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 v0.21.1. 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: 347887.0875
  Upper bound: 347887.0875
  Number of objectives: 1
  Number of constraints: 31362
  Number of variables: 2486
  Number of nonzeros: 440
  Sense: minimize
# ----------------------------------------------------------
#   Solver Information
# ----------------------------------------------------------
Solver:
- Status: ok
  User time: -1.0
  System time: 0.7
  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: 1124
  Error rc: 0
  Time: 0.7294807434082031
# ----------------------------------------------------------
#   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	-68.803422	0.000000	-68.803422	-68.803422	-68.803422	-68.803422	-68.803422	-68.803422	-68.803422	-68.803422	-68.803422	-68.803422	-68.803422	-68.803422	-68.803422	-68.803422
	2	190.707277	190.707277	0.000000	212.790051	13.505569	-122.706595	190.839638	191.016610	190.975568	190.815148	191.158943	154.292820	190.026621	190.064367	191.158189	190.758698
	3	325.824496	325.824496	334.145551	0.000000	383.397383	250.482733	325.812939	325.797488	325.801071	325.853068	325.946006	313.484607	327.596353	327.498094	325.945803	325.839950
	4	-750.815231	-750.815231	-724.824601	-773.225244	0.000000	-487.570138	-750.782634	-750.739050	-750.749158	-750.921325	-751.264937	-708.345988	-756.662617	-756.338346	-751.264186	-750.871162
	5	1069.888680	1069.888680	1045.960019	1054.623175	932.859967	0.000000	1067.815615	1065.043845	1065.686656	1069.894036	1069.913738	1156.214741	1134.263550	1130.693592	1069.913696	1069.893808
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
Transformer	404	3.995927	3.995927	3.998271	3.994990	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	52.977690	52.977690	53.170624	53.069459	53.942928	52.873378	52.990054	53.006586	53.002752	53.084125	53.401446	53.971017	52.411840	52.443219	53.400739	53.007013
	450	82.518656	82.518656	82.460247	82.496259	82.250370	82.130691	82.517149	82.515133	82.515601	82.523624	82.539012	82.337593	82.595006	82.590772	82.538978	82.520587
	458	83.475437	83.475437	83.415972	83.452641	83.202356	83.080694	83.473902	83.471850	83.472326	83.480495	83.496159	83.291108	83.553178	83.548867	83.496124	83.477403

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