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 network from PyPSA version v0.17.1 while current version is v0.22.1. 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: 347887.0935
  Upper bound: 347887.0935
  Number of objectives: 1
  Number of constraints: 31362
  Number of variables: 2486
  Number of nonzeros: 438
  Sense: minimize
# ----------------------------------------------------------
#   Solver Information
# ----------------------------------------------------------
Solver:
- Status: ok
  User time: -1.0
  System time: 0.76
  Wallclock time: 0.73
  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: 1108
  Error rc: 0
  Time: 0.7446849346160889
# ----------------------------------------------------------
#   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	-68.803464	0.000000	-68.803464	-68.803464	-68.803464	-68.803464	-68.803464	-68.803464	-68.803464	-68.803464	-68.803464	-68.803464	-68.803464	-68.803464	-68.803464	-68.803464
	2	190.707296	190.707296	0.000000	212.790070	13.505586	-122.706584	190.839657	191.016628	190.975586	190.815167	191.158962	154.292839	190.026639	190.064385	191.158208	190.758717
	3	325.824500	325.824500	334.145556	0.000000	383.397387	250.482736	325.812943	325.797492	325.801075	325.853072	325.946010	313.484611	327.596357	327.498098	325.945807	325.839954
	4	-750.815237	-750.815237	-724.824605	-773.225251	0.000000	-487.570138	-750.782640	-750.739056	-750.749164	-750.921332	-751.264943	-708.345995	-756.662624	-756.338352	-751.264192	-750.871168
	5	1069.888706	1069.888706	1045.960042	1054.623201	932.859992	0.000000	1067.815641	1065.043871	1065.686682	1069.894062	1069.913764	1156.214767	1134.263579	1130.693621	1069.913722	1069.893834
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
Transformer	404	3.995926	3.995926	3.998270	3.994989	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	94.841070	94.467175	94.474713	94.688169	94.608893
	421	52.977690	52.977690	53.170624	53.069459	53.942929	52.873378	52.990055	53.006586	53.002752	53.084125	53.401446	53.971018	52.411840	52.443220	53.400739	53.007013
	450	82.518669	82.518669	82.460260	82.496272	82.250383	82.130704	82.517162	82.515147	82.515614	82.523638	82.539026	82.337607	82.595019	82.590785	82.538992	82.520601
	458	83.475451	83.475451	83.415986	83.452655	83.202369	83.080707	83.473916	83.471864	83.472340	83.480508	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

PyPSA: Python for Power System Analysis

Security-Constrained Optimisation

Security-Constrained Optimisation#