Operate mode math¶

Pre-defined mode math to apply operate mode math on top of the base mathematical formulation. This math is only applied when config.build.mode is set to "operate".

A guide to math documentation¶

If a math component's initial conditions are met (the first if statement), it will be applied to a model. For each objective, constraint and global expression, a number of sub-conditions then apply (the subsequent, indented if statements) to decide on the specific expression to apply at a given iteration of the component dimensions.

In the expressions, terms in bold font are decision variables and terms in italic font are parameters. The decision variables and parameters are listed at the end of the page; they also refer back to the global expressions / constraints in which they are used. Those parameters which are defined over time (timesteps) in the expressions can be defined by a user as a single, time invariant value, or as a timeseries that is loaded from file or dataframe.

Note

For every math component in the documentation, we include the YAML snippet that was used to generate the math in a separate tab.

Download the operate mode math formulation as a YAML file

Subject to¶

area_use_capacity_per_loc¶

REMOVED Set an upper bound on the total area that all technologies with area_use can occupy at a given node.

area_use_per_flow_capacity¶

REMOVED Set a fixed relationship between a technology's flow capacity and its area use.

flow_capacity_per_storage_capacity_max¶

REMOVED Set the upper bound of storage flow capacity relative to its storage capacity.

flow_capacity_per_storage_capacity_min¶

REMOVED Set the lower bound of storage flow capacity relative to its storage capacity.

flow_capacity_systemwide_max¶

REMOVED Set an upper bound on flow capacity of a technology across all nodes in which the technology exists.

flow_capacity_systemwide_min¶

REMOVED Set a lower bound on flow capacity of a technology across all nodes in which the technology exists.

force_zero_area_use¶

REMOVED Set a technology's area use to zero if its flow capacity upper bound is zero.

source_capacity_equals_flow_capacity¶

REMOVED Set a supply technology's flow capacity to equal its source capacity.

symmetric_transmission¶

REMOVED Fix the flow capacity of two transmission technologies representing the same link in the system.

Where¶

cost¶

UPDATED The total annualised costs of a technology, including installation and operation costs.

Unit: cost

Default: 0

MathYAML

\[ \begin{array}{l} \forall{} \text{ node }\negthickspace \in \negthickspace\text{ nodes, } \text{ tech }\negthickspace \in \negthickspace\text{ techs, } \text{ cost }\negthickspace \in \negthickspace\text{ costs } \!\!,\\ \text{if } (\textbf{cost\_operation\_variable}_\text{node,tech,cost,timestep})\!\!:\\[2em] \quad \sum\limits_{\substack{\text{timestep} \in \text{timesteps}}} (\textbf{cost\_operation\_variable}_\text{node,tech,cost,timestep})\\ \end{array} \]

title: Total costs
description: "UPDATED\nThe total annualised costs of a technology, including installation
  and operation costs."
active: true
equations:
- where: 'True'
  expression: sum(cost_operation_variable, over=timesteps)
sub_expressions: {}
slices: {}
foreach:
- nodes
- techs
- costs
where: cost_operation_variable
unit: cost
default: 0

cost_investment¶

REMOVED The installation costs of a technology, including those linked to the nameplate capacity, land use, and storage size.

cost_investment_annualised¶

REMOVED An annuity factor has been applied to scale lifetime investment costs to annual values that can be directly compared to operation costs. If the modeling period is not equal to one full year, this will be scaled accordingly.

cost_investment_area_use¶

REMOVED The investment costs associated with the area used by a technology.

cost_investment_flow_cap¶

REMOVED The investment costs associated with the nominal/rated capacity of a technology.

cost_investment_source_cap¶

REMOVED The investment costs associated with the source consumption capacity of a technology.

cost_investment_storage_cap¶

REMOVED The investment costs associated with the storage capacity of a technology.

cost_operation_fixed¶

REMOVED The fixed, annual operation costs of a technology, which are calculated relative to investment costs. If the modeling period is not equal to one full year, this will be scaled accordingly.

Parameters¶

area_use¶

REDEFINED (variables -> parameters) Sets area_use to a parameter in operate mode. NOTE: this parameter cannot be used in base mode as it clashes with the decision variable of the same name.

Unit: \(\text{area}\).

Default: inf

flow_cap¶

REDEFINED (variables -> parameters) Sets flow_cap to a parameter in operate mode. NOTE: this parameter cannot be used in base mode as it clashes with the decision variable of the same name.

Unit: power.

Default: inf

source_cap¶

REDEFINED (variables -> parameters) Sets source_cap to a parameter in operate mode. NOTE: this parameter cannot be used in base mode as it clashes with the decision variable of the same name.

Unit: power.

Default: inf

storage_cap¶

REDEFINED (variables -> parameters) Sets storage_cap to a parameter in operate mode. NOTE: this parameter cannot be used in base mode as it clashes with the decision variable of the same name.

Unit: \(\text{area}\).

Default: inf