# Calliope: a multi-scale energy systems modelling framework

v0.6.5 (Release history)

This is the documentation for version 0.6.5. See the main project website for contact details and other useful information.

Calliope focuses on flexibility, high spatial and temporal resolution, the ability to execute many runs based on the same base model, and a clear separation of framework (code) and model (data). Its primary focus is on planning energy systems at scales ranging from urban districts to entire continents. In an optional operational mode it can also test a pre-defined system under different operational conditions. Calliope’s built-in tools allow interactive exploration of results:

A model based on Calliope consists of a collection of text files (in YAML and CSV formats) that define the technologies, locations and resource potentials. Calliope takes these files, constructs an optimisation problem, solves it, and reports results in the form of xarray Datasets which in turn can easily be converted into Pandas data structures, for easy analysis with Calliope’s built-in tools or the standard Python data analysis stack.

Calliope is developed in the open on GitHub and contributions are very welcome (see the Development guide).

Key features of Calliope include:

- Model specification in an easy-to-read and machine-processable YAML format

- Generic technology definition allows modelling any mix of production, storage and consumption

- Resolved in space: define locations with individual resource potentials

- Resolved in time: read time series with arbitrary resolution

- Able to run on high-performance computing (HPC) clusters

- Uses a state-of-the-art Python toolchain based on Pyomo, xarray, and Pandas

- Freely available under the Apache 2.0 license

## User guide

### Introduction

The basic process of modelling with Calliope is based on three steps:

1. Create a model from scratch or by adjusting an existing model (Building a model)

2. Run your model (Running a model)

3. Analyse and visualise model results (Analysing a model)

#### Energy system models

Energy system models allow analysts to form internally coherent scenarios of how energy is extracted, converted, transported, and used, and how these processes might change in the future. These models have been gaining renewed importance as methods to help navigate the climate policy-driven transformation of the energy system.

Calliope is an attempt to design an energy system model from the ground of up with specific design goals in mind (see below). Therefore, the model approach and data format layout may be different from approaches used in other models. The design of the nodes approach used in Calliope was influenced by the power nodes modelling framework by [Heussen2010], but Calliope is different from traditional power system modelling tools, and does not provide features such as power flow analysis.

Calliope was designed to address questions around the transition to renewable energy, so there are tools that are likely to be more suitable for other types of questions. In particular, the following related energy modelling systems are available under open source or free software licenses:

- SWITCH: A power system model focused on renewables integration, using multi-stage stochastic linear optimisation, as well as hourly resource potential and demand data. Written in the commercial AMPL language and GPL-licensed [Fripp2012].

- Temoa: An energy system model with multi-stage stochastic optimisation functionality which can be deployed to computing clusters, to address parametric uncertainty. Written in Python/Pyomo and AGPL-licensed [Hunter2013].

- OSeMOSYS: A simplified energy system model similar to the MARKAL/TIMES model families, which can be used as a stand-alone tool or integrated in the LEAP energy model. Written in GLPK, a free subset of the commercial AMPL language, and Apache 2.0-licensed [Howells2011].

Additional energy models that are partially or fully open can be found on the Open Energy Modelling Initiative’s wiki.

#### Rationale

Calliope was designed with the following goals in mind:

- Designed from the ground up to analyze energy systems with high shares of renewable energy or other variable generation

- Formulated to allow arbitrary spatial and temporal resolution, and equipped with the necessary tools to deal with time series input data

- Allow easy separation of model code and data, and modular extensibility of model code

- Make models easily modifiable, archiveable and auditable (e.g. in a Git repository), by using well-defined and human-readable text formats

- Simplify the definition and deployment of large numbers of model runs to high-performance computing clusters

- Able to run stand-alone from the command-line, but also provide an API for programmatic access and embedding in larger analyses

- Be a first-class citizen of the Python world (installable with `conda` and `pip`, with properly documented and tested code that mostly conforms to PEP8)

- Have a free and open-source code base under a permissive license

#### Acknowledgments

Initial development was partially funded by the Grantham Institute at Imperial College London and the European Institute of Innovation & Technology’s Climate-KIC program.

#### License

Calliope is released under the Apache 2.0 license, which is a permissive open-source license much like the MIT or BSD licenses. This means that Calliope can be incorporated in both commercial and non-commercial projects.

    Copyright 2013-2019 Calliope contributors listed in AUTHORS

    Licensed under the Apache License, Version 2.0 (the "License");
    you may not use this file except in compliance with the License.
    You may obtain a copy of the License at

       http://www.apache.org/licenses/LICENSE-2.0

    Unless required by applicable law or agreed to in writing, software
    distributed under the License is distributed on an "AS IS" BASIS,
    WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
    See the License for the specific language governing permissions and
    limitations under the License.

#### References

Fripp2012

  Fripp, M., 2012. Switch: A Planning Tool for Power Systems with Large Shares of Intermittent Renewable Energy. Environ. Sci. Technol., 46(11), p.6371–6378. DOI: 10.1021/es204645c

Heussen2010

  Heussen, K. et al., 2010. Energy storage in power system operation: The power nodes modeling framework. In Innovative Smart Grid Technologies Conference Europe (ISGT Europe), 2010 IEEE PES. pp. 1–8. DOI: 10.1109/ISGTEUROPE.2010.5638865

Howells2011

  Howells, M. et al., 2011. OSeMOSYS: The Open Source Energy Modeling System: An introduction to its ethos, structure and development. Energy Policy, 39(10), p.5850–5870. DOI: 10.1016/j.enpol.2011.06.033

Hunter2013

  Hunter, K., Sreepathi, S. & DeCarolis, J.F., 2013. Modeling for insight using Tools for Energy Model Optimization and Analysis (Temoa). Energy Economics, 40, p.339–349. DOI: 10.1016/j.eneco.2013.07.014

### Download and installation

#### Requirements

Calliope has been tested on Linux, macOS, and Windows.

Running Calliope requires four things:

1. The Python programming language, version 3.7 or higher.

2. A number of Python add-on modules (see below for the complete list).

3. A solver: Calliope has been tested with CBC, GLPK, Gurobi, and CPLEX. Any other solver that is compatible with Pyomo should also work.

4. The Calliope software itself.

#### Recommended installation method

The easiest way to get a working Calliope installation is to use the free `conda` package manager, which can install all of the four things described above in a single step.

To get `conda`, download and install the “Miniconda” distribution for your operating system (using the version for Python 3).

With Miniconda installed, you can create a new environment called `"calliope"` with all the necessary modules, including the free and open source GLPK solver, by running the following command in a terminal or command-line window

>     $ conda create -c conda-forge -n calliope calliope

To use Calliope, you need to activate the `calliope` environment each time

>     $ conda activate calliope

You are now ready to use Calliope together with the free and open source GLPK solver. However, we recommend to not use this solver where possible, since it performs relatively poorly (both in solution time and stability of result). Indeed, our example models use the free and open source CBC solver instead, but installing it on Windows requires an extra step. Read the next section for more information on installing alternative solvers.

#### Updating an existing installation

If following the recommended installation method above, the following command, assuming the conda environment is active, will update Calliope to the newest version

>     $ conda update -c conda-forge calliope

#### Solvers

You need at least one of the solvers supported by Pyomo installed. CBC (open-source) or Gurobi (commercial) are recommended for large problems, and have been confirmed to work with Calliope. Refer to the documentation of your solver on how to install it.

##### CBC

CBC is our recommended option if you want a free and open-source solver. CBC can be installed via conda on Linux and macOS by running ``conda install -c conda-forge coincbc``. Windows binary packages are somewhat more difficult to install, due to limited information on the CBC website. We recommend you download the relevant binary for CBC 2.9.9 and add cbc.exe to a directory known to PATH (e.g. an Anaconda environment ‘bin’ directory).

##### GLPK

GLPK is free and open-source, but can take too much time and/or too much memory on larger problems. If using the recommended installation approach above, GLPK is already installed in the `calliope` environment. To install GLPK manually, refer to the GLPK website.

##### Gurobi

Gurobi is commercial but significantly faster than CBC and GLPK, which is relevant for larger problems. It needs a license to work, which can be obtained for free for academic use by creating an account on gurobi.com.

While Gurobi can be installed via conda (`conda install -c gurobi gurobi`) we recommend downloading and installing the installer from the Gurobi website, as the conda package has repeatedly shown various issues.

After installing, log on to the Gurobi website and obtain a (free academic or paid commercial) license, then activate it on your system via the instructions given online (using the `grbgetkey` command).

##### CPLEX

Another commercial alternative is CPLEX. IBM offer academic licenses for CPLEX. Refer to the IBM website for details.

#### Python module requirements

Refer to requirements/base.yml in the Calliope repository for a full and up-to-date listing of required third-party packages.

Some of the key packages Calliope relies on are:

- Pyomo

- Pandas

- Xarray

- Plotly

- Jupyter (optional, but highly recommended, and used for the example notebooks in the tutorials)

### Building a model

In short, a Calliope model works like this: supply technologies can take a resource from outside of the modeled system and turn it into a specific energy carrier in the system. The model specifies one or more locations along with the technologies allowed at those locations. Transmission technologies can move energy of the same carrier from one location to another, while conversion technologies can convert one carrier into another at the same location. Demand technologies remove energy from the system, while storage technologies can store energy at a specific location. Putting all of these possibilities together allows a modeller to specify as simple or as complex a model as necessary to answer a given research question.

In more technical terms, Calliope allows a modeller to define technologies with arbitrary characteristics by “inheriting” basic traits from a number of included base tech groups – `supply`, `supply_plus`, `demand`, `conversion`, `conversion_plus`, and `transmission`. These groups are described in more detail in Abstract base technology groups.

#### Terminology

The terminology defined here is used throughout the documentation and the model code and configuration files:

- Technology: a technology that produces, consumes, converts or transports energy

- Location: a site which can contain multiple technologies and which may contain other locations for energy balancing purposes

- Resource: a source or sink of energy that can (or must) be used by a technology to introduce into or remove energy from the system

- Carrier: an energy carrier that groups technologies together into the same network, for example `electricity` or `heat`.

As more generally in constrained optimisation, the following terms are also used:

- Parameter: a fixed coefficient that enters into model equations

- Variable: a variable coefficient (decision variable) that enters into model equations

- Set: an index in the algebraic formulation of the equations

- Constraint: an equality or inequality expression that constrains one or several variables

#### Files that define a model

Calliope models are defined through YAML files, which are both human-readable and computer-readable, and CSV files (a simple tabular format) for time series data.

It makes sense to collect all files belonging to a model inside a single model directory. The layout of that directory typically looks roughly like this (`+` denotes directories, `-` files):

    + example_model
        + model_config
            - locations.yaml
            - techs.yaml
        + timeseries_data
            - solar_resource.csv
            - electricity_demand.csv
        - model.yaml
        - scenarios.yaml

In the above example, the files `model.yaml`, `locations.yaml` and `techs.yaml` together are the model definition. This definition could be in one file, but it is more readable when split into multiple. We use the above layout in the example models and in our research!

Inside the `timeseries_data` directory, timeseries are stored as CSV files. The location of this directory can be specified in the model configuration, e.g. in `model.yaml`.

Note

The easiest way to create a new model is to use the `calliope new` command, which makes a copy of one of the built-in examples models:

    $ calliope new my_new_model

This creates a new directory, `my_new_model`, in the current working directory.

By default, `calliope new` uses the national-scale example model as a template. To use a different template, you can specify the example model to use, e.g.: `--template=urban_scale`.

See also

YAML configuration file format, Built-in example models, Time series data

#### Model configuration (`model`)

The model configuration specifies all aspects of the model to run. It is structured into several top-level headings (keys in the YAML file): `model`, `techs`, `locations`, `links`, and `run`. We will discuss each of these in turn, starting with `model`:

    model:
        name: 'My energy model'
        timeseries_data_path: 'timeseries_data'
        reserve_margin:
            power: 0
        subset_time: ['2005-01-01', '2005-01-05']

Besides the model’s name (`name`) and the path for CSV time series data (`timeseries_data_path`), group constraints can be set, like `reserve_margin`.

To speed up model runs, the above example specifies a time subset to run the model over only five days of time series data (`subset_time: [‘2005-01-01’, ‘2005-01-05’]`)– this is entirely optional. Usually, a full model will contain at least one year of data, but subsetting time can be useful to speed up a model for testing purposes.

See also

National scale example model, Model configuration

#### Technologies (`techs`)

The `techs` section in the model configuration specifies all of the model’s technologies. In our current example, this is in a separate file, `model_config/techs.yaml`, which is imported into the main `model.yaml` file alongside the file for locations described further below:

    import:
        - 'model_config/techs.yaml'
        - 'model_config/locations.yaml'

Note

The `import` statement can specify a list of paths to additional files to import (the imported files, in turn, may include further files, so arbitrary degrees of nested configurations are possible). The `import` statement can either give an absolute path or a path relative to the importing file.

The following example shows the definition of a `ccgt` technology, i.e. a combined cycle gas turbine that delivers electricity:

    ccgt:
        essentials:
            name: 'Combined cycle gas turbine'
            color: '#FDC97D'
            parent: supply
            carrier_out: power
        constraints:
            resource: inf
            energy_eff: 0.5
            energy_cap_max: 40000  # kW
            energy_cap_max_systemwide: 100000  # kW
            energy_ramping: 0.8
            lifetime: 25
        costs:
            monetary:
                interest_rate: 0.10
                energy_cap: 750  # USD per kW
                om_con: 0.02  # USD per kWh

Each technology must specify some `essentials`, most importantly a name, the abstract base technology it is inheriting from (`parent`), and its energy carrier (`carrier_out` in the case of a `supply` technology). Specifying a `color` is optional but useful for using the built-in visualisation tools (see Analysing a model).

The `constraints` section gives all constraints for the technology, such as allowed capacities, conversion efficiencies, the life time (used in levelised cost calculations), and the resource it consumes (in the above example, the resource is set to infinite via `inf`).

The `costs` section gives costs for the technology. Calliope uses the concept of “cost classes” to allow accounting for more than just monetary costs. The above example specifies only the `monetary` cost class, but any number of other classes could be used, for example `co2` to account for emissions. Additional cost classes can be created simply by adding them to the definition of costs for a technology.

By default, only the `monetary` cost class is used in the objective function, i.e., the default objective is to minimize total costs.

Multiple cost classes can be considered in the objective by setting the cost_class key. It must be a dictionary of cost classes and their weights in the objective, e.g. `objective_options: {‘cost_class’: {‘monetary’: 1, ‘emissions’: 0.1}}`. In this example, monetary costs are summed as usual and emissions are added to this, scaled by 0.1 (emulating a carbon price).

To use a different sense (minimize/maximize) you can set sense: `objective_options: {‘cost_class’: …, ‘sense’: ‘minimize’}`.

To use a single alternative cost class, disabling the consideration of the default monetary, set the weight of the monetary cost class to zero to stop considering it and the weight of another cost class to a non-zero value, e.g. `objective_options: {‘cost_class’: {‘monetary’: 0, ‘emissions’: 1}}`.

See also

Per-tech constraints, Per-tech costs, tutorials, built-in examples

##### Allowing for unmet demand

For a model to find a feasible solution, supply must always be able to meet demand. To avoid the solver failing to find a solution, you can ensure feasibility:

    run:
        ensure_feasibility: true

This will create an `unmet_demand` decision variable in the optimisation, which can pick up any mismatch between supply and demand, across all energy carriers. It has a very high cost associated with its use, so it will only appear when absolutely necessary.

Note

When ensuring feasibility, you can also set a big M value (`run.bigM`). This is the “cost” of unmet demand. It is possible to make model convergence very slow if bigM is set too high. default bigM is 1x10 9, but should be close to the maximum total system cost that you can imagine. This is perhaps closer to 1x10 6 for urban scale models.

#### Time series data

For parameters that vary in time, time series data can be read from CSV files, by specifying `resource: file=filename.csv` to pick the desired CSV file from within the configured timeseries data path (`model.timeseries_data_path`).

By default, Calliope looks for a column in the CSV file with the same name as the location. It is also possible to specify a column to use when setting `resource` per location, by giving the column name with a colon following the filename: `resource: file=filename.csv:column`

For example, a simple photovoltaic (PV) tech using a time series of hour-by-hour electricity generation data might look like this:

    pv:
        essentials:
            name: 'Rooftop PV'
            color: '#B59C2B'
            parent: supply
            carrier_out: power
        constraints:
            resource: file=pv_resource.csv
            energy_cap_max: 10000  # kW

By default, Calliope expects time series data in a model to be indexed by ISO 8601 compatible time stamps in the format `YYYY-MM-DD hh:mm:ss`, e.g. `2005-01-01 00:00:00`. This can be changed by setting `model.timeseries_dateformat` based on `strftime` directives <http://strftime.org/>`_, which defaults to ``'%Y-%m-%d %H:%M:%S'`.

For example, the first few lines of a CSV file giving a resource potential for two locations might look like this, with the first column in the file always being read as the date-time index:

    ,location1,location2
    2005-01-01 00:00:00,0,0
    2005-01-01 01:00:00,0,11
    2005-01-01 02:00:00,0,18
    2005-01-01 03:00:00,0,49
    2005-01-01 04:00:00,11,110
    2005-01-01 05:00:00,45,300
    2005-01-01 06:00:00,90,458

Note

- If a parameter is not explicit in time and space, it can be specified as a single value in the model definition (or, using location-specific definitions, be made spatially explicit). This applies both to parameters that never vary through time (for example, cost of installed capacity) and for those that may be time-varying (for example, a technology’s available resource). However, each model must contain at least one time series.

- Only the subset of parameters listed in file_allowed in the model configuration can be loaded from file. It is advised not to update this default list unless you are developing the core code, since the model will likely behave unexpectedly.

- You _cannot_ have a space around the `=` symbol when pointing to a timeseries file, i.e. `resource: file = filename.csv` is not valid.

#### Locations and links (`locations`, `links`)

A model can specify any number of locations. These locations are linked together by transmission technologies. By consuming an energy carrier in one location and outputting it in another, linked location, transmission technologies allow resources to be drawn from the system at a different location from where they are brought into it.

The `locations` section specifies each location:

    locations:
        region1:
            coordinates: {lat: 40, lon: -2}
            techs:
                unmet_demand_power:
                demand_power:
                ccgt:
                    constraints:
                        energy_cap_max: 30000

Locations can optionally specify `coordinates` (used in visualisation or to compute distance between them) and must specify `techs` allowed at that location. As seen in the example above, each allowed tech must be listed, and can optionally specify additional location-specific parameters (constraints or costs). If given, location-specific parameters supersede any group constraints a technology defines in the `techs` section for that location.

The `links` section specifies possible transmission links between locations in the form `location1,location2`:

    links:
        region1,region2:
            techs:
                ac_transmission:
                    constraints:
                        energy_cap_max: 10000
                    costs.monetary:
                        energy_cap: 100

In the above example, an high-voltage AC transmission line is specified to connect `region1` with `region2`. For this to work, a `transmission` technology called `ac_transmission` must have previously been defined in the model’s `techs` section. There, it can be given group constraints or costs. As in the case of locations, the `links` section can specify per-link parameters (constraints or costs) that supersede any model-wide parameters.

The modeller can also specify a distance for each link, and use per-distance constraints and costs for transmission technologies.

See also

Per-tech constraints, Per-tech costs.

#### Run configuration (`run`)

The only required setting in the run configuration is the solver to use:

    run:
        solver: cbc
        mode: plan

the most important parts of the `run` section are `solver` and `mode`. A model can run either in planning mode (`plan`) or operational mode (`operate`). In planning mode, capacities are determined by the model, whereas in operational mode, capacities are fixed and the system is operated with a receding horizon control algorithm.

Possible options for solver include `glpk`, `gurobi`, `cplex`, and `cbc`. The interface to these solvers is done through the Pyomo library. Any solver compatible with Pyomo should work with Calliope.

For solvers with which Pyomo provides more than one way to interface, the additional `solver_io` option can be used. In the case of Gurobi, for example, it is usually fastest to use the direct Python interface:

    run:
        solver: gurobi
        solver_io: python

Note

The opposite is currently true for CPLEX, which runs faster with the default `solver_io`.

Further optional settings, including debug settings, can be specified in the run configuration.

See also

Run configuration, Troubleshooting, Specifying custom solver options, documentation on operational mode.

#### Scenarios and overrides

To make it easier to run a given model multiple times with slightly changed settings or constraints, for example, varying the cost of a key technology, it is possible to define and apply scenarios and overrides. “Overrides” are blocks of YAML that specify configurations that expand or override parts of the base model. “Scenarios” are combinations of any number of such overrides. Both are specified at the top level of the model configuration, as in this example `model.yaml` file:

    scenarios:
        high_cost_2005: ["high_cost", "year2005"]
        high_cost_2006: ["high_cost", "year2006"]

    overrides:
        high_cost:
            techs.onshore_wind.costs.monetary.energy_cap: 2000
        year2005:
            model.subset_time: ['2005-01-01', '2005-12-31']
        year2006:
            model.subset_time: ['2006-01-01', '2006-12-31']

    model:
        ...

    run:
        ...

Each override is given by a name (e.g. `high_cost`) and any number of model settings – anything in the model configuration can be overridden by an override. In the above example, one override defines higher costs for an `onshore_wind` tech while the two other overrides specify different time subsets, so would run an otherwise identical model over two different periods of time series data.

One or several overrides can be applied when running a model, as described in Running a model. Overrides can also be combined into scenarios to make applying them at run-time easier. Scenarios consist of a name and a list of override names which together form that scenario.

Scenarios and overrides can be used to generate scripts that run a single Calliope model many times, either sequentially, or in parallel on a high-performance cluster (see Generating scripts to run a model many times).

Note

Overrides can also import other files. This can be useful if many overrides are defined which share large parts of model configuration, such as different levels of interconnection between model zones. See Importing other YAML files in overrides for details.

See also

Generating scripts to run a model many times, Importing other YAML files in overrides

### Running a model

There are essentially three ways to run a Calliope model:

1. With the `calliope run` command-line tool.

2. By programmatically creating and running a model from within other Python code, or in an interactive Python session.

3. By generating and then executing scripts with the `calliope generate_runs` command-line tool, which is primarily designed for running many scenarios on a high-performance cluster.

#### Running with the command-line tool

We can easily run a model after creating it (see Building a model), saving results to a single NetCDF file for further processing

>     $ calliope run testmodel/model.yaml --save_netcdf=results.nc

The `calliope run` command takes the following options:

- `--save_netcdf={filename.nc}`: Save complete model, including results, to the given NetCDF file. This is the recommended way to save model input and output data into a single file, as it preserves all data fully, and allows later reconstruction of the Calliope model for further analysis.

- `--save_csv={directory name}`: Save results as a set of CSV files to the given directory. This can be handy if the modeler needs results in a simple text-based format for further processing with a tool like Microsoft Excel.

- `--save_plots={filename.html}`: Save interactive plots to the given HTML file (see Analysing a model for further details on the plotting functionality).

- `--debug`: Run in debug mode, which prints more internal information, and is useful when troubleshooting failing models.

- `--scenario={scenario}` and `--override_dict={yaml_string}`: Specify a scenario, or one or several overrides, to apply to the model, or apply specific overrides from a YAML string (see below for more information)

- `--help`: Show all available options.

Multiple options can be specified, for example, saving NetCDF, CSV, and HTML plots simultaneously

>     $ calliope run testmodel/model.yaml --save_netcdf=results.nc --save_csv=outputs --save_plots=plots.html

Warning

Unlike in versions prior to 0.6.0, the command-line tool in Calliope 0.6.0 and upward does not save results by default – the modeller must specify one of the `-save` options.

##### Applying a scenario or override

The `--scenario` can be used in three different ways:

- It can be given the name of a scenario defined in the model configuration, as in `--scenario=my_scenario`

- It can be given the name of a single override defined in the model configuration, as in `--scenario=my_override`

- It can be given a comma-separated string of several overrides defined in the model configuration, as in `--scenario=my_override_1,my_override_2`

In the latter two cases, the given override(s) is used to implicitly create a “scenario” on-the-fly when running the model. This allows quick experimentation with different overrides without explicitly defining a scenario combining them.

Assuming we have specified an override called `milp` in our model configuration, we can apply it to our model with

>     $ calliope run testmodel/model.yaml --scenario=milp --save_netcdf=results.nc

Note that if both a scenario and an override with the same name, such as `milp` in the above example, exist, Calliope will raise an error, as it will not be clear which one the user wishes to apply.

It is also possible to use the –override_dict option to pass a YAML string that will be applied after anything applied through `--scenario`

>     $ calliope run testmodel/model.yaml --override_dict="{'model.subset_time': ['2005-01-01', '2005-01-31']}" --save_netcdf=results.nc

See also

Analysing a model, Scenarios and overrides

#### Running interactively with Python

The most basic way to run a model programmatically from within a Python interpreter is to create a `Model` instance with a given `model.yaml` configuration file, and then call its `run()` method:

    import calliope
    model = calliope.Model('path/to/model.yaml')
    model.run()

Note

If `config` is not specified (i.e. `model = Model()`), an error is raised. See Built-in example models for information on instantiating a simple example model without specifying a custom model configuration.

Other ways to load a model interactively are:

- Passing an `AttrDict` or standard Python dictionary to the `Model` constructor, with the same nested format as the YAML model configuration (top-level keys: `model`, `run`, `locations`, `techs`).

- Loading a previously saved model from a NetCDF file with `model = calliope.read_netcdf(‘path/to/saved_model.nc’)`. This can either be a pre-processed model saved before its `run` method was called, which will include input data only, or a completely solved model, which will include input and result data.

After instantiating the `Model` object, and before calling the `run()` method, it is possible to manually inspect and adjust the configuration of the model. The pre-processed inputs are all held in the xarray Dataset `model.inputs`.

After the model has been solved, an xarray Dataset containing results (`model.results`) can be accessed. At this point, the model can be saved with either `to_csv()` or `to_netcdf()`, which saves all inputs and results, and is equivalent to the corresponding `--save` options of the command-line tool.

See also

An example of interactive running in a Python session, which also demonstrates some of the analysis possibilities after running a model, is given in the tutorials. You can download and run the embedded notebooks on your own machine (if both Calliope and the Jupyter Notebook are installed).

##### Scenarios and overrides

There are two ways to override a base model when running interactively, analogously to the use of the command-line tool (see Applying a scenario or override above):

1. By setting the scenario argument, e.g.:

   >     model = calliope.Model('model.yaml', scenario='milp')

2. By passing the override_dict argument, which is a Python dictionary, an `AttrDict`, or a YAML string of overrides:

   >     model = calliope.Model(
   >         'model.yaml',
   >         override_dict={'run.solver': 'gurobi'}
   >     )

Note

Both scenario and override_dict can be defined at once. They will be applied in order, such that scenarios are applied first, followed by dictionary overrides. As such, the override_dict can be used to override scenarios.

##### Tracking progress

When running Calliope in the command line, logging of model pre-processing and solving occurs automatically. Interactively, for example in a Jupyter notebook, you can enable verbose logging by setting the log level using `calliope.set_log_verbosity(level)` immediately after importing the Calliope package. By default, `calliope.set_log_verbosity()` also sets the log level for the backend model to DEBUG, which turns on output of solver output. This can be disabled by `calliope.set_log_verbosity(level, include_solver_output=False)`. Possible log levels are (from least to most verbose):

1. CRITICAL: only show critical errors.

2. ERROR: only show errors.

3. WARNING: show errors and warnings (default level).

4. INFO: show errors, warnings, and informative messages. Calliope uses the INFO level to show a message at each stage of pre-processing, sending the model to the solver, and post-processing, including timestamps.

5. DEBUG: SOLVER logging, with heavily verbose logging of a number of function outputs. Only for use when troubleshooting failing runs or developing new functionality in Calliope.

#### Generating scripts for many model runs

Scripts to simplify the creation and execution of a large number of Calliope model runs are generated with the `calliope generate_runs` command-line tool. More detail on this is available in Generating scripts to run a model many times.

#### Improving solution times

Large models will take time to solve. The easiest is often to just let a model run on a remote device (another computer, or a high performance computing cluster) and forget about it until it is done. However, if you need results now, there are ways to improve solution time.

Details on strategies to improve solution times are given in Troubleshooting.

#### Debugging failing runs

What will typically go wrong, in order of decreasing likelihood:

> - The model is improperly defined or missing data. Calliope will attempt to diagnose some common errors and raise an appropriate error message.

> - The model is consistent and properly defined but infeasible. Calliope will be able to construct the model and pass it on to the solver, but the solver (after a potentially long time) will abort with a message stating that the model is infeasible.

> - There is a bug in Calliope causing the model to crash either before being passed to the solver, or after the solver has completed and when results are passed back to Calliope.

Calliope provides help in diagnosing all of these model issues. For details, see Troubleshooting.

### Analysing a model

Calliope inputs and results are designed for easy handling. Whatever software you prefer to use for data processing, either the NetCDF or CSV output options should provide a path to importing your Calliope results. If you prefer to not worry about writing your own scripts, then we have that covered too! The built-in plotting functions in `plot` are built on Plotly’s interactive visualisation tools to bring your data to life.

#### Accessing model data and results

A model which solved successfully has two primary Datasets with data of interest:

- `model.inputs`: contains all input data, such as renewable resource capacity factors

- `model.results`: contains all results data, such as dispatch decisions and installed capacities

In both of these, variables are indexed over concatenated sets of locations and technologies, over a dimension we call `loc_techs`. For example, if a technology called `boiler` only exists in location `X1` and not in locations `X2` or `X3`, then it will have a single entry in the loc_techs dimension called `X1::boiler`. For parameters which also consider different energy carriers, we use a `loc_tech_carrier` dimension, such that we would have, in the case of the prior boiler example, `X1::boiler::heat`.

This concatenated set formulation is memory-efficient but cumbersome to deal with, so the `model.get_formatted_array(name_of_variable)` function can be used to retrieve a DataArray indexed over separate dimensions (any of techs, locs, carriers, costs, timesteps, depending on the desired variable).

Note

On saving to CSV (see the command-line interface documentation), all variables are saved to a single file each, which are always indexed over all dimensions rather than just the concatenated dimensions.

#### Visualising results

In an interactive Python session, there are four primary visualisation functions: `capacity`, `timeseries`, `transmission`, and `summary`. To gain access to result visualisation without the need to interact with Python, the `summary` plot can also be accessed from the command line interface (see below).

Refer to the API documentation for the analysis module for an overview of available analysis functionality.

Refer to the tutorials for some basic analysis techniques.

##### Plotting time series

The following example shows a timeseries plot of the built-in urban scale example model:

In Python, we get this function by calling `model.plot.timeseries()`. It includes all relevant timeseries information, from both inputs and results. We can force it to only have particular results in the dropdown menu:

    # Only inputs or only results
    model.plot.timeseries(array='inputs')
    model.plot.timeseries(array='results')

    # Only consumed resource
    model.plot.timeseries(array='resource_con')

    # Only consumed resource and 'power' carrier flow
    model.plot.timeseries(array=['power', 'resource_con'])

The data used to build the plots can also be subset and ordered by using the `subset` argument. This uses xarray’s ‘loc’ indexing functionality to access subsets of data:

    # Only show region1 data (rather than the default, which is a sum of all locations)
    model.plot.timeseries(subset={'locs': ['region1']})

    # Only show a subset of technologies
    model.plot.timeseries(subset={'techs': ['ccgt', 'csp']})

    # Assuming our model has three techs, 'ccgt', 'csp', and 'battery',
    # specifying `subset` lets us order them in the stacked barchart
    model.plot.timeseries(subset={'techs': ['ccgt', 'battery', 'csp']})

When aggregating model timesteps with clustering methods, the timeseries plots are adjusted accordingly (example from the built-in `time_clustering` example model):

See also

API documentation for the analysis module

##### Plotting capacities

The following example shows a capacity plot of the built-in urban scale example model:

Functionality is similar to timeseries, this time called by `model.plot.capacity()`. Here we show capacity limits set at input and chosen capacities at output. Choosing dropdowns and subsetting works in the same way as for timeseries plots

##### Plotting transmission

The following example shows a transmission plot of the built-in urban scale example model:

By calling `model.plot.transmission()` you will see installed links, their capacities (on hover), and the locations of the nodes. This functionality only works if you have physically pinpointed your locations using the `coordinates` key for your location.

The above plot uses Mapbox to overlay our transmission plot on Openstreetmap. By creating an account at Mapbox and acquiring a Mapbox access token, you can also create similar visualisations by giving the token to the plotting function: `model.plot.transmission(mapbox_access_token=’your token here’)`.

Without the token, the plot will fall back on simple country-level outlines. In this urban scale example, the background is thus just grey (zoom out to see the UK!):

Note

If the coordinates were in x and y, not lat and lon, the transmission trace would be given on a cartesian plot.

##### Plotting flows

The following example shows an energy flow plot of the built-in urban scale example model:

By calling `model.plot.flows()` you will see a plot similar to transmission. However, you can see carrier production at each node and along links, at every timestep (controlled by moving a slider). This functionality only works if you have physically pinpointed your locations using the `coordinates` key for your location. It is possible to look at only a subset of the timesteps in the model using the timestep_index_subset argument, or to show only every `X` timestep (where `X` is an integer) using the timestep_cycle argument.

Note

If the timestep dimension is particularly large in your model, you will find this visualisation to be slow. Time subsetting is recommended for such a case.

If you cannot see the carrier production for a technology on hovering, it is likely masked by another technology at the same location or on the same link. Hide the masking technology to get the hover info for the technology below.

##### Summary plots

If you want all the data in one place, you can run `model.plot.summary(to_file=’path/to/file.html’)`, which will build a HTML file of all the interactive plots (maintaining the interactivity) and save it to ‘path/to/file.html’. This HTML file can be opened in a web browser to show all the plots. This funcionality is made available in the command line interface by using the command `--save_plots=filename.html` when running the model.

See an example of such a HTML plot here.

See also

Running with the command-line tool

##### Saving publication-quality SVG figures

On calling any of the three primary plotting functions, you can also set `to_file=path/to/file.svg` for a high quality vector graphic to be saved. This file can be prepared for publication in programs like Inkscape.

Note

For similar results in the command line interface, you’ll currently need to save your model to netcdf (`--save_netcdf={filename.nc}`) then load it into a Calliope Model object in Python. Once there, you can use the above functions to get your SVGs.

#### Reading solutions

Calliope provides functionality to read a previously-saved model from a single NetCDF file:

    solved_model = calliope.read_netcdf('my_saved_model.nc')

In the above example, the model’s input data will be available under `solved_model.inputs`, while the results (if the model had previously been solved) are available under `solved_model.results`.

Both of these are xarray.Datasets and can be further processed with Python.

See also

The xarray documentation should be consulted for further information on dealing with Datasets. Calliope’s NetCDF files follow the CF conventions and can easily be processed with any other tool that can deal with NetCDF.

### Tutorials

The tutorials are based on the built-in example models, they explain the key steps necessary to set up and run simple models. Refer to the other parts of the documentation for more detailed information on configuring and running more complex models. The built-in examples are simple on purpose, to show the key components of a Calliope model with which models of arbitrary complexity can be built.

The first tutorial builds a model for part of a national grid, exhibiting the following Calliope functionality:

- Use of supply, supply_plus, demand, storage and transmission technologies

- Nested locations

- Multiple cost types

The second tutorial builds a model for part of a district network, exhibiting the following Calliope functionality:

- Use of supply, demand, conversion, conversion_plus, and transmission technologies

- Use of multiple energy carriers

- Revenue generation, by carrier export

The third tutorial extends the second tutorial, exhibiting binary and integer decision variable functionality (extended an LP model to a MILP model)

#### Tutorial 1: national scale

This example consists of two possible power supply technologies, a power demand at two locations, the possibility for battery storage at one of the locations, and a transmission technology linking the two. The diagram below gives an overview:

Overview of the built-in national-scale example model

##### Supply-side technologies

The example model defines two power supply technologies.

The first is `ccgt` (combined-cycle gas turbine), which serves as an example of a simple technology with an infinite resource. Its only constraints are the cost of built capacity (`energy_cap`) and a constraint on its maximum built capacity.

The layout of a supply node, in this case `ccgt`, which has an infinite resource, a carrier conversion efficiency (\(energy_{eff}\)), and a constraint on its maximum built \(energy_{cap}\) (which puts an upper limit on \(energy_{prod}\)).

The definition of this technology in the example model’s configuration looks as follows:

    ccgt:
        essentials:
            name: 'Combined cycle gas turbine'
            color: '#E37A72'
            parent: supply
            carrier_out: power
        constraints:
            resource: inf
            energy_eff: 0.5
            energy_cap_max: 40000  # kW
            energy_cap_max_systemwide: 100000  # kW
            energy_ramping: 0.8
            lifetime: 25
        costs:
            monetary:
                interest_rate: 0.10
                energy_cap: 750  # USD per kW
                om_con: 0.02  # USD per kWh

There are a few things to note. First, `ccgt` defines essential information: a name, a color (given as an HTML color code, for later visualisation), its parent, `supply`, and its carrier_out, `power`. It has set itself up as a power supply technology. This is followed by the definition of constraints and costs (the only cost class used is monetary, but this is where other “costs”, such as emissions, could be defined).

Note

There are technically no restrictions on the units used in model definitions. Usually, the units will be kW and kWh, alongside a currency like USD for costs. It is the responsibility of the modeler to ensure that units are correct and consistent. Some of the analysis functionality in the `analysis` module assumes that kW and kWh are used when drawing figure and axis labels, but apart from that, there is nothing preventing the use of other units.

The second technology is `csp` (concentrating solar power), and serves as an example of a complex supply_plus technology making use of:

- a finite resource based on time series data

- built-in storage

- plant-internal losses (`parasitic_eff`)

The layout of a more complex node, in this case `csp`, which makes use of most node-level functionality available.

This definition in the example model’s configuration is more verbose:

    csp:
        essentials:
            name: 'Concentrating solar power'
            color: '#F9CF22'
            parent: supply_plus
            carrier_out: power
        constraints:
            storage_cap_max: 614033
            energy_cap_per_storage_cap_max: 1
            storage_loss: 0.002
            resource: file=csp_resource.csv
            resource_unit: energy_per_area
            energy_eff: 0.4
            parasitic_eff: 0.9
            resource_area_max: inf
            energy_cap_max: 10000
            lifetime: 25
        costs:
            monetary:
                interest_rate: 0.10
                storage_cap: 50
                resource_area: 200
                resource_cap: 200
                energy_cap: 1000
                om_prod: 0.002

Again, `csp` has the definitions for name, color, parent, and carrier_out. Its constraints are more numerous: it defines a maximum storage capacity (`storage_cap_max`), an hourly storage loss rate (`storage_loss`), then specifies that its resource should be read from a file (more on that below). It also defines a carrier conversion efficiency of 0.4 and a parasitic efficiency of 0.9 (i.e., an internal loss of 0.1). Finally, the resource collector area and the installed carrier conversion capacity are constrained to a maximum.

The costs are more numerous as well, and include monetary costs for all relevant components along the conversion from resource to carrier (power): storage capacity, resource collector area, resource conversion capacity, energy conversion capacity, and variable operational and maintenance costs. Finally, it also overrides the default value for the monetary interest rate.

##### Storage technologies

The second location allows a limited amount of battery storage to be deployed to better balance the system. This technology is defined as follows:

A storage node with an \(energy_{eff}\) and \(storage_{loss}\).

    battery:
        essentials:
            name: 'Battery storage'
            color: '#3B61E3'
            parent: storage
            carrier: power
        constraints:
            energy_cap_max: 1000  # kW
            storage_cap_max: inf
            energy_cap_per_storage_cap_max: 4
            energy_eff: 0.95  # 0.95 * 0.95 = 0.9025 round trip efficiency
            storage_loss: 0  # No loss over time assumed
            lifetime: 25
        costs:
            monetary:
                interest_rate: 0.10
                storage_cap: 200  # USD per kWh storage capacity

The contraints give a maximum installed generation capacity for battery storage together with a maximum ratio of energy capacity to storage capacity (`energy_cap_per_storage_cap_max`) of 4, which in turn limits the storage capacity. The ratio is the charge/discharge rate / storage capacity (a.k.a the battery reservoir). In the case of a storage technology, `energy_eff` applies twice: on charging and discharging. In addition, storage technologies can lose stored energy over time – in this case, we set this loss to zero.

##### Other technologies

Three more technologies are needed for a simple model. First, a definition of power demand:

A simple demand node.

    demand_power:
        essentials:
            name: 'Power demand'
            color: '#072486'
            parent: demand
            carrier: power

Power demand is a technology like any other. We will associate an actual demand time series with the demand technology later.

What remains to set up is a simple transmission technology. Transmission technologies (like conversion technologies) look different than other nodes, as they link the carrier at one location to the carrier at another (or, in the case of conversion, one carrier to another at the same location):

A simple transmission node with an \(energy_{eff}\).

    ac_transmission:
        essentials:
            name: 'AC power transmission'
            color: '#8465A9'
            parent: transmission
            carrier: power
        constraints:
            energy_eff: 0.85
            lifetime: 25
        costs:
            monetary:
                interest_rate: 0.10
                energy_cap: 200
                om_prod: 0.002

    free_transmission:
        essentials:
            name: 'Local power transmission'
            color: '#6783E3'
            parent: transmission
            carrier: power
        constraints:
            energy_cap_max: inf
            energy_eff: 1.0
        costs:
            monetary:
                om_prod: 0

`ac_transmission` has an efficiency of 0.85, so a loss during transmission of 0.15, as well as some cost definitions.

`free_transmission` allows local power transmission from any of the csp facilities to the nearest location. As the name suggests, it applies no cost or efficiency losses to this transmission.

##### Locations

In order to translate the model requirements shown in this section’s introduction into a model definition, five locations are used: `region-1`, `region-2`, `region1-1`, `region1-2`, and `region1-3`.

The technologies are set up in these locations as follows:

Locations and their technologies in the example model

Let’s now look at the first location definition:

    region1:
        coordinates: {lat: 40, lon: -2}
        techs:
            demand_power:
                constraints:
                    resource: file=demand-1.csv:demand
            ccgt:
                constraints:
                    energy_cap_max: 30000 # increased to ensure no unmet_demand in first timestep

There are several things to note here:

- The location specifies a dictionary of technologies that it allows (`techs`), with each key of the dictionary referring to the name of technologies defined in our `techs.yaml` file. Note that technologies listed here must have been defined elsewhere in the model configuration.

- It also overrides some options for both `demand_power` and `ccgt`. For the latter, it simply sets a location-specific maximum capacity constraint. For `demand_power`, the options set here are related to reading the demand time series from a CSV file. CSV is a simple text-based format that stores tables by comma-separated rows. Note that we did not define any `resource` option in the definition of the `demand_power` technology. Instead, this is done directly via a location-specific override. For this location, the file `demand-1.csv` is loaded and the column `demand` is taken (the text after the colon). If no column is specified, Calliope will assume that the column name matches the location name `region1-1`. Note that in Calliope, a supply is positive and a demand is negative, so the stored CSV data will be negative.

- Coordinates are defined by latitude (`lat`) and longitude (`lon`), which will be used to calculate distance of transmission lines (unless we specify otherwise later on) and for location-based visualisation.

The remaining location definitions look like this:

    region2:
        coordinates: {lat: 40, lon: -8}
        techs:
            demand_power:
                constraints:
                    resource: file=demand-2.csv:demand
            battery:

    region1-1.coordinates: {lat: 41, lon: -2}
    region1-2.coordinates: {lat: 39, lon: -1}
    region1-3.coordinates: {lat: 39, lon: -2}

    region1-1, region1-2, region1-3:
        techs:
            csp:

`region2` is very similar to `region1`, except that it does not allow the `ccgt` technology. The three `region1-` locations are defined together, except for their location coordinates, i.e. they each get the exact same configuration. They allow only the `csp` technology, this allows us to model three possible sites for CSP plants.

For transmission technologies, the model also needs to know which locations can be linked, and this is set up in the model configuration as follows:

    region1,region2:
        techs:
            ac_transmission:
                constraints:
                    energy_cap_max: 10000
    region1,region1-1:
        techs:
            free_transmission:
    region1,region1-2:
        techs:
            free_transmission:
    region1,region1-3:
        techs:
            free_transmission:

We are able to override constraints for transmission technologies at this point, such as the maximum capacity of the specific `region1` to `region2` link shown here.

##### Running the model

We now take you through running the model in a Jupyter notebook, which you can view here. After clicking on that link, you can also download and run the notebook yourself (you will need to have Calliope installed).

#### Tutorial 2: urban scale

This example consists of two possible sources of electricity, one possible source of heat, and one possible source of simultaneous heat and electricity. There are three locations, each describing a building, with transmission links between them. The diagram below gives an overview:

Overview of the built-in urban-scale example model

##### Supply technologies

This example model defines three supply technologies.

The first two are `supply_gas` and `supply_grid_power`, referring to the supply of `gas` (natural gas) and `electricity`, respectively, from the national distribution system. These ‘inifinitely’ available national commodities can become energy carriers in the system, with the cost of their purchase being considered at supply, not conversion.

The layout of a simple supply technology, in this case `supply_gas`, which has a resource input and a carrier output. A carrier conversion efficiency (\(energy_{eff}\)) can also be applied (although isn’t considered for our supply technologies in this problem).

The definition of these technologies in the example model’s configuration looks as follows:

    supply_grid_power:
        essentials:
            name: 'National grid import'
            color: '#C5ABE3'
            parent: supply
            carrier: electricity
        constraints:
            resource: inf
            energy_cap_max: 2000
            lifetime: 25
        costs:
            monetary:
                interest_rate: 0.10
                energy_cap: 15
                om_con: 0.1 # 10p/kWh electricity price #ppt

    supply_gas:
        essentials:
            name: 'Natural gas import'
            color: '#C98AAD'
            parent: supply
            carrier: gas
        constraints:
            resource: inf
            energy_cap_max: 2000
            lifetime: 25
        costs:
            monetary:
                interest_rate: 0.10
                energy_cap: 1
                om_con: 0.025 # 2.5p/kWh gas price #ppt

The final supply technology is `pv` (solar photovoltaic power), which serves as an inflexible supply technology. It has a time-dependant resource availablity, loaded from file, a maximum area over which it can capture its resource (`resource_area_max`) and a requirement that all available resource must be used (`force_resource: True`). This emulates the reality of solar technologies: once installed, their production matches the availability of solar energy.

The efficiency of the DC to AC inverter (which occurs after conversion from resource to energy carrier) is considered in `parasitic_eff` and the `resource_area_per_energy_cap` gives a link between the installed area of solar panels to the installed capacity of those panels (i.e. kWp).

In most cases, domestic PV panels are able to export excess energy to the national grid. We allow this here by specifying an `export_carrier`. Revenue for export will be considered on a per-location basis.

The definition of this technology in the example model’s configuration looks as follows:

    pv:
        essentials:
            name: 'Solar photovoltaic power'
            color: '#F9D956'
            parent: supply_power_plus
        constraints:
            export_carrier: electricity
            resource: file=pv_resource.csv:per_area  # Already accounts for panel efficiency - kWh/m2. Source: Renewables.ninja Solar PV Power - Version: 1.1 - License: https://creativecommons.org/licenses/by-nc/4.0/ - Reference: https://doi.org/10.1016/j.energy.2016.08.060
            resource_unit: energy_per_area
            parasitic_eff: 0.85 # inverter losses
            energy_cap_max: 250
            resource_area_max: 1500
            force_resource: true
            resource_area_per_energy_cap: 7 # 7m2 of panels needed to fit 1kWp of panels
            lifetime: 25
        costs:
            monetary:
                interest_rate: 0.10
                energy_cap: 1350

Finally, the parent of the PV technology is not `supply_plus`, but rather `supply_power_plus`. We use this to show the possibility of an intermediate technology group, which provides the information on the energy carrier (`electricity`) and the ultimate abstract base technology (`supply_plus`):

    tech_groups:
        supply_power_plus:
            essentials:
                parent: supply_plus
                carrier: electricity

Intermediate technology groups allow us to avoid repetition of technology information, be it in `essentials`, `constraints`, or `costs`, by linking multiple technologies to the same intermediate group.

##### Conversion technologies

The example model defines two conversion technologies.

The first is `boiler` (natural gas boiler), which serves as an example of a simple conversion technology with one input carrier and one output carrier. Its only constraints are the cost of built capacity (`costs.monetary.energy_cap`), a constraint on its maximum built capacity (`constraints.energy_cap.max`), and an energy conversion efficiency (`energy_eff`).

The layout of a simple node, in this case `boiler`, which has one carrier input, one carrier output, a carrier conversion efficiency (\(energy_{eff}\)), and a constraint on its maximum built \(energy_{cap}\) (which puts an upper limit on \(carrier_{prod}\)).

The definition of this technology in the example model’s configuration looks as follows:

    boiler:
        essentials:
            name: 'Natural gas boiler'
            color: '#8E2999'
            parent: conversion
            carrier_out: heat
            carrier_in: gas
        constraints:
            energy_cap_max: 600
            energy_eff: 0.85
            lifetime: 25
        costs:
            monetary:
                interest_rate: 0.10
                om_con: 0.004  # .4p/kWh

There are a few things to note. First, `boiler` defines a name, a color (given as an HTML color code), and a stack_weight. These are used by the built-in analysis tools when analyzing model results. Second, it specifies its parent, `conversion`, its carrier_in `gas`, and its carrier_out `heat`, thus setting itself up as a gas to heat conversion technology. This is followed by the definition of constraints and costs (the only cost class used is monetary, but this is where other “costs”, such as emissions, could be defined).

The second technology is `chp` (combined heat and power), and serves as an example of a possible conversion_plus technology making use of two output carriers.

The layout of a more complex node, in this case `chp`, which makes use of multiple output carriers.

This definition in the example model’s configuration is more verbose:

    chp:
        essentials:
            name: 'Combined heat and power'
            color: '#E4AB97'
            parent: conversion_plus
            primary_carrier_out: electricity
            carrier_in: gas
            carrier_out: electricity
            carrier_out_2: heat
        constraints:
            export_carrier: electricity
            energy_cap_max: 1500
            energy_eff: 0.405
            carrier_ratios.carrier_out_2.heat: 0.8
            lifetime: 25
        costs:
            monetary:
                interest_rate: 0.10
                energy_cap: 750
                om_prod: 0.004  # .4p/kWh for 4500 operating hours/year
                export: file=export_power.csv

See also

The conversion_plus tech

Again, `chp` has the definitions for name, color, parent, and carrier_in/out. It now has an additional carrier (`carrier_out_2`) defined in its essential information, allowing a second carrier to be produced at the same time as the first carrier (`carrier_out`). The carrier ratio constraint tells us the ratio of carrier_out_2 to carrier_out that we can achieve, in this case 0.8 units of heat are produced every time a unit of electricity is produced. to produce these units of energy, gas is consumed at a rate of `carrier_prod(carrier_out) / energy_eff`, so gas consumption is only a function of power output.

As with the `pv`, the `chp` an export eletricity. The revenue gained from this export is given in the file `export_power.csv`, in which negative values are given per time step.

##### Demand technologies

Electricity and heat demand are defined here:

    demand_electricity:
        essentials:
            name: 'Electrical demand'
            color: '#072486'
            parent: demand
            carrier: electricity

    demand_heat:
        essentials:
            name: 'Heat demand'
            color: '#660507'
            parent: demand
            carrier: heat

Electricity and heat demand are technologies like any other. We will associate an actual demand time series with each demand technology later.

##### Transmission technologies

In this district, electricity and heat can be distributed between locations. Gas is made available in each location without consideration of transmission.

A simple transmission node with an \(energy_{eff}\).

    power_lines:
        essentials:
            name: 'Electrical power distribution'
            color: '#6783E3'
            parent: transmission
            carrier: electricity
        constraints:
            energy_cap_max: 2000
            energy_eff: 0.98
            lifetime: 25
        costs:
            monetary:
                interest_rate: 0.10
                energy_cap_per_distance: 0.01

    heat_pipes:
        essentials:
            name: 'District heat distribution'
            color: '#823739'
            parent: transmission
            carrier: heat
        constraints:
            energy_cap_max: 2000
            energy_eff_per_distance: 0.975
            lifetime: 25
        costs:
            monetary:
                interest_rate: 0.10
                energy_cap_per_distance: 0.3

`power_lines` has an efficiency of 0.95, so a loss during transmission of 0.05. `heat_pipes` has a loss rate per unit distance of 2.5%/unit distance (or `energy_eff_per_distance` of 97.5%). Over the distance between the two locations of 0.5km (0.5 units of distance), this translates to \(2.5^{0.5}\) = 1.58% loss rate.

##### Locations

In order to translate the model requirements shown in this section’s introduction into a model definition, four locations are used: `X1`, `X2`, `X3`, and `N1`.

The technologies are set up in these locations as follows:

Locations and their technologies in the urban-scale example model

Let’s now look at the first location definition:

    X1:
        techs:
            chp:
            pv:
            supply_grid_power:
                costs.monetary.energy_cap: 100 # cost of transformers
            supply_gas:
            demand_electricity:
                constraints.resource: file=demand_power.csv
            demand_heat:
                constraints.resource: file=demand_heat.csv
        available_area: 500
        coordinates: {x: 2, y: 7}

There are several things to note here:

- The location specifies a dictionary of technologies that it allows (`techs`), with each key of the dictionary referring to the name of technologies defined in our `techs.yaml` file. Note that technologies listed here must have been defined elsewhere in the model configuration.

- It also overrides some options for both `demand_electricity`, `demand_heat`, and `supply_grid_power`. For the latter, it simply sets a location-specific cost. For demands, the options set here are related to reading the demand time series from a CSV file. CSV is a simple text-based format that stores tables by comma-separated rows. Note that we did not define any `resource` option in the definition of these demands. Instead, this is done directly via a location-specific override. For this location, the files `demand_heat.csv` and `demand_power.csv` are loaded. As no column is specified (see national scale example model) Calliope will assume that the column name matches the location name `X1`. Note that in Calliope, a supply is positive and a demand is negative, so the stored CSV data will be negative.

- Coordinates are defined by cartesian coordinates `x` and `y`, which will be used to calculate distance of transmission lines (unless we specify otherwise later on) and for location-based visualisation. These coordinates are abstract, unlike latitude and longitude, and can be used when we don’t know (or care) about the geographical location of our problem.

- An `available_area` is defined, which will limit the maximum area of all `resource_area` technologies to the e.g. roof space available at our location. In this case, we just have `pv`, but the case where solar thermal panels compete with photovoltaic panels for space, this would the sum of the two to the available area.

The remaining location definitions look like this:

    X2:
        techs:
            boiler:
                costs.monetary.energy_cap: 43.1 # different boiler costs
            pv:
                costs.monetary:
                        om_prod: -0.0203 # revenue for just producing electricity
                        export: -0.0491 # FIT return for PV export
            supply_gas:
            demand_electricity:
                constraints.resource: file=demand_power.csv
            demand_heat:
                constraints.resource: file=demand_heat.csv
        available_area: 1300
        coordinates: {x: 8, y: 7}

    X3:
        techs:
            boiler:
                costs.monetary.energy_cap: 78 # different boiler costs
            pv:
                constraints:
                    energy_cap_max: 50 # changing tariff structure below 50kW
                costs.monetary:
                        om_annual: -80.5 # reimbursement per kWp from FIT
            supply_gas:
            demand_electricity:
                constraints.resource: file=demand_power.csv
            demand_heat:
                constraints.resource: file=demand_heat.csv
        available_area: 900
        coordinates: {x: 5, y: 3}

`X2` and `X3` are very similar to `X1`, except that they do not connect to the national electricity grid, nor do they contain the `chp` technology. Specific `pv` cost structures are also given, emulating e.g. commercial vs. domestic feed-in tariffs.

`N1` differs to the others by virtue of containing no technologies. It acts as a branching station for the heat network, allowing connections to one or both of `X2` and `X3` without double counting the pipeline from `X1` to `N1`. Its definition look like this:

    N1: # location for branching heat transmission network
        coordinates: {x: 5, y: 7}

For transmission technologies, the model also needs to know which locations can be linked, and this is set up in the model configuration as follows:

    X1,X2:
        techs:
            power_lines:
                distance: 10
    X1,X3:
        techs:
            power_lines:
    X1,N1:
        techs:
            heat_pipes:
    N1,X2:
        techs:
            heat_pipes:
    N1,X3:
        techs:
            heat_pipes:

The distance measure for the power line is larger than the straight line distance given by the coordinates of `X1` and `X2`, so we can provide more information on non-direct routes for our distribution system. These distances will override any automatic straight-line distances calculated by coordinates.

##### Revenue by export

Defined for both PV and CHP, there is the option to accrue revenue in the system by exporting electricity. This export is considered as a removal of the energy carrier `electricity` from the system, in exchange for negative cost (i.e. revenue). To allow this, `carrier_export: electricity` has been given under both technology definitions and an `export` value given under costs.

The revenue from PV export varies depending on location, emulating the different feed-in tariff structures in the UK for commercial and domestic properties. In domestic properties, the revenue is generated by simply having the installation (per kW installed capacity), as export is not metered. Export is metered in commercial properties, thus revenue is generated directly from export (per kWh exported). The revenue generated by CHP depends on the electricity grid wholesale price per kWh, being 80% of that. These revenue possibilities are reflected in the technologies’ and locations’ definitions.

##### Running the model

We now take you through running the model in a Jupyter notebook, which you can view here. After clicking on that link, you can also download and run the notebook yourself (you will need to have Calliope installed).

#### Tutorial 3: Mixed Integer Linear Programming

This example is based on the urban scale example model, but with an override. In the model’s `scenarios.yaml` file overrides are defined which trigger binary and integer decision variables, creating a MILP model, rather than a conventional LP model.

##### Units

The capacity of a technology is usually a continuous decision variable, which can be within the range of 0 and `energy_cap_max` (the maximum capacity of a technology). In this model, we introduce a unit limit on the CHP instead:

        chp:
            constraints:
                units_max: 4
                energy_cap_per_unit: 300
                energy_cap_min_use: 0.2
            costs:
                monetary:
                    energy_cap: 700
                    purchase: 40000

A unit maximum allows a discrete, integer number of CHP to be purchased, each having a capacity of `energy_cap_per_unit`. Any of `energy_cap_max`, `energy_cap_min`, or `energy_cap_equals` are now ignored, in favour of `units_max`, `units_min`, or `units_equals`. A useful feature unlocked by introducing this is the ability to set a minimum operating capacity which is only enforced when the technology is operating. In the LP model, `energy_cap_min_use` would force the technology to operate at least at that proportion of its maximum capacity at each time step. In this model, the newly introduced `energy_cap_min_use` of 0.2 will ensure that the output of the CHP is 20% of its maximum capacity in any time step in which it has a non-zero output.

##### Purchase cost

The boiler does not have a unit limit, it still utilises the continuous variable for its capacity. However, we have introduced a `purchase` cost:

        boiler:
            costs:
                monetary:
                    energy_cap: 35
                    purchase: 2000

By introducing this, the boiler now has a binary decision variable associated with it, which is 1 if the boiler has a non-zero `energy_cap` (i.e. the optimisation results in investment in a boiler) and 0 if the capacity is 0. The purchase cost is applied to the binary result, providing a fixed cost on purchase of the technology, irrespective of the technology size. In physical terms, this may be associated with the cost of pipework, land purchase, etc. The purchase cost is also imposed on the CHP, which is applied to the number of integer CHP units in which the solver chooses to invest.

MILP functionality can be easily applied, but convergence is slower as a result of integer/binary variables. It is recommended to use a commercial solver (e.g. Gurobi, CPLEX) if you wish to utilise these variables outside this example model.

##### Asynchronous energy production/consumption

The heat pipes which distribute thermal energy in the network may be prone to dissipating heat in an unphysical way. I.e. given that they have distribution losses associated with them, in any given timestep, a link could produce and consume energy in the same timestep, losing energy to the atmosphere in both instances, but having a net energy transmission of zero. This allows e.g. a CHP facility to overproduce heat to produce more cheap electricity, and have some way of dumping that heat. The `asynchronous_prod_con` binary constraint ensures this phenomenon is avoided:

        heat_pipes:
            constraints:
                force_asynchronous_prod_con: true

Now, only one of `carrier_prod` and `carrier_con` can be non-zero in a given timestep. This constraint can also be applied to storage technologies, to similarly control charge/discharge.

##### Running the model

We now take you through running the model in a Jupyter notebook, which you can view here. After clicking on that link, you can also download and run the notebook yourself (you will need to have Calliope installed).

### Advanced constraints

This section, as the title suggests, contains more info and more details, and in particular, information on some of Calliope’s more advanced functionality.

We suggest you read the Building a model, Running a model and Analysing a model sections first.

#### The `supply_plus` tech

The `plus` tech groups offer complex functionality, for technologies which cannot be described easily. `Supply_plus` allows a supply technology with internal storage of resource before conversion to the carrier happens. This could be emulated with dummy carriers and a combination of supply, storage, and conversion techs, but the `supply_plus` tech allows for concise and mathematically more efficient formulation.

Representation of the `supply_plus` technology

An example use of `supply_plus` is to define a concentrating solar power (CSP) technology which consumes a solar resource, has built-in thermal storage, and produces electricity. See the national-scale built-in example model for an application of this.

See the listing of supply_plus configuration in the abstract base tech group definitions for the additional constraints that are possible.

Warning

When analysing results from supply_plus, care must be taken to correctly account for the losses along the transformation from resource to carrier. For example, charging of storage from the resource may have a `resource_eff`-associated loss with it, while discharging storage to produce the carrier may have a different loss resulting from a combination of `energy_eff` and `parasitic_eff`. Such intermediate conversion losses need to be kept in mind when comparing discharge from storage with `carrier_prod` in the same time step.

#### The `conversion_plus` tech

The `plus` tech groups offer complex functionality, for technologies which cannot be described easily. `Conversion_plus` allows several carriers to be converted to several other carriers. Describing such a technology requires that the user understands the `carrier_ratios`, i.e. the interactions and relative efficiencies of carrier inputs and outputs.

Representation of the most complex `conversion_plus` technology available

The `conversion_plus` technologies allows for up to three carrier groups as inputs (`carrier_in`, `carrier_in_2` and `carrier_in_3`) and up to three carrier groups as outputs (`carrier_out`, `carrier_out_2` and `carrier_out_3`). A carrier group can contain any number of carriers.

The efficiency of a `conversion_plus` tech dictates how many units of carrier_out are produced per unit of consumed carrier_in. A unit of carrier_out_2 and of carrier_out_3 is produced each time a unit of carrier_out is produced. Similarly, a unit of Carrier_in_2 and of carrier_in_3 is consumed each time a unit of carrier_in is consumed. Within a given carrier group (e.g. carrier_out_2) any number of carriers can meet this one unit. The `carrier_ratio` of any carrier compares it either to the production of one unit of carrier_out or to the consumption of one unit of carrier_in.

In this section, we give examples of a few `conversion_plus` technologies alongside the YAML formulation required to construct them:

##### Combined heat and power

A combined heat and power plant produces electricity, in this case from natural gas. Waste heat that is produced can be used to meet nearby heat demand (e.g. via district heating network). For every unit of electricity produced, 0.8 units of heat are always produced. This is analogous to the heat to power ratio (HTP). Here, the HTP is 0.8.

    chp:
        essentials:
            name: Combined heat and power
            carrier_in: gas
            carrier_out: electricity
            carrier_out_2: heat
            primary_carrier_out: electricity
        constraints:
            energy_eff: 0.45
            energy_cap_max: 100
            carrier_ratios.carrier_out_2.heat: 0.8

##### Air source heat pump

The output energy from the heat pump can be either heat or cooling, simulating a heat pump that can be useful in both summer and winter. For each unit of electricity input, one unit of output is produced. Within this one unit of `carrier_out`, there can be a combination of heat and cooling. Heat is produced with a COP of 5, cooling with a COP of 3. If only heat were produced in a timestep, 5 units of it would be available in carrier_out; similarly 3 units for cooling. In another timestep, both heat and cooling might be produced with e.g. 2.5 units heat + 1.5 units cooling = 1 unit of carrier_out.

    ahp:
        essentials:
            name: Air source heat pump
            carrier_in: electricity
            carrier_out: [heat, cooling]
            primary_carrier_out: heat

        constraints:
            energy_eff: 1
            energy_cap_max: 100
            carrier_ratios:
                carrier_out:
                    heat: 5
                    cooling: 3

##### Combined cooling, heat and power (CCHP)

A CCHP plant can use generated heat to produce cooling via an absorption chiller. As with the CHP plant, electricity is produced at 45% efficiency. For every unit of electricity produced, 1 unit of `carrier_out_2` must be produced, which can be a combination of 0.8 units of heat and 0.5 units of cooling. Some example ways in which the model could decide to operate this unit in a given time step are:

- 1 unit of gas (`carrier_in`) is converted to 0.45 units of electricity (`carrier_out`) and (0.8 * 0.45) units of heat (`carrier_out_2`)

- 1 unit of gas is converted to 0.45 units electricity and (0.5 * 0.45) units of cooling

- 1 unit of gas is converted to 0.45 units electricity, (0.3 * 0.8 * 0.45) units of heat, and (0.7 * 0.5 * 0.45) units of cooling

    cchp:
        essentials:
            name: Combined cooling, heat and power
            carrier_in: gas
            carrier_out: electricity
            carrier_out_2: [heat, cooling]
            primary_carrier_out: electricity

        constraints:
            energy_eff: 0.45
            energy_cap_max: 100
            carrier_ratios.carrier_out_2: {heat: 0.8, cooling: 0.5}

##### Advanced gas turbine

This technology can choose to burn methane (CH:sub:4) or send hydrogen (H:sub:2) through a fuel cell to produce electricity. One unit of carrier_in can be met by any combination of methane and hydrogen. If all methane, 0.5 units of carrier_out would be produced for 1 unit of carrier_in (energy_eff). If all hydrogen, 0.25 units of carrier_out would be produced for the same amount of carrier_in (energy_eff * hydrogen carrier ratio).

    gt:
        essentials:
            name: Advanced gas turbine
            carrier_in: [methane, hydrogen]
            carrier_out: electricity

        constraints:
            energy_eff: 0.5
            energy_cap_max: 100
            carrier_ratios:
                carrier_in: {methane: 1, hydrogen: 0.5}

##### Complex fictional technology

There are few instances where using the full capacity of a conversion_plus tech is physically possible. Here, we have a fictional technology that combines fossil fuels with biomass/waste to produce heat, cooling, and electricity. Different ‘grades’ of heat can be produced, the higher grades having an alternative. High grade heat (`high_T_heat`) is produced and can be used directly, or used to produce electricity (via e.g. organic rankine cycle). `carrier_out` is thus a combination of these two. carrier_out_2 can be 0.3 units mid grade heat for every unit carrier_out or 0.2 units cooling. Finally, 0.1 units `carrier_out_3`, low grade heat, is produced for every unit of carrier_out.

    complex:
        essentials:
            name: Complex fictional technology
            carrier_in: [coal, gas, oil]
            carrier_in_2: [biomass, waste]
            carrier_out: [high_T_heat, electricity]
            carrier_out_2: [mid_T_heat, cooling]
            carrier_out_3: low_T_heat
            primary_carrier_out: electricity

        constraints:
            energy_eff: 1
            energy_cap_max: 100
            carrier_ratios:
                carrier_in: {coal: 1.2, gas: 1, oil: 1.6}
                carrier_in_2: {biomass: 1, waste: 1.25}
                carrier_out: {high_T_heat: 0.8, electricity: 0.6}
                carrier_out_2: {mid_T_heat: 0.3, cooling: 0.2}
                carrier_out_3.low_T_heat: 0.15

A `primary_carrier_out` must be defined when there are multiple `carrier_out` values defined, similarly `primary_carrier_in` can be defined for `carrier_in`. primary_carriers can be defined as any carrier in a technology’s input/output carriers (including secondary and tertiary carriers). The chosen output carrier will be the one to which production costs are applied (reciprocally, input carrier for consumption costs).

Note

`Conversion_plus` technologies can also export any one of their output carriers, by specifying that carrier as `carrier_export`.

#### Resource area constraints

Several optional constraints can be used to specify area-related restrictions on technology use.

To make use of these constraints, one should set `resource_unit: energy_per_area` for the given technologies. This scales the available resource at a given location for a given technology with its `resource_area` decision variable.

The following related settings are available:

- `resource_area_equals`, `resource_area_max`, `resource_area_min`: Set uppper or lower bounds on resource_area or force it to a specific value

- `resource_area_per_energy_cap`: False by default, but if set to true, it forces `resource_area` to follow `energy_cap` with the given numerical ratio (e.g. setting to 1.5 means that `resource_area == 1.5 * energy_cap`)

By default, `resource_area_max` is infinite and `resource_area_min` is 0 (zero).

#### Group constraints

Group constraints are applied to named sets of locations and techs, called “constraint groups”, specified through a top-level `group_constraints` key (sitting alongside other top-level keys like `model` and `run`).

The below example shows two such named groups. The first does not specify a subset of techs or locations and is thus applied across the entire model. In the example, we use `cost_max` with the `co2` cost class to specify a model-wide emissions limit (assuming the technologies in the model have `co2` costs associated with them). We also use the `demand_share_min` constraint to force wind and PV to supply at least 40% of electricity demand in Germany, which is modelled as two locations (North and South):

    run:
        ...

    model:
        ...

    group_constraints:
        # A constraint group to apply a systemwide CO2 cap
        systemwide_co2_cap:
            cost_max:
                co2: 100000
        # A constraint group to enforce renewable generation in Germany
        renewable_minimum_share_in_germany:
            techs: ['wind', 'pv']
            locs: ['germany_north', 'germany_south']
            demand_share_min:
                electricity: 0.4

When specifying group constraints, a named group must give at least one constraint, but can list an arbitrary amount of constraints, and optionally give a subset of techs and locations:

    group_constraints:
        group_name:
            techs: []  # Optional, can be left out if empty
            locs: []  # Optional, can be left out if empty
            # Any number of constraints can be specified for the given group
            constraint_1: ...
            constraint_2: ...
            ...

The below table lists all available group constraints.

Note that when computing the share for `demand_share` constraints, only `demand` technologies are counted, and that when computing the share for `supply_share` constraints, `supply` and `supply_plus` technologies are counted.

Group constraints
Constraint | Dimensions | Description
--- | --- | ---
`demand_share_min` | carriers | Minimum share of carrier demand met from a set of technologies across a set of locations, on average over the entire model period.
`demand_share_max` | carriers | Maximum share of carrier demand met from a set of technologies across a set of locations, on average over the entire model period.
`demand_share_equals` | carriers | Share of carrier demand met from a set of technologies across a set of locations, on average over the entire model period.
`demand_share_per_timestep_min` | carriers | Minimum share of carrier demand met from a set of technologies across a set of locations, in each individual timestep.
`demand_share_per_timestep_max` | carriers | Maximum share of carrier demand met from a set of technologies across a set of locations, in each individual timestep.
`demand_share_per_timestep_equals` | carriers | Share of carrier demand met from a set of technologies across a set of locations, in each individual timestep.
`demand_share_per_timestep_decision` | carriers | Turns the per-timestep share of carrier demand met from a set of technologies across a set of locations into a model decision variable.
`carrier_prod_share_min` | carriers | Minimum share of carrier production met from a set of technologies across a set of locations, on average over the entire model period.
`carrier_prod_share_max` | carriers | Maximum share of carrier production met from a set of technologies across a set of locations, on average over the entire model period.
`carrier_prod_share_equals` | carriers | Share of carrier production met from a set of technologies across a set of locations, on average over the entire model period.
`carrier_prod_share_per_timestep_min` | carriers | Minimum share of carrier production met from a set of technologies across a set of locations, in each individual timestep.
`carrier_prod_share_per_timestep_max` | carriers | Maximum share of carrier production met from a set of technologies across a set of locations, in each individual timestep.
`carrier_prod_share_per_timestep_equals` | carriers | Share of carrier production met from a set of technologies across a set of locations, in each individual timestep.
`net_import_share_min` | carriers | Minimum share of demand met from transmission technologies into a set of locations, on average over the entire model period. All transmission technologies of the chosen carrier are added automatically and technologies must thus not be defined explicitly.
`net_import_share_max` | carriers | Maximum share of demand met from transmission technologies into a set of locations, on average over the entire model period. All transmission technologies of the chosen carrier are added automatically and technologies must thus not be defined explicitly.
`net_import_share_equals` | carriers | Share of demand met from transmission technologies into a set of locations, on average over the entire model. All transmission technologies of the chosen carrier are added automatically and technologies must thus not be defined explicitly. period.
`carrier_prod_min` | carriers | Maximum absolute sum of supplied energy (carrier_prod) over all timesteps for a set of technologies across a set of locations.
`carrier_prod_max` | carriers | Maximum absolute sum of supplied energy (carrier_prod) over all timesteps for a set of technologies across a set of locations.
`carrier_prod_equals` | carriers | Exact absolute sum of supplied energy (carrier_prod) over all timesteps for a set of technologies across a set of locations.
`cost_max` | costs | Maximum total cost from a set of technologies across a set of locations.
`cost_min` | costs | Minimum total cost from a set of technologies across a set of locations.
`cost_equals` | costs | Total cost from a set of technologies across a set of locations must equal given value.
`cost_var_max` | costs | Maximum variable cost from a set of technologies across a set of locations.
`cost_var_min` | costs | Minimum variable cost from a set of technologies across a set of locations.
`cost_var_equals` | costs | Variable cost from a set of technologies across a set of locations must equal given value.
`cost_investment_max` | costs | Maximum investment cost from a set of technologies across a set of locations.
`cost_investment_min` | costs | Minimum investment cost from a set of technologies across a set of locations.
`cost_investment_equals` | costs | Investment cost from a set of technologies across a set of locations must equal given value.
`energy_cap_share_min` | – | Minimum share of installed capacity from a set of technologies across a set of locations.
`energy_cap_share_max` | – | Maximum share of installed capacity from a set of technologies across a set of locations.
`energy_cap_share_equals` | – | Exact share of installed capacity from a set of technologies across a set of locations.
`energy_cap_min` | – | Minimum installed capacity from a set of technologies across a set of locations.
`energy_cap_max` | – | Maximum installed capacity from a set of technologies across a set of locations.
`energy_cap_equals` | – | Exact installed capacity from a set of technologies across a set of locations.
`resource_area_min` | – | Minimum resource area used by a set of technologies across a set of locations.
`resource_area_max` | – | Maximum resource area used by a set of technologies across a set of locations.
`resource_area_equals` | – | Exact resource area used by a set of technologies across a set of locations.

For specifics of the mathematical formulation of the available group constraints, see Group constraints in the mathematical formulation section.

See also

The built-in national-scale example’s `scenarios.yaml` shows two example uses of group constraints: limiting shared capacity with `energy_cap_max` and enforcing a minimum shared power generation with `carrier_prod_share_min`.

##### `demand_share_per_timestep_decision`

The `demand_share_per_timestep_decision` constraint is a special case amongst group constraints, as it introduces a new decision variable, allowing the model to set the share of demand met by each technology given in the constraint’s group, across the locations given in the group. The fraction set in the constraint is the fraction of total demand over which the model has control. Setting this to anything else than `1.0` only makes sense when a subset of technologies is targeted by the constraint.

It can also be set to `.inf` to permit Calliope to decide on the fraction of total demand to cover by the constraint. This can be necessary in cases where there are sources of carrier consumption other than demand in the locations covered by the group constraint: when using conversion techs or when there are losses from storage and transmission, as the share may then be higher than 1, leading to an infeasible model if it is forced to `1.0`.

This constraint can be useful in large-scale models where individual technologies should not fluctuate in their relative share from time step to time step, for example, when modelling the relative share of heating demand from different heating technologies.

Warning

It is easy to create an infeasible model by setting several conflicting group constraints, in particular when `demand_share_per_timestep_decision` is involved. Make sure you think through the implications when setting up these constraints!

#### Per-distance constraints and costs

Transmission technologies can additionally specify per-distance efficiency (loss) with `energy_eff_per_distance` and per-distance costs with `energy_cap_per_distance`:

    techs:
        my_transmission_tech:
            essentials:
                ...
            constraints:
                # "efficiency" (1-loss) per unit of distance
                energy_eff_per_distance: 0.99
            costs:
                monetary:
                    # cost per unit of distance
                    energy_cap_per_distance: 10

The distance is specified in transmission links:

    links:
        location1,location2:
            my_transmission_tech:
                distance: 500
                constraints:
                    energy_cap.max: 10000

If no distance is given, but the locations have been given lat and lon coordinates, Calliope will compute distances automatically (based on the length of a straight line connecting the locations).

#### One-way transmission links

Transmission links are bidirectional by default. To force unidirectionality for a given technology along a given link, you have to set the `one_way` constraint in the constraint definition of that technology, for that link:

    links:
        location1,location2:
            transmission-tech:
                constraints:
                    one_way: true

This will only allow transmission from `location1` to `location2`. To swap the direction, the link name must be inverted, i.e. `location2,location1`.

#### Cyclic storage

With `storage` and `supply_plus` techs, it is possible to link the storage at either end of the timeseries, using cyclic storage. This allows the user to better represent multiple years by just modelling one year. Cyclic storage is activated by default (to deactivate: `run.cyclic_storage: false`). As a result, a technology’s initial stored energy at a given location will be equal to its stored energy at the end of the model’s last timestep.

For example, for a model running over a full year at hourly resolution, the initial storage at Jan 1st 00:00:00 will be forced equal to the storage at the end of the timestep Dec 31st 23:00:00. By setting `storage_initial` for a technology, it is also possible to fix the value in the last timestep. For instance, with `run.cyclic_storage: true` and a `storage_initial` of zero, the stored energy must be zero by the end of the time horizon.

Without cyclic storage in place (as was the case prior to v0.6.2), the storage tech can have any amount of stored energy by the end of the timeseries. This may prove useful in some cases, but has less physical meaning than assuming cyclic storage.

Note

Cyclic storage also functions when time clustering, if allowing storage to be tracked between clusters (see Time resolution adjustment). However, it cannot be used in `operate` run mode.

#### Revenue and export

It is possible to specify revenues for technologies simply by setting a negative cost value. For example, to consider a feed-in tariff for PV generation, it could be given a negative operational cost equal to the real operational cost minus the level of feed-in tariff received.

Export is an extension of this, allowing an energy carrier to be removed from the system without meeting demand. This is analogous to e.g. domestic PV technologies being able to export excess electricity to the national grid. A cost (or negative cost: revenue) can then be applied to export.

Note

Negative costs can be applied to capacity costs, but the user must an ensure a capacity limit has been set. Otherwise, optimisation will be unbounded.

#### The `group_share` constraint (deprecated)

Warning

`group_share` is deprecated as of v0.6.4 and will be removed in v0.7.0. Use the new, more flexible functionality Group constraints to replace it.

The `group_share` constraint can be used to force groups of technologies to fulfill certain shares of supply or capacity.

For example, assuming a model containing a `csp` and a `cold_fusion` power generation technology, we could force at least 85% of power generation in the model to come from these two technologies with the following constraint definition in the `model` settings:

    model:
        group_share:
            csp,cold_fusion:
                carrier_prod_min:
                    power: 0.85

Possible `group_share` constraints with carrier-specific settings are:

- `carrier_prod_min`

- `carrier_prod_max`

- `carrier_prod_equals`

Possible `group_share` constraints with carrier-independent settings are:

- `energy_cap_min`

- `energy_cap_max`

- `energy_cap_equals`

These can be implemented as, for example, to force at most 20% of `energy_cap` to come from the two listed technologies:

    model:
        group_share:
            csp,cold_fusion:
                energy_cap_max: 0.20

#### Binary and mixed-integer constraints

Calliope models are purely linear by default. However, several constraints can turn a model into a binary or mixed-integer model. Because solving problems with binary or integer variables takes considerably longer than solving purely linear models, it usually makes sense to carefully consider whether the research question really necessitates going beyond a purely linear model.

By applying a `purchase` cost to a technology, that technology will have a binary variable associated with it, describing whether or not it has been “purchased”.

By applying `units.max`, `units.min`, or `units.equals` to a technology, that technology will have a integer variable associated with it, describing how many of that technology have been “purchased”. If a `purchase` cost has been applied to this same technology, the purchasing cost will be applied per unit.

Warning

Integer and binary variables are a recent addition to Calliope and may not cover all edge cases as intended. Please raise an issue on GitHub if you see unexpected behavior.

See also

Tutorial 3: Mixed Integer Linear Programming

##### Asynchronous energy production/consumption

The `asynchronous_prod_con` binary constraint ensures that only one of `carrier_prod` and `carrier_con` can be non-zero in a given timestep.

This constraint can be applied to storage or transmission technologies. This example shows use with a heat transmission technology:

        heat_pipes:
            constraints:
                force_asynchronous_prod_con: true

In the above example, heat pipes which distribute thermal energy in the network may be prone to dissipating heat in an unphysical way. I.e. given that they have distribution losses associated with them, in any given timestep, a link could produce and consume energy in the same timestep, losing energy to the atmosphere in both instances, but having a net energy transmission of zero. This might allow e.g. a CHP facility to overproduce heat to produce more cheap electricity, and have some way of dumping that heat. Enabling the `asynchronous_prod_con` constraint ensures that this does not happen.

### Advanced features

Once you’re comfortable with building, running, and analysing one of the built-in example models, you may want to explore Calliope’s advanced functionality. With these features, you will be able to build and run complex models in no time.

#### Time resolution adjustment

Models have a default timestep length (defined implicitly by the timesteps of the model’s time series data). This default resolution can be adjusted over parts of the dataset by specifying time resolution adjustment in the model configuration, for example:

    model:
        time:
            function: resample
            function_options: {'resolution': '6H'}

In the above example, this would resample all time series data to 6-hourly timesteps.

Calliope’s time resolution adjustment functionality allows running a function that can perform arbitrary adjustments to the time series data in the model.

The available options include:

1. Uniform time resolution reduction through the `resample` function, which takes a pandas-compatible rule describing the target resolution (see above example).

2. Deriving representative days from the input time series, by applying the clustering method implemented in `calliope.time.clustering`, for example:

    model:
        time:
            function: apply_clustering
            function_options:
                clustering_func: kmeans
                how: mean
                k: 20

When using representative days, a number of additional constraints are added, based on the study undertaken by Kotzur et al. These constraints require a new decision variable `storage_inter_cluster`, which tracks storage between all the dates of the original timeseries. This particular functionality can be disabled by including `storage_inter_cluster: false` in the function_options given above.

Note

It is also possible to load user-defined representative days, by pointing to a file in clustering_func in the same format as pointing to timeseries files in constraints, e.g. `clustering_func: file=clusters.csv:column_name`. Clusters are unique per datestep, so the clustering file is most readable if the index is at datestep resolution. But, the clustering file index can be in timesteps (e.g. if sharing the same file as a constraint timeseries), with the cluster number repeated per timestep in a day. Cluster values should be integer, starting at zero.

3. Heuristic selection of time steps, that is, the application of one or more of the masks defined in `calliope.time.masks`, which will mark areas of the time series to retain at maximum resolution (unmasked) and areas where resolution can be lowered (masked). Options can be passed to the masking functions by specifying `options`. A `time.function` can still be specified and will be applied to the masked areas (i.e. those areas of the time series not selected to remain at the maximum resolution), as in this example, which looks for the week of minimum and maximum potential wind generation (assuming a `wind` technology was specified), then reduces the rest of the input time series to 6-hourly resolution:

    model:
        time:
            masks:
                - {function: extreme, options: {padding: 'calendar_week', tech: 'wind', how: 'max'}}
                - {function: extreme, options: {padding: 'calendar_week', tech: 'wind', how: 'min'}}
            function: resample
            function_options: {'resolution': '6H'}

Warning

When using time clustering or time masking, the resulting timesteps will be assigned different weights depending on how long a period of time they represent. Weights are used for example to give appropriate weight to the operational costs of aggregated typical days in comparison to individual extreme days, if both exist in the same processed time series. The weighting is accessible in the model data, e.g. through `model.inputs.timestep_weights`. The interpretation of results when weights are not 1 for all timesteps requires caution. Production values are not scaled according to weights, but costs are multiplied by weight, in order to weight different timesteps appropriately in the objective function. This means that costs and production values are not consistent without manually post-processing them by either multipyling production by weight (production would then be inconsistent with capacity) or dividing costs by weight. The computation of levelised costs and of capacity factors takes weighting into account, so these values are consisten and can be used as usual.

See also

See the implementation of constraints in `calliope.backend.pyomo.constraints` for more detail on timestep weights and how they affect model constraints.

#### Setting a random seed

By specifying `model.random_seed` in the model configuration, any alphanumeric string can be used to initialise the random number generator at the very start of model processing.

This is useful for full reproducibility of model results where time series clustering is used, as clustering methods such as k-means depend on randomly generated initial conditions.

Note that this affects only the random number generator used in Calliope’s model preprocessing and not in any way the solver used to solve the model (any solver-specific options need to be set specifically for that solver; see Specifying custom solver options).

#### Using `tech_groups` to group configuration

In a large model, several very similar technologies may exist, for example, different kinds of PV technologies with slightly different cost data or with different potentials at different model locations.

To make it easier to specify closely related technologies, `tech_groups` can be used to specify configuration shared between multiple technologies. The technologies then give the `tech_group` as their parent, rather than one of the abstract base technologies.

You can as well extend abstract base technologies, by adding an attribute that will be in effect for all technologies derived from the base technology. To do so, use the name of the abstract base technology for your group, but omit the parent.

For example:

    tech_groups:
        supply:
            constraints:
                monetary:
                    interest_rate: 0.1
        pv:
            essentials:
                parent: supply
                carrier: power
            constraints:
                resource: file=pv_resource.csv
                lifetime: 30
            costs:
                monetary:
                    om_annual_investment_fraction: 0.05
                    depreciation_rate: 0.15

    techs:
        pv_large_scale:
            essentials:
                parent: pv
                name: 'Large-scale PV'
            constraints:
                energy_cap_max: 2000
            costs:
                monetary:
                    energy_cap: 750
        pv_rooftop:
            essentials:
                parent: pv
                name: 'Rooftop PV'
            constraints:
                energy_cap_max: 10000
            costs:
                monetary:
                    energy_cap: 1000

None of the `tech_groups` appear in model results, they are only used to group model configuration values.

#### Removing techs, locations and links

By specifying `exists: false` in the model configuration, which can be done for example through overrides, model components can be removed for debugging or scenario analysis.

This works for:

- Techs: `techs.tech_name.exists: false`

- Locations: `locations.location_name.exists: false`

- Links: `links.location1,location2.exists: false`

- Techs at a specific location: `locations.location_name.techs.tech_name.exists: false`

- Transmission techs at a specific location: `links.location1,location2.techs.transmission_tech.exists: false`

- Group constraints: `group_constraints.my_constraint.exists: false`

#### Operational mode

In planning mode, constraints are given as upper and lower boundaries and the model decides on an optimal system configuration. In operational mode, all capacity constraints are fixed and the system is operated with a receding horizon control algorithm.

To specify a runnable operational model, capacities for all technologies at all locations must have be defined. This can be done by specifying `energy_cap_equals`. In the absence of `energy_cap_equals`, constraints given as `energy_cap_max` are assumed to be fixed in operational mode.

Operational mode runs a model with a receding horizon control algorithm. This requires two additional settings:

    run:
        operation:
            horizon: 48  # hours
            window: 24  # hours

`horizon` specifies how far into the future the control algorithm optimises in each iteration. `window` specifies how many of the hours within `horizon` are actually used. In the above example, decisions on how to operate for each 24-hour window are made by optimising over 48-hour horizons (i.e., the second half of each optimisation run is discarded). For this reason, `horizon` must always be larger than `window`.

#### Generating scripts to run a model many times

Scenarios and overrides can be used to run a given model multiple times with slightly changed settings or constraints.

This functionality can be used together with the `calliope generate_runs` and `calliope generate_scenarios` command-line tools to generate scripts that run a model many times over in a fully automated way, for example, to explore the effect of different technology costs on model results.

`calliope generate_runs`, at a minimum, must be given the following arguments:

- the model configuration file to use

- the name of the script to create

- `--kind`: Currently, three options are available. `windows` creates a Windows batch (`.bat`) script that runs all models sequentially, `bash` creates an equivalent script to run on Linux or macOS, `bsub` creates a submission script for a LSF-based high-performance cluster, and `sbatch` creates a submission script for a SLURM-based high-performance cluster.

- `--scenarios`: A semicolon-separated list of scenarios (or overrides/combinations of overrides) to generate scripts for, for example, `scenario1;scenario2` or `override1,override2a;override1,override2b`. Note that when not using manually defined scenario names, a comma is used to group overrides together into a single model – in the above example, `override1,override2a` would be applied to the first run and `override1,override2b` be applied to the second run

A fully-formed command generating a Windows batch script to run a model four times with each of the scenarios “run1”, “run2”, “run3”, and “run4”:

    calliope generate_runs model.yaml run_model.bat --kind=windows --scenarios "run1;run2;run3;run4"

Optional arguments are:

- `--cluster_threads`: specifies the number of threads to request on a HPC cluster

- `--cluster_mem`: specifies the memory to request on a HPC cluster

- `--cluster_time`: specifies the run time to request on a HPC cluster

- `--additional_args`: A text string of any additional arguments to pass directly through to `calliope run` in the generated scripts, for example, `--additional_args=”–debug”`.

- `--debug`: Print additional debug information when running the run generation script.

An example generating a script to run on a `bsub`-type high-performance cluster, with additional arguments to specify the resources to request from the cluster:

    calliope generate_runs model.yaml submit_runs.sh --kind=bsub --cluster_mem=1G --cluster_time=100 --cluster_threads=5  --scenarios "run1;run2;run3;run4"

Running this will create two files:

- `submit_runs.sh`: The cluster submission script to pass to `bsub` on the cluster.

- `submit_runs.array.sh`: The accompanying script defining the runs for the cluster to execute.

In all cases, results are saved into the same directory as the script, with filenames of the form `out_{run_number}_{scenario_name}.nc` (model results) and `plots_{run_number}_{scenario_name}.html` (HTML plots), where `{run_number}` is the run number and `{scenario_name}` is the name of the scenario (or the string defining the overrides applied). On a cluster, log files are saved to files with names starting with `log_` in the same directory.

Finally, the `calliope generate_scenarios` tool can be used to quickly generate a file with `scenarios` definition for inclusion in a model, if a large enough number of overrides exist to make it tedious to manually combine them into scenarios. Assuming that in `model.yaml` a range of overrides exist that specify a subset of time for the years 2000 through 2010, called “y2000” through “y2010”, and a set of cost-related overrides called “cost_low”, “cost_medium” and “cost_high”, the following command would generate scenarios with combinations of all years and cost overrides, calling them “run_1”, “run_2”, and so on, and saving them to `scenarios.yaml`:

    calliope generate_scenarios model.yaml scenarios.yaml y2000;y2001;y2002;2003;y2004;y2005;y2006;2007;2008;y2009;2010 cost_low;cost_medium;cost_high --scenario_name_prefix="run_"

#### Importing other YAML files in overrides

When using overrides (see Scenarios and overrides), it is possible to have `import` statements within overrides for more flexibility. The following example illustrates this:

    overrides:
        some_override:
            techs:
                some_tech.constraints.energy_cap_max: 10
            import: [additional_definitions.yaml]

`additional_definitions.yaml`:

    techs:
        some_other_tech.constraints.energy_eff: 0.1

This is equivalent to the following override:

    overrides:
        some_override:
            techs:
                some_tech.constraints.energy_cap_max: 10
                some_other_tech.constraints.energy_eff: 0.1

#### Interfacing with the solver backend

On loading a model, there is no solver backend, only the input dataset. The backend is generated when a user calls run() on their model. Currently this will call back to Pyomo to build the model and send it off to the solver, given by the user in the run configuration `run.solver`. Once built, solved, and returned, the user has access to the results dataset `model.results` and interface functions with the backend `model.backend`.

You can use this interface to:

1. Get the raw data on the inputs used in the optimisation.

     By running `model.backend.get_input_params()` a user get an xarray Dataset which will look very similar to `model.inputs`, except that assumed default values will be included. You may also spot a bug, where a value in `model.inputs` is different to the value returned by this function.

2. Update a parameter value.

     If you are interested in updating a few values in the model, you can run `model.backend.update_param()`. For example, to update the energy efficiency of your ccgt technology in location region1 from 0.5 to 0.1, you can run `model.backend.update_param(‘energy_eff’, {‘region1::ccgt`: 0.1})`. This will not affect results at this stage, you’ll need to rerun the backend (point 4) to optimise with these new values.

Note

If you are interested in updating the objective function cost class weights, you will need to set ‘objective_cost_class’ as the parameter, e.g. `model.backend.update_param(‘objective_cost_class’, {‘monetary’: 0.5})`.

3. Activate / Deactivate a constraint or objective.

     Constraints can be activated and deactivate such that they will or will not have an impact on the optimisation. All constraints are active by default, but you might like to remove, for example, a capacity constraint if you don’t want there to be a capacity limit for any technologies. Similarly, if you had multiple objectives, you could deactivate one and activate another. The result would be to have a different objective when rerunning the backend.

Note

Currently Calliope does not allow you to build multiple objectives, you will need to understand Pyomo and add an additional objective yourself to make use of this functionality. The Pyomo ConcreteModel() object can be accessed at `model._backend_model`.

4. Rerunning the backend.

     If you have edited parameters or constraint activation, you will need to rerun the optimisation to propagate the effects. By calling `model.backend.rerun()`, the optimisation will run again, with the updated backend. This will not affect your model, but instead will return a new calliope Model object associated with that specific rerun. You can analyse the results and inputs in this new model, but there is no backend interface available. You’ll need to return to the original model to access the backend again, or run the returned model using `new_model.run(force_rerun=True)`. In the original model, `model.results` will not change, and can only be overwritten by `model.run(force_rerun=True)`.

Note

By calling `model.run(force_rerun=True)` any updates you have made to the backend will be overwritten.

See also

Pyomo backend interface

#### Specifying custom solver options

##### Gurobi

Refer to the Gurobi manual, which contains a list of parameters. Simply use the names given in the documentation (e.g. “NumericFocus” to set the numerical focus value). For example:

    run:
        solver: gurobi
        solver_options:
            Threads: 3
            NumericFocus: 2

##### CPLEX

Refer to the CPLEX parameter list. Use the “Interactive” parameter names, replacing any spaces with underscores (for example, the memory reduction switch is called “emphasis memory”, and thus becomes “emphasis_memory”). For example:

    run:
        solver: cplex
        solver_options:
            mipgap: 0.01
            mip_polishafter_absmipgap: 0.1
            emphasis_mip: 1
            mip_cuts: 2
            mip_cuts_cliques: 3

### Configuration and defaults

This section lists the available configuration options and constraints along with their default values. Defaults are automatically applied in constraints whenever there is no user input for a particular value.

#### Model configuration

Setting | Default | Comments
--- | --- | ---
calliope_version |  | Calliope framework version this model is intended for
group_share | {} | Optional settings for the group_share constraint - deprecated and will be removed in v0.7.0
name |  | Model name
random_seed |  | Seed for random number generator used during clustering
reserve_margin | {} | Per-carrier system-wide reserve margins
subset_time |  | Subset of timesteps as a two-element list giving the range, e.g. [‘2005-01-01’, ‘2005-01-05’], or a single string, e.g. ‘2005-01’
time | {} | Optional settings to adjust time resolution, see Time resolution adjustment for the available options
timeseries_data_path |  | Path to time series data
timeseries_data |  | Dict of dataframes with time series data (when passing in dicts rather than YAML files to Model constructor)
timeseries_dateformat | %Y-%m-%d %H:%M:%S | Timestamp format of all time series data when read from file
file_allowed | [‘clustering_func’, ‘energy_con’, ‘energy_eff’, ‘energy_prod’, ‘energy_ramping’, ‘export’, ‘force_resource’, ‘om_con’, ‘om_prod’, ‘parasitic_eff’, ‘resource’, ‘resource_eff’, ‘storage_loss’, ‘carrier_ratios’] | List of configuration options allowed to specify “file=” to load timeseries data. This can be updated if you’re adding a new custom constraint that requires a newly defined parameter to be a timeseries. If updating existing parameters, you can expect existing constraints to not change behaviour or to break on being constructed. ## # Base technology groups ##

#### Run configuration

Setting | Default | Comments
--- | --- | ---
backend | pyomo | Backend to use to build and solve the model. As of v0.6.0, only pyomo is available
bigM | 1000000000.0 | Used for unmet demand, but should be of a similar order of magnitude as the largest cost that the model could achieve. Too high and the model will not converge
cyclic_storage | True | If true, storage in the last timestep of the timeseries is considered to be the ‘previous timestep’ in the first timestep of the timeseries
ensure_feasibility | False | If true, unmet_demand will be a decision variable, to account for an ability to meet demand with the available supply. If False and a mismatch occurs, the optimisation will fail due to infeasibility
mode | plan | Which mode to run the model in: ‘plan’ or ‘operation’
objective_options | {} | Arguments to pass to objective function. If cost-based objective function in use, should include ‘cost_class’ and ‘sense’ (maximize/minimize)
objective | minmax_cost_optimization | Name of internal objective function to use, currently only min/max cost-based optimisation is available
operation | {} | Settings for operational mode
save_logs |  | Directory into which to save logs and temporary files. Also turns on symbolic solver labels in the Pyomo backend
solver_io |  | What method the Pyomo backend should use to communicate with the solver
solver_options |  | A list of options, which are passed on to the chosen solver, and are therefore solver-dependent
solver | cbc | Which solver to use
zero_threshold | 1e-10 | Any value coming out of the backend that is smaller than this threshold (due to floating point errors, probably) will be set to zero

#### Per-tech constraints

The following table lists all available technology constraint settings and their default values. All of these can be set by `tech_identifier.constraints.constraint_name`, e.g. `nuclear.constraints.energy_cap.max`.

Setting | Default | Name | Unit | Comments
--- | --- | --- | --- | ---
carrier_ratios | {} | Carrier ratios | fraction | Ratio of summed output of carriers in [‘out_2’, ‘out_3’] / [‘in_2’, ‘in_3’] to the summed output of carriers in ‘out’ / ‘in’. given in a nested dictionary.
charge_rate | False | Charge rate | hour -1 | (do not use, replaced by energy_cap_per_storage_cap_max) ratio of maximum charge/discharge (kW) for a given maximum storage capacity (kWh).
energy_cap_per_storage_cap_min | False | Minimum energy capacity per storage capacity | hour -1 | ratio of minimum charge/discharge (kW) for a given storage capacity (kWh).
energy_cap_per_storage_cap_max | False | Maximum energy capacity per storage capacity | hour -1 | ratio of maximum charge/discharge (kW) for a given storage capacity (kWh).
energy_cap_per_storage_cap_equals | False | Tie energy capacity to storage capacity | fraction |
energy_cap_equals | False | Specific installed energy capacity | kW | fixes maximum/minimum if decision variables `carrier_prod`/`carrier_con` and overrides `_max` and `_min` constraints.
energy_cap_equals_systemwide | False | System-wide specific installed energy capacity | kW | fixes the sum to a maximum/minimum, for a particular technology, of the decision variables `carrier_prod`/`carrier_con` over all locations.
energy_cap_max | inf | Maximum installed energy capacity | kW | Limits decision variables `carrier_prod`/`carrier_con` to a maximum/minimum.
energy_cap_max_systemwide | inf | System-wide maximum installed energy capacity | kW | Limits the sum to a maximum/minimum, for a particular technology, of the decision variables `carrier_prod`/`carrier_con` over all locations.
energy_cap_min | 0 | Minimum installed energy capacity | kW | Limits decision variables `carrier_prod`/`carrier_con` to a minimum/maximum.
energy_cap_min_use | False | Minimum carrier production | fraction | Set to a value between 0 and 1 to force minimum carrer production as a fraction of the technology maximum energy capacity. If non-zero and technology is not defined by `units`, this will force the technology to operate above its minimum value at every timestep.
energy_cap_per_unit | False | Energy capacity per purchased unit | kW/unit | Set the capacity of each integer unit of a technology purchased
energy_cap_scale | 1.0 | Energy capacity scale | float | Scale all `energy_cap` min/max/equals/total_max/total_equals constraints by this value
energy_con | False | Energy consumption | boolean | Allow this technology to consume energy from the carrier (static boolean, or from file as timeseries).
energy_eff | 1.0 | Energy efficiency | fraction | conversion efficiency (static, or from file as timeseries), from `resource`/`storage`/`carrier_in` (tech dependent) to `carrier_out`.
energy_eff_per_distance | 1.0 | Energy efficiency per distance | distance -1 | Set as value between 1 (no loss) and 0 (all energy lost).
energy_prod | False | Energy production | boolean | Allow this technology to supply energy to the carrier (static boolean, or from file as timeseries).
energy_ramping | False | Ramping rate | fraction / hour | Set to `false` to disable ramping constraints, otherwise limit maximum carrier production to a fraction of maximum capacity, which increases by that fraction at each timestep.
export_cap | inf | Export capacity | kW | Maximum allowed export of produced energy carrier for a technology.
export_carrier |  | Export carrier | N/A | Name of carrier to be exported. Must be an output carrier of the technology
force_asynchronous_prod_con | False | if True, carrier_prod and carrier_con cannot both occur in the same timestep |  |
force_resource | False | Force resource | boolean | Forces this technology to use all available `resource`, rather than making it a maximum upper boundary (for production) or minimum lower boundary (for consumption). Static boolean, or from file as timeseries
lifetime |  | Technology lifetime | years | Must be defined if fixed capital costs are defined. A reasonable value for many technologies is around 20-25 years.
one_way | False | Forces a transmission technology to only move energy in one direction on the link, in this case from default_location_from to default_location_to |  |
parasitic_eff | 1.0 | Plant parasitic efficiency | fraction | Additional losses as energy gets transferred from the plant to the carrier (static, or from file as timeseries), e.g. due to plant parasitic consumption
resource | 0 | Available resource | kWh | kWh/m2 | kWh/kW | Maximum available resource (static, or from file as timeseries). Unit dictated by `resource_unit`
resource_area_equals | False | Specific installed resource area | m2 |
resource_area_max | inf | Maximum usable resource area | m2 | If set to a finite value, restricts the usable area of the technology to this value.
resource_area_min | 0 | Minimum usable resource area | m2 |
resource_area_per_energy_cap | False | Resource area per energy capacity | boolean | If set, forces `resource_area` to follow `energy_cap` with the given numerical ratio (e.g. setting to 1.5 means that `resource_area == 1.5 * energy_cap`)
resource_cap_equals | False | Specific installed resource consumption capacity | kW | overrides `_max` and `_min` constraints.
resource_cap_equals_energy_cap | False | Resource capacity equals energy cpacity | boolean | If true, `resource_cap` is forced to equal `energy_cap`
resource_cap_max | inf | Maximum installed resource consumption capacity | kW |
resource_cap_min | 0 | Minimum installed resource consumption capacity | kW |
resource_eff | 1.0 | Resource efficiency | fraction | Efficiency (static, or from file as timeseries) in capturing resource before it reaches storage (if storage is present) or conversion to carrier.
resource_min_use | False | Minimum resource consumption | fraction | Set to a value between 0 and 1 to force minimum resource consumption for production technologies
resource_scale | 1.0 | Resource scale | fraction | Scale resource (either static value or all values in timeseries) by this value
resource_unit | energy | Resource unit | N/A | Sets the unit of `resource` to either `energy` (i.e. kWh), `energy_per_area` (i.e. kWh/m2), or `energy_per_cap` (i.e. kWh/kW). `energy_per_area` uses the `resource_area` decision variable to scale the available resource while `energy_per_cap` uses the `energy_cap` decision variable.
storage_cap_equals | False | Specific storage capacity | kWh | If not defined, `energy_cap_equals` * `energy_cap_per_storage_cap_max` will be used as the capacity and overrides `_max` and `_min` constraints.
storage_cap_max | inf | Maximum storage capacity | kWh | If not defined, `energy_cap_max` * `energy_cap_per_storage_cap_max` will be used as the capacity.
storage_cap_min | 0 | Minimum storage capacity | kWh |
storage_cap_per_unit | False | Storage capacity per purchased unit | kWh/unit | Set the storage capacity of each integer unit of a technology purchased.
storage_discharge_depth | 0 | Storage depth of discharge | fraction | Defines the minimum level of storage state of charge, as a fraction of total storage capacity
storage_initial | 0 | Initial storage level | fraction | Set stored energy in device at the first timestep, as a fraction of total storage capacity
storage_loss | 0 | Storage loss rate | hour -1 | rate of storage loss per hour (static, or from file as timeseries), used to calculate lost stored energy as `(1 - storage_loss)^hours_per_timestep`
units_equals | False | Specific number of purchased units | integer | Turns the model from LP to MILP.
units_equals_systemwide | False | System-wide specific installed energy capacity | kW | fixes the sum to a specific value, for a particular technology, of the decision variables `carrier_prod`/`carrier_con` over all locations.
units_max | False | Maximum number of purchased units | integer | Turns the model from LP to MILP.
units_max_systemwide | inf | System-wide maximum installed energy capacity | kW | Limits the sum to a maximum/minimum, for a particular technology, of the decision variables `carrier_prod`/`carrier_con` over all locations.
units_min | False | Minimum number of purchased units | integer | Turns the model from LP to MILP.

#### Per-tech costs

These are all the available costs, which are set to \(0\) by default for every defined cost class. Costs are set by `tech_identifier.costs.cost_class.cost_name`, e.g. `nuclear.costs.monetary.energy_cap`.

Setting | Default | Name | Unit | Comments
--- | --- | --- | --- | ---
energy_cap | 0 | Cost of energy capacity | kW gross -1 |
energy_cap_per_distance | 0 | Cost of energy capacity, per unit distance | kW gross -1 / distance | Applied to transmission links only
export | 0 | Carrier export cost | kWh -1 | Usually used in the negative sense, as a subsidy.
interest_rate | 0 | Interest rate | fraction | Used when computing levelized costs
om_annual | 0 | Yearly O&M costs | kW energy_cap -1 |
om_annual_investment_fraction | 0 | Fractional yearly O&M costs | fraction / total investment |
om_con | 0 | Carrier consumption cost | kWh -1 | Applied to carrier consumption of a technology
om_prod | 0 | Carrier production cost | kWh -1 | Applied to carrier production of a technology
purchase | 0 | Purchase cost | unit -1 | Triggers a binary variable for that technology to say that it has been purchased or is applied to integer variable `units`
resource_area | 0 | Cost of resource area | m-2 |
resource_cap | 0 | Cost of resource consumption capacity | kW -1 |
storage_cap | 0 | Cost of storage capacity | kWh -1 |

Technology depreciation settings apply when calculating levelized costs. The interest rate and life times must be set for each technology with investment costs.

#### Group constraints

See Group constraints for a full listing of available group constraints.

#### Abstract base technology groups

Technologies must always define a parent, and this can either be one of the pre-defined abstract base technology groups or a user-defined group (see Using tech_groups to group configuration). The pre-defined groups are:

- `supply`: Supplies energy to a carrier, has a positive resource.

- `supply_plus`: Supplies energy to a carrier, has a positive resource. Additional possible constraints, including efficiencies and storage, distinguish this from `supply`.

- `demand`: Demands energy from a carrier, has a negative resource.

- `storage`: Stores energy.

- `transmission`: Transmits energy from one location to another.

- `conversion`: Converts energy from one carrier to another.

- `conversion_plus`: Converts energy from one or more carrier(s) to one or more different carrier(s).

A technology inherits the configuration that its parent group specifies (which, in turn, may inherit from its own parent).

Note

The identifiers of the abstract base tech groups are reserved and cannot be used for user-defined technologies. However, you can amend an abstract base technology group for example by a lifetime attribute that will be in effect for all technologies derived from that group (see Using tech_groups to group configuration).

The following lists the pre-defined base tech groups and the defaults they provide.

##### supply

Default constraints provided by the parent tech group:

    essentials:
      parent:
    constraints:
      energy_prod: true
      resource: inf
      resource_unit: energy
    costs: {}

Required constraints, allowed constraints, and allowed costs:

    required_constraints: []
    allowed_constraints:
    -   energy_cap_equals
    -   energy_cap_equals_systemwide
    -   energy_cap_max
    -   energy_cap_max_systemwide
    -   energy_cap_min
    -   energy_cap_min_use
    -   energy_cap_per_unit
    -   energy_cap_scale
    -   energy_eff
    -   energy_prod
    -   energy_ramping
    -   export_cap
    -   export_carrier
    -   force_resource
    -   lifetime
    -   resource
    -   resource_area_equals
    -   resource_area_max
    -   resource_area_min
    -   resource_area_per_energy_cap
    -   resource_min_use
    -   resource_scale
    -   resource_unit
    -   units_equals
    -   units_equals_systemwide
    -   units_max
    -   units_max_systemwide
    -   units_min
    allowed_costs:
    -   depreciation_rate
    -   energy_cap
    -   export
    -   interest_rate
    -   om_annual
    -   om_annual_investment_fraction
    -   om_con
    -   om_prod
    -   purchase
    -   resource_area

##### supply_plus

Default constraints provided by the parent tech group:

    essentials:
      parent:
    constraints:
      energy_prod: true
      resource: inf
      resource_eff: 1.0
      resource_unit: energy
    costs: {}

Required constraints, allowed constraints, and allowed costs:

    required_constraints: []
    allowed_constraints:
    -   charge_rate
    -   energy_cap_per_storage_cap_min
    -   energy_cap_per_storage_cap_max
    -   energy_cap_per_storage_cap_equals
    -   energy_cap_equals
    -   energy_cap_equals_systemwide
    -   energy_cap_max
    -   energy_cap_max_systemwide
    -   energy_cap_min
    -   energy_cap_min_use
    -   energy_cap_per_unit
    -   energy_cap_scale
    -   energy_eff
    -   energy_prod
    -   energy_ramping
    -   export_cap
    -   export_carrier
    -   force_resource
    -   lifetime
    -   parasitic_eff
    -   resource
    -   resource_area_equals
    -   resource_area_max
    -   resource_area_min
    -   resource_area_per_energy_cap
    -   resource_cap_equals
    -   resource_cap_equals_energy_cap
    -   resource_cap_max
    -   resource_cap_min
    -   resource_eff
    -   resource_min_use
    -   resource_scale
    -   resource_unit
    -   storage_cap_equals
    -   storage_cap_max
    -   storage_cap_min
    -   storage_cap_per_unit
    -   storage_initial
    -   storage_loss
    -   units_equals
    -   units_equals_systemwide
    -   units_max
    -   units_max_systemwide
    -   units_min
    allowed_costs:
    -   depreciation_rate
    -   energy_cap
    -   export
    -   interest_rate
    -   om_annual
    -   om_annual_investment_fraction
    -   om_con
    -   om_prod
    -   purchase
    -   resource_area
    -   resource_cap
    -   storage_cap

##### demand

Default constraints provided by the parent tech group:

    essentials:
      parent:
    constraints:
      energy_con: true
      force_resource: true
      resource_unit: energy
    costs: {}

Required constraints, allowed constraints, and allowed costs:

    required_constraints:
    -   resource
    allowed_constraints:
    -   energy_con
    -   force_resource
    -   resource
    -   resource_area_equals
    -   resource_scale
    -   resource_unit
    allowed_costs:
    -   om_con

##### storage

Default constraints provided by the parent tech group:

    essentials:
      parent:
    constraints:
      energy_con: true
      energy_prod: true
      storage_cap_max: inf
    costs: {}

Required constraints, allowed constraints, and allowed costs:

    required_constraints: []
    allowed_constraints:
    -   charge_rate
    -   energy_cap_per_storage_cap_min
    -   energy_cap_per_storage_cap_max
    -   energy_cap_per_storage_cap_equals
    -   energy_cap_equals
    -   energy_cap_equals_systemwide
    -   energy_cap_max
    -   energy_cap_max_systemwide
    -   energy_cap_min
    -   energy_cap_min_use
    -   energy_cap_per_unit
    -   energy_cap_scale
    -   energy_con
    -   energy_eff
    -   energy_prod
    -   energy_ramping
    -   export_cap
    -   export_carrier
    -   force_asynchronous_prod_con
    -   lifetime
    -   storage_cap_equals
    -   storage_cap_max
    -   storage_cap_min
    -   storage_cap_per_unit
    -   storage_initial
    -   storage_loss
    -   storage_time_max
    -   storage_discharge_depth
    -   units_equals
    -   units_equals_systemwide
    -   units_max
    -   units_max_systemwide
    -   units_min
    allowed_costs:
    -   depreciation_rate
    -   energy_cap
    -   export
    -   interest_rate
    -   om_annual
    -   om_annual_investment_fraction
    -   om_prod
    -   purchase
    -   storage_cap

##### transmission

Default constraints provided by the parent tech group:

    essentials:
      parent:
    constraints:
      energy_con: true
      energy_prod: true

    ##
    # Default technology
    ##
    costs: {}

Required constraints, allowed constraints, and allowed costs:

    required_constraints: []
    allowed_constraints:
    -   energy_cap_equals
    -   energy_cap_min
    -   energy_cap_max
    -   energy_cap_per_unit
    -   energy_cap_scale
    -   energy_con
    -   energy_eff
    -   energy_eff_per_distance
    -   energy_prod
    -   force_asynchronous_prod_con
    -   lifetime
    -   one_way
    allowed_costs:
    -   depreciation_rate
    -   energy_cap
    -   energy_cap_per_distance
    -   interest_rate
    -   om_annual
    -   om_annual_investment_fraction
    -   om_prod
    -   purchase
    -   purchase_per_distance

##### conversion

Default constraints provided by the parent tech group:

    essentials:
      parent:
    constraints:
      energy_con: true
      energy_prod: true
    costs: {}

Required constraints, allowed constraints, and allowed costs:

    required_constraints: []
    allowed_constraints:
    -   energy_cap_equals
    -   energy_cap_equals_systemwide
    -   energy_cap_max
    -   energy_cap_max_systemwide
    -   energy_cap_min
    -   energy_cap_min_use
    -   energy_cap_per_unit
    -   energy_cap_scale
    -   energy_con
    -   energy_eff
    -   energy_prod
    -   energy_ramping
    -   export_cap
    -   export_carrier
    -   lifetime
    -   units_equals
    -   units_equals_systemwide
    -   units_max
    -   units_max_systemwide
    -   units_min
    allowed_costs:
    -   depreciation_rate
    -   energy_cap
    -   export
    -   interest_rate
    -   om_annual
    -   om_annual_investment_fraction
    -   om_con
    -   om_prod
    -   purchase

##### conversion_plus

Default constraints provided by the parent tech group:

    essentials:
      parent:
    constraints:
      energy_con: true
      energy_prod: true
    costs: {}

Required constraints, allowed constraints, and allowed costs:

    required_constraints: []
    allowed_constraints:
    -   carrier_ratios
    -   energy_cap_equals
    -   energy_cap_equals_systemwide
    -   energy_cap_max
    -   energy_cap_max_systemwide
    -   energy_cap_min
    -   energy_cap_min_use
    -   energy_cap_per_unit
    -   energy_cap_scale
    -   energy_con
    -   energy_eff
    -   energy_prod
    -   energy_ramping
    -   export_cap
    -   export_carrier
    -   lifetime
    -   units_equals
    -   units_equals_systemwide
    -   units_max
    -   units_max_systemwide
    -   units_min
    allowed_costs:
    -   depreciation_rate
    -   energy_cap
    -   export
    -   interest_rate
    -   om_annual
    -   om_annual_investment_fraction
    -   om_con
    -   om_prod
    -   purchase

### Troubleshooting

#### General strategies

- Building a smaller model: `model.subset_time` allows specifying a subset of timesteps to be used. This can be useful for debugging purposes as it can dramatically speed up model solution times. The timestep subset can be specified as `[startdate, enddate]`, e.g. `[‘2005-01-01’, ‘2005-01-31’]`, or as a single time period, such as `2005-01` to select January only. The subsets are processed before building the model and applying time resolution adjustments, so time resolution reduction functions will only see the reduced set of data.

- Retaining logs and temporary files: The setting `run.save_logs`, disabled by default, sets the directory into which to save logs and temporary files from the backend, to inspect solver logs and solver-generated model files. This also turns on symbolic solver labels in the Pyomo backend, so that all model components in the backend model are named according to the corresponding Calliope model components (by default, Pyomo uses short random names for all generated model components).

- Analysing the optimisation problem without running the model: If you are comfortable with navigating Pyomo objects, then you can build the Pyomo model backend without running the optimisation problem, using `model.run(build_only=True)`. Pyomo objects are then accessible within `model._backend_model`. For instance, the constraint limiting energy capacity can be viewed by calling `model._backend_model.energy_capacity_constraint.pprint(‘hi’)`. Alternatively, if you are working from the command line or have little experience with Pyomo, you can generate an LP file. The LP file contains the mathematical model formulation of a fully built Calliope model. It is a standard format that can be passed to various solvers. Examining the LP file manually or using additional tools (see below) can help find issues when a model is infeasible or unbounded. To build a model and save it to LP without actually solving it, use:

      calliope run my_model.yaml --save_lp=my_saved_model.lp

  or, interactively:

      model.to_lp('my_saved_model.lp')

#### Improving solution times

One way to improve solution time is to reduce the size of a problem (another way is to address potential numerical issues, which is dealt with further below in Understanding infeasibility and numerical instability).

##### Number of variables

The sets `locs`, `techs`, `timesteps`, `carriers`, and `costs` all contribute to model complexity. A reduction of any of these sets will reduce the number of resulting decision variables in the optimisation, which in turn will improve solution times.

Note

By reducing the number of locations (e.g. merging nearby locations) you also remove the technologies linking those locations to the rest of the system, which is additionally beneficial.

Currently, we only provide automatic set reduction for timesteps. Timesteps can be resampled (e.g. 1hr -> 2hr intervals), masked (e.g. 1hr -> 12hr intervals except one week of particular interest), or clustered (e.g. 365 days to 5 days, each representing 73 days of the year, with 1hr resolution). In so doing, significant solution time improvements can be acheived.

See also

Time resolution adjustment, Stefan Pfenninger (2017). Dealing with multiple decades of hourly wind and PV time series in energy models: a comparison of methods to reduce time resolution and the planning implications of inter-annual variability. Applied Energy.

##### Complex technologies

Calliope is primarily an LP framework, but application of certain constraints will trigger binary or integer decision variables. When triggered, a MILP model will be created.

In both cases, there will be a time penalty, as linear programming solvers are less able to converge on solutions of problems which include binary or integer decision variables. But, the additional functionality can be useful. A purchasing cost allows for a cost curve of the form \(y = Mx + C\) to be applied to a technology, instead of the LP costs which are all of the form \(y = Mx\). Integer units also trigger per-timestep decision variables, which allow technologies to be “on” or “off” at each timestep.

Additionally, in LP models, interactions between timesteps (in `storage` technologies) can lead to longer solution time. The exact extent of this is as-yet untested.

##### Model mode

Solution time increases more than linearly with the number of decision variables. As it splits the model into ~daily chunks, operational mode can help to alleviate solution time of big problems. This is clearly at the expense of fixing technology capacities. However, one solution is to use a heavily time clustered `plan` mode to get indicative model capacities. Then run `operate` mode with these capacities to get a higher resolution operation strategy. If necessary, this process could be iterated.

See also

Operational mode

#### Influence of solver choice on speed

The open-source solvers (GLPK and CBC) are slower than the commercial solvers. If you are an academic researcher, it is recommended to acquire a free licence for Gurobi or CPLEX to very quickly improve solution times. GLPK in particular is slow when solving MILP models. CBC is an improvement, but can still be several orders of magnitude slower at reaching a solution than Gurobi or CPLEX.

We tested solution time for various solver choices on our example models, extended to run over a full year (8760 hours). These runs took place on the University of Cambridge high performance computing cluster, with a maximum run time of 5 hours. As can be seen, CBC is far superior to GLPK. If introducing binary constraints, although CBC is an improvement on GLPK, access to a commercial solver is preferable.

National scale example model size

- Variables : 420526 [Nneg: 219026, Free: 105140, Other: 96360]

- Linear constraints : 586972 [Less: 315373, Greater: 10, Equal: 271589]

MILP urban scale example model

- Variables: 586996 [Nneg: 332913, Free: 78880, Binary: 2, General Integer: 8761, Other: 166440]

- Linear constraints: 788502 [Less: 394226, Greater: 21, Equal: 394255]

Solution time

Solver | Solution time
--- | ---
National | Urban
GLPK | 4:35:40 | >5hrs
CBC | 0:04:45 | 0:52:13
Gurobi (1 thread) | 0:02:08 | 0:03:21
CPLEX (1 thread) | 0:04:55 | 0:05:56
Gurobi (4 thread) | 0:02:27 | 0:03:08
CPLEX (4 thread) | 0:02:16 | 0:03:26

See also

Specifying custom solver options

#### Understanding infeasibility and numerical instability

Note

A good first step when faced with an infeasible model is often to remove constraints, in particular more complex constraints. For example, different combinations of group constraints can easily introduce mutually exclusive requirements on capacities or output from specific technologies. Once a minimal model works, more complex constraints can be turned on again one after the other.

##### Using the Gurobi solver

To understand infeasible models:

- Set `run.solver_options.DualReductions: 0` to see whether a model is infeasible or unbounded.

- To analyse infeasible models, save an LP file with the `--save_lp` command-line option, then use Gurobi to generate an Irreducible Inconsistent Subsystem that shows which constraints are infeasible:

      gurobi_cl ResultFile=result.ilp my_saved_model.lp

  More detail on this is in the official Gurobi documentation.

To deal with numerically unstable models, try setting `run.solver_options.Presolve: 0`, as large numeric ranges can cause the pre-solver to generate an infeasible or numerically unstable model. The Gurobi Guidelines for Numerical Issues give detailed guidance for strategies to address numerically difficult optimisation problems.

##### Using the CPLEX solver

There are two ways to understand infeasibility when using the CPLEX solver, the first is quick and the second is more involved:

1. Save solver logs for your model (`run.save_logs: path/to/log_directory`). In the directory, open the file ending in ‘.cplex.log’ to see the CPLEX solver report. If the model is infeasible or unbounded, the offending constraint will be identified (e.g. “SOLVER: Infeasible variable = slack c_u_carrier_production_max_constraint(region1_2__csp__power_2005_01_01_07_00_00)_”). This may be enough to understand why the model is failing, if not…

2. Open the LP file in CPLEX interactive (run cplex in the command line to invoke a CPLEX interactive session). The LP file for the problem ends with ‘.lp’ in the log folder (read path/to/file.lp). Once loaded, you can try relaxing variables / constraints to see if the problem can be solved with relaxation (FeasOpt). You can also identify conflicting constraints (tools conflict) and print those constraints directly (display conflict all). There are many more commands available to analyse individual constraints and variables in the Official CPLEX documentation.

Similar to Gurobi, numerically unstable models may lead to unexpected infeasibility, so you can try `run.solver_options.preprocessing_presolve: 0` or you can request CPLEX to more aggressively scale the problem itself using the solver option `read_scale: 1` . The CPLEX documentation page on numeric difficulties goes into more detail on numeric instability.

#### Rerunning a model

After running, if there is an infeasibility you want to address, or simply a few values you dont think were quite right, you can change them and rerun your model. If you change them in model.inputs, just rerun the model as `model.run(force_rerun=True)`.

Note

`model.run(force_rerun=True)` will replace you current model.results and rebuild he entire model backend. You may want to save your model before doing this.

Particularly if your problem is large, you may not want to rebuild the backend to change a few small values. Instead you can interface directly with the backend using the `model.backend` functions, to update individual parameter values and switch constraints on/off. By rerunning the backend specifically, you can optimise your problem with these backend changes, without rebuilding the backend entirely.

Note

`model.inputs` and `model.results` will not be changed when updating and rerunning the backend. Instead, a new xarray Dataset is returned.

See also

Interfacing with the solver backend

#### Debugging model errors

Calliope provides a method to save its fully built and commented internal representation of a model to a single YAML file with `Model.save_commented_model_yaml(path)`. Comments in the resulting YAML file indicate where original values were overridden.

Because this is Calliope’s internal representation of a model directly before the `model_data` `xarray.Dataset` is built, it can be useful for debugging possible issues in the model formulation, for example, undesired constraints that exist at specific locations because they were specified model-wide without having been superseded by location-specific settings.

Further processing of the data does occur before solving the model. The final values of parameters used by the backend solver to generate constraints can be analysed when running an interactive Python session by running `model.backend.get_input_params()`. This provides a user with an xarray Dataset which will look very similar to `model.inputs`, except that assumed default values will be included. An attempt at running the model has to be made in order to be able to run this command.

See also

If using Calliope interactively in a Python session, we recommend reading up on the Python debugger and (if using Jupyter notebooks) making use of the %debug magic.

### More info (reference)

This section contains additional information useful as reference: a list of all example models and their configuration, a listing of different possible configuration values, and the detailed mathematical formulation.

We suggest you read the Building a model, Running a model and Analysing a model sections first before referring to this section.

#### Built-in example models

This section gives a listing of all the YAML configuration files included in the built-in example models. Refer to the tutorials section for a brief overview of how these parts together provide a working model.

The example models are accessible in the `calliope.examples` module. To create an instance of an example model, call its constructor function, e.g.

>     urban_model = calliope.examples.urban_scale()

The available example models and their constructor functions are:

`calliope.examples.``national_scale`(*args, **kwargs)

  Returns the built-in national-scale example model.

`calliope.examples.``time_clustering`(*args, **kwargs)

  Returns the built-in national-scale example model with time clustering.

`calliope.examples.``time_resampling`(*args, **kwargs)

  Returns the built-in national-scale example model with time resampling.

`calliope.examples.``urban_scale`(*args, **kwargs)

  Returns the built-in urban-scale example model.

`calliope.examples.``milp`(*args, **kwargs)

  Returns the built-in urban-scale example model with MILP constraints enabled.

`calliope.examples.``operate`(*args, **kwargs)

  Returns the built-in urban-scale example model in operate mode.

`calliope.examples.``time_masking`(*args, **kwargs)

  Returns the built-in urban-scale example model with time masking.

##### National-scale example

Available as `calliope.examples.national_scale`.

###### Model settings

The layout of the model directory is as follows (`+` denotes directories, `-` files):

    - model.yaml
    - scenarios.yaml
    + timeseries_data
        - csp_resource.csv
        - demand-1.csv
        - demand-2.csv
    + model_config
        - locations.yaml
        - techs.yaml

`model.yaml`:

    import:  # Import other files from paths relative to this file, or absolute paths
        - 'model_config/techs.yaml'  # This file specifies the model's technologies
        - 'model_config/locations.yaml'  # This file specifies the model's locations
        - 'scenarios.yaml'  # Scenario and override group definitions

    # Model configuration: all settings that affect the built model
    model:
        name: National-scale example model

        # What version of Calliope this model is intended for
        calliope_version: 0.6.5

        # Time series data path - can either be a path relative to this file, or an absolute path
        timeseries_data_path: 'timeseries_data'

        subset_time: ['2005-01-01', '2005-01-05']  # Subset of timesteps

    # Run configuration: all settings that affect how the built model is run
    run:
        solver: cbc

        ensure_feasibility: true  # Switches on the "unmet demand" constraint

        bigM: 1e6  # Sets the scale of unmet demand, which cannot be too high, otherwise the optimisation will not converge

        zero_threshold: 1e-10  # Any value coming out of the backend that is smaller than this (due to floating point errors, probably) will be set to zero

        mode: plan  # Choices: plan, operate

        objective_options.cost_class: {monetary: 1}

`scenarios.yaml`:

    ##
    # Scenarios are optional, named combinations of overrides
    ##
    scenarios:
        cold_fusion_with_production_share: ['cold_fusion', 'cold_fusion_prod_share']
        cold_fusion_with_capacity_share: ['cold_fusion', 'cold_fusion_cap_share']

    ##
    # Overrides are the building blocks from which scenarios can be defined
    ##
    overrides:
        profiling:
            model.name: 'National-scale example model (profiling run)'
            model.subset_time: ['2005-01-01', '2005-01-15']
            run.solver: cbc

        time_resampling:
            model.name: 'National-scale example model with time resampling'
            model.subset_time: '2005-01'
            # Resample time resolution to 6-hourly
            model.time: {function: resample, function_options: {'resolution': '6H'}}

        time_clustering:
            model.random_seed: 23
            model.name: 'National-scale example model with time clustering'
            model.subset_time: null  # No time subsetting
            # Cluster timesteps using k-means
            model.time: {function: apply_clustering, function_options: {clustering_func: 'kmeans', how: 'closest', k: 10}}

        operate:
            run.mode: operate
            run.operation:
                window: 12
                horizon: 24
            model.subset_time: ['2005-01-01', '2005-01-10']
            locations:
                region1.techs.ccgt.constraints.energy_cap_equals: 30000

                region2.techs.battery.constraints.energy_cap_equals: 1000
                region2.techs.battery.constraints.storage_cap_equals: 5240

                region1-1.techs.csp.constraints.energy_cap_equals: 10000
                region1-1.techs.csp.constraints.storage_cap_equals: 244301
                region1-1.techs.csp.constraints.resource_area_equals: 130385

                region1-2.techs.csp.constraints.energy_cap_equals: 0
                region1-2.techs.csp.constraints.storage_cap_equals: 0
                region1-2.techs.csp.constraints.resource_area_equals: 0

                region1-3.techs.csp.constraints.energy_cap_equals: 2534
                region1-3.techs.csp.constraints.storage_cap_equals: 25301
                region1-3.techs.csp.constraints.resource_area_equals: 8487

            links:
                region1,region2.techs.ac_transmission.constraints.energy_cap_equals: 3231
                region1,region1-1.techs.free_transmission.constraints.energy_cap_equals: 9000
                region1,region1-2.techs.free_transmission.constraints.energy_cap_equals: 0
                region1,region1-3.techs.free_transmission.constraints.energy_cap_equals: 2281

        check_feasibility:
            run:
                ensure_feasibility: False
                objective: 'check_feasibility'
            model:
                subset_time: '2005-01-04'

        reserve_margin:
            model:
                # Model-wide settings for the system-wide reserve margin
                # Even setting a reserve margin of zero activates the constraint,
                # forcing enough installed capacity to cover demand in
                # the maximum demand timestep
                reserve_margin:
                    power: 0.10  # 10% reserve margin for power

        ##
        # Overrides to demonstrate the run generator ("calliope generate_runs")
        ##

        run1:
            model.subset_time: ['2005-01-01', '2005-01-31']
        run2:
            model.subset_time: ['2005-02-01', '2005-02-31']
        run3:
            model.subset_time: ['2005-01-01', '2005-01-31']
            locations.region1.techs.ccgt.constraints.energy_cap_max: 0  # Disallow CCGT
        run4:
            subset_time: ['2005-02-01', '2005-02-31']
            locations.region1.techs.ccgt.constraints.energy_cap_max: 0  # Disallow CCGT

        ##
        # Overrides to demonstrate group constraints
        ##

        cold_fusion:  # Defines a hypothetical cold fusion tech to use in group constraints
            techs:
                cold_fusion:
                    essentials:
                        name: 'Cold fusion'
                        color: '#233B39'
                        parent: supply
                        carrier_out: power
                    constraints:
                        energy_cap_max: 10000
                        lifetime: 50
                    costs:
                        monetary:
                            interest_rate: 0.20
                            energy_cap: 100
            locations.region1.techs.cold_fusion: null
            locations.region2.techs.cold_fusion: null

        cold_fusion_prod_share:
            group_constraints:
                min_carrier_prod_share_group:
                    techs: ['csp', 'cold_fusion']
                    carrier_prod_share_min:
                        # At least 85% of power supply must come from CSP and cold fusion together
                        power: 0.85

        cold_fusion_cap_share:
            group_constraints:
                max_cap_share_group:
                    techs: ['csp', 'cold_fusion']
                    # At most 20% of total energy_cap can come from CSP and cold fusion together
                    energy_cap_share_max: 0.20
            locations:
                region1:
                    techs:
                        ccgt:
                            constraints:
                                energy_cap_max: 100000  # Increased to keep model feasible

        minimize_emissions_costs:
            run:
                objective_options:
                    cost_class: {'emissions': 1, 'monetary': 0}
            techs:
                ccgt:
                    costs:
                        emissions:
                            om_prod: 100 # kgCO2/kWh
                csp:
                    costs:
                        emissions:
                            om_prod: 10 # kgCO2/kWh

        maximize_utility_costs:
            run:
                objective_options:
                    cost_class: {'utility': 1 , 'monetary': 0}
                    sense: maximize
            techs:
                ccgt:
                    costs:
                        utility:
                            om_prod: 10 # arbitrary utility value
                csp:
                    costs:
                        utility:
                            om_prod: 100 # arbitrary utility value

`techs.yaml`:

    ##
    # TECHNOLOGY DEFINITIONS
    ##

    # Note: '-start' and '-end' is used in tutorial documentation only

    techs:

        ##
        # Supply
        ##

        # ccgt-start
        ccgt:
            essentials:
                name: 'Combined cycle gas turbine'
                color: '#E37A72'
                parent: supply
                carrier_out: power
            constraints:
                resource: inf
                energy_eff: 0.5
                energy_cap_max: 40000  # kW
                energy_cap_max_systemwide: 100000  # kW
                energy_ramping: 0.8
                lifetime: 25
            costs:
                monetary:
                    interest_rate: 0.10
                    energy_cap: 750  # USD per kW
                    om_con: 0.02  # USD per kWh
        # ccgt-end

        # csp-start
        csp:
            essentials:
                name: 'Concentrating solar power'
                color: '#F9CF22'
                parent: supply_plus
                carrier_out: power
            constraints:
                storage_cap_max: 614033
                energy_cap_per_storage_cap_max: 1
                storage_loss: 0.002
                resource: file=csp_resource.csv
                resource_unit: energy_per_area
                energy_eff: 0.4
                parasitic_eff: 0.9
                resource_area_max: inf
                energy_cap_max: 10000
                lifetime: 25
            costs:
                monetary:
                    interest_rate: 0.10
                    storage_cap: 50
                    resource_area: 200
                    resource_cap: 200
                    energy_cap: 1000
                    om_prod: 0.002
        # csp-end

        ##
        # Storage
        ##
        # battery-start
        battery:
            essentials:
                name: 'Battery storage'
                color: '#3B61E3'
                parent: storage
                carrier: power
            constraints:
                energy_cap_max: 1000  # kW
                storage_cap_max: inf
                energy_cap_per_storage_cap_max: 4
                energy_eff: 0.95  # 0.95 * 0.95 = 0.9025 round trip efficiency
                storage_loss: 0  # No loss over time assumed
                lifetime: 25
            costs:
                monetary:
                    interest_rate: 0.10
                    storage_cap: 200  # USD per kWh storage capacity
        # battery-end

        ##
        # Demand
        ##
        # demand-start
        demand_power:
            essentials:
                name: 'Power demand'
                color: '#072486'
                parent: demand
                carrier: power
        # demand-end

        ##
        # Transmission
        ##

        # transmission-start
        ac_transmission:
            essentials:
                name: 'AC power transmission'
                color: '#8465A9'
                parent: transmission
                carrier: power
            constraints:
                energy_eff: 0.85
                lifetime: 25
            costs:
                monetary:
                    interest_rate: 0.10
                    energy_cap: 200
                    om_prod: 0.002

        free_transmission:
            essentials:
                name: 'Local power transmission'
                color: '#6783E3'
                parent: transmission
                carrier: power
            constraints:
                energy_cap_max: inf
                energy_eff: 1.0
            costs:
                monetary:
                    om_prod: 0
        # transmission-end

`locations.yaml`:

    ##
    # LOCATIONS
    ##

    locations:
        # region-1-start
        region1:
            coordinates: {lat: 40, lon: -2}
            techs:
                demand_power:
                    constraints:
                        resource: file=demand-1.csv:demand
                ccgt:
                    constraints:
                        energy_cap_max: 30000 # increased to ensure no unmet_demand in first timestep
        # region-1-end
        # other-locs-start
        region2:
            coordinates: {lat: 40, lon: -8}
            techs:
                demand_power:
                    constraints:
                        resource: file=demand-2.csv:demand
                battery:

        region1-1.coordinates: {lat: 41, lon: -2}
        region1-2.coordinates: {lat: 39, lon: -1}
        region1-3.coordinates: {lat: 39, lon: -2}

        region1-1, region1-2, region1-3:
            techs:
                csp:
        # other-locs-end

    ##
    # TRANSMISSION CAPACITIES
    ##

    links:
        # links-start
        region1,region2:
            techs:
                ac_transmission:
                    constraints:
                        energy_cap_max: 10000
        region1,region1-1:
            techs:
                free_transmission:
        region1,region1-2:
            techs:
                free_transmission:
        region1,region1-3:
            techs:
                free_transmission:
        # links-end

##### Urban-scale example

Available as `calliope.examples.urban_scale`.

###### Model settings

`model.yaml`:

    import:  # Import other files from paths relative to this file, or absolute paths
        - 'model_config/techs.yaml'
        - 'model_config/locations.yaml'
        - 'scenarios.yaml'

    model:
        name: Urban-scale example model

        # What version of Calliope this model is intended for
        calliope_version: 0.6.5

        # Time series data path - can either be a path relative to this file, or an absolute path
        timeseries_data_path: 'timeseries_data'

        subset_time: ['2005-07-01', '2005-07-02']  # Subset of timesteps

    run:
        mode: plan  # Choices: plan, operate

        solver: cbc

        ensure_feasibility: true # Switching on unmet demand

        bigM: 1e6 # setting the scale of unmet demand, which cannot be too high, otherwise the optimisation will not converge

        objective_options.cost_class: {monetary: 1}

`scenarios.yaml`:

    ##
    # Overrides for different example model configuratiions
    ##

    overrides:
        milp:
            model.name: 'Urban-scale example model with MILP'
            run.solver_options.mipgap: 0.05
            techs:
                # chp-start
                chp:
                    constraints:
                        units_max: 4
                        energy_cap_per_unit: 300
                        energy_cap_min_use: 0.2
                    costs:
                        monetary:
                            energy_cap: 700
                            purchase: 40000
                # chp-end
                # boiler-start
                boiler:
                    costs:
                        monetary:
                            energy_cap: 35
                            purchase: 2000
                # boiler-end
                # heat_pipes-start
                heat_pipes:
                    constraints:
                        force_asynchronous_prod_con: true
                # heat_pipes-end

        mapbox_ready:
            locations:
                X1.coordinates: {lat: 51.4596158, lon: -0.1613446}
                X2.coordinates: {lat: 51.4652373, lon: -0.1141548}
                X3.coordinates: {lat: 51.4287016, lon: -0.1310635}
                N1.coordinates: {lat: 51.4450766, lon: -0.1247183}
            links:
                X1,X2.techs.power_lines.distance: 10
                X1,X3.techs.power_lines.distance: 5
                X1,N1.techs.heat_pipes.distance: 3
                N1,X2.techs.heat_pipes.distance: 3
                N1,X3.techs.heat_pipes.distance: 4

        operate:
            run.mode: operate
            run.operation:
                window: 24
                horizon: 48
            model.subset_time: ['2005-07-01', '2005-07-10']
            locations:
                X1:
                    techs:
                        chp.constraints.energy_cap_max: 300
                        pv.constraints.energy_cap_max: 0
                        supply_grid_power.constraints.energy_cap_max: 40
                        supply_gas.constraints.energy_cap_max: 700

                X2:
                    techs:
                        boiler.constraints.energy_cap_max: 200
                        pv.constraints.energy_cap_max: 70
                        supply_gas.constraints.energy_cap_max: 250

                X3:
                    techs:
                        boiler.constraints.energy_cap_max: 0
                        pv.constraints.energy_cap_max: 50
                        supply_gas.constraints.energy_cap_max: 0

            links:
                X1,X2.techs.power_lines.constraints.energy_cap_max: 300
                X1,X3.techs.power_lines.constraints.energy_cap_max: 60
                X1,N1.techs.heat_pipes.constraints.energy_cap_max: 300
                N1,X2.techs.heat_pipes.constraints.energy_cap_max: 250
                N1,X3.techs.heat_pipes.constraints.energy_cap_max: 320

        time_masking:
            model.name: 'Urban-scale example model with time masking'
            model.subset_time: '2005-01'
            # Resample time resolution to 6-hourly
            model.time:
                masks:
                    - {function: extreme_diff, options: {tech0: demand_heat, tech1: demand_electricity, how: max, n: 2}}
                function: resample
                function_options: {resolution: 6H}

`techs.yaml`:

    ##
    # TECHNOLOGY DEFINITIONS
    ##

    # Note: '-start' and '-end' is used in tutorial documentation only

    # supply_power_plus-start
    tech_groups:
        supply_power_plus:
            essentials:
                parent: supply_plus
                carrier: electricity
    # supply_power_plus-end

    techs:

    ##-GRID SUPPLY-##
        # supply-start
        supply_grid_power:
            essentials:
                name: 'National grid import'
                color: '#C5ABE3'
                parent: supply
                carrier: electricity
            constraints:
                resource: inf
                energy_cap_max: 2000
                lifetime: 25
            costs:
                monetary:
                    interest_rate: 0.10
                    energy_cap: 15
                    om_con: 0.1 # 10p/kWh electricity price #ppt

        supply_gas:
            essentials:
                name: 'Natural gas import'
                color: '#C98AAD'
                parent: supply
                carrier: gas
            constraints:
                resource: inf
                energy_cap_max: 2000
                lifetime: 25
            costs:
                monetary:
                    interest_rate: 0.10
                    energy_cap: 1
                    om_con: 0.025 # 2.5p/kWh gas price #ppt
        # supply-end

    ##-Renewables-##
        # pv-start
        pv:
            essentials:
                name: 'Solar photovoltaic power'
                color: '#F9D956'
                parent: supply_power_plus
            constraints:
                export_carrier: electricity
                resource: file=pv_resource.csv:per_area  # Already accounts for panel efficiency - kWh/m2. Source: Renewables.ninja Solar PV Power - Version: 1.1 - License: https://creativecommons.org/licenses/by-nc/4.0/ - Reference: https://doi.org/10.1016/j.energy.2016.08.060
                resource_unit: energy_per_area
                parasitic_eff: 0.85 # inverter losses
                energy_cap_max: 250
                resource_area_max: 1500
                force_resource: true
                resource_area_per_energy_cap: 7 # 7m2 of panels needed to fit 1kWp of panels
                lifetime: 25
            costs:
                monetary:
                    interest_rate: 0.10
                    energy_cap: 1350
        # pv-end

    # Conversion
        # boiler-start
        boiler:
            essentials:
                name: 'Natural gas boiler'
                color: '#8E2999'
                parent: conversion
                carrier_out: heat
                carrier_in: gas
            constraints:
                energy_cap_max: 600
                energy_eff: 0.85
                lifetime: 25
            costs:
                monetary:
                    interest_rate: 0.10
                    om_con: 0.004  # .4p/kWh
        # boiler-end

    # Conversion_plus
        # chp-start
        chp:
            essentials:
                name: 'Combined heat and power'
                color: '#E4AB97'
                parent: conversion_plus
                primary_carrier_out: electricity
                carrier_in: gas
                carrier_out: electricity
                carrier_out_2: heat
            constraints:
                export_carrier: electricity
                energy_cap_max: 1500
                energy_eff: 0.405
                carrier_ratios.carrier_out_2.heat: 0.8
                lifetime: 25
            costs:
                monetary:
                    interest_rate: 0.10
                    energy_cap: 750
                    om_prod: 0.004  # .4p/kWh for 4500 operating hours/year
                    export: file=export_power.csv
        # chp-end

    ##-DEMAND-##
        # demand-start
        demand_electricity:
            essentials:
                name: 'Electrical demand'
                color: '#072486'
                parent: demand
                carrier: electricity

        demand_heat:
            essentials:
                name: 'Heat demand'
                color: '#660507'
                parent: demand
                carrier: heat
        # demand-end

    ##-DISTRIBUTION-##
        # transmission-start
        power_lines:
            essentials:
                name: 'Electrical power distribution'
                color: '#6783E3'
                parent: transmission
                carrier: electricity
            constraints:
                energy_cap_max: 2000
                energy_eff: 0.98
                lifetime: 25
            costs:
                monetary:
                    interest_rate: 0.10
                    energy_cap_per_distance: 0.01

        heat_pipes:
            essentials:
                name: 'District heat distribution'
                color: '#823739'
                parent: transmission
                carrier: heat
            constraints:
                energy_cap_max: 2000
                energy_eff_per_distance: 0.975
                lifetime: 25
            costs:
                monetary:
                    interest_rate: 0.10
                    energy_cap_per_distance: 0.3
        # transmission-end

`locations.yaml`:

    locations:
        # X1-start
        X1:
            techs:
                chp:
                pv:
                supply_grid_power:
                    costs.monetary.energy_cap: 100 # cost of transformers
                supply_gas:
                demand_electricity:
                    constraints.resource: file=demand_power.csv
                demand_heat:
                    constraints.resource: file=demand_heat.csv
            available_area: 500
            coordinates: {x: 2, y: 7}
        # X1-end
        # other-locs-start
        X2:
            techs:
                boiler:
                    costs.monetary.energy_cap: 43.1 # different boiler costs
                pv:
                    costs.monetary:
                            om_prod: -0.0203 # revenue for just producing electricity
                            export: -0.0491 # FIT return for PV export
                supply_gas:
                demand_electricity:
                    constraints.resource: file=demand_power.csv
                demand_heat:
                    constraints.resource: file=demand_heat.csv
            available_area: 1300
            coordinates: {x: 8, y: 7}

        X3:
            techs:
                boiler:
                    costs.monetary.energy_cap: 78 # different boiler costs
                pv:
                    constraints:
                        energy_cap_max: 50 # changing tariff structure below 50kW
                    costs.monetary:
                            om_annual: -80.5 # reimbursement per kWp from FIT
                supply_gas:
                demand_electricity:
                    constraints.resource: file=demand_power.csv
                demand_heat:
                    constraints.resource: file=demand_heat.csv
            available_area: 900
            coordinates: {x: 5, y: 3}
        # other-locs-end
        # N1-start
        N1: # location for branching heat transmission network
            coordinates: {x: 5, y: 7}
        # N1-end

    links:
        # links-start
        X1,X2:
            techs:
                power_lines:
                    distance: 10
        X1,X3:
            techs:
                power_lines:
        X1,N1:
            techs:
                heat_pipes:
        N1,X2:
            techs:
                heat_pipes:
        N1,X3:
            techs:
                heat_pipes:
        # links-end

#### Configuration reference

##### Configuration layout

There must always be at least one model configuration YAML file, probably called `model.yaml` or similar. This file can import any number of additional files.

This file or this set of files must specify the following top-level configuration keys:

- `name`: the name of the model

- `model`: model settings

- `run`: run settings

- `techs`: technology definitions

- (optionally) `tech_groups`: tech group definitions

- `locations`: location definitions

- (optionally) `links`: transmission link definitions

Note

Model settings (`model`) affect how the model and its data are built by Calliope, while run settings (`run`) only take effect once a built model is run (e.g. interactively via `model.run()`). This means that run settings, unlike model settings, can be updated after a model is built and before it is run, by modifying attributes in the built model dataset.

##### YAML configuration file format

All configuration files (with the exception of time series data files) are in the YAML format, “a human friendly data serialisation standard for all programming languages”.

Configuration for Calliope is usually specified as `option: value` entries, where `value` might be a number, a text string, or a list (e.g. a list of further settings).

Calliope allows an abbreviated form for long, nested settings:

    one:
       two:
          three: x

can be written as:

    one.two.three: x

Calliope also allows a special `import:` directive in any YAML file. This can specify one or several YAML files to import. If both the imported file and the current file define the same option, the definition in the current file takes precedence.

Using quotation marks (`'` or `"`) to enclose strings is optional, but can help with readability. The three ways of setting `option` to `text` below are equivalent:

    option: "text"
    option: 'text'
    option: text

Sometimes, a setting can be either enabled or disabled, in this case, the boolean values `true` or `false` are used.

Comments can be inserted anywhere in YAML files with the `#` symbol. The remainder of a line after `#` is interpreted as a comment.

See the YAML website for more general information about YAML.

Calliope internally represents the configuration as `AttrDict`s, which are a subclass of the built-in Python dictionary data type (`dict`) with added functionality such as YAML reading/writing and attribute access to keys.

#### Mathematical formulation

This section details the mathematical formulation of the different components. For each component, a link to the actual implementing function in the Calliope code is given.

Note

Make sure to also refer to the detailed listing of constraints and costs along with their units and default values.

##### Decision variables

`calliope.backend.pyomo.variables.``initialize_decision_variables`(backend_model)

  Defines decision variables.

  Variable | Dimensions
  --- | ---
  energy_cap | loc_techs
  carrier_prod | loc_tech_carriers_prod, timesteps
  carrier_con | loc_tech_carriers_con, timesteps
  cost | costs, loc_techs_cost
  resource_area | loc_techs_area,
  storage_cap | loc_techs_store
  storage | loc_techs_store, timesteps
  resource_con | loc_techs_supply_plus, timesteps
  resource_cap | loc_techs_supply_plus
  carrier_export | loc_tech_carriers_export, timesteps
  cost_var | costs, loc_techs_om_cost, timesteps
  cost_investment | costs, loc_techs_investment_cost
  purchased | loc_techs_purchase
  units | loc_techs_milp
  operating_units | loc_techs_milp, timesteps
  unmet_demand | loc_carriers, timesteps
  unused_supply | loc_carriers, timesteps

##### Objective functions

`calliope.backend.pyomo.objective.``minmax_cost_optimization`(backend_model)

  Minimize or maximise total system cost for specified cost class or a set of cost classes. cost_class is a string or dictionary. If a string, it is automatically converted to a dictionary with a single key:value pair where value == 1. The dictionary provides a weight for each cost class of interest: {cost_1: weight_1, cost_2: weight_2, etc.}.

  If unmet_demand is in use, then the calculated cost of unmet_demand is added or subtracted from the total cost in the opposite sense to the objective.

  \[ \begin{align}\begin{aligned}min: z = \sum_{loc::tech_{cost},k} (cost(loc::tech, cost=cost_{k}) \times weight_{k}) + \sum_{loc::carrier,timestep} (unmet\_demand(loc::carrier, timestep) \times bigM)\\max: z = \sum_{loc::tech_{cost},k} (cost(loc::tech, cost=cost_{k}) \times weight_{k}) - \sum_{loc::carrier,timestep} (unmet\_demand(loc::carrier, timestep) \times bigM)\end{aligned}\end{align} \]

`calliope.backend.pyomo.objective.``check_feasibility`(backend_model)

  Dummy objective, to check that there are no conflicting constraints.

  \[min: z = 1\]

###### Constraints

##### Energy Balance

`calliope.backend.pyomo.constraints.energy_balance.``system_balance_constraint_rule`(backend_model, loc_carrier, timestep)

  System balance ensures that, within each location, the production and consumption of each carrier is balanced.

  \[\sum_{loc::tech::carrier_{prod} \in loc::carrier} \boldsymbol{carrier_{prod}}(loc::tech::carrier, timestep) + \sum_{loc::tech::carrier_{con} \in loc::carrier} \boldsymbol{carrier_{con}}(loc::tech::carrier, timestep) + \sum_{loc::tech::carrier_{export} \in loc::carrier} \boldsymbol{carrier_{export}}(loc::tech::carrier, timestep) \quad \forall loc::carrier \in loc::carriers, \forall timestep \in timesteps\]

`calliope.backend.pyomo.constraints.energy_balance.``balance_supply_constraint_rule`(backend_model, loc_tech, timestep)

  Limit production from supply techs to their available resource

  \[min\_use(loc::tech) \times available\_resource(loc::tech, timestep) \leq \frac{\boldsymbol{carrier_{prod}}(loc::tech::carrier, timestep)}{\eta_{energy}(loc::tech, timestep)} \geq available\_resource(loc::tech, timestep) \quad \forall loc::tech \in loc::techs_{supply}, \forall timestep \in timesteps\]

  If \(force\_resource(loc::tech)\) is set:

  \[\frac{\boldsymbol{carrier_{prod}}(loc::tech::carrier, timestep)}{\eta_{energy}(loc::tech, timestep)} = available\_resource(loc::tech, timestep) \quad \forall loc::tech \in loc::techs_{supply}, \forall timestep \in timesteps\]

  Where:

  \[available\_resource(loc::tech, timestep) = resource(loc::tech, timestep) \times resource\_scale(loc::tech)\]

  if \(loc::tech\) is in \(loc::techs_{area}\):

  \[available\_resource(loc::tech, timestep) = resource(loc::tech, timestep) \times resource\_scale(loc::tech) \times \boldsymbol{resource_{area}}(loc::tech)\]

`calliope.backend.pyomo.constraints.energy_balance.``balance_demand_constraint_rule`(backend_model, loc_tech, timestep)

  Limit consumption from demand techs to their required resource.

  \[\boldsymbol{carrier_{con}}(loc::tech::carrier, timestep) \times \eta_{energy}(loc::tech, timestep) \geq required\_resource(loc::tech, timestep) \quad \forall loc::tech \in loc::techs_{demand}, \forall timestep \in timesteps\]

  If \(force\_resource(loc::tech)\) is set:

  \[\boldsymbol{carrier_{con}}(loc::tech::carrier, timestep) \times \eta_{energy}(loc::tech, timestep) = required\_resource(loc::tech, timestep) \quad \forall loc::tech \in loc::techs_{demand}, \forall timestep \in timesteps\]

  Where:

  \[required\_resource(loc::tech, timestep) = resource(loc::tech, timestep) \times resource\_scale(loc::tech)\]

  if \(loc::tech\) is in \(loc::techs_{area}\):

  \[required\_resource(loc::tech, timestep) = resource(loc::tech, timestep) \times resource\_scale(loc::tech) \times \boldsymbol{resource_{area}}(loc::tech)\]

`calliope.backend.pyomo.constraints.energy_balance.``resource_availability_supply_plus_constraint_rule`(backend_model, loc_tech, timestep)

  Limit production from supply_plus techs to their available resource.

  \[\boldsymbol{resource_{con}}(loc::tech, timestep) \leq available\_resource(loc::tech, timestep) \quad \forall loc::tech \in loc::techs_{supply^{+}}, \forall timestep \in timesteps\]

  If \(force\_resource(loc::tech)\) is set:

  \[\boldsymbol{resource_{con}}(loc::tech, timestep) = available\_resource(loc::tech, timestep) \quad \forall loc::tech \in loc::techs_{supply^{+}}, \forall timestep \in timesteps\]

  Where:

  \[available\_resource(loc::tech, timestep) = resource(loc::tech, timestep) \times resource_{scale}(loc::tech)\]

  if \(loc::tech\) is in \(loc::techs_{area}\):

  \[available\_resource(loc::tech, timestep) = resource(loc::tech, timestep) \times resource_{scale}(loc::tech) \times resource_{area}(loc::tech)\]

`calliope.backend.pyomo.constraints.energy_balance.``balance_transmission_constraint_rule`(backend_model, loc_tech, timestep)

  Balance carrier production and consumption of transmission technologies

  \[-1 * \boldsymbol{carrier_{con}}(loc_{from}::tech:loc_{to}::carrier, timestep) \times \eta_{energy}(loc::tech, timestep) = \boldsymbol{carrier_{prod}}(loc_{to}::tech:loc_{from}::carrier, timestep) \quad \forall loc::tech:loc \in locs::techs:locs_{transmission}, \forall timestep \in timesteps\]

  Where a link is the connection between \(loc_{from}::tech:loc_{to}\) and \(loc_{to}::tech:loc_{from}\) for locations to and from.

`calliope.backend.pyomo.constraints.energy_balance.``balance_supply_plus_constraint_rule`(backend_model, loc_tech, timestep)

  Balance carrier production and resource consumption of supply_plus technologies alongside any use of resource storage.

  \[\boldsymbol{storage}(loc::tech, timestep) = \boldsymbol{storage}(loc::tech, timestep_{previous}) \times (1 - storage\_loss(loc::tech, timestep))^{timestep\_resolution(timestep)} + \boldsymbol{resource_{con}}(loc::tech, timestep) \times \eta_{resource}(loc::tech, timestep) - \frac{\boldsymbol{carrier_{prod}}(loc::tech::carrier, timestep)}{\eta_{energy}(loc::tech, timestep) \times \eta_{parasitic}(loc::tech, timestep)} \quad \forall loc::tech \in loc::techs_{supply^{+}}, \forall timestep \in timesteps\]

  If no storage is defined for the technology, this reduces to:

  \[\boldsymbol{resource_{con}}(loc::tech, timestep) \times \eta_{resource}(loc::tech, timestep) = \frac{\boldsymbol{carrier_{prod}}(loc::tech::carrier, timestep)}{\eta_{energy}(loc::tech, timestep) \times \eta_{parasitic}(loc::tech, timestep)} \quad \forall loc::tech \in loc::techs_{supply^{+}}, \forall timestep \in timesteps\]

`calliope.backend.pyomo.constraints.energy_balance.``balance_storage_constraint_rule`(backend_model, loc_tech, timestep)

  Balance carrier production and consumption of storage technologies, alongside any use of the stored volume.

  \[\boldsymbol{storage}(loc::tech, timestep) = \boldsymbol{storage}(loc::tech, timestep_{previous}) \times (1 - storage\_loss(loc::tech, timestep))^{resolution(timestep)} - \boldsymbol{carrier_{con}}(loc::tech::carrier, timestep) \times \eta_{energy}(loc::tech, timestep) - \frac{\boldsymbol{carrier_{prod}}(loc::tech::carrier, timestep)}{\eta_{energy}(loc::tech, timestep)} \quad \forall loc::tech \in loc::techs_{storage}, \forall timestep \in timesteps\]

`calliope.backend.pyomo.constraints.energy_balance.``balance_storage_inter_cluster_rule`(backend_model, loc_tech, datestep)

  When clustering days, to reduce the timeseries length, balance the daily stored energy across all days of the original timeseries.

  Ref: DOI 10.1016/j.apenergy.2018.01.023

  \[\boldsymbol{storage_{inter\_cluster}}(loc::tech, datestep) = \boldsymbol{storage_{inter\_cluster}}(loc::tech, datestep_{previous}) \times (1 - storage\_loss(loc::tech, timestep))^{24} + \boldsymbol{storage}(loc::tech, timestep_{final, cluster(datestep))}) \quad \forall loc::tech \in loc::techs_{store}, \forall datestep \in datesteps\]

  Where \(timestep_{final, cluster(datestep_{previous}))}\) is the final timestep of the cluster in the clustered timeseries corresponding to the previous day

`calliope.backend.pyomo.constraints.energy_balance.``storage_initial_rule`(backend_model, loc_tech)

  If storage is cyclic, allow an initial storage to still be set. This is applied to the storage of the final timestep/datestep of the series as that, in cyclic storage, is the ‘storage_previous_step’ for the first timestep/datestep.

  If clustering and `storage_inter_cluster` exists:

  \[\boldsymbol{storage_{inter\_cluster}}(loc::tech, datestep_{final}) \times ((1 - storage_loss) ** 24) = storage_{initial}(loc::tech) \times storage_{cap}(loc::tech) \quad \forall loc::tech \in loc::techs_{store}, \forall datestep \in datesteps\]

  Where \(datestep_{final}\) is the last datestep of the timeseries

  Else: .. container:: scrolling-wrapper

  > \[\boldsymbol{storage}(loc::tech, timestep_{final}) \times ((1 - storage_loss) ** 24) = storage_{initial}(loc::tech) \times storage_{cap}(loc::tech) \quad \forall loc::tech \in loc::techs_{store}, \forall timestep \in timesteps\]

  Where \(timestep_{final}\) is the last timestep of the timeseries

##### Capacity

`calliope.backend.pyomo.constraints.capacity.``storage_capacity_constraint_rule`(backend_model, loc_tech)

  Set maximum storage capacity. Supply_plus & storage techs only

  The first valid case is applied:

  \[\begin{split}\boldsymbol{storage_{cap}}(loc::tech) \begin{cases} = storage_{cap, equals}(loc::tech),& \text{if } storage_{cap, equals}(loc::tech)\\ \leq storage_{cap, max}(loc::tech),& \text{if } storage_{cap, max}(loc::tech)\\ \text{unconstrained},& \text{otherwise} \end{cases} \forall loc::tech \in loc::techs_{store}\end{split}\]

  and (if `equals` not enforced):

  \[\boldsymbol{storage_{cap}}(loc::tech) \geq storage_{cap, min}(loc::tech) \quad \forall loc::tech \in loc::techs_{store}\]

`calliope.backend.pyomo.constraints.capacity.``energy_capacity_storage_constraint_rule_old`(backend_model, loc_tech)

  Set an additional energy capacity constraint on storage technologies, based on their use of charge_rate.

  This is deprecated and will be removed in Calliope 0.7.0. Instead of charge_rate, please use energy_cap_per_storage_cap_max.

  \[\boldsymbol{energy_{cap}}(loc::tech) \leq \boldsymbol{storage_{cap}}(loc::tech) \times charge\_rate(loc::tech) \quad \forall loc::tech \in loc::techs_{store}\]

`calliope.backend.pyomo.constraints.capacity.``energy_capacity_storage_min_constraint_rule`(backend_model, loc_tech)

  Limit energy capacities of storage technologies based on their storage capacities.

  \[\begin{split}\boldsymbol{energy_{cap}}(loc::tech) \geq \boldsymbol{storage_{cap}}(loc::tech) \times energy\_cap\_per\_storage\_cap\_min(loc::tech)\\ \forall loc::tech \in loc::techs_{store}\end{split}\]

`calliope.backend.pyomo.constraints.capacity.``energy_capacity_storage_max_constraint_rule`(backend_model, loc_tech)

  Limit energy capacities of storage technologies based on their storage capacities.

  \[\begin{split}\boldsymbol{energy_{cap}}(loc::tech) \leq \boldsymbol{storage_{cap}}(loc::tech) \times energy\_cap\_per\_storage\_cap\_max(loc::tech)\\ \forall loc::tech \in loc::techs_{store}\end{split}\]

`calliope.backend.pyomo.constraints.capacity.``energy_capacity_storage_equals_constraint_rule`(backend_model, loc_tech)

  Limit energy capacities of storage technologies based on their storage capacities.

  \[\boldsymbol{energy_{cap}}(loc::tech) = \boldsymbol{storage_{cap}}(loc::tech) \times energy\_cap\_per\_storage\_cap\_equals(loc::tech) \forall loc::tech \in loc::techs_{store}\]

`calliope.backend.pyomo.constraints.capacity.``resource_capacity_constraint_rule`(backend_model, loc_tech)

  Add upper and lower bounds for resource_cap.

  The first valid case is applied:

  \[\begin{split}\boldsymbol{resource_{cap}}(loc::tech) \begin{cases} = resource_{cap, equals}(loc::tech),& \text{if } resource_{cap, equals}(loc::tech)\\ \leq resource_{cap, max}(loc::tech),& \text{if } resource_{cap, max}(loc::tech)\\ \text{unconstrained},& \text{otherwise} \end{cases} \forall loc::tech \in loc::techs_{finite\_resource\_supply\_plus}\end{split}\]

  and (if `equals` not enforced):

  \[\boldsymbol{resource_{cap}}(loc::tech) \geq resource_{cap, min}(loc::tech) \quad \forall loc::tech \in loc::techs_{finite\_resource\_supply\_plus}\]

`calliope.backend.pyomo.constraints.capacity.``resource_capacity_equals_energy_capacity_constraint_rule`(backend_model, loc_tech)

  Add equality constraint for resource_cap to equal energy_cap, for any technologies which have defined resource_cap_equals_energy_cap.

  \[\boldsymbol{resource_{cap}}(loc::tech) = \boldsymbol{energy_{cap}}(loc::tech) \quad \forall loc::tech \in loc::techs_{finite\_resource\_supply\_plus} \text{ if } resource\_cap\_equals\_energy\_cap = \text{True}\]

`calliope.backend.pyomo.constraints.capacity.``resource_area_constraint_rule`(backend_model, loc_tech)

  Set upper and lower bounds for resource_area.

  The first valid case is applied:

  \[\begin{split}\boldsymbol{resource_{area}}(loc::tech) \begin{cases} = resource_{area, equals}(loc::tech),& \text{if } resource_{area, equals}(loc::tech)\\ \leq resource_{area, max}(loc::tech),& \text{if } resource_{area, max}(loc::tech)\\ \text{unconstrained},& \text{otherwise} \end{cases} \forall loc::tech \in loc::techs_{area}\end{split}\]

  and (if `equals` not enforced):

  \[\boldsymbol{resource_{area}}(loc::tech) \geq resource_{area, min}(loc::tech) \quad \forall loc::tech \in loc::techs_{area}\]

`calliope.backend.pyomo.constraints.capacity.``resource_area_per_energy_capacity_constraint_rule`(backend_model, loc_tech)

  Add equality constraint for resource_area to equal a percentage of energy_cap, for any technologies which have defined resource_area_per_energy_cap

  \[\boldsymbol{resource_{area}}(loc::tech) = \boldsymbol{energy_{cap}}(loc::tech) \times area\_per\_energy\_cap(loc::tech) \quad \forall loc::tech \in locs::techs_{area} \text{ if } area\_per\_energy\_cap(loc::tech)\]

`calliope.backend.pyomo.constraints.capacity.``resource_area_capacity_per_loc_constraint_rule`(backend_model, loc)

  Set upper bound on use of area for all locations which have available_area constraint set. Does not consider resource_area applied to demand technologies

  \[\sum_{tech} \boldsymbol{resource_{area}}(loc::tech) \leq available\_area \quad \forall loc \in locs \text{ if } available\_area(loc)\]

`calliope.backend.pyomo.constraints.capacity.``energy_capacity_constraint_rule`(backend_model, loc_tech)

  Set upper and lower bounds for energy_cap.

  The first valid case is applied:

  \[\begin{split}\frac{\boldsymbol{energy_{cap}}(loc::tech)}{energy_{cap, scale}(loc::tech)} \begin{cases} = energy_{cap, equals}(loc::tech),& \text{if } energy_{cap, equals}(loc::tech)\\ \leq energy_{cap, max}(loc::tech),& \text{if } energy_{cap, max}(loc::tech)\\ \text{unconstrained},& \text{otherwise} \end{cases} \forall loc::tech \in loc::techs\end{split}\]

  and (if `equals` not enforced):

  \[\frac{\boldsymbol{energy_{cap}}(loc::tech)}{energy_{cap, scale}(loc::tech)} \geq energy_{cap, min}(loc::tech) \quad \forall loc::tech \in loc::techs\]

`calliope.backend.pyomo.constraints.capacity.``energy_capacity_systemwide_constraint_rule`(backend_model, tech)

  Set constraints to limit the capacity of a single technology type across all locations in the model.

  The first valid case is applied:

  \[\begin{split}\sum_{loc}\boldsymbol{energy_{cap}}(loc::tech) \begin{cases} = energy_{cap, equals, systemwide}(loc::tech),& \text{if } energy_{cap, equals, systemwide}(loc::tech)\\ \leq energy_{cap, max, systemwide}(loc::tech),& \text{if } energy_{cap, max, systemwide}(loc::tech)\\ \text{unconstrained},& \text{otherwise} \end{cases} \forall tech \in techs\end{split}\]

##### Dispatch

`calliope.backend.pyomo.constraints.dispatch.``carrier_production_max_constraint_rule`(backend_model, loc_tech_carrier, timestep)

  Set maximum carrier production. All technologies.

  \[\boldsymbol{carrier_{prod}}(loc::tech::carrier, timestep) \leq energy_{cap}(loc::tech) \times timestep\_resolution(timestep) \times parasitic\_eff(loc::tec)\]

`calliope.backend.pyomo.constraints.dispatch.``carrier_production_min_constraint_rule`(backend_model, loc_tech_carrier, timestep)

  Set minimum carrier production. All technologies except `conversion_plus`.

  \[\boldsymbol{carrier_{prod}}(loc::tech::carrier, timestep) \geq energy_{cap}(loc::tech) \times timestep\_resolution(timestep) \times energy_{cap,min\_use}(loc::tec)\]

`calliope.backend.pyomo.constraints.dispatch.``carrier_consumption_max_constraint_rule`(backend_model, loc_tech_carrier, timestep)

  Set maximum carrier consumption for demand, storage, and transmission techs.

  \[\boldsymbol{carrier_{con}}(loc::tech::carrier, timestep) \geq -1 \times energy_{cap}(loc::tech) \times timestep\_resolution(timestep)\]

`calliope.backend.pyomo.constraints.dispatch.``resource_max_constraint_rule`(backend_model, loc_tech, timestep)

  Set maximum resource consumed by supply_plus techs.

  \[\boldsymbol{resource_{con}}(loc::tech, timestep) \leq timestep\_resolution(timestep) \times resource_{cap}(loc::tech)\]

`calliope.backend.pyomo.constraints.dispatch.``storage_max_constraint_rule`(backend_model, loc_tech, timestep)

  Set maximum stored energy. Supply_plus & storage techs only.

  \[\boldsymbol{storage}(loc::tech, timestep) \leq storage_{cap}(loc::tech)\]

`calliope.backend.pyomo.constraints.dispatch.``storage_discharge_depth_constraint_rule`(backend_model, loc_tech, timestep)

  Forces storage state of charge to be greater than the allowed depth of discharge.

  \[\boldsymbol{storage}(loc::tech, timestep) >= \boldsymbol{storage_discharge_depth}\forall loc::tech \in loc::techs_{storage}, \forall timestep \in timesteps\]

`calliope.backend.pyomo.constraints.dispatch.``ramping_up_constraint_rule`(backend_model, loc_tech_carrier, timestep)

  Ramping up constraint.

  \[diff(loc::tech::carrier, timestep) \leq max\_ramping\_rate(loc::tech::carrier, timestep)\]

`calliope.backend.pyomo.constraints.dispatch.``ramping_down_constraint_rule`(backend_model, loc_tech_carrier, timestep)

  Ramping down constraint.

  \[-1 \times max\_ramping\_rate(loc::tech::carrier, timestep) \leq diff(loc::tech::carrier, timestep)\]

`calliope.backend.pyomo.constraints.dispatch.``ramping_constraint`(backend_model, loc_tech_carrier, timestep, direction=0)

  Ramping rate constraints.

  Direction: 0 is up, 1 is down.

  \[ \begin{align}\begin{aligned}\boldsymbol{max\_ramping\_rate}(loc::tech::carrier, timestep) = energy_{ramping}(loc::tech, timestep) \times energy_{cap}(loc::tech)\\\boldsymbol{diff}(loc::tech::carrier, timestep) = (carrier_{prod}(loc::tech::carrier, timestep) + carrier_{con}(loc::tech::carrier, timestep)) / timestep\_resolution(timestep) - (carrier_{prod}(loc::tech::carrier, timestep-1) + carrier_{con}(loc::tech::carrier, timestep-1)) / timestep\_resolution(timestep-1)\end{aligned}\end{align} \]

`calliope.backend.pyomo.constraints.dispatch.``storage_intra_max_rule`(backend_model, loc_tech, timestep)

  When clustering days, to reduce the timeseries length, set limits on intra-cluster auxiliary maximum storage decision variable. Ref: DOI 10.1016/j.apenergy.2018.01.023

  \[\boldsymbol{storage}(loc::tech, timestep) \leq \boldsymbol{storage_{intra\_cluster, max}}(loc::tech, cluster(timestep)) \quad \forall loc::tech \in loc::techs_{store}, \forall timestep \in timesteps\]

  Where \(cluster(timestep)\) is the cluster number in which the timestep is located.

`calliope.backend.pyomo.constraints.dispatch.``storage_intra_min_rule`(backend_model, loc_tech, timestep)

  When clustering days, to reduce the timeseries length, set limits on intra-cluster auxiliary minimum storage decision variable. Ref: DOI 10.1016/j.apenergy.2018.01.023

  \[\boldsymbol{storage}(loc::tech, timestep) \geq \boldsymbol{storage_{intra\_cluster, min}}(loc::tech, cluster(timestep)) \quad \forall loc::tech \in loc::techs_{store}, \forall timestep \in timesteps\]

  Where \(cluster(timestep)\) is the cluster number in which the timestep is located.

`calliope.backend.pyomo.constraints.dispatch.``storage_inter_max_rule`(backend_model, loc_tech, datestep)

  When clustering days, to reduce the timeseries length, set maximum limit on the intra-cluster and inter-date stored energy. intra-cluster = all timesteps in a single cluster datesteps = all dates in the unclustered timeseries (each has a corresponding cluster) Ref: DOI 10.1016/j.apenergy.2018.01.023

  \[\boldsymbol{storage_{inter\_cluster}}(loc::tech, datestep) + \boldsymbol{storage_{intra\_cluster, max}}(loc::tech, cluster(datestep)) \leq \boldsymbol{storage_{cap}}(loc::tech) \quad \forall loc::tech \in loc::techs_{store}, \forall datestep \in datesteps\]

  Where \(cluster(datestep)\) is the cluster number in which the datestep is located.

`calliope.backend.pyomo.constraints.dispatch.``storage_inter_min_rule`(backend_model, loc_tech, datestep)

  When clustering days, to reduce the timeseries length, set minimum limit on the intra-cluster and inter-date stored energy. intra-cluster = all timesteps in a single cluster datesteps = all dates in the unclustered timeseries (each has a corresponding cluster) Ref: DOI 10.1016/j.apenergy.2018.01.023

  \[\boldsymbol{storage_{inter\_cluster}}(loc::tech, datestep) \times (1 - storage\_loss(loc::tech, timestep))^{24} + \boldsymbol{storage_{intra\_cluster, min}}(loc::tech, cluster(datestep)) \geq 0 \quad \forall loc::tech \in loc::techs_{store}, \forall datestep \in datesteps\]

  Where \(cluster(datestep)\) is the cluster number in which the datestep is located.

##### Costs

`calliope.backend.pyomo.constraints.costs.``cost_constraint_rule`(backend_model, cost, loc_tech)

  Combine investment and time varying costs into one cost per technology.

  \[\boldsymbol{cost}(cost, loc::tech) = \boldsymbol{cost_{investment}}(cost, loc::tech) + \sum_{timestep \in timesteps} \boldsymbol{cost_{var}}(cost, loc::tech, timestep)\]

`calliope.backend.pyomo.constraints.costs.``cost_investment_constraint_rule`(backend_model, cost, loc_tech)

  Calculate costs from capacity decision variables.

  Transmission technologies “exist” at two locations, so their cost is divided by 2.

  \[ \begin{align}\begin{aligned}\boldsymbol{cost_{investment}}(cost, loc::tech) = cost_{fractional\_om}(cost, loc::tech) + cost_{fixed\_om}(cost, loc::tech) + cost_{cap}(cost, loc::tech)\\cost_{cap}(cost, loc::tech) = depreciation\_rate * ts\_weight * (cost_{energy\_cap}(cost, loc::tech) \times \boldsymbol{energy_{cap}}(loc::tech) + cost_{storage\_cap}(cost, loc::tech) \times \boldsymbol{storage_{cap}}(loc::tech) + cost_{resource\_cap}(cost, loc::tech) \times \boldsymbol{resource_{cap}}(loc::tech) + cost_{resource\_area}(cost, loc::tech)) \times \boldsymbol{resource_{area}}(loc::tech)\\\begin{split}depreciation\_rate = \begin{cases} = 1 / plant\_life,& \text{if } interest\_rate = 0\\ = \frac{interest\_rate \times (1 + interest\_rate)^{plant\_life}}{(1 + interest\_rate)^{plant\_life} - 1},& \text{if } interest\_rate \gt 0\\ \end{cases}\end{split}\\ts\_weight = \sum_{timestep \in timesteps} (time\_res(timestep) \times weight(timestep)) \times \frac{1}{8760}\end{aligned}\end{align} \]

`calliope.backend.pyomo.constraints.costs.``cost_var_constraint_rule`(backend_model, cost, loc_tech, timestep)

  Calculate costs from time-varying decision variables

  \[ \begin{align}\begin{aligned}\boldsymbol{cost_{var}}(cost, loc::tech, timestep) = cost_{prod}(cost, loc::tech, timestep) + cost_{con}(cost, loc::tech, timestep)\\cost_{prod}(cost, loc::tech, timestep) = cost_{om\_prod}(cost, loc::tech, timestep) \times weight(timestep) \times \boldsymbol{carrier_{prod}}(loc::tech::carrier, timestep)\\\begin{split}prod\_con\_eff = \begin{cases} = \boldsymbol{resource_{con}}(loc::tech, timestep),& \text{if } loc::tech \in loc\_techs\_supply\_plus \\ = \frac{\boldsymbol{carrier_{prod}}(loc::tech::carrier, timestep)}{energy_eff(loc::tech, timestep)},& \text{if } loc::tech \in loc\_techs\_supply \\ \end{cases}\end{split}\\cost_{con}(cost, loc::tech, timestep) = cost_{om\_con}(cost, loc::tech, timestep) \times weight(timestep) \times prod\_con\_eff\end{aligned}\end{align} \]

##### Export

`calliope.backend.pyomo.constraints.export.``update_system_balance_constraint`(backend_model, loc_carrier, timestep)

  Update system balance constraint (from energy_balance.py) to include export

  Math given in `system_balance_constraint_rule()`

`calliope.backend.pyomo.constraints.export.``export_balance_constraint_rule`(backend_model, loc_tech_carrier, timestep)

  Ensure no technology can ‘pass’ its export capability to another technology with the same carrier_out, by limiting its export to the capacity of its production

  \[\boldsymbol{carrier_{prod}}(loc::tech::carrier, timestep) \geq \boldsymbol{carrier_{export}}(loc::tech::carrier, timestep) \quad \forall loc::tech::carrier \in locs::tech::carriers_{export}, \forall timestep \in timesteps\]

`calliope.backend.pyomo.constraints.export.``update_costs_var_constraint`(backend_model, cost, loc_tech, timestep)

  Update time varying cost constraint (from costs.py) to include export

  \[\boldsymbol{cost_{var}}(cost, loc::tech, timestep) += cost_{export}(cost, loc::tech, timestep) \times \boldsymbol{carrier_{export}}(loc::tech::carrier, timestep) * timestep_{weight} \quad \forall cost \in costs, \forall loc::tech \in loc::techs_{cost_{var}, export}, \forall timestep \in timesteps\]

`calliope.backend.pyomo.constraints.export.``export_max_constraint_rule`(backend_model, loc_tech_carrier, timestep)

  Set maximum export. All exporting technologies.

  \[\boldsymbol{carrier_{export}}(loc::tech::carrier, timestep) \leq export_{cap}(loc::tech) \quad \forall loc::tech::carrier \in locs::tech::carriers_{export}, \forall timestep \in timesteps\]

  If the technology is defined by integer units, not a continuous capacity, this constraint becomes:

  \[\boldsymbol{carrier_{export}}(loc::tech::carrier, timestep) \leq export_{cap}(loc::tech) \times \boldsymbol{operating_{units}}(loc::tech, timestep)\]

##### MILP

`calliope.backend.pyomo.constraints.milp.``unit_commitment_milp_constraint_rule`(backend_model, loc_tech, timestep)

  Constraining the number of integer units \(operating_units(loc_tech, timestep)\) of a technology which can operate in a given timestep, based on maximum purchased units \(units(loc_tech)\)

  \[\boldsymbol{operating\_units}(loc::tech, timestep) \leq \boldsymbol{units}(loc::tech) \quad \forall loc::tech \in loc::techs_{milp}, \forall timestep \in timesteps\]

`calliope.backend.pyomo.constraints.milp.``unit_capacity_milp_constraint_rule`(backend_model, loc_tech)

  Add upper and lower bounds for purchased units of a technology

  \[\begin{split}\boldsymbol{units}(loc::tech) \begin{cases} = units_{equals}(loc::tech),& \text{if } units_{equals}(loc::tech)\\ \leq units_{max}(loc::tech),& \text{if } units_{max}(loc::tech)\\ \text{unconstrained},& \text{otherwise} \end{cases} \quad \forall loc::tech \in loc::techs_{milp}\end{split}\]

  and (if `equals` not enforced):

  \[\boldsymbol{units}(loc::tech) \geq units_{min}(loc::tech) \quad \forall loc::tech \in loc::techs_{milp}\]

`calliope.backend.pyomo.constraints.milp.``carrier_production_max_milp_constraint_rule`(backend_model, loc_tech_carrier, timestep)

  Set maximum carrier production of MILP techs that aren’t conversion plus

  \[\boldsymbol{carrier_{prod}}(loc::tech::carrier, timestep) \leq energy_{cap, per unit}(loc::tech) \times timestep\_resolution(timestep) \times \boldsymbol{operating\_units}(loc::tech, timestep) \times \eta_{parasitic}(loc::tech, timestep) \quad \forall loc::tech \in loc::techs_{milp}, \forall timestep \in timesteps\]

  \(\eta_{parasitic}\) is only activated for supply_plus technologies

`calliope.backend.pyomo.constraints.milp.``carrier_production_max_conversion_plus_milp_constraint_rule`(backend_model, loc_tech, timestep)

  Set maximum carrier production of conversion_plus MILP techs

  \[\sum_{loc::tech::carrier \in loc::tech::carriers_{out}} \boldsymbol{carrier_{prod}}(loc::tech::carrier, timestep) \leq energy_{cap, per unit}(loc::tech) \times timestep\_resolution(timestep) \times \boldsymbol{operating\_units}(loc::tech, timestep) \times \eta_{parasitic}(loc::tech, timestep) \quad \forall loc::tech \in loc::techs_{milp, conversion^{+}}, \forall timestep \in timesteps\]

`calliope.backend.pyomo.constraints.milp.``carrier_production_min_milp_constraint_rule`(backend_model, loc_tech_carrier, timestep)

  Set minimum carrier production of MILP techs that aren’t conversion plus

  \[\boldsymbol{carrier_{prod}}(loc::tech::carrier, timestep) \geq energy_{cap, per unit}(loc::tech) \times timestep\_resolution(timestep) \times \boldsymbol{operating\_units}(loc::tech, timestep) \times energy_{cap, min use}(loc::tech) \quad \forall loc::tech \in loc::techs_{milp}, \forall timestep \in timesteps\]

`calliope.backend.pyomo.constraints.milp.``carrier_production_min_conversion_plus_milp_constraint_rule`(backend_model, loc_tech, timestep)

  Set minimum carrier production of conversion_plus MILP techs

  \[\sum_{loc::tech::carrier \in loc::tech::carriers_{out}} \boldsymbol{carrier_{prod}}(loc::tech::carrier, timestep) \geq energy_{cap, per unit}(loc::tech) \times timestep\_resolution(timestep) \times \boldsymbol{operating\_units}(loc::tech, timestep) \times energy_{cap, min use}(loc::tech) \quad \forall loc::tech \in loc::techs_{milp, conversion^{+}}, \forall timestep \in timesteps\]

`calliope.backend.pyomo.constraints.milp.``carrier_consumption_max_milp_constraint_rule`(backend_model, loc_tech_carrier, timestep)

  Set maximum carrier consumption of demand, storage, and transmission MILP techs

  \[\boldsymbol{carrier_{con}}(loc::tech::carrier, timestep) \geq -1 * energy_{cap, per unit}(loc::tech) \times timestep\_resolution(timestep) \times \boldsymbol{operating\_units}(loc::tech, timestep) \times \eta_{parasitic}(loc::tech, timestep) \quad \forall loc::tech \in loc::techs_{milp, con}, \forall timestep \in timesteps\]

`calliope.backend.pyomo.constraints.milp.``energy_capacity_units_milp_constraint_rule`(backend_model, loc_tech)

  Set energy capacity decision variable as a function of purchased units

  \[\boldsymbol{energy_{cap}}(loc::tech) = \boldsymbol{units}(loc::tech) \times energy_{cap, per unit}(loc::tech) \quad \forall loc::tech \in loc::techs_{milp}\]

`calliope.backend.pyomo.constraints.milp.``storage_capacity_units_milp_constraint_rule`(backend_model, loc_tech)

  Set storage capacity decision variable as a function of purchased units

  \[\boldsymbol{storage_{cap}}(loc::tech) = \boldsymbol{units}(loc::tech) \times storage_{cap, per unit}(loc::tech) \quad \forall loc::tech \in loc::techs_{milp, store}\]

`calliope.backend.pyomo.constraints.milp.``energy_capacity_max_purchase_milp_constraint_rule`(backend_model, loc_tech)

  Set maximum energy capacity decision variable upper bound as a function of binary purchase variable

  The first valid case is applied:

  \[\begin{split}\frac{\boldsymbol{energy_{cap}}(loc::tech)}{energy_{cap, scale}(loc::tech)} \begin{cases} = energy_{cap, equals}(loc::tech) \times \boldsymbol{purchased}(loc::tech),& \text{if } energy_{cap, equals}(loc::tech)\\ \leq energy_{cap, max}(loc::tech) \times \boldsymbol{purchased}(loc::tech),& \text{if } energy_{cap, max}(loc::tech)\\ \text{unconstrained},& \text{otherwise} \end{cases} \forall loc::tech \in loc::techs_{purchase}\end{split}\]

`calliope.backend.pyomo.constraints.milp.``energy_capacity_min_purchase_milp_constraint_rule`(backend_model, loc_tech)

  Set minimum energy capacity decision variable upper bound as a function of binary purchase variable

  and (if `equals` not enforced):

  \[\frac{\boldsymbol{energy_{cap}}(loc::tech)}{energy_{cap, scale}(loc::tech)} \geq energy_{cap, min}(loc::tech) \times \boldsymbol{purchased}(loc::tech) \quad \forall loc::tech \in loc::techs\]

`calliope.backend.pyomo.constraints.milp.``storage_capacity_max_purchase_milp_constraint_rule`(backend_model, loc_tech)

  Set maximum storage capacity.

  The first valid case is applied:

  \[\begin{split}\boldsymbol{storage_{cap}}(loc::tech) \begin{cases} = storage_{cap, equals}(loc::tech) \times \boldsymbol{purchased},& \text{if } storage_{cap, equals} \\ \leq storage_{cap, max}(loc::tech) \times \boldsymbol{purchased},& \text{if } storage_{cap, max}(loc::tech)\\ \text{unconstrained},& \text{otherwise} \end{cases} \forall loc::tech \in loc::techs_{purchase, store}\end{split}\]

`calliope.backend.pyomo.constraints.milp.``storage_capacity_min_purchase_milp_constraint_rule`(backend_model, loc_tech)

  Set minimum storage capacity decision variable as a function of binary purchase variable

  if `equals` not enforced for storage_cap:

  \[\boldsymbol{storage_{cap}}(loc::tech) \geq storage_{cap, min}(loc::tech) \times \boldsymbol{purchased}(loc::tech) \quad \forall loc::tech \in loc::techs_{purchase, store}\]

`calliope.backend.pyomo.constraints.milp.``update_costs_investment_units_milp_constraint`(backend_model, cost, loc_tech)

  Add MILP investment costs (cost * number of units purchased)

  \[\boldsymbol{cost_{investment}}(cost, loc::tech) += \boldsymbol{units}(loc::tech) \times cost_{purchase}(cost, loc::tech) * timestep_{weight} * depreciation \quad \forall cost \in costs, \forall loc::tech \in loc::techs_{cost_{investment}, milp}\]

`calliope.backend.pyomo.constraints.milp.``update_costs_investment_purchase_milp_constraint`(backend_model, cost, loc_tech)

  Add binary investment costs (cost * binary_purchased_unit)

  \[\boldsymbol{cost_{investment}}(cost, loc::tech) += \boldsymbol{purchased}(loc::tech) \times cost_{purchase}(cost, loc::tech) * timestep_{weight} * depreciation \quad \forall cost \in costs, \forall loc::tech \in loc::techs_{cost_{investment}, purchase}\]

`calliope.backend.pyomo.constraints.milp.``unit_capacity_systemwide_milp_constraint_rule`(backend_model, tech)

  Set constraints to limit the number of purchased units of a single technology type across all locations in the model.

  The first valid case is applied:

  \[\begin{split}\sum_{loc}\boldsymbol{units}(loc::tech) + \boldsymbol{purchased}(loc::tech) \begin{cases} = units_{equals, systemwide}(tech),& \text{if } units_{equals, systemwide}(tech)\\ \leq units_{max, systemwide}(tech),& \text{if } units_{max, systemwide}(tech)\\ \text{unconstrained},& \text{otherwise} \end{cases} \forall tech \in techs\end{split}\]

`calliope.backend.pyomo.constraints.milp.``asynchronous_con_milp_constraint_rule`(backend_model, loc_tech, timestep)

  BigM limit set on carrier_con, forcing it to either be zero or non-zero, depending on whether con is zero or one, respectively.

  \[- \boldsymbol{carrier_con}[loc::tech::carrier, timestep] \leq \text{bigM} \times (1 - \boldsymbol{prod_con_switch}[loc::tech, timestep]) \forall loc::tech \in loc::techs_{asynchronous_prod_con}, \forall timestep \in timesteps\]

`calliope.backend.pyomo.constraints.milp.``asynchronous_prod_milp_constraint_rule`(backend_model, loc_tech, timestep)

  BigM limit set on carrier_prod, forcing it to either be zero or non-zero, depending on whether prod is zero or one, respectively.

  \[\boldsymbol{carrier_prod}[loc::tech::carrier, timestep] \leq \text{bigM} \times \boldsymbol{prod_con_switch}[loc::tech, timestep] \forall loc::tech \in loc::techs_{asynchronous_prod_con}, \forall timestep \in timesteps\]

##### Conversion

`calliope.backend.pyomo.constraints.conversion.``balance_conversion_constraint_rule`(backend_model, loc_tech, timestep)

  Balance energy carrier consumption and production

  \[-1 * \boldsymbol{carrier_{con}}(loc::tech::carrier, timestep) \times \eta_{energy}(loc::tech, timestep) = \boldsymbol{carrier_{prod}}(loc::tech::carrier, timestep) \times \eta_{energy}(loc::tech, timestep) \quad \forall loc::tech \in locs::techs_{conversion}, \forall timestep \in timesteps\]

`calliope.backend.pyomo.constraints.conversion.``cost_var_conversion_constraint_rule`(backend_model, cost, loc_tech, timestep)

  Add time-varying conversion technology costs

  \[\boldsymbol{cost_{var}}(loc::tech, cost, timestep) = \boldsymbol{carrier_{prod}}(loc::tech::carrier, timestep) \times timestep_{weight}(timestep) \times cost_{om, prod}(loc::tech, cost, timestep) + \boldsymbol{carrier_{con}}(loc::tech::carrier, timestep) \times timestep_{weight}(timestep) \times cost_{om, con}(loc::tech, cost, timestep) \quad \forall loc::tech \in loc::techs_{cost_{var}, conversion}\]

##### Conversion_plus

`calliope.backend.pyomo.constraints.conversion_plus.``balance_conversion_plus_primary_constraint_rule`(backend_model, loc_tech, timestep)

  Balance energy carrier consumption and production for carrier_in and carrier_out

  \[\sum_{loc::tech::carrier \in loc::tech::carriers_{out}} \frac{\boldsymbol{carrier_{prod}}(loc::tech::carrier, timestep)}{ carrier\_ratio(loc::tech::carrier, `out')} = -1 * \sum_{loc::tech::carrier \in loc::tech::carriers_{in}} ( \boldsymbol{carrier_{con}}(loc::tech::carrier, timestep) * carrier\_ratio(loc::tech::carrier, `in') * \eta_{energy}(loc::tech, timestep)) \quad \forall loc::tech \in loc::techs_{conversion^{+}}, \forall timestep \in timesteps\]

`calliope.backend.pyomo.constraints.conversion_plus.``carrier_production_max_conversion_plus_constraint_rule`(backend_model, loc_tech, timestep)

  Set maximum conversion_plus carrier production.

  \[\sum_{loc::tech::carrier \in loc::tech::carriers_{out}} \boldsymbol{carrier_{prod}}(loc::tech::carrier, timestep) \leq \boldsymbol{energy_{cap}}(loc::tech) \times timestep\_resolution(timestep) \quad \forall loc::tech \in loc::techs_{conversion^{+}}, \forall timestep \in timesteps\]

`calliope.backend.pyomo.constraints.conversion_plus.``carrier_production_min_conversion_plus_constraint_rule`(backend_model, loc_tech, timestep)

  Set minimum conversion_plus carrier production.

  \[\sum_{loc::tech::carrier \in loc::tech::carriers_{out}} \boldsymbol{carrier_{prod}}(loc::tech::carrier, timestep) \leq \boldsymbol{energy_{cap}}(loc::tech) \times timestep\_resolution(timestep) \times energy_{cap, min use}(loc::tech) \quad \forall loc::tech \in loc::techs_{conversion^{+}}, \forall timestep \in timesteps\]

`calliope.backend.pyomo.constraints.conversion_plus.``cost_var_conversion_plus_constraint_rule`(backend_model, cost, loc_tech, timestep)

  Add time-varying conversion_plus technology costs

  \[\boldsymbol{cost_{var}}(loc::tech, cost, timestep) = \boldsymbol{carrier_{prod}}(loc::tech::carrier_{primary}, timestep) \times timestep_{weight}(timestep) \times cost_{om, prod}(loc::tech, cost, timestep) + \boldsymbol{carrier_{con}}(loc::tech::carrier_{primary}, timestep) \times timestep_{weight}(timestep) \times cost_{om, con}(loc::tech, cost, timestep) \quad \forall loc::tech \in loc::techs_{cost_{var}, conversion^{+}}\]

`calliope.backend.pyomo.constraints.conversion_plus.``balance_conversion_plus_tiers_constraint_rule`(backend_model, tier, loc_tech, timestep)

  Force all carrier_in_2/carrier_in_3 and carrier_out_2/carrier_out_3 to follow carrier_in and carrier_out (respectively).

  If tier in [‘out_2’, ‘out_3’]:

  \[\sum_{loc::tech::carrier \in loc::tech::carriers_{out}} ( \frac{\boldsymbol{carrier_{prod}}(loc::tech::carrier, timestep)}{ carrier\_ratio(loc::tech::carrier, `out')} = \sum_{loc::tech::carrier \in loc::tech::carriers_{tier}} ( \frac{\boldsymbol{carrier_{prod}}(loc::tech::carrier, timestep)}{ carrier\_ratio(loc::tech::carrier, tier)} \quad \forall \text { tier } \in [`out_2', `out_3'], \forall loc::tech \in loc::techs_{conversion^{+}}, \forall timestep \in timesteps\]

  If tier in [‘in_2’, ‘in_3’]:

  \[\sum_{loc::tech::carrier \in loc::tech::carriers_{in}} \frac{\boldsymbol{carrier_{con}}(loc::tech::carrier, timestep)}{ carrier\_ratio(loc::tech::carrier, `in')} = \sum_{loc::tech::carrier \in loc::tech::carriers_{tier}} \frac{\boldsymbol{carrier_{prod}}(loc::tech::carrier, timestep)}{ carrier\_ratio(loc::tech::carrier, tier)} \quad \forall \text{ tier } \in [`in_2', `in_3'], \forall loc::tech \in loc::techs_{conversion^{+}}, \forall timestep \in timesteps\]

`calliope.backend.pyomo.constraints.conversion_plus.``conversion_plus_prod_con_to_zero_constraint_rule`(backend_model, loc_tech_carrier_tier, timestep)

  Force any carrier production or consumption for a conversion plus technology to zero in timesteps where its carrier_ratio is zero

##### Network

`calliope.backend.pyomo.constraints.network.``symmetric_transmission_constraint_rule`(backend_model, loc_tech)

  Constrain e_cap symmetrically for transmission nodes. Transmission techs only.

  \[energy_{cap}(loc1::tech:loc2) = energy_{cap}(loc2::tech:loc1)\]

##### Policy

`calliope.backend.pyomo.constraints.policy.``group_share_energy_cap_constraint_rule`(backend_model, techlist, what)

  Enforce shares in energy_cap for groups of technologies. Applied to `supply` and `supply_plus` technologies only.

  \[\sum_{loc::tech \in given\_group} energy_{cap}(loc::tech) = fraction \times \sum_{loc::tech \in loc\_techs\_supply \or loc\_techs\_supply\_plus} energy_{cap}(loc::tech)\]

`calliope.backend.pyomo.constraints.policy.``group_share_carrier_prod_constraint_rule`(backend_model, techlist_carrier, what)

  Enforce shares in carrier_prod for groups of technologies. Applied to `loc_tech_carriers_supply_conversion_all`, which includes supply, supply_plus, conversion, and conversion_plus.

  \[\sum_{loc::tech::carrier \in given\_group, timestep \in timesteps} carrier_{prod}(loc::tech::carrier, timestep) = fraction \times \sum_{loc::tech:carrier \in loc\_tech\_carriers\_supply\_all, timestep\in timesteps} carrier_{prod}(loc::tech::carrier, timestep)\]

`calliope.backend.pyomo.constraints.policy.``reserve_margin_constraint_rule`(backend_model, carrier)

  Enforces a system reserve margin per carrier.

  \[\sum_{loc::tech::carrier \in loc\_tech\_carriers\_supply\_all} energy_{cap}(loc::tech::carrier, timestep_{max\_demand}) \geq \sum_{loc::tech::carrier \in loc\_tech\_carriers\_demand} carrier_{con}(loc::tech::carrier, timestep_{max\_demand}) \times -1 \times \frac{1}{time\_resolution_{max\_demand}} \times (1 + reserve\_margin)\]

##### Group constraints

`calliope.backend.pyomo.constraints.group.``get_demand_share_lhs_and_rhs_loc_tech_carriers`(backend_model, group_name, carrier)
  Returns
    (lhs_loc_tech_carriers, rhs_loc_tech_carriers):

      lhs are the supply technologies, rhs are the demand technologies

`calliope.backend.pyomo.constraints.group.``demand_share_constraint_rule`(backend_model, group_name, carrier, what)

  Enforces shares of demand of a carrier to be met by the given groups of technologies at the given locations, on average over the entire model period. The share is relative to `demand` technologies only.

  \[\sum_{loc::tech::carrier \in given\_group, timestep \in timesteps} carrier_{prod}(loc::tech::carrier, timestep) \leq share \times \sum_{loc::tech:carrier \in loc\_techs\_demand \in given\_locations, timestep\in timesteps} carrier_{con}(loc::tech::carrier, timestep)\]

`calliope.backend.pyomo.constraints.group.``demand_share_per_timestep_constraint_rule`(backend_model, group_name, carrier, timestep, what)

  Enforces shares of demand of a carrier to be met by the given groups of technologies at the given locations, in each timestep. The share is relative to `demand` technologies only.

  \[\sum_{loc::tech::carrier \in given\_group} carrier_{prod}(loc::tech::carrier, timestep) \leq share \times \sum_{loc::tech:carrier \in loc\_techs\_demand \in given\_locations} carrier_{con}(loc::tech::carrier, timestep) for timestep \in timesteps\]

`calliope.backend.pyomo.constraints.group.``demand_share_per_timestep_decision_main_constraint_rule`(backend_model, group_name, carrier, tech, timestep)

  Allows the model to decide on how a fraction demand for a carrier is met by the given groups, which will all have the same share in each timestep. The share is relative to the actual demand from `demand` technologies only.

  The main constraint enforces that the shares are the same in each timestep.

  \[ \begin{align}\begin{aligned}\sum_{loc::tech::carrier \in given\_group} carrier_{prod}(loc::tech::carrier, timestep)\\=\\\sum_{loc::tech::carrier \in given\_group} required\_resource(loc::tech::carrier, timestep)\\\times \sum_{loc::tech::carrier \in given\_group} demand\_share\_per\_timestep\_decision(loc::tech::carrier)\\\forall timestep \in timesteps\\\forall tech \in techs\end{aligned}\end{align} \]

`calliope.backend.pyomo.constraints.group.``demand_share_per_timestep_decision_sum_constraint_rule`(backend_model, group_name, carrier)

  > Allows the model to decide on how a fraction of demand for a carrier is met by the given groups, which will all have the same share in each timestep. The share is relative to the actual demand from `demand` technologies only.

  > The sum constraint ensures that all decision shares add up to the share of carrier demand specified in the constraint.

  > This constraint is only applied if the share of carrier demand has been set to a not-None value.

  \[share = \sum_{loc::tech::carrier \in given\_group} demand\_share\_per\_timestep\_decision(loc::tech::carrier)\]

`calliope.backend.pyomo.constraints.group.``carrier_prod_share_constraint_rule`(backend_model, constraint_group, carrier, what)

  Enforces shares of carrier_prod for groups of technologies and locations, on average over the entire model period. The share is relative to `supply` and `supply_plus` technologies only.

  \[\sum_{loc::tech::carrier \in given\_group, timestep \in timesteps} carrier_{prod}(loc::tech::carrier, timestep) \leq share \times \sum_{loc::tech:carrier \in loc\_tech\_carriers\_supply\_all \in given\_locations, timestep\in timesteps} carrier_{prod}(loc::tech::carrier, timestep)\]

`calliope.backend.pyomo.constraints.group.``carrier_prod_share_per_timestep_constraint_rule`(backend_model, constraint_group, carrier, timestep, what)

  Enforces shares of carrier_prod for groups of technologies and locations, in each timestep. The share is relative to `supply` and `supply_plus` technologies only.

  \[\sum_{loc::tech::carrier \in given\_group} carrier_{prod}(loc::tech::carrier, timestep) \leq share \times \sum_{loc::tech:carrier \in loc\_tech\_carriers\_supply\_all \in given\_locations} carrier_{prod}(loc::tech::carrier, timestep) for timestep \in timesteps\]

`calliope.backend.pyomo.constraints.group.``net_import_share_constraint_rule`(backend_model, constraint_group, carrier, what)

  Enforces demand shares of net imports from transmission technologies for groups of locations, on average over the entire model period. Transmission within the group are ignored. The share is relative to `demand` technologies only.

  \[\sum_{loc::tech::carrier \in loc\_tech\_carriers\_transmission \in given\_locations, timestep \in timesteps} carrier_{prod}(loc::tech::carrier, timestep) + \sum_{loc::tech::carrier \in loc\_tech\_carriers\_transmission \in given\_locations, timestep \in timesteps} carrier_{con}(loc::tech::carrier, timestep) \leq share \times \sum_{loc::tech:carrier \in loc\_tech\_demand \in given\_locations, timestep\in timesteps} carrier_{con}(loc::tech::carrier, timestep)\]

`calliope.backend.pyomo.constraints.group.``carrier_prod_constraint_rule`(backend_model, constraint_group, carrier, what)

  Enforces carrier_prod for groups of technologies and locations, as a sum over the entire model period.

  \[\sum_{loc::tech::carrier \in given\_group, timestep \in timesteps} carrier_{prod}(loc::tech::carrier, timestep) \leq supply_max\]

`calliope.backend.pyomo.constraints.group.``energy_cap_share_constraint_rule`(backend_model, constraint_group, what)

  Enforces shares of energy_cap for groups of technologies and locations. The share is relative to `supply` and `supply_plus` technologies only.

  \[\sum_{loc::tech \in given\_group} energy_{cap}(loc::tech) \leq share \times \sum_{loc::tech \in loc\_tech\_supply\_all \in given\_locations} energy_{cap}(loc::tech)\]

`calliope.backend.pyomo.constraints.group.``energy_cap_constraint_rule`(backend_model, constraint_group, what)

  Enforce upper and lower bounds for energy_cap of energy_cap for groups of technologies and locations.

  \[ \begin{align}\begin{aligned}\begin{split}\sum_{loc::tech \in given\_group} energy_{cap}(loc::tech) \leq energy\_cap\_max\\\end{split}\\\sum_{loc::tech \in given\_group} energy_{cap}(loc::tech) \geq energy\_cap\_min\end{aligned}\end{align} \]

`calliope.backend.pyomo.constraints.group.``cost_cap_constraint_rule`(backend_model, group_name, cost, what)

  Limit cost for a specific cost class to a certain value, i.e. Ɛ-constrained costs, for groups of technologies and locations.

  \[\sum{loc::tech \in loc\_techs_{group\_name}, timestep \in timesteps} \boldsymbol{cost}(cost, loc::tech, timestep) \begin{cases} \leq cost\_max(cost) \geq cost\_min(cost) = cost\_equals(cost) \end{cases}\]

`calliope.backend.pyomo.constraints.group.``cost_investment_cap_constraint_rule`(backend_model, group_name, cost, what)

  Limit investment costs specific to a cost class to a certain value, i.e. Ɛ-constrained costs, for groups of technologies and locations.

  \[\sum{loc::tech \in loc\_techs_{group\_name}, timestep \in timesteps} \boldsymbol{cost\_{investment}}(cost, loc::tech, timestep) \begin{cases} \leq cost\_investment\_max(cost) \geq cost\_investment\_min(cost) = cost\_investment\_equals(cost) \end{cases}\]

`calliope.backend.pyomo.constraints.group.``cost_var_cap_constraint_rule`(backend_model, group_name, cost, what)

  Limit variable costs specific to a cost class to a certain value, i.e. Ɛ-constrained costs, for groups of technologies and locations.

  \[\sum{loc::tech \in loc\_techs_{group\_name}, timestep \in timesteps} \boldsymbol{cost\_{var}}(cost, loc::tech, timestep) \begin{cases} \leq cost\_var\_max(cost) \geq cost\_var\_min(cost) = cost\_var\_equals(cost) \end{cases}\]

`calliope.backend.pyomo.constraints.group.``resource_area_constraint_rule`(backend_model, constraint_group, what)

  Enforce upper and lower bounds of resource_area for groups of technologies and locations.

  \[ \begin{align}\begin{aligned}\begin{split}\boldsymbol{resource_{area}}(loc::tech) \leq group\_resource\_area\_max\\\end{split}\\\boldsymbol{resource_{area}}(loc::tech) \geq group\_resource\_area\_min\end{aligned}\end{align} \]

### Development guide

Contributions are very welcome! See our contributors guide on GitHub for information on how to contribute.

The code lives on GitHub at calliope-project/calliope. Development takes place in the `master` branch. Stable versions are tagged off of `master` with semantic versioning.

Tests are included and can be run with `py.test` from the project’s root directory.

Also see the list of open issues, planned milestones and projects for an overview of where development is heading, and join us on Gitter to ask questions or discuss code.

#### Installing a development version

As when installing a stable version, using `conda` is recommended.

To actively contribute to Calliope development, or simply track the latest development version, you’ll instead want to clone our GitHub repository. This will provide you with the master branch in a known location on your local device.

First, clone the repository

>     $ git clone https://github.com/calliope-project/calliope

Using conda, install all requirements, including the free and open source GLPK solver, into a new environment, e.g. `calliope_dev`

>     $ conda env create -f calliope/requirements/base.yml -n calliope_dev
>     $ conda activate calliope_dev

Then install Calliope itself with pip

>     $ pip install -e calliope

Most of our tests depend on having the CBC solver also installed, as we have found it to be more stable than GPLK. To install solvers other than GLPK, see our solver installation instructions <install_solvers>.

#### Creating modular extensions

As of version 0.6.0, dynamic loading of custom constraint generator extensions has been removed due it not not being used by users of Calliope. The ability to dynamically load custom functions to adjust time resolution remains (see below).

##### Time functions and masks

Custom functions that adjust time resolution can be loaded dynamically during model initialisation. By default, Calliope first checks whether the name of a function or time mask refers to a function from the `calliope.core.time.masks` or `calliope.core.time.funcs` module, and if not, attempts to load the function from an importable module:

    time:
       masks:
           - {function: week, options: {day_func: 'extreme', tech: 'wind', how: 'min'}}
           - {function: my_custom_module.my_custom_mask, options: {...}}
       function: my_custom_module.my_custom_function
       function_options: {...}

#### Understanding Calliope internal implementation

Worried about delving into the Calliope code? Confused by the structure? Fear not! The package is structured as best as possible to follow a clear workflow, which takes inputs on a journey from YAML and CSV files, via Pyomo objects, to a NetCDF file of results.

##### Overview

Calliope enables data stored in YAML and CSV files to be prepared for optimisation in a linear solver, and the results of optimisation to be analysed and/or saved. The internal workflow is shown below. The python packages ruamel.yaml and pandas are used to parse the YAML and CSV files, respectively. Xarray is then used to restructure the data into multidimensional arrays, ready for saving, plotting, or sending to the backend. The pyomo package is currently used in the backend to transform the xarray dataset into a pyomo ConcreteModel. All parameters, sets, constraints, and decision variables are defined as pyomo objects at this stage. Pyomo produces an LP file, which can be read in by the modeller’s chosen solver. Results are extracted from pyomo into an xarray dataset, again ready to be analysed or saved.

##### Internal implementation

Taking a more detailed look at the workflow, a number of data objects are populated. On initialising a model, the model_run dictionary is created from the provided YAML and CSV files. Overrides (both from scenarios and location/link specific ones) are applied at this point. The model_run dictionary is then reformulated into multidimensional arrays of data and collated in the model_data xarray dataset. At this point, model initialisation has completed; model inputs can be accessed by the user, and edited if necessary.

On executing model.run(), only model_data is sent over to the backend, where the pyomo ConcreteModel is created and pyomo parameters (Param) and sets (Set) are populated using data from model_data. Decision variables (Var), constraints (Constraint), and the objective (Obj) are also initialised at this point. The model is then sent to the solver.

Upon solving the problem, the backend_model (pyomo ConcreteModel) is attached to the Model object and the results are added to model_data. Post-processing also occurs to clean up the results and to calculate certain indicators, such as the capacity factor of technologies. At this point, the model run has completed; model results can be accessed by the user, and saved or analysed as required.

Representation of Calliope internal implementation workflow. Five primary steps are shown, starting at the model definition and implemented clockwise. From inner edge to outer edge of the rainbow are: the data object produced by the step, primary and auxiliary python files in which functionality to produce the data object are found, and the folder containing the relevant python files for the step.

##### Exposing all methods and data attached to the Model object

The Model object begins as an empty class. Once called, it becomes an empty object which is populated with methods to access, analyse, and save the model data. The Model object is further augmented once run has been called, at which point, the backend model object can be accessed, directly or via a user-friendly interface. The notebook found here goes through each method and data object which can be accessed through the Model object. Most are hidden (using an underscore before the method name), as they aren’t useful for the average user.

Representation of the Calliope Model object, growing from an empty class to having methods to view, plot and save data, and to interface with the solver backend.

#### Contribution workflow

Have a bug fix or feature addition you’d like to see in the next stable release of Calliope? First, be sure to check out our list of open and closed issues to see whether this is something someone else has mentioned, or perhaps has even fixed. If it’s there, you can add to the discussion, give it a thumbs up, or look to implement the change yourself. If it isn’t there, then feel free to open your own issue, or you can head straight to implementing it. The below instructions are a more detailed description of our contribution guidelines, which you can refer to if you’re already comfortable with using pytest and GitHub flows.

##### Implementing a change

When you want to change some part of Calliope, whether it is the software or the documentation, it’s best to do it in a fork of the main Calliope project repository. You can find out more about how to fork a repository on GitHub’s help pages. Your fork will be a duplicate of the Calliope master branch and can be ‘cloned’ to provide you with the repository on your own device

>     $ git clone https://github.com/your_username/calliope

If you want the local version of your fork to be in the same folder as your local version of the main Calliope repository, then you just need to specify a new directory name

>     $ git clone https://github.com/your_username/calliope your_new_directory_name

Following the instructions for installing a development environment of Calliope, you can create an environment specific to this installation of Calliope.

In making changes to your local version, it’s a good idea to create a branch first, to not have your master branch diverge from that of the main Calliope repository

>     $ git branch new-fix-or-feature

Then, ‘checkout’ the branch so that the folder contents are specific to that branch

>     $ git checkout new-fix-or-feature

Finally, push the branch online, so it’s existence is also in your remote fork of the Calliope repository (you’ll find it in the dropdown list of branches at https://github.com/your_repository/calliope)

>     $ git push -u origin new-fix-or-feature

Now the files in your local directory can be edited with complete freedom. Once you have made the necessary changes, you’ll need to test that they don’t break anything. This can be done easily by changing to the directory into which you cloned your fork using the terminal / command line, and running pytest (make sure you have activated the conda environment and you have pytest installed: conda install pytest). Any change you make should also be covered by a test. Add it into the relevant test file, making sure the function starts with ‘test_’. Since the whole test suite takes ~25 minutes to run, you can run specific tests, such as those you add in

>     $ pytest calliope/test/test_filename.py::ClassName::function_name

If tests are failing, you can debug them by using the pytest arguments `-x` (stop at the first failed test) and `--pdb` (enter into the debug console).

Once everything has been updated as you’d like (see the contribution checklist below for more on this), you can commit those changes. This stores all edited files in the directory, ready for pushing online

>     $ git add .
>     $ git checkout -m "Short message explaining what has been done in this commit."

If you only want a subset of edited files to go into this commit, you can specify them in the call to git add; the period adds all edited files.

If you’re happy with your commit(s) then it is time to ‘push’ everything online using the command git push. If you’re working with someone else on a branch and they have made changes, you can bring them into your local repository using the command git pull.

Now it is time to request that these changes are added into the main Calliope project repository! You can do this by starting a pull request. One of the core Calliope team will review the pull request and either accept it or request some changes before it’s merged into the main Calliope repository. If any changes are requested, you can make those changes on your local branch, commit them, and push them online – your pull request will update automatically with those changes.

Once a pull request has been accepted, you can return your fork back to its master branch and sync it with the updated Calliope project master

>     $ git remote add upstream https://github.com/calliope-project/calliope
>     $ git fetch upstream master
>     $ git checkout master
>     $ git merge upstream/master

##### Contribution checklist

A contribution to the core Calliope code should meet the following requirements:

> 1. Test(s) added to cover contribution

>    Tests ensure that a bug you’ve fixed will be caught in future, if an update to the code causes it to occur again. They also allow you to ensure that additional functionality works as you expect, and any change elsewhere in the code that causes it to act differently in future will be caught.

> 2. Documentation updated

>    If you’ve added functionality, it should be mentioned in the documentation. You can find the reStructuredText (.rst) files for the documentation under ‘doc/user’.

> 3. Changelog updated

>    A brief description of the bug fixed or feature added should be placed in the changelog (changelog.rst). Depending on what the pull request introduces, the description should be prepended with fixed, changed, or new.

> 4. Coverage maintained or improved

>    Coverage will be shown once all tests are complete online. It is the percentage of lines covered by at least one test. If you’ve added a test or two, you should be fine. But if coverage does go down it means that not all of your contribution has been tested!

> Example of coverage notification in a pull request.

If you’re not sure you’ve done everything to have a fully formed pull request, feel free to start it anyway. We can help guide you through making the necessary changes, once we have seen where you’ve got to.

#### Profiling

To profile a Calliope run with the built-in national-scale example model, then visualise the results with snakeviz:

    make profile  # will dump profile output in the current directory
    snakeviz calliope.profile  # launch snakeviz to visually examine profile

Use `mprof plot` to plot memory use.

Other options for visualising:

- Interactive visualisation with KCachegrind (on macOS, use QCachegrind, installed e.g. with `brew install qcachegrind`)

  >     pyprof2calltree -i calliope.profile -o calliope.calltree
  >     kcachegrind calliope.calltree

- Generate a call graph from the call tree via graphviz

  >     # brew install gprof2dot
  >     gprof2dot -f callgrind calliope.calltree | dot -Tsvg -o callgraph.svg

#### Checklist for new release

##### Pre-release

- Make sure all unit tests pass

- Build up-to-date Plotly plots for the documentation with (`make doc-plots`)

- Re-run tutorial Jupyter notebooks, found in doc/_static/notebooks

- Make sure documentation builds without errors

- Make sure the release notes are up-to-date, especially that new features and backward incompatible changes are clearly marked

##### Create release

- Change `_version.py` version number

- Update changelog with final version number and release date

- Commit with message “Release vXXXX”, then add a “vXXXX” tag, push both to GitHub

- Create a release through the GitHub web interface, using the same tag, titling it “Release vXXXX” (required for Zenodo to pull it in)

- Upload new release to PyPI: `make all-dist`

- Update the conda-forge package:
    - Fork conda-forge/calliope-feedstock, and update `recipe/meta.yaml` with:

        - Version number: `{% set version = "XXXX" %}`

        - SHA256 of latest version from PyPI: `{% set sha256 = "XXXX" %}`

        - Reset `build: number: 0` if it is not already at zero

        - If necessary, carry over any changed requirements from `setup.py` or `requirements/base.yml`

    - Submit a pull request from an appropriately named branch in your fork (e.g. `vXXXX`) to the conda-forge/calliope-feedstock repository

##### Post-release

- Update changelog, adding a new vXXXX-dev heading, and update `_version.py` accordingly, in preparation for the next master commit

- Update the `calliope_version` setting in all example models to match the new version, but without the `-dev` string (so `0.6.0-dev` is `0.6.0` for the example models)

Note

Adding ‘-dev’ to the version string, such as `__version__ = '0.1.0-dev'`, is required for the custom code in `doc/conf.py` to work when building in-development versions of the documentation.

## API documentation

Documents functions, classes and methods:

### API Documentation

#### Model class

class `calliope.``Model`(config, model_data=None, *args, **kwargs)

  A Calliope Model.

  `save_commented_model_yaml`(path)

    Save a fully built and commented version of the model to a YAML file at the given `path`. Comments in the file indicate where values were overridden. This is Calliope’s internal representation of a model directly before the model_data xarray.Dataset is built, and can be useful for debugging possible issues in the model formulation.

  `run`(force_rerun=False, **kwargs)

    Run the model. If `force_rerun` is True, any existing results will be overwritten.

    Additional kwargs are passed to the backend.

  `get_formatted_array`(var, index_format='index')

    Return an xr.DataArray with locs, techs, and carriers as separate dimensions.

    Parameters
      var str

        Decision variable for which to return a DataArray.

      index_format str, default = ‘index’

        ‘index’ to return the loc_tech(_carrier) dimensions as individual indexes, ‘multiindex’ to return them as a MultiIndex. The latter has the benefit of having a smaller memory footprint, but you cannot undertake dimension specific operations (e.g. formatted_array.sum(‘locs’))

  `to_netcdf`(path)

    Save complete model data (inputs and, if available, results) to a NetCDF file at the given `path`.

  `to_csv`(path, dropna=True)

    Save complete model data (inputs and, if available, results) as a set of CSV files to the given `path`.

    Parameters
      dropna bool, optional

        If True (default), NaN values are dropped when saving, resulting in significantly smaller CSV files.

  `to_lp`(path)

    Save built model to LP format at the given `path`. If the backend model has not been built yet, it is built prior to saving.

#### Time series

`calliope.core.time.clustering.``get_clusters`(data, func, timesteps_per_day, tech=None, timesteps=None, k=None, variables=None, **kwargs)

  Run a clustering algorithm on the timeseries data supplied. All timeseries data is reshaped into one row per day before clustering into similar days.

  Parameters
    data xarray.Dataset

      Should be normalized

    func str

      ‘kmeans’ or ‘hierarchical’ for KMeans or Agglomerative clustering, respectively

    timesteps_per_day int

      Total number of timesteps in a day

    tech list, optional

      list of strings referring to technologies by which clustering is undertaken. If none (default), all technologies within timeseries variables will be used.

    timesteps list or str, optional

      Subset of the time domain within which to apply clustering.

    k int, optional

      Number of clusters to create. If none (default), will use Hartigan’s rule to infer a reasonable number of clusters.

    variables list, optional

      data variables (e.g. resource, energy_eff) by whose values the data will be clustered. If none (default), all timeseries variables will be used.

    kwargs dict

      Additional keyword arguments available depend on the func. For available KMeans kwargs see: http://scikit-learn.org/stable/modules/generated/sklearn.cluster.KMeans.html For available hierarchical kwargs see: http://scikit-learn.org/stable/modules/generated/sklearn.cluster.AgglomerativeClustering.html

    Returns
    ——-
    clusters dataframe

      Indexed by timesteps and with locations as columns, giving cluster membership for first timestep of each day.

    clustered_data sklearn.cluster object

      Result of clustering using sklearn.KMeans(k).fit(X) or sklearn.KMeans(k).AgglomerativeClustering(X). Allows user to access specific attributes, for detailed statistical analysis.

`calliope.core.time.masks.``extreme`(data, tech, var='resource', how='max', length='1D', n=1, groupby_length=None, padding=None, normalize=True, **kwargs)

  Returns timesteps for period of `length` where `var` for the technology `tech` across the given list of `locations` is either minimal or maximal.

  Parameters
    data xarray.Dataset
    tech str

      Technology whose var to find extreme for.

    var str, optional

      default ‘resource’

    how str, optional

      ‘max’ (default) or ‘min’.

    length str, optional

      Defaults to ‘1D’.

    n int, optional

      Number of periods of length to look for, default is 1.

    groupby_length str, optional

      Group time series and return n periods of length for each group.

    padding str, optional

      Either Pandas frequency (e.g. ‘1D’) or ‘calendar_week’. If Pandas frequency, symmetric padding is undertaken, either side of length If ‘calendar_week’, padding is fit to the calendar week in which the extreme day(s) are found.

    normalize bool, optional

      If True (default), data is normalized using `normalized_copy()`.

    kwargs dict, optional

      Dimensions of the selected var over which to index. Any remaining dimensions will be flattened by mean

`calliope.core.time.masks.``extreme_diff`(data, tech0, tech1, var='resource', how='max', length='1D', n=1, groupby_length=None, padding=None, normalize=True, **kwargs)

  Returns timesteps for period of `length` where the diffence in extreme value for `var` between technologies `tech0` and `tech1` is either a minimum or a maximum.

  Parameters
    data xarray.Dataset
    tech0 str

      First technology for which we find the extreme of var

    tech1 str

      Second technology for which we find the extreme of var

    var str, optional

      default ‘resource’

    how str, optional

      ‘max’ (default) or ‘min’.

    length str, optional

      Defaults to ‘1D’.

    n int, optional

      Number of periods of length to look for, default is 1.

    groupby_length str, optional

      Group time series and return n periods of length for each group.

    padding str, optional

      Either Pandas frequency (e.g. ‘1D’) or ‘calendar_week’. If Pandas frequency, symmetric padding is undertaken, either side of length If ‘calendar_week’, padding is fit to the calendar week in which the extreme day(s) are found.

    normalize bool, optional

      If True (default), data is normalized using `normalized_copy()`.

    kwargs dict, optional

      Dimensions of the selected var over which to index. Any remaining dimensions will be flattened by mean

`calliope.core.time.funcs.``resample`(data, timesteps, resolution)

  Function to resample timeseries data from the input resolution (e.g. 1H), to the given resolution (e.g. 2H)

  Parameters
    data xarray.Dataset

      calliope model data, containing only timeseries data variables

    timesteps str or list; optional

      If given, apply resampling to a subset of the timeseries data

    resolution str

      time resolution of the output data, given in Pandas time frequency format. E.g. 1H = 1 hour, 1W = 1 week, 1M = 1 month, 1T = 1 minute. Multiples allowed.

#### Analyzing models

class `calliope.analysis.plotting.plotting.``ModelPlotMethods`(model)
  `timeseries`(**kwargs)
    Parameters
      array str or list; default = ‘all’

        options: ‘all’, ‘results’, ‘inputs’, the name/list of any energy carrier(s) (e.g. ‘power’), the name/list of any input/output DataArray(s).

        User can specify ‘all’ for all input/results timeseries plots, ‘inputs’ for just input timeseries, ‘results’ for just results timeseries, or the name of any data array to plot (in either inputs or results). In all but the last case, arrays can be picked from dropdown in visualisation. In the last case, output can be saved to SVG and a rangeslider can be used.

      timesteps_zoom int, optional

        Number of timesteps to show initially on the x-axis (if not given, the full time range is shown by default).

      rangeslider bool, optional

        If True, displays a range slider underneath the plot for navigating (helpful primarily in interactive use).

      subset dict, optional

        Dictionary by which data is subset (uses xarray loc indexing). Keys any of [‘timeseries’, ‘locs’, ‘techs’, ‘carriers’, ‘costs’].

      sum_dims str, optional

        List of dimension names to sum plot variable over.

      squeeze bool, optional

        Whether to squeeze out dimensions of length = 1.

      html_only bool, optional; default = False

        Returns a html string for embedding the plot in a webpage

      to_file False or str, optional; default = False

        Will save plot to file with the given name and extension. to_file=’plot.svg’ to save to SVG, to_file=’plot.png’ for a static PNG image. Allowed file extensions are: [‘png’, ‘jpeg’, ‘svg’, ‘webp’].

      layout_updates dict, optional

        The given dict will be merged with the Plotly layout dict generated by the Calliope plotting function, overwriting keys that already exist.

      plotly_kwarg_updates dict, optional

        The given dict will be merged with the Plotly plot function’s keyword arguments generated by the Calliope plotting function, overwriting keys that already exist.

  `capacity`(**kwargs)
    Parameters
      array str or list; default = ‘all’

        options: ‘all’, ‘results’, ‘inputs’, the name/list of any energy capacity DataArray(s) from inputs/results. User can specify ‘all’ for all input/results capacities, ‘inputs’ for just input capacities, ‘results’ for just results capacities, or the name(s) of any data array(s) to plot (in either inputs or results). In all but the last case, arrays can be picked from dropdown in visualisation. In the last case, output can be saved to SVG.

      orient str, optional

        ‘h’ for horizontal or ‘v’ for vertical barchart

      subset dict, optional

        Dictionary by which data is selected (using xarray indexing loc[]). Keys any of [‘timeseries’, ‘locs’, ‘techs’, ‘carriers’, ‘costs’]).

      sum_dims str, optional

        List of dimension names to sum plot variable over.

      squeeze bool, optional

        Whether to squeeze out dimensions containing only single values.

      html_only bool, optional; default = False

        Returns a html string for embedding the plot in a webpage

      to_file False or str, optional; default = False

        Will save plot to file with the given name and extension. to_file=’plot.svg’ to save to SVG, to_file=’plot.png’ for a static PNG image. Allowed file extensions are: [‘png’, ‘jpeg’, ‘svg’, ‘webp’].

      layout_updates dict, optional

        The given dict will be merged with the Plotly layout dict generated by the Calliope plotting function, overwriting keys that already exist.

      plotly_kwarg_updates dict, optional

        The given dict will be merged with the Plotly plot function’s keyword arguments generated by the Calliope plotting function, overwriting keys that already exist.

  `transmission`(**kwargs)
    Parameters
      mapbox_access_token str, optional

        If given and a valid Mapbox API key, a Mapbox map is drawn for lat-lon coordinates, else (by default), a more simple built-in map.

      html_only bool, optional; default = False

        Returns a html string for embedding the plot in a webpage

      to_file False or str, optional; default = False

        Will save plot to file with the given name and extension. to_file=’plot.svg’ to save to SVG, to_file=’plot.png’ for a static PNG image. Allowed file extensions are: [‘png’, ‘jpeg’, ‘svg’, ‘webp’].

      layout_updates dict, optional

        The given dict will be merged with the Plotly layout dict generated by the Calliope plotting function, overwriting keys that already exist.

      plotly_kwarg_updates dict, optional

        The given dict will be merged with the Plotly plot function’s keyword arguments generated by the Calliope plotting function, overwriting keys that already exist.

  `summary`(**kwargs)

    Plot a summary containing timeseries, installed capacities, and transmission plots. Returns a HTML string by default, returns None if `to_file` given (and saves the HTML string to file).

    Parameters
      to_file str, optional

        Path to output file to save HTML to.

      mapbox_access_token str, optional

        (passed to plot_transmission) If given and a valid Mapbox API key, a Mapbox map is drawn for lat-lon coordinates, else (by default), a more simple built-in map.

#### Pyomo backend interface

class `calliope.backend.pyomo.interface.``BackendInterfaceMethods`(model)
  `access_model_inputs`()

    If the user wishes to inspect the parameter values used as inputs in the backend model, they can access a new Dataset of all the backend model inputs, including defaults applied where the user did not specify anything for a loc::tech

  `update_param`(*args, **kwargs)

    A Pyomo Param value can be updated without the user directly accessing the backend model.

    Parameters
      param str

        Name of the parameter to update

      update_dict dict

        keys are parameter indeces (either strings or tuples of strings, depending on whether there is one or more than one dimension). Values are the new values being assigned to the parameter at the given indeces.

    Returns
      Value(s) will be updated in-place, requiring the user to run the model again to
      see the effect on results.
  `activate_constraint`(*args, **kwargs)

    Takes a constraint or objective name, finds it in the backend model and sets its status to either active or deactive.

    Parameters
      constraint str

        Name of the constraint/objective to activate/deactivate Built-in constraints include ‘_constraint’

      active: bool, default=True

        status to set the constraint/objective

  `rerun`(*args, **kwargs)

    Rerun the Pyomo backend, perhaps after updating a parameter value, (de)activating a constraint/objective or updating run options in the model model_data object (e.g. run.solver).

    Returns
      new_model calliope.Model

        New calliope model, including both inputs and results, but no backend interface.

#### Utility classes: AttrDict, Exceptions, Logging

class `calliope.core.attrdict.``AttrDict`(source_dict=None)

  A subclass of `dict` with key access by attributes:

      d = AttrDict({'a': 1, 'b': 2})
      d.a == 1  # True

  Includes a range of additional methods to read and write to YAML, and to deal with nested keys.

  `copy`()

    Override copy method so that it returns an AttrDict

  `init_from_dict`(d)

    Initialize a new AttrDict from the given dict. Handles any nested dicts by turning them into AttrDicts too:

        d = AttrDict({'a': 1, 'b': {'x': 1, 'y': 2}})
        d.b.x == 1  # True

  classmethod `from_yaml`(f, resolve_imports=True)

    Returns an AttrDict initialized from the given path or file object `f`, which must point to a YAML file. The path can be a string or a pathlib.Path.

    Parameters
      f str or pathlib.Path
      resolve_imports bool or str, optional

        If `resolve_imports` is True, top-level `import:` statements are resolved recursively. If `resolve_imports is False, top-level ``import:` statements are treated like any other key and not further processed. If `resolve_imports` is a string, such as `foobar`, import statements underneath that key are resolved, i.e. `foobar.import:`. When resolving import statements, anything defined locally overrides definitions in the imported file.

  classmethod `from_yaml_string`(string, resolve_imports=True)

    Returns an AttrDict initialized from the given string, which must be valid YAML.

  `set_key`(key, value)

    Set the given `key` to the given `value`. Handles nested keys, e.g.:

        d = AttrDict()
        d.set_key('foo.bar', 1)
        d.foo.bar == 1  # True

  `get_key`(key, default=<calliope.core.attrdict.__Missing object>)

    Looks up the given `key`. Like set_key(), deals with nested keys.

    If default is anything but `_MISSING`, the given default is returned if the key does not exist.

  `del_key`(key)

    Delete the given key. Properly deals with nested keys.

  `as_dict`(flat=False)

    Return the AttrDict as a pure dict (with nested dicts if necessary).

  `to_yaml`(path=None)

    Saves the AttrDict to the `path` as a YAML file, or returns a YAML string if `path` is None.

  `keys_nested`(subkeys_as='list')

    Returns all keys in the AttrDict, sorted, including the keys of nested subdicts (which may be either regular dicts or AttrDicts).

    If `subkeys_as='list'` (default), then a list of all keys is returned, in the form `['a', 'b.b1', 'b.b2']`.

    If `subkeys_as='dict'`, a list containing keys and dicts of subkeys is returned, in the form `['a', {'b': ['b1', 'b2']}]`.

  `union`(other, allow_override=False, allow_replacement=False, allow_subdict_override_with_none=False)

    Merges the AttrDict in-place with the passed `other` AttrDict. Keys in `other` take precedence, and nested keys are properly handled.

    If `allow_override` is False, a KeyError is raised if other tries to redefine an already defined key.

    If `allow_replacement`, allow “_REPLACE_” key to replace an entire sub-dict.

    If `allow_subdict_override_with_none` is False (default), a key of the form `this.that: None` in other will be ignored if subdicts exist in self like `this.that.foo: 1`, rather than wiping them.

exception `calliope.exceptions.``ModelError`

  ModelErrors should stop execution of the model, e.g. due to a problem with the model formulation or input data.

exception `calliope.exceptions.``BackendError`

exception `calliope.exceptions.``ModelWarning`

  ModelWarnings should be raised for possible model errors, but where execution can still continue.

exception `calliope.exceptions.``BackendWarning`

`calliope.exceptions.``print_warnings_and_raise_errors`(warnings=None, errors=None)

  Print warnings and raise ModelError from errors.

  Parameters
    warnings list, optional
    errors list, optional

`calliope.core.util.logging.``set_log_verbosity`(verbosity='info', include_solver_output=True, capture_warnings=True)

  Set the verbosity of logging and setup the root logger to log to console (stdout) with timestamp output formatting.

  Parameters
    verbosity str, default ‘info’

      Logging level to display across all of Calliope. Can be one of ‘debug’, ‘info’, ‘warning’, ‘error’, or ‘critical’.

    include_solver_output bool, default True

      If True, the logging level for just the backend model is set to DEBUG, which turns on display of solver output.

    capture_warnings bool, default True

      If True, also capture all warnings and log them to the WARNING level. This results in more consistent output when running interactively.

### Index

## Release history

#### 0.6.5 (2020-01-14)

new New group constraints energy_cap_equals, resource_area_equals, and energy_cap_share_equals to add the equality constraint to existing min/max group constraints.

new New group constraints carrier_prod_min, carrier_prod_max, and carrier_prod_equals which restrict the absolute energy produced by a subgroup of technologies and locations.

new Introduced a storage_discharge_depth constraint, which allows to set a minimum stored-energy level to be preserved by a storage technology.

new New group constraints net_import_share_min, net_import_share_max, and net_import_share_equals which restrict the net imported energy of a certain carrier into subgroups of locations.

changed backwards-incompatible Group constraints with the prefix supply_share are renamed to use the prefix carrier_prod_share. This ensures consistent naming for all group constraints.

changed Allowed ‘energy_cap_min’ for transmission technologies.

changed Minor additions made to troubleshooting and development documentation.

changed backwards-incompatible The backend interface to update a parameter value (Model.backend.update_param()) has been updated to allow multiple values in a parameter to be updated at once, using a dictionary.

changed Allowed om_con cost for demand technologies. This is conceived to allow better representing generic international exports as demand sinks with a given revenue (e.g. the average electricity price on a given bidding zone), not restricted to any particular type of technology.

changed backwards-incompatible model.backend.rerun() returns a calliope Model object instead of an xarray Dataset, allowing a user to access calliope Model methods, such as get_formatted_array.

changed Carrier ratios can be loaded from file, to allow timeseries carrier ratios to be defined, e.g. `carrier_ratios.carrier_out_2.heat: file=ratios.csv`.

changed Objective function options turned into Pyomo parameters. This allows them to update through the Model.backend.update_param() functionality.

changed All model defaults have been moved to defaults.yaml, removing the need for model.yaml. A default location, link and group constraint have been added to defaults.yaml to validate input model keys.

changed backwards-incompatible Revised internal logging and warning structure. Less critical warnings during model checks are now logged directly to the INFO log level, which is displayed by default in the CLI, and can be enabled interactively by calling calliope.set_log_verbosity() without any options. The calliope.set_log_level function has been renamed to calliope.set_log_verbosity and includes the ability to easily turn on and off the display of solver output.

changed All group constraint values are parameters so they can be updated in the backend model

fixed Operate mode checks cleaned up to warn less frequently and to not be so aggressive at editing a users model to fit the operate mode requirements.

fixed Documentation distinctly renders inline Python, YAML, and shell code snippets.

fixed Tech groups are used to filter technologies to which group constraints can be applied. This ensures that transmission and storage technologies are included in cost and energy capacity group constraints. More comprehensive tests have been added accordingly.

fixed Models saved to NetCDF now include the fully built internal YAML model and debug data so that Model.save_commented_model_yaml() is available after loading a NetCDF model from disk

fixed Fix an issue preventing the deprecated charge_rate constraint from working in 0.6.4.

fixed Fix an issue that prevented 0.6.4 from loading NetCDF models saved with older versions of Calliope. It is still recommended to only load models with the same version of Calliope that they were saved with, as not all functionality will work when mixing versions.

fixed backwards-incompatible Updated to require pandas 0.25, xarray 0.14, and scikit-learn 0.22, and verified Python 3.8 compatibility. Because of a bugfix in scikit-learn 0.22, models using k-means clustering with a specified random seed may return different clusters from Calliope 0.6.5 on.

#### 0.6.4 (2019-05-27)

new New model-wide constraint that can be applied to all, or a subset of, locations and technologies in a model, covering:

- demand_share, supply_share, demand_share_per_timestep, supply_share_per_timestep, each of which can specify min, max, and equals, as well as energy_cap_share_min and energy_cap_share_max. These supersede the group_share constraints, which are now deprecated and will be removed in v0.7.0.

- demand_share_per_timestep_decision, allowing the model to make decisions on the per-timestep shares of carrier demand met from different technologies.

- cost_max, cost_min, cost_equals, cost_var_max, cost_var_min, cost_var_equals, cost_investment_max, cost_investment_min, cost_investment_equals, which allow a user to constrain costs, including those not used in the objective.

- energy_cap_min, energy_cap_max, resource_area_min, resource_area_max which allow to constrain installed capacities of groups of technologies in specific locations.

new asynchronous_prod_con parameter added to the constraints, to allow a user to fix a storage or transmission technology to only be able to produce or consume energy in a given timestep. This ensures that unphysical dissipation of energy cannot occur in these technologies, by activating a binary variable (prod_con_switch) in the backend.

new Multi-objective optimisation problems can be defined by linear scalarisation of cost classes, using run.objective_options.cost_class (e.g. {‘monetary’: 1, ‘emissions’: 0.1}, which models an emissions price of 0.1 units of currency per unit of emissions)

new Storage capacity can be tied to energy capacity with a new energy_cap_per_storage_cap_equals constraint.

new The ratio of energy capacity and storage capacity can be constrained with a new energy_cap_per_storage_cap_min constraint.

new Easier way to save an LP file with a `--save_lp` command-line option and a `Model.to_lp` method

new Documentation has a new layout, better search, and is restructured with various content additions, such as a section on troubleshooting.

new Documentation for developers has been improved to include an overview of the internal package structure and a guide to contributing code via a pull request.

changed backwards-incompatible Scenarios in YAML files defined as list of override names, not comma-separated strings: fusion_scenario: cold_fusion,high_cost becomes fusion_scenario: [‘cold_fusion’, ‘high_cost’]. No change to the command-line interface.

changed charge_rate has been renamed to energy_cap_per_storage_cap_max. charge_rate will be removed in Calliope 0.7.0.

changed Default value of resource_area_max now is `inf` instead of `0`, deactivating the constraint by default.

changed Constraint files are auto-loaded in the pyomo backend and applied in the order set by ‘ORDER’ variables given in each constraint file (such that those constraints which depend on pyomo expressions existing are built after the expressions are built).

changed Error on defining a technology in both directions of the same link.

changed Any inexistent locations and / or technologies defined in model-wide (group) constraints will be caught and filtered out, raising a warning of their existence in the process.

changed Error on required column not existing in CSV is more explicit.

changed backwards-incompatible Exit code for infeasible problems now is 1 (no success). This is a breaking change when relying on the exit code.

changed get_formatted_array improved in both speed and memory consumption.

changed model and run configurations are now available as attributes of the Model object, specifically as editable dictionaries which automatically update a YAML string in the model_data xarray dataset attribute list (i.e. the information is stored when sending to the solver backend and when saving to and loading from NetCDF file)

changed All tests and example models have been updated to solve with Coin-CBC, instead of GLPK. Documentation has been updated to reflect this, and aid in installing CBC (which is not simple for Windows users).

changed Additional and improved pre-processing checks and errors for common model mistakes.

fixed Total levelised cost of energy considers all costs, but energy generation only from `supply`, `supply_plus`, `conversion`, and `conversion_plus`.

fixed If a space is left between two locations in a link (i.e. A, B instead of A,B), the space is stripped, instead of leading to the expectation of a location existing with the name ` B`.

fixed Timeseries efficiencies can be included in operate mode without failing on preprocessing checks.

fixed Name of data variables is retained when accessed through model.get_formatted_array()

fixed Systemwide constraints work in models without transmission systems.

fixed Updated documentation on amendments of abstract base technology groups.

fixed Models without time series data fail gracefully.

fixed Unknown technology parameters are detected and the user is warned.

fixed Loc::techs with empty cost classes (i.e. value == None) are handled by a warning and cost class deletion, instead of messy failure.

#### 0.6.3 (2018-10-03)

new Addition of `flows` plotting function. This shows production and how much they exchange with other locations. It also provides a slider in order to see flows’ evolution through time.

new `calliope generate_runs` in the command line interface can now produce scripts for remote clusters which require SLURM-based submission (`sbatch...`).

new backwards-incompatible Addition of `scenarios`, which complement and expand the existing `overrides` functionality. `overrides` becomes a top-level key in model configuration, instead of a separate file. The `calliope run` command has a new `--scenario` option which replaces –override_file, while `calliope generate_runs` has a new `--scenarios` option which replaces –override_file and takes a semicolon-separated list of scenario names or of group1,group2 combinations. To convert existing overrides to the new approach, simply group them under a top-level `overrides` key and import your existing overrides file from the main model configuration file with `import: ['your_overrides_file.yaml']`.

new Addition of `calliope generate_scenarios` command to allow automating the construction of scenarios which consist of many combinations of overrides.

new Added `--override_dict` option to `calliope run` and `calliope generate_runs` commands

new Added solver performance comparison in the docs. CPLEX & Gurobi are, as expected, the best options. If going open-source & free, CBC is much quicker than GLPK!

new Calliope is tested and confirmed to run on Python 3.7

changed resource_unit - available to supply, supply_plus, and demand technologies - can now be defined as ‘energy_per_area’, ‘energy’, or ‘energy_per_cap’. ‘power’ has been removed. If ‘energy_per_area’ then available resource is the resource (CSV or static value) * resource_area, if ‘energy_per_cap’ it is resource * energy_cap. Default is ‘energy’, i.e. resource = available_resource.

changed Updated to xarray v0.10.8, including updates to timestep aggregation and NetCDF I/O to handle updated xarray functionality.

changed Removed `calliope convert` command. If you need to convert a 0.5.x model, first use `calliope convert` in Calliope 0.6.2 and then upgrade to 0.6.3 or higher.

changed Removed comment persistence in AttrDict and the associated API in order to improve compatibility with newer versions of ruamel.yaml

fixed Operate mode is more robust, by being explicit about timestep and loc_tech indexing in storage_initial preparation and resource_cap checks, respectively, instead of assuming an order.

fixed When setting ensure_feasibility, the resulting unmet_demand variable can also be negative, accounting for possible infeasibility when there is unused supply, once all demand has been met (assuming no load shedding abilities). This is particularly pertinent when the force_resource constraint is in place.

fixed When applying systemwide constraints to transmission technologies, they are no longer silently ignored. Instead, the constraint value is doubled (to account for the constant existence of a pair of technologies to describe one link) and applied to the relevant transmission techs.

fixed Permit groups in override files to specify imports of other YAML files

fixed If only interest_rate is defined within a cost class of a technology, the entire cost class is correctly removed after deleting the interest_rate key. This ensures an empty cost key doesn’t break things later on. Fixes issue #113.

fixed If time clustering with ‘storage_inter_cluster’ = True, but no storage technologies, the model doesn’t break. Fixes issue #142.

#### 0.6.2 (2018-06-04)

new `units_max_systemwide` and `units_equals_systemwide` can be applied to an integer/binary constrained technology (capacity limited by `units` not `energy_cap`, or has an associated `purchase` (binary) cost). Constraint works similarly to existing `energy_cap_max_systemwide`, limiting the number of units of a technology that can be purchased across all locations in the model.

new backwards-incompatible `primary_carrier` for conversion_plus techs is now split into `primary_carrier_in` and `primary_carrier_out`. Previously, it only accounted for output costs, by separating it, om_con and om_prod are correctly accounted for. These are required conversion_plus essentials if there’s more than one input and output carrier, respectively.

new Storage can be set to cyclic using `run.cyclic_storage`. The last timestep in the series will then be used as the ‘previous day’ conditions for the first timestep in the series. This also applies to `storage_inter_cluster`, if clustering. Defaults to False, with intention of defaulting to True in 0.6.3.

new On clustering timeseries into representative days, an additional set of decision variables and constraints is generated. This addition allows for tracking stored energy between clusters, by considering storage between every datestep of the original (unclustered) timeseries as well as storage variation within a cluster.

new CLI now uses the IPython debugger rather than built-in `pdb`, which provides highlighting, tab completion, and other UI improvements

new AttrDict now persists comments when reading from and writing to YAML files, and gains an API to view, add and remove comments on keys

fixed Fix CLI error when running a model without transmission technologies

fixed Allow plotting for inputs-only models, single location models, and models without location coordinates

fixed Fixed negative `om_con` costs in conversion and conversion_plus technologies

#### 0.6.1 (2018-05-04)

new Addition of user-defined datestep clustering, accessed by clustering_func:file=filename.csv:column in time aggregation config

new Added `layout_updates` and `plotly_kwarg_updates` parameters to plotting functions to override the generated Plotly configuration and layout

changed Cost class and sense (maximize/minimize) for objective function may now be specified in run configuration (default remains monetary cost minimization)

changed Cleaned up and documented `Model.save_commented_model_yaml()` method

fixed Fixed error when calling `--save_plots` in CLI

fixed Minor improvements to warnings

fixed Pure dicts can be used to create a `Model` instance

fixed `AttrDict.union` failed on all-empty nested dicts

#### 0.6.0 (2018-04-20)

Version 0.6.0 is an almost complete rewrite of most of Calliope’s internals. See New in v0.6.0 for a more detailed description of the many changes.

##### Major changes

changed backwards-incompatible Substantial changes to model configuration format, including more verbose names for most settings, and removal of run configuration files.

new backwards-incompatible Complete rewrite of Pyomo backend, including new various new and improved functionality to interact with a built model (see New in v0.6.0).

new Addition of a `calliope convert` CLI tool to convert 0.5.x models to 0.6.0.

new Experimental ability to link to non-Pyomo backends.

new New constraints: `resource_min_use` constraint for `supply` and `supply_plus` techs.

changed backwards-incompatible Removal of settings and constraints includes `subset_x`, `subset_y`, `s_time`, `r2`, `r_scale_to_peak`, `weight`.

changed backwards-incompatible `system_margin` constraint replaced with `reserve_margin` constraint.

changed backwards-incompatible Removed the ability to load additional custom constraints or objectives.

#### 0.5.5 (2018-02-28)

- fixed Allow r_area to be non-zero if either of e_cap.max or e_cap.equals is set, not just e_cap.max.

- fixed Ensure static parameters in resampled timeseries are caught in constraint generation

- fixed Fix time masking when set_t.csv contains sub-hourly resolutions

#### 0.5.4 (2017-11-10)

##### Major changes

- fixed r_area_per_e_cap and r_cap_equals_e_cap constraints have been separated from r_area and r_cap constraints to ensure that user specified r_area.max and r_cap.max constraints are observed.

- changed technologies and location subsets are now communicated with the solver as a combined location:technology subset, to reduce the problem size, by ignoring technologies at locations in which they have not been allowed. This has shown drastic improvements in Pyomo preprocessing time and memory consumption for certain models.

##### Other changes

- fixed Allow plotting carrier production using calliope.analysis.plot_carrier_production if that carrier does not have an associated demand technology (previously would raise an exception).

- fixed Define time clustering method (sum/mean) for more constraints that can be time varying. Previously only included r and e_eff.

- changed storage technologies default s_cap.max to inf, not 0 and are automatically included in the loc_tech_store subset. This ensures relevant constraints are not ignored by storage technologies.

- changed Some values in the urban scale MILP example were updated to provide results that would show the functionality more clearly

- changed technologies have set colours in the urban scale example model, as random colours were often hideous.

- changed ruamel.yaml, not ruamel_yaml, is now used for parsing YAML files.

- fixed e_cap constraints for unmet_demand technologies are ignored in operational mode. Capacities are fixed for all other technologies, which previously raised an exception, as a fixed infinite capacity is not physically allowable.

- fixed stack_weights were strings rather than numeric datatypes on reading NetCDF solution files.

#### 0.5.3 (2017-08-22)

##### Major changes

- new (BETA) Mixed integer linear programming (MILP) capabilities, when using `purchase` cost and/or `units.max/min/equals` constraints. Integer/Binary decision variables will be applied to the relevant technology-location sets, avoiding unnecessary complexity by describing all technologies with these decision variables.

##### Other changes

- changed YAML parser is now ruamel_yaml, not pyyaml. This allows scientific notation of numbers in YAML files (#57)

- fixed Description of PV technology in urban scale example model now more realistic

- fixed Optional ramping constraint no longer uses backward-incompatible definitions (#55)

- fixed One-way transmission no longer forces unidirectionality in the wrong direction

- fixed Edge case timeseries resource combinations, where infinite resource sneaks into an incompatible constraint, are now flagged with a warning and ignored in that constraint (#61)

- fixed e_cap.equals: 0 sets a technology to a capacity of zero, instead of ignoring the constraint (#63)

- fixed depreciation_getter now changes with location overrides, instead of just checking the technology level constraints (#64)

- fixed Time clustering now functions in models with time-varying costs (#66)

- changed Solution now includes time-varying costs (costs_variable)

- fixed Saving to NetCDF does not affect in-memory solution (#62)

#### 0.5.2 (2017-06-16)

- changed Calliope now uses Python 3.6 by default. From Calliope 0.6.0 on, Python 3.6 will likely become the minimum required version.

- fixed Fixed a bug in distance calculation if both lat/lon metadata and distances for links were specified.

- fixed Fixed a bug in storage constraints when both `s_cap` and `e_cap` were constrained but no `c_rate` was given.

- fixed Fixed a bug in the system margin constraint.

#### 0.5.1 (2017-06-14)

new backwards-incompatible Better coordinate definitions in metadata. Location coordinates are now specified by a dictionary with either lat/lon (for geographic coordinates) or x/y (for generic Cartesian coordinates), e.g. `{lat: 40, lon: -2}` or `{x: 0, y: 1}`. For geographic coordinates, the `map_boundary` definition for plotting was also updated in accordance. See the built-in example models for details.

new Unidirectional transmission links are now possible. See the documentation on transmission links.

##### Other changes

- fixed Missing urban-scale example model files are now included in the distribution

- fixed Edge cases in `conversion_plus` constraints addressed

- changed Documentation improvements

#### 0.5.0 (2017-05-04)

##### Major changes

new Urban-scale example model, major revisions to the documentation to accommodate it, and a new `calliope.examples` module to hold multiple example models. In addition, the `calliope new` command now accepts a `--template` option to select a template other than the default national-scale example model, e.g.: `calliope new my_urban_model --template=UrbanScale`.

new Allow technologies to generate revenue (by specifying negative costs)

new Allow technologies to export their carrier directly to outside the system boundary

new Allow storage & supply_plus technologies to define a charge rate (c_rate), linking storage capacity (s_cap) with charge/discharge capacity (e_cap) by s_cap * c_rate => e_cap. As such, either s_cap.max & c_rate or e_cap.max & c_rate can be defined for a technology. The smallest of s_cap.max * c_rate and e_cap.max will be taken if all three are defined.

changed backwards-incompatible Revised technology definitions and internal definition of sets and subsets, in particular subsets of various technology types. Supply technologies are now split into two types: `supply` and `supply_plus`. Most of the more advanced functionality of the original `supply` technology is now contained in `supply_plus`, making it necessary to update model definitions accordingly. In addition to the existing `conversion` technology type, a new more complex `conversion_plus` was added.

##### Other changes

- changed backwards-incompatible Creating a `Model()` with no arguments now raises a `ModelError` rather than returning an instance of the built-in national-scale example model. Use the new `calliope.examples` module to access example models.

- changed Improvements to the national-scale example model and its tutorial notebook

- changed Removed SolutionModel class

- fixed Other minor fixes

#### 0.4.1 (2017-01-12)

- new Allow profiling with the `--profile` and `--profile_filename` command-line options

- new Permit setting random seed with `random_seed` in the run configuration

- changed Updated installation documentation using conda-forge package

- fixed Other minor fixes

#### 0.4.0 (2016-12-09)

##### Major changes

new Added new methods to deal with time resolution: clustering, resampling, and heuristic timestep selection

changed backwards-incompatible Major change to solution data structure. Model solution is now returned as a single xarray DataSet instead of multiple pandas DataFrames and Panels. Instead of as a generic HDF5 file, complete solutions can be saved as a NetCDF4 file via xarray’s NetCDF functionality.

While the recommended way to save and process model results is by NetCDF4, CSV saving functionality has now been upgraded for more flexibility. Each variable is saved as a separate CSV file with a single value column and as many index columns as required.

changed backwards-incompatible Model data structures simplified and based on xarray

##### Other changes

- new Functionality to post-process parallel runs into aggregated NetCDF files in `calliope.read`

- changed Pandas 0.18/0.19 compatibility

- changed 1.11 is now the minimum required numpy version. This version makes datetime64 tz-naive by default, thus preventing some odd behavior when displaying time series.

- changed Improved logging, status messages, and error reporting

- fixed Other minor fixes

#### 0.3.7 (2016-03-10)

##### Major changes

changed Per-location configuration overrides improved. All technology constraints can now be set on a per-location basis, as can costs. This applies to the following settings:

- `techname.x_map`

- `techname.constraints.*`

- `techname.constraints_per_distance.*`

- `techname.costs.*`

The following settings cannot be overridden on a per-location basis:

- Any other options directly under `techname`, such as `techname.parent` or `techname.carrier`

- `techname.costs_per_distance.*`

- `techname.depreciation.*`

##### Other changes

- fixed Improved installation instructions

- fixed Pyomo 4.2 API compatibility

- fixed Other minor fixes

#### 0.3.6 (2015-09-23)

- fixed Version 0.3.5 changes were not reflected in tutorial

#### 0.3.5 (2015-09-18)

##### Major changes

new New constraint to constrain total (model-wide) installed capacity of a technology (`e_cap.total_max`), in addition to its per-node capacity (`e_cap.max`)

changed Removed the `level` option for locations. Level is now implicitly derived from the nested structure given by the `within` settings. Locations that define no or an empty `within` are implicitly at the topmost (0) level.

changed backwards-incompatible Revised configuration of capacity constraints: `e_cap_max` becomes `e_cap.max`, addition of `e_cap.min` and `e_cap.equals` (analogous for r_cap, s_cap, rb_cap, r_area). The `e_cap.equals` constraint supersedes `e_cap_max_force` (analogous for the other constraints). No backwards-compatibility is retained, models must change all constraints to the new formulation. See Per-tech constraints for a complete list of all available constraints. Some additional constraints have name changes:

- `e_cap_max_scale` becomes `e_cap_scale`

- `rb_cap_follows` becomes `rb_cap_follow`, and addition of `rb_cap_follow_mode`

- `s_time_max` becomes `s_time.max`

changed backwards-incompatible All optional constraints are now grouped together, under `constraints.optional`:

- `constraints.group_fraction.group_fraction` becomes `constraints.optional.group_fraction`

- `constraints.ramping.ramping_rate` becomes `constraints.optional.ramping_rate`

##### Other changes

- new analysis.map_results function to extract solution details from multiple parallel runs

- new Various other additions to analysis functionality, particularly in the analysis_utils module

- new analysis.get_levelized_cost to get technology and location specific costs

- new Allow dynamically loading time mask functions

- changed Improved summary table in the model solution: now shows only aggregate information for transmission technologies, also added missing `s_cap` column and technology type

- fixed Bug causing some total levelized transmission costs to be infinite instead of zero

- fixed Bug causing some CSV solution files to be empty

#### 0.3.4 (2015-04-27)

- fixed Bug in construction and fixed O&M cost calculations in operational mode

#### 0.3.3 (2015-04-03)

##### Major changes

changed In preparation for future enhancements, the ordering of location levels is flipped. The top-level locations at which balancing takes place is now level 0, and may contain level 1 locations. This is a backwards-incompatible change.

changed backwards-incompatible Refactored time resolution adjustment functionality. Can now give a list of masks in the run configuration which will all be applied, via `time.masks`, with a base resolution via `time.resolution` (or instead, as before, load a resolution series from file via `time.file`). Renamed the `time_functions` submodule to `time_masks`.

##### Other changes

- new Models and runs can have a `name`

- changed More verbose `calliope run`

- changed Analysis tools restructured

- changed Renamed `debug.keepfiles` setting to `debug.keep_temp_files` and better documented debug configuration

#### 0.3.2 (2015-02-13)

- new Run setting `model_override` allows specifying the path to a YAML file with overrides for the model configuration, applied at model initialization (path is given relative to the run configuration file used). This is in addition to the existing `override` setting, and is applied first (so `override` can override `model_override`).

- new Run settings `output.save_constraints` and `output.save_constraints_options`

- new Run setting `parallel.post_run`

- changed Solution column names more in line with model component names

- changed Can specify more than one output format as a list, e.g. `output.format: ['csv', 'hdf']`

- changed Run setting `parallel.additional_lines` renamed to `parallel.pre_run`

- changed Better error messages and CLI error handling

- fixed Bug on saving YAML files with numpy dtypes fixed

- Other minor improvements and fixes

#### 0.3.1 (2015-01-06)

- Fixes to time_functions

- Other minor improvements and fixes

#### 0.3.0 (2014-12-12)

- Python 3 and Pyomo 4 are now minimum requirements

- Significantly improved documentation

- Improved model solution management by saving to HDF5 instead of CSV

- Calculate shares of technologies, including the ability to define groups for the purpose of computing shares

- Improved operational mode

- Simplified time_tools

- Improved output plotting, including dispatch, transmission flows, and installed capacities, and added model configuration to support these plots

- `r` can be specified as power or energy

- Improved solution speed

- Better error messages and basic logging

- Better sanity checking and error messages for common mistakes

- Basic distance-dependent constraints (only implemented for e_loss and cost of e_cap for now)

- Other improvements and fixes

#### 0.2.0 (2014-03-18)

- Added cost classes with a new set `k`

- Added energy carriers with a new set `c`

- Added conversion technologies

- Speed improvements and simplifications

- Ability to arbitrarily nest model configuration files with `import` statements

- Added additional constraints

- Improved configuration handling

- Ability to define timestep options in run configuration

- Cleared up terminology (nodes vs locations)

- Improved TimeSummarizer masking and added new masks

- Removed technology classes

- Improved operational mode with results output matching planning mode and dynamic updating of parameters in model instance

- Working parallel_tools

- Improved documentation

- Apache 2.0 licensed

- Other improvements and fixes

#### 0.1.0 (2013-12-10)

- Some semblance of documentation

- Usable built-in example model

- Improved and working TimeSummarizer

- More flexible masking for TimeSummarizer

- Ability to add additional constraints without editing core source code

- Some basic test coverage

- Working parallel run configuration system

Release history

## License

Copyright 2013-2019 Calliope contributors listed in AUTHORS

Licensed under the Apache License, Version 2.0 (the “License”); you may not use this file except in compliance with the License. You may obtain a copy of the License at

> http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an “AS IS” BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.