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 network from PyPSA version v0.17.1 while current version is v0.21.3. Read the release notes at https://pypsa.readthedocs.io/en/latest/release_notes.html to prepare your network for import.
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
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: 347887.0881
  Upper bound: 347887.0881
  Number of objectives: 1
  Number of constraints: 31362
  Number of variables: 2486
  Number of nonzeros: 441
  Sense: minimize
# ----------------------------------------------------------
#   Solver Information
# ----------------------------------------------------------
Solver:
- Status: ok
  User time: -1.0
  System time: 0.8
  Wallclock time: 0.77
  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: 1242
  Error rc: 0
  Time: 0.7817301750183105
# ----------------------------------------------------------
#   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)
Line	1	-68.803346	0.000000	-68.803346	-68.803346	-68.803346	-68.803346	-68.803346	-68.803346	-68.803346	-68.803346	-68.803346	-68.803346	-68.803346	-68.803346	-68.803346	-68.803346
	2	190.707265	190.707265	0.000000	212.790039	13.505556	-122.706611	190.839626	191.016597	190.975555	190.815136	191.158931	154.292808	190.026608	190.064355	191.158177	190.758686
	3	325.824492	325.824492	334.145547	0.000000	383.397379	250.482728	325.812935	325.797484	325.801067	325.853064	325.946002	313.484603	327.596349	327.498089	325.945799	325.839946
	4	-750.815233	-750.815233	-724.824605	-773.225246	0.000000	-487.570136	-750.782636	-750.739052	-750.749159	-750.921327	-751.264938	-708.345991	-756.662619	-756.338348	-751.264188	-750.871164
	5	1069.888693	1069.888693	1045.960033	1054.623188	932.859980	0.000000	1067.815628	1065.043858	1065.686669	1069.894049	1069.913751	1156.214752	1134.263564	1130.693606	1069.913709	1069.893820
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
Transformer	404	3.995927	3.995927	3.998272	3.994991	3.992287	3.984332	3.995921	3.995912	3.995914	3.988667	3.966849	3.993605	3.996374	3.996349	3.966898	3.993758
	413	94.603093	94.603093	94.650025	94.624896	94.833999	94.575138	94.606061	94.610031	94.609110	94.624524	94.688312	94.841071	94.467176	94.474713	94.688169	94.608894
	421	52.977689	52.977689	53.170623	53.069458	53.942928	52.873377	52.990054	53.006585	53.002751	53.084124	53.401445	53.971017	52.411839	52.443219	53.400738	53.007013
	450	82.518672	82.518672	82.460263	82.496275	82.250386	82.130707	82.517165	82.515150	82.515617	82.523641	82.539029	82.337610	82.595022	82.590788	82.538995	82.520604
	458	83.475454	83.475454	83.415989	83.452658	83.202372	83.080710	83.473919	83.471867	83.472343	83.480511	83.496176	83.291125	83.553195	83.548884	83.496141	83.477420

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