Running the MILP example model¶
This notebook will show you how to load, build, solve, and examine the results of the MILP example model.
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import calliope
# We increase logging verbosity
calliope.set_log_verbosity("INFO", include_solver_output=False)
import calliope
# We increase logging verbosity
calliope.set_log_verbosity("INFO", include_solver_output=False)
Load model and examine inputs¶
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model = calliope.examples.milp()
model = calliope.examples.milp()
[2026-04-22 17:28:03] INFO (scenarios, milp ) | Applying the following overrides: ['milp'].
[2026-04-22 17:28:03] INFO Math init | loading pre-defined math.
[2026-04-22 17:28:03] INFO Math init | loading math files {'additional_math', 'spores', 'milp', 'operate', 'base', 'storage_inter_cluster'}.
[2026-04-22 17:28:03] INFO Model: preprocessing data
[2026-04-22 17:28:03] INFO Math build | building applied math with ['base', 'milp', 'additional_math'].
[2026-04-22 17:28:04] INFO input data `color` not defined in model math; it will not be available in the optimisation problem.
[2026-04-22 17:28:04] INFO input data `name` not defined in model math; it will not be available in the optimisation problem.
[2026-04-22 17:28:04] INFO input data `color` not defined in model math; it will not be available in the optimisation problem.
[2026-04-22 17:28:04] INFO input data `name` not defined in model math; it will not be available in the optimisation problem.
[2026-04-22 17:28:04] INFO Model: initialisation complete
Model inputs can be viewed at model.inputs.
Variables are indexed over any combination of techs, nodes, carriers, costs and timesteps.
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model.inputs
model.inputs
Out[3]:
<xarray.Dataset> Size: 87kB
Dimensions: (costs: 1, techs: 12, carriers: 3, nodes: 4,
timesteps: 48)
Coordinates:
* costs (costs) object 8B 'monetary'
* techs (techs) object 96B 'N1_to_X2' ... 'supply_gri...
* carriers (carriers) object 24B 'electricity' 'gas' 'heat'
* nodes (nodes) object 32B 'N1' 'X1' 'X2' 'X3'
* timesteps (timesteps) datetime64[ns] 384B 2005-07-01 .....
Data variables: (12/42)
cost_interest_rate (costs) float64 8B 0.1
bigM float64 8B 1e+06
objective_cost_weights (costs) float64 8B 1.0
base_tech (techs) object 96B 'transmission' ... 'supply'
cap_method (techs) object 96B nan nan nan ... nan nan nan
carrier_export (techs, carriers) bool 36B False False ... False
... ...
longitude (nodes) float64 32B -0.1247 -0.1613 ... -0.1311
source_use_equals (techs, timesteps) float64 5kB nan nan ... nan
sink_use_equals (timesteps, techs, nodes) float64 18kB nan .....
definition_matrix (nodes, techs, carriers) bool 144B False ... ...
timestep_resolution (timesteps) float64 384B 1.0 1.0 1.0 ... 1.0 1.0
timestep_weights (timesteps) float64 384B 1.0 1.0 1.0 ... 1.0 1.0Individual data variables can be accessed easily, to_series().dropna() allows us to view the data in a nice tabular format.
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model.inputs.flow_cap_max.to_series().dropna()
model.inputs.flow_cap_max.to_series().dropna()
Out[4]:
techs carriers nodes N1_to_X2 heat N1 2000.0 X2 2000.0 N1_to_X3 heat N1 2000.0 X3 2000.0 X1_to_N1 heat N1 2000.0 X1 2000.0 X1_to_X2 electricity X1 2000.0 X2 2000.0 X1_to_X3 electricity X1 2000.0 X3 2000.0 boiler heat X2 600.0 X3 600.0 pv electricity X1 250.0 X2 250.0 X3 50.0 supply_gas gas X1 2000.0 X2 2000.0 X3 2000.0 supply_grid_power electricity X1 2000.0 Name: flow_cap_max, dtype: float64
You can apply node/tech/carrier/timesteps only operations, like summing information over timesteps
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model.inputs.sink_use_equals.sum(
"timesteps", min_count=1, skipna=True
).to_series().dropna()
model.inputs.sink_use_equals.sum(
"timesteps", min_count=1, skipna=True
).to_series().dropna()
Out[5]:
techs nodes demand_electricity X1 35.271156 X2 8796.878622 X3 1244.604116 demand_heat X1 33.999992 X2 7147.808356 X3 50.567751 Name: sink_use_equals, dtype: float64
Build and solve the optimisation problem.¶
Results are loaded into model.results.
By setting the log verbosity at the start of this tutorial to "INFO", we can see the timing of parts of the run, as well as the solver's log.
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model.build()
model.solve()
model.build()
model.solve()
[2026-04-22 17:28:04] INFO Model: backend build starting
[2026-04-22 17:28:04] INFO Optimisation Model | parameters/lookups | Generated.
[2026-04-22 17:28:05] INFO Optimisation Model | variables | Generated.
[2026-04-22 17:28:05] INFO Optimisation Model | global_expressions | Generated.
[2026-04-22 17:28:07] INFO Optimisation Model | constraints | Generated.
[2026-04-22 17:28:07] INFO Optimisation Model | piecewise_constraints | Generated.
[2026-04-22 17:28:07] INFO Optimisation Model | objectives | Generated.
[2026-04-22 17:28:07] INFO Model: backend build complete
[2026-04-22 17:28:07] INFO Optimisation model | starting model in base mode.
[2026-04-22 17:28:11] INFO Optimisation Model | postprocess | Generated.
[2026-04-22 17:28:11] INFO Backend: solver finished running. Time since start of solving optimisation problem: 0:00:03.381077
[2026-04-22 17:28:11] INFO Postprocessing: applied zero threshold 1e-10 to model results.
[2026-04-22 17:28:11] INFO Postprocessing: ended. Time since start of solving optimisation problem: 0:00:03.416447
[2026-04-22 17:28:11] INFO Backend: model solve completed. Time since start of solving optimisation problem: 0:00:03.416781
Model results are held in the same structure as model inputs. The results consist of the optimal values for all decision variables, including capacities and carrier flow. There are also results, like system capacity factor and levelised costs, which are calculated in postprocessing before being added to the results Dataset
Examine results¶
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model.results
model.results
Out[7]:
<xarray.Dataset> Size: 426kB
Dimensions: (techs: 12, nodes: 4, carriers: 3,
timesteps: 48, costs: 1)
Coordinates:
* techs (techs) object 96B 'N1_to_X2' ... 'supply_gri...
* nodes (nodes) object 32B 'N1' 'X1' 'X2' 'X3'
* carriers (carriers) object 24B 'electricity' 'gas' 'heat'
* timesteps (timesteps) datetime64[ns] 384B 2005-07-01 .....
* costs (costs) object 8B 'monetary'
Data variables: (12/29)
flow_cap (nodes, techs, carriers) float64 1kB nan ... nan
link_flow_cap (techs) float64 96B 214.8 10.4 238.7 ... nan nan
flow_out (nodes, techs, carriers, timesteps) float64 55kB ...
flow_in (nodes, techs, carriers, timesteps) float64 55kB ...
flow_export (nodes, techs, carriers, timesteps) float64 55kB ...
area_use (nodes, techs) float64 384B nan nan ... nan nan
... ...
capacity_factor (nodes, techs, carriers, timesteps) float64 55kB ...
systemwide_capacity_factor (techs, carriers) float64 288B nan nan ... nan
total_generation (techs, carriers) float64 288B nan nan ... nan
systemwide_levelised_cost (techs, carriers, costs) float64 288B nan ......
total_levelised_cost (carriers, costs) float64 24B 0.04333 ... 0.0442
unmet_sum (nodes, carriers, timesteps) float64 5kB nan ...Integer variables purchased_units and operating_units are available in the results
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model.results.purchased_units.to_series().dropna()
model.results.purchased_units.to_series().dropna()
Out[8]:
nodes techs X1 chp 1.0 X2 boiler 1.0 X3 boiler 0.0 Name: purchased_units, dtype: float64
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model.results.operating_units.to_series().dropna().unstack("techs").head()
model.results.operating_units.to_series().dropna().unstack("techs").head()
Out[9]:
| techs | chp | |
|---|---|---|
| nodes | timesteps | |
| X1 | 2005-07-01 00:00:00 | 1.0 |
| 2005-07-01 01:00:00 | 1.0 | |
| 2005-07-01 02:00:00 | 1.0 | |
| 2005-07-01 03:00:00 | 1.0 | |
| 2005-07-01 04:00:00 | 1.0 |
We can sum heat output over all locations and turn the result into a pandas DataFrame.
Note: heat output of transmission technologies (e.g., N1_to_X2) is the import of heat at nodes.
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df_heat = (
model.results.flow_out.sel(carriers="heat")
.sum("nodes", min_count=1, skipna=True)
.to_series()
.dropna()
.unstack("techs")
)
df_heat.head()
df_heat = (
model.results.flow_out.sel(carriers="heat")
.sum("nodes", min_count=1, skipna=True)
.to_series()
.dropna()
.unstack("techs")
)
df_heat.head()
Out[10]:
| techs | N1_to_X2 | N1_to_X3 | X1_to_N1 | boiler | chp |
|---|---|---|---|---|---|
| timesteps | |||||
| 2005-07-01 00:00:00 | 64.731991 | 0.015600 | 69.857405 | 0.000000 | 75.585392 |
| 2005-07-01 01:00:00 | 66.352993 | 0.860322 | 72.541074 | 4.100446 | 78.466297 |
| 2005-07-01 02:00:00 | 67.566474 | 0.015600 | 72.915564 | 9.626502 | 78.876806 |
| 2005-07-01 03:00:00 | 67.471047 | 0.015600 | 72.812606 | 37.085389 | 78.877367 |
| 2005-07-01 04:00:00 | 70.036981 | 0.860407 | 76.515868 | 53.191464 | 83.204646 |
You can apply node/tech/carrier only operations, like summing information over nodes
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df_heat.info()
df_heat.info()
<class 'pandas.core.frame.DataFrame'> DatetimeIndex: 48 entries, 2005-07-01 00:00:00 to 2005-07-02 23:00:00 Data columns (total 5 columns): # Column Non-Null Count Dtype --- ------ -------------- ----- 0 N1_to_X2 48 non-null float64 1 N1_to_X3 48 non-null float64 2 X1_to_N1 48 non-null float64 3 boiler 48 non-null float64 4 chp 48 non-null float64 dtypes: float64(5) memory usage: 2.2 KB
We can also examine total technology costs.
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costs = model.results.cost.to_series().dropna()
costs
costs = model.results.cost.to_series().dropna()
costs
Out[12]:
nodes techs costs N1 N1_to_X2 monetary 0.058362 N1_to_X3 monetary 0.003767 X1_to_N1 monetary 0.064846 X1 X1_to_N1 monetary 0.064846 X1_to_X2 monetary 0.008273 X1_to_X3 monetary 0.000691 chp monetary 183.482186 pv monetary 0.000000 supply_gas monetary 528.971602 supply_grid_power monetary 64.468219 X2 N1_to_X2 monetary 0.058362 X1_to_X2 monetary 0.008273 boiler monetary 11.853703 pv monetary 52.821906 supply_gas monetary 39.663214 X3 N1_to_X3 monetary 0.003767 X1_to_X3 monetary 0.000691 boiler monetary 0.000000 pv monetary 18.692301 supply_gas monetary 0.000000 Name: cost, dtype: float64
We can also examine levelized costs for each location and technology, which is calculated in a post-processing step.
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lcoes = (
model.results.systemwide_levelised_cost.sel(carriers="electricity")
.to_series()
.dropna()
)
lcoes
lcoes = (
model.results.systemwide_levelised_cost.sel(carriers="electricity")
.to_series()
.dropna()
)
lcoes
Out[13]:
techs costs X1_to_X2 monetary 0.000002 X1_to_X3 monetary 0.000002 chp monetary 0.021319 pv monetary 0.027795 supply_grid_power monetary 0.108373 Name: systemwide_levelised_cost, dtype: float64
See the Calliope documentation for more details on setting up and running a Calliope model.