Modular Expansion¶
In this example, we demonstrate how to handle the modular expansion feature in PyPSA. Modular expansion allows you to specify discrete steps for the expansion of components. This is particularly useful for technologies that can only be built in fixed block sizes, such as nuclear generators.
We start by loading the 3-hourly resolved model.energy example and adding a nuclear generator as expansion option (with ramp limits of 1%/h and a minimum part load of 70%). Initially, we allow the nuclear generator to be built in continuous sizes.
import pypsa
from pypsa.common import annuity
n = pypsa.examples.model_energy()
n.add(
"Generator",
"nuclear",
bus="electricity",
p_nom_extendable=True,
marginal_cost=15,
capital_cost=annuity(0.07, 50) * 8_000_000,
p_min_pu=0.7,
ramp_limit_up=0.03,
ramp_limit_down=0.03,
)
n.optimize(log_to_console=False)
n.generators.p_nom_opt
INFO:pypsa.network.io:Retrieving network data from https://github.com/PyPSA/PyPSA/raw/v1.0.5/examples/networks/model-energy/model-energy.nc.
INFO:pypsa.network.io:Imported network 'Model-Energy' has buses, carriers, generators, links, loads, storage_units, stores
INFO:linopy.model: Solve problem using Highs solver
INFO:linopy.model:Solver options: - log_to_console: False
INFO:linopy.io:Writing objective.
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Writing constraints.: 39%|███▉ | 9/23 [00:00<00:00, 84.00it/s]
Writing constraints.: 78%|███████▊ | 18/23 [00:00<00:00, 76.05it/s]
Writing constraints.: 100%|██████████| 23/23 [00:00<00:00, 64.73it/s]
Writing continuous variables.: 0%| | 0/11 [00:00<?, ?it/s]
Writing continuous variables.: 100%|██████████| 11/11 [00:00<00:00, 191.88it/s]
INFO:linopy.io: Writing time: 0.43s
INFO:linopy.constants: Optimization successful: Status: ok Termination condition: optimal Solution: 32127 primals, 75925 duals Objective: 6.55e+09 Solver model: available Solver message: Optimal
INFO:pypsa.optimization.optimize:The shadow-prices of the constraints Generator-fix-p-lower, Generator-fix-p-upper, Generator-ext-p-lower, Generator-ext-p-upper, Generator-ext-p-ramp_limit_up, Generator-ext-p-ramp_limit_down, Link-ext-p-lower, Link-ext-p-upper, Store-ext-e-lower, Store-ext-e-upper, StorageUnit-ext-p_dispatch-lower, StorageUnit-ext-p_dispatch-upper, StorageUnit-ext-p_store-lower, StorageUnit-ext-p_store-upper, StorageUnit-ext-state_of_charge-lower, StorageUnit-ext-state_of_charge-upper, StorageUnit-energy_balance, Store-energy_balance were not assigned to the network.
name load shedding 10901.160000 wind 3864.989283 solar 5212.328279 nuclear 7639.029235 Name: p_nom_opt, dtype: float64
As optimal capacity for the nuclear generator, we obtain 7,639 MW.
Now, let's assume that the nuclear generator can only be built in discrete steps of 1,000 MW. We can set the p_nom_mod attribute to 1,000 MW, which introduces an integer variable that constraints the optimised capacity to be a multiple of 1,000 MW. To constrain the option space for the integer variable, and help the solver a bit, we can also set the upper limit p_nom_max to 10,000 MW.
This problem is solved as a mixed-integer linear program (MILP), which will take longer to solve than the previous continuous linear program (LP).
n.generators.loc["nuclear", "p_nom_mod"] = 1000
n.generators.loc["nuclear", "p_nom_max"] = 10000
n.optimize(mip_rel_gap=0.001, log_to_console=False)
n.generators.p_nom_opt
INFO:linopy.model: Solve problem using Highs solver
INFO:linopy.model:Solver options: - mip_rel_gap: 0.001 - log_to_console: False
INFO:linopy.io:Writing objective.
Writing constraints.: 0%| | 0/25 [00:00<?, ?it/s]
Writing constraints.: 44%|████▍ | 11/25 [00:00<00:00, 100.20it/s]
Writing constraints.: 88%|████████▊ | 22/25 [00:00<00:00, 83.57it/s]
Writing constraints.: 100%|██████████| 25/25 [00:00<00:00, 70.14it/s]
Writing continuous variables.: 0%| | 0/12 [00:00<?, ?it/s]
Writing continuous variables.: 100%|██████████| 12/12 [00:00<00:00, 205.27it/s]
Writing integer variables.: 0%| | 0/1 [00:00<?, ?it/s]
Writing integer variables.: 100%|██████████| 1/1 [00:00<00:00, 1131.15it/s]
INFO:linopy.io: Writing time: 0.44s
INFO:linopy.constants: Optimization successful: Status: ok Termination condition: optimal Solution: 32128 primals, 75927 duals Objective: 6.55e+09 Solver model: available Solver message: Optimal
INFO:pypsa.optimization.optimize:The shadow-prices of the constraints Generator-fix-p-lower, Generator-fix-p-upper, Generator-ext-p-lower, Generator-ext-p-upper, Generator-ext-p-ramp_limit_up, Generator-ext-p-ramp_limit_down, Link-ext-p-lower, Link-ext-p-upper, Store-ext-e-lower, Store-ext-e-upper, StorageUnit-ext-p_dispatch-lower, StorageUnit-ext-p_dispatch-upper, StorageUnit-ext-p_store-lower, StorageUnit-ext-p_store-upper, StorageUnit-ext-state_of_charge-lower, StorageUnit-ext-state_of_charge-upper, StorageUnit-energy_balance, Store-energy_balance were not assigned to the network.
name load shedding 10901.160000 wind 2907.095790 solar 4437.946962 nuclear 8000.000000 Name: p_nom_opt, dtype: float64
From the re-optimised results, we can see that the optimal capacity for the nuclear generator is now 8,000 MW, a multiple of 1,000 MW.
As a short concluding excursion into the results, we can also illustrate how the optimal dispatch of this nuclear generator is constrained by ramp limits and minimum part loads in January 2019.
n.generators_t.p.loc["2019-01"].plot(figsize=(6, 3))
<Axes: xlabel='snapshot'>
