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, 20, 0], 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")

WARNING:pypsa.components:Solving optimisation problem with pyomo.In PyPSA version 0.21 the default will change to ``n.lopf(pyomo=False)``.Explicitly set ``n.lopf(pyomo=True)`` to retain current behaviour.
INFO:pypsa.opf:Building pyomo model using `kirchhoff` formulation
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: 347887.0926
  Upper bound: 347887.0926
  Number of objectives: 1
  Number of constraints: 31362
  Number of variables: 2486
  Number of nonzeros: 439
  Sense: minimize
# ----------------------------------------------------------
#   Solver Information
# ----------------------------------------------------------
Solver:
- Status: ok
  User time: -1.0
  System time: 0.74
  Wallclock time: 0.71
  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: 1158
  Error rc: 0
  Time: 0.7267937660217285
# ----------------------------------------------------------
#   Solution Information
# ----------------------------------------------------------
Solution:
- number of solutions: 0
  number of solutions displayed: 0

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)
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)
Transformer	2	-398.673557	-398.673557	-418.812170	-359.776332	-494.531592	-456.944271	-398.465081	-398.186341	-398.250985	-398.719309	-398.867087	-390.267047	-407.034895	-406.571210	-398.866764	-398.697283
	5	883.055800	883.055800	898.249129	811.125660	988.177524	745.490073	883.034699	883.006486	883.013029	883.107970	883.277664	860.524527	886.291015	886.111604	883.277294	883.084018
	10	-227.642977	-227.642977	-227.040368	-227.465351	-225.951447	-302.148218	-239.209405	-254.674181	-251.087689	-227.628693	-227.583800	-209.997527	42.837910	27.838187	-227.583898	-227.636786
	12	-1211.646080	-1211.646080	-1211.821857	-1211.717451	-1212.306156	-1192.941429	-1191.974372	-1165.672511	-1171.772271	-1211.648632	-1211.656386	-1216.321290	-1479.256769	-1464.416214	-1211.656369	-1211.646922
	13	41.861950	41.861950	41.500970	41.608206	39.441350	41.627203	41.832212	41.792450	41.801671	67.075992	5.594734	39.431473	43.269601	43.191538	5.655277	73.316136
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
Line	855	65.129873	65.129873	65.010504	65.078881	64.536480	64.147069	65.127057	65.123292	65.124165	65.140617	65.173879	64.753233	65.277580	65.269389	65.173805	65.134037
	856	93.141666	93.141666	92.945010	93.049299	92.092939	91.247887	93.137330	93.131532	93.132876	93.160471	93.218668	92.505187	93.376630	93.363600	93.218540	93.148934
	857	359.231588	359.231588	357.976182	359.455060	359.413098	372.664329	359.179306	359.109403	359.125615	359.237745	359.258511	356.942347	361.344964	361.227765	359.258466	359.235642
	858	33.680485	33.680485	33.624796	33.654329	33.383509	33.144210	33.679257	33.677615	33.677996	33.685810	33.702290	33.500249	33.747022	33.743332	33.702254	33.682543
	859	182.371439	182.371439	181.969317	182.274409	181.001252	181.315362	182.360064	182.344855	182.348382	182.396656	182.474891	181.282508	182.909996	182.880130	182.474718	182.381371

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