Note
You can download this example as a Jupyter notebook or start it in interactive mode.
Security-Constrained Optimisation
In this example, the dispatch of generators is optimised using the security-constrained linear OPF, to guaranteed that no branches are overloaded by certain branch outages.
[1]:
import pypsa, os
import numpy as np
[2]:
network = pypsa.examples.scigrid_de(from_master=True)
WARNING:pypsa.io:
Importing PyPSA from older version of PyPSA than current version.
Please read the release notes at https://pypsa.readthedocs.io/en/latest/release_notes.html
carefully to prepare your network for import.
Currently used PyPSA version [0, 19, 3], imported network file PyPSA version [0, 17, 1].
INFO:pypsa.io:Imported network scigrid-de.nc has buses, generators, lines, loads, storage_units, transformers
There are some infeasibilities without line extensions.
[3]:
for line_name in ["316", "527", "602"]:
network.lines.loc[line_name, "s_nom"] = 1200
now = network.snapshots[0]
Performing security-constrained linear OPF
[4]:
branch_outages = network.lines.index[:15]
network.sclopf(now, branch_outages=branch_outages, solver_name="cbc")
INFO:pypsa.opf:Building pyomo model using `kirchhoff` formulation
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.19.3/lib/python3.10/site-packages/scipy/sparse/linalg/_dsolve/linsolve.py:322: SparseEfficiencyWarning: splu requires CSC matrix format
warn('splu requires CSC matrix format', SparseEfficiencyWarning)
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.19.3/lib/python3.10/site-packages/pypsa/contingency.py:78: RuntimeWarning: divide by zero encountered in true_divide
(1 / (1 - np.diag(branch_PTDF)), (r_[:num_branches], r_[:num_branches]))
WARNING:pypsa.contingency:No type given for 1, assuming it is a line
WARNING:pypsa.contingency:No type given for 2, assuming it is a line
WARNING:pypsa.contingency:No type given for 3, assuming it is a line
WARNING:pypsa.contingency:No type given for 4, assuming it is a line
WARNING:pypsa.contingency:No type given for 5, assuming it is a line
WARNING:pypsa.contingency:No type given for 6, assuming it is a line
WARNING:pypsa.contingency:No type given for 7, assuming it is a line
WARNING:pypsa.contingency:No type given for 8, assuming it is a line
WARNING:pypsa.contingency:No type given for 9, assuming it is a line
WARNING:pypsa.contingency:No type given for 10, assuming it is a line
WARNING:pypsa.contingency:No type given for 11, assuming it is a line
WARNING:pypsa.contingency:No type given for 12, assuming it is a line
WARNING:pypsa.contingency:No type given for 13, assuming it is a line
WARNING:pypsa.contingency:No type given for 14, assuming it is a line
WARNING:pypsa.contingency:No type given for 15, assuming it is a line
INFO:pypsa.opf:Solving model using cbc
INFO:pypsa.opf:Optimization successful
# ==========================================================
# = Solver Results =
# ==========================================================
# ----------------------------------------------------------
# Problem Information
# ----------------------------------------------------------
Problem:
- Name: unknown
Lower bound: 347887.0925
Upper bound: 347887.0925
Number of objectives: 1
Number of constraints: 31362
Number of variables: 2486
Number of nonzeros: 442
Sense: minimize
# ----------------------------------------------------------
# Solver Information
# ----------------------------------------------------------
Solver:
- Status: ok
User time: -1.0
System time: 0.72
Wallclock time: 0.68
Termination condition: optimal
Termination message: Model was solved to optimality (subject to tolerances), and an optimal solution is available.
Statistics:
Branch and bound:
Number of bounded subproblems: None
Number of created subproblems: None
Black box:
Number of iterations: 1064
Error rc: 0
Time: 0.6944501399993896
# ----------------------------------------------------------
# Solution Information
# ----------------------------------------------------------
Solution:
- number of solutions: 0
number of solutions displayed: 0
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.19.3/lib/python3.10/site-packages/pypsa/opf.py:1971: FutureWarning: Using the level keyword in DataFrame and Series aggregations is deprecated and will be removed in a future version. Use groupby instead. df.sum(level=1) should use df.groupby(level=1).sum().
pd.concat(
For the PF, set the P to the optimised P.
[5]:
network.generators_t.p_set = network.generators_t.p_set.reindex(
columns=network.generators.index
)
network.generators_t.p_set.loc[now] = network.generators_t.p.loc[now]
network.storage_units_t.p_set = network.storage_units_t.p_set.reindex(
columns=network.storage_units.index
)
network.storage_units_t.p_set.loc[now] = network.storage_units_t.p.loc[now]
Check no lines are overloaded with the linear contingency analysis
[6]:
p0_test = network.lpf_contingency(now, branch_outages=branch_outages)
p0_test
INFO:pypsa.pf:Performing linear load-flow on AC sub-network SubNetwork 0 for snapshot(s) DatetimeIndex(['2011-01-01'], dtype='datetime64[ns]', name='snapshot', freq=None)
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.19.3/lib/python3.10/site-packages/scipy/sparse/linalg/_dsolve/linsolve.py:322: SparseEfficiencyWarning: splu requires CSC matrix format
warn('splu requires CSC matrix format', SparseEfficiencyWarning)
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.19.3/lib/python3.10/site-packages/pypsa/contingency.py:78: RuntimeWarning: divide by zero encountered in true_divide
(1 / (1 - np.diag(branch_PTDF)), (r_[:num_branches], r_[:num_branches]))
WARNING:pypsa.contingency:No type given for 1, assuming it is a line
WARNING:pypsa.contingency:No type given for 2, assuming it is a line
WARNING:pypsa.contingency:No type given for 3, assuming it is a line
WARNING:pypsa.contingency:No type given for 4, assuming it is a line
WARNING:pypsa.contingency:No type given for 5, assuming it is a line
WARNING:pypsa.contingency:No type given for 6, assuming it is a line
WARNING:pypsa.contingency:No type given for 7, assuming it is a line
WARNING:pypsa.contingency:No type given for 8, assuming it is a line
WARNING:pypsa.contingency:No type given for 9, assuming it is a line
WARNING:pypsa.contingency:No type given for 10, assuming it is a line
WARNING:pypsa.contingency:No type given for 11, assuming it is a line
WARNING:pypsa.contingency:No type given for 12, assuming it is a line
WARNING:pypsa.contingency:No type given for 13, assuming it is a line
WARNING:pypsa.contingency:No type given for 14, assuming it is a line
WARNING:pypsa.contingency:No type given for 15, assuming it is a line
[6]:
| base | (Line, 1) | (Line, 2) | (Line, 3) | (Line, 4) | (Line, 5) | (Line, 6) | (Line, 7) | (Line, 8) | (Line, 9) | (Line, 10) | (Line, 11) | (Line, 12) | (Line, 13) | (Line, 14) | (Line, 15) | ||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Line | 1 | -68.803446 | 0.000000 | -68.803446 | -68.803446 | -68.803446 | -68.803446 | -68.803446 | -68.803446 | -68.803446 | -68.803446 | -68.803446 | -68.803446 | -68.803446 | -68.803446 | -68.803446 | -68.803446 |
| 2 | 190.707291 | 190.707291 | 0.000000 | 212.790065 | 13.505582 | -122.706586 | 190.839652 | 191.016624 | 190.975581 | 190.815162 | 191.158957 | 154.292834 | 190.026634 | 190.064381 | 191.158203 | 190.758712 | |
| 3 | 325.824498 | 325.824498 | 334.145554 | 0.000000 | 383.397385 | 250.482735 | 325.812942 | 325.797490 | 325.801074 | 325.853070 | 325.946008 | 313.484609 | 327.596356 | 327.498096 | 325.945806 | 325.839953 | |
| 4 | -750.815235 | -750.815235 | -724.824604 | -773.225249 | 0.000000 | -487.570139 | -750.782638 | -750.739054 | -750.749162 | -750.921330 | -751.264941 | -708.345993 | -756.662622 | -756.338350 | -751.264190 | -750.871166 | |
| 5 | 1069.888694 | 1069.888694 | 1045.960031 | 1054.623189 | 932.859981 | 0.000000 | 1067.815630 | 1065.043859 | 1065.686670 | 1069.894050 | 1069.913752 | 1156.214755 | 1134.263566 | 1130.693608 | 1069.913710 | 1069.893822 | |
| ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... |
| Transformer | 404 | 3.995926 | 3.995926 | 3.998271 | 3.994990 | 3.992286 | 3.984331 | 3.995920 | 3.995911 | 3.995913 | 3.988666 | 3.966848 | 3.993604 | 3.996373 | 3.996348 | 3.966897 | 3.993757 |
| 413 | 94.603092 | 94.603092 | 94.650025 | 94.624896 | 94.833998 | 94.575138 | 94.606061 | 94.610030 | 94.609110 | 94.624523 | 94.688311 | 94.841071 | 94.467175 | 94.474713 | 94.688169 | 94.608894 | |
| 421 | 52.977690 | 52.977690 | 53.170624 | 53.069459 | 53.942928 | 52.873378 | 52.990054 | 53.006586 | 53.002752 | 53.084125 | 53.401446 | 53.971018 | 52.411840 | 52.443219 | 53.400739 | 53.007013 | |
| 450 | 82.518670 | 82.518670 | 82.460261 | 82.496273 | 82.250384 | 82.130705 | 82.517162 | 82.515147 | 82.515615 | 82.523638 | 82.539026 | 82.337607 | 82.595019 | 82.590785 | 82.538992 | 82.520601 | |
| 458 | 83.475451 | 83.475451 | 83.415986 | 83.452656 | 83.202370 | 83.080708 | 83.473916 | 83.471864 | 83.472340 | 83.480509 | 83.496173 | 83.291122 | 83.553192 | 83.548881 | 83.496138 | 83.477417 |
948 rows × 16 columns
Check loading as per unit of s_nom in each contingency
[7]:
max_loading = (
abs(p0_test.divide(network.passive_branches().s_nom, axis=0)).describe().loc["max"]
)
max_loading
[7]:
base 1.0
(Line, 1) 1.0
(Line, 2) 1.0
(Line, 3) 1.0
(Line, 4) 1.0
(Line, 5) 1.0
(Line, 6) 1.0
(Line, 7) 1.0
(Line, 8) 1.0
(Line, 9) 1.0
(Line, 10) 1.0
(Line, 11) 1.0
(Line, 12) 1.0
(Line, 13) 1.0
(Line, 14) 1.0
(Line, 15) 1.0
Name: max, dtype: float64
[8]:
np.allclose(max_loading, np.ones((len(max_loading))))
[8]:
True