Note
You can download this example as a Jupyter notebook or start it in interactive mode.
Redispatch Example with SciGRID network#
In this example, we compare a 2-stage market with an initial market clearing in two bidding zones with flow-based market coupling and a subsequent redispatch market (incl. curtailment) to an idealised nodal pricing scheme.
[1]:
import cartopy.crs as ccrs
import matplotlib.pyplot as plt
import pypsa
from pypsa.descriptors import get_switchable_as_dense as as_dense
Load example network#
[2]:
o = pypsa.examples.scigrid_de(from_master=True)
o.lines.s_max_pu = 0.7
o.lines.loc[["316", "527", "602"], "s_nom"] = 1715
o.set_snapshots([o.snapshots[12]])
WARNING:pypsa.io:Importing network from PyPSA version v0.17.1 while current version is v0.34.0. 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
[3]:
n = o.copy() # for redispatch model
m = o.copy() # for market model
[4]:
o.plot();
/tmp/ipykernel_3743/3521453863.py:1: DeprecatedWarning: plot is deprecated. Use `n.plot.map()` as a drop-in replacement instead.
o.plot();
Solve original nodal market model o#
First, let us solve a nodal market using the original model o:
[5]:
o.optimize()
WARNING:pypsa.consistency:The following transformers have zero r, which could break the linear load flow:
Index(['2', '5', '10', '12', '13', '15', '18', '20', '22', '24', '26', '30',
'32', '37', '42', '46', '52', '56', '61', '68', '69', '74', '78', '86',
'87', '94', '95', '96', '99', '100', '104', '105', '106', '107', '117',
'120', '123', '124', '125', '128', '129', '138', '143', '156', '157',
'159', '160', '165', '184', '191', '195', '201', '220', '231', '232',
'233', '236', '247', '248', '250', '251', '252', '261', '263', '264',
'267', '272', '279', '281', '282', '292', '303', '307', '308', '312',
'315', '317', '322', '332', '334', '336', '338', '351', '353', '360',
'362', '382', '384', '385', '391', '403', '404', '413', '421', '450',
'458'],
dtype='object', name='Transformer')
INFO:linopy.model: Solve problem using Highs solver
INFO:linopy.io: Writing time: 0.09s
INFO:linopy.constants: Optimization successful:
Status: ok
Termination condition: optimal
Solution: 2485 primals, 5957 duals
Objective: 3.01e+05
Solver model: available
Solver message: optimal
INFO:pypsa.optimization.optimize:The shadow-prices of the constraints Generator-fix-p-lower, Generator-fix-p-upper, Line-fix-s-lower, Line-fix-s-upper, Transformer-fix-s-lower, Transformer-fix-s-upper, StorageUnit-fix-p_dispatch-lower, StorageUnit-fix-p_dispatch-upper, StorageUnit-fix-p_store-lower, StorageUnit-fix-p_store-upper, StorageUnit-fix-state_of_charge-lower, StorageUnit-fix-state_of_charge-upper, Kirchhoff-Voltage-Law, StorageUnit-energy_balance were not assigned to the network.
Running HiGHS 1.10.0 (git hash: fd86653): Copyright (c) 2025 HiGHS under MIT licence terms
LP linopy-problem-qv09ehg5 has 5957 rows; 2485 cols; 10948 nonzeros
Coefficient ranges:
Matrix [1e-02, 2e+02]
Cost [3e+00, 1e+02]
Bound [0e+00, 0e+00]
RHS [4e-10, 6e+03]
Presolving model
817 rows, 2282 cols, 5248 nonzeros 0s
559 rows, 2017 cols, 4867 nonzeros 0s
535 rows, 1354 cols, 4137 nonzeros 0s
Dependent equations search running on 523 equations with time limit of 1000.00s
Dependent equations search removed 0 rows and 0 nonzeros in 0.00s (limit = 1000.00s)
523 rows, 1337 cols, 4180 nonzeros 0s
Presolve : Reductions: rows 523(-5434); columns 1337(-1148); elements 4180(-6768)
Solving the presolved LP
Using EKK dual simplex solver - serial
Iteration Objective Infeasibilities num(sum)
0 -2.2254393827e-01 Pr: 485(2.80835e+06) 0s
622 3.0120938233e+05 Pr: 0(0); Du: 0(5.32907e-15) 0s
Solving the original LP from the solution after postsolve
Model name : linopy-problem-qv09ehg5
Model status : Optimal
Simplex iterations: 622
Objective value : 3.0120938233e+05
Relative P-D gap : 1.9324650668e-16
HiGHS run time : 0.04
Writing the solution to /tmp/linopy-solve-cos4t6j4.sol
[5]:
('ok', 'optimal')
Costs are 301 k€.
Build market model m with two bidding zones#
For this example, we split the German transmission network into two market zones at latitude 51 degrees.
You can build any other market zones by providing an alternative mapping from bus to zone.
[6]:
zones = (n.buses.y > 51).map(lambda x: "North" if x else "South")
Next, we assign this mapping to the market model m.
We re-assign the buses of all generators and loads, and remove all transmission lines within each bidding zone.
Here, we assume that the bidding zones are coupled through the transmission lines that connect them.
[7]:
for c in m.iterate_components(m.one_port_components):
c.static.bus = c.static.bus.map(zones)
for c in m.iterate_components(m.branch_components):
c.static.bus0 = c.static.bus0.map(zones)
c.static.bus1 = c.static.bus1.map(zones)
internal = c.static.bus0 == c.static.bus1
m.remove(c.name, c.static.loc[internal].index)
m.remove("Bus", m.buses.index)
m.add("Bus", ["North", "South"]);
Now, we can solve the coupled market with two bidding zones.
[8]:
m.optimize()
INFO:linopy.model: Solve problem using Highs solver
INFO:linopy.io: Writing time: 0.06s
INFO:linopy.constants: Optimization successful:
Status: ok
Termination condition: optimal
Solution: 1561 primals, 3185 duals
Objective: 2.14e+05
Solver model: available
Solver message: optimal
INFO:pypsa.optimization.optimize:The shadow-prices of the constraints Generator-fix-p-lower, Generator-fix-p-upper, Line-fix-s-lower, Line-fix-s-upper, StorageUnit-fix-p_dispatch-lower, StorageUnit-fix-p_dispatch-upper, StorageUnit-fix-p_store-lower, StorageUnit-fix-p_store-upper, StorageUnit-fix-state_of_charge-lower, StorageUnit-fix-state_of_charge-upper, Kirchhoff-Voltage-Law, StorageUnit-energy_balance were not assigned to the network.
Running HiGHS 1.10.0 (git hash: fd86653): Copyright (c) 2025 HiGHS under MIT licence terms
LP linopy-problem-xarlj7xp has 3185 rows; 1561 cols; 4829 nonzeros
Coefficient ranges:
Matrix [9e-01, 3e+06]
Cost [3e+00, 1e+02]
Bound [0e+00, 0e+00]
RHS [4e-10, 3e+04]
Presolving model
40 rows, 1510 cols, 1587 nonzeros 0s
40 rows, 135 cols, 212 nonzeros 0s
Dependent equations search running on 40 equations with time limit of 1000.00s
Dependent equations search removed 0 rows and 0 nonzeros in 0.00s (limit = 1000.00s)
40 rows, 135 cols, 212 nonzeros 0s
Presolve : Reductions: rows 40(-3145); columns 135(-1426); elements 212(-4617)
Solving the presolved LP
Using EKK dual simplex solver - serial
Iteration Objective Infeasibilities num(sum)
0 -4.3458587374e-04 Pr: 2(51830.2) 0s
42 2.1398868596e+05 Pr: 0(0) 0s
Solving the original LP from the solution after postsolve
Model name : linopy-problem-xarlj7xp
Model status : Optimal
Simplex iterations: 42
Objective value : 2.1398868596e+05
Relative P-D gap : 6.2562943224e-15
HiGHS run time : 0.01
Writing the solution to /tmp/linopy-solve-oigq75qi.sol
[8]:
('ok', 'optimal')
Costs are 214 k€, which is much lower than the 301 k€ of the nodal market.
This is because network restrictions apart from the North/South division are not taken into account yet.
We can look at the market clearing prices of each zone:
[9]:
m.buses_t.marginal_price
[9]:
| Bus | North | South |
|---|---|---|
| snapshot | ||
| 2011-01-01 12:00:00 | 8.0 | 25.0 |
Build redispatch model n#
Next, based on the market outcome with two bidding zones m, we build a secondary redispatch market n that rectifies transmission constraints through curtailment and ramping up/down thermal generators.
First, we fix the dispatch of generators to the results from the market simulation. (For simplicity, this example disregards storage units.)
[10]:
p = m.generators_t.p / m.generators.p_nom
n.generators_t.p_min_pu = p
n.generators_t.p_max_pu = p
Then, we add generators bidding into redispatch market using the following assumptions:
All generators can reduce their dispatch to zero. This includes also curtailment of renewables.
All generators can increase their dispatch to their available/nominal capacity.
No changes to the marginal costs, i.e. reducing dispatch lowers costs.
With these settings, the 2-stage market should result in the same cost as the nodal market.
[11]:
g_up = n.generators.copy()
g_down = n.generators.copy()
g_up.index = g_up.index.map(lambda x: x + " ramp up")
g_down.index = g_down.index.map(lambda x: x + " ramp down")
up = (
as_dense(m, "Generator", "p_max_pu") * m.generators.p_nom - m.generators_t.p
).clip(0) / m.generators.p_nom
down = -m.generators_t.p / m.generators.p_nom
up.columns = up.columns.map(lambda x: x + " ramp up")
down.columns = down.columns.map(lambda x: x + " ramp down")
n.add("Generator", g_up.index, p_max_pu=up, **g_up.drop("p_max_pu", axis=1))
n.add(
"Generator",
g_down.index,
p_min_pu=down,
p_max_pu=0,
**g_down.drop(["p_max_pu", "p_min_pu"], axis=1),
);
Now, let’s solve the redispatch market:
[12]:
n.optimize()
WARNING:pypsa.consistency:The following transformers have zero r, which could break the linear load flow:
Index(['2', '5', '10', '12', '13', '15', '18', '20', '22', '24', '26', '30',
'32', '37', '42', '46', '52', '56', '61', '68', '69', '74', '78', '86',
'87', '94', '95', '96', '99', '100', '104', '105', '106', '107', '117',
'120', '123', '124', '125', '128', '129', '138', '143', '156', '157',
'159', '160', '165', '184', '191', '195', '201', '220', '231', '232',
'233', '236', '247', '248', '250', '251', '252', '261', '263', '264',
'267', '272', '279', '281', '282', '292', '303', '307', '308', '312',
'315', '317', '322', '332', '334', '336', '338', '351', '353', '360',
'362', '382', '384', '385', '391', '403', '404', '413', '421', '450',
'458'],
dtype='object', name='Transformer')
INFO:linopy.model: Solve problem using Highs solver
INFO:linopy.io: Writing time: 0.12s
INFO:linopy.constants: Optimization successful:
Status: ok
Termination condition: optimal
Solution: 5331 primals, 11649 duals
Objective: 3.01e+05
Solver model: available
Solver message: optimal
INFO:pypsa.optimization.optimize:The shadow-prices of the constraints Generator-fix-p-lower, Generator-fix-p-upper, Line-fix-s-lower, Line-fix-s-upper, Transformer-fix-s-lower, Transformer-fix-s-upper, StorageUnit-fix-p_dispatch-lower, StorageUnit-fix-p_dispatch-upper, StorageUnit-fix-p_store-lower, StorageUnit-fix-p_store-upper, StorageUnit-fix-state_of_charge-lower, StorageUnit-fix-state_of_charge-upper, Kirchhoff-Voltage-Law, StorageUnit-energy_balance were not assigned to the network.
Running HiGHS 1.10.0 (git hash: fd86653): Copyright (c) 2025 HiGHS under MIT licence terms
LP linopy-problem-1vjtuu4u has 11649 rows; 5331 cols; 19486 nonzeros
Coefficient ranges:
Matrix [1e-02, 2e+02]
Cost [3e+00, 1e+02]
Bound [0e+00, 0e+00]
RHS [2e-19, 6e+03]
Presolving model
817 rows, 2285 cols, 5251 nonzeros 0s
560 rows, 2020 cols, 4873 nonzeros 0s
539 rows, 1358 cols, 4149 nonzeros 0s
Dependent equations search running on 527 equations with time limit of 1000.00s
Dependent equations search removed 0 rows and 0 nonzeros in 0.00s (limit = 1000.00s)
527 rows, 1341 cols, 4192 nonzeros 0s
Presolve : Reductions: rows 527(-11122); columns 1341(-3990); elements 4192(-15294)
Solving the presolved LP
Using EKK dual simplex solver - serial
Iteration Objective Infeasibilities num(sum)
0 0.0000000000e+00 Ph1: 0(0) 0s
620 3.0120938233e+05 Pr: 0(0) 0s
Solving the original LP from the solution after postsolve
Model name : linopy-problem-1vjtuu4u
Model status : Optimal
Simplex iterations: 620
Objective value : 3.0120938232e+05
Relative P-D gap : 7.1501207472e-15
HiGHS run time : 0.05
Writing the solution to /tmp/linopy-solve-hz25avcl.sol
[12]:
('ok', 'optimal')
And, as expected, the costs are the same as for the nodal market: 301 k€.
Now, we can plot both the market results of the 2 bidding zone market and the redispatch results:
[13]:
fig, axs = plt.subplots(
1, 3, figsize=(20, 10), subplot_kw={"projection": ccrs.AlbersEqualArea()}
)
market = (
n.generators_t.p[m.generators.index]
.T.squeeze()
.groupby(n.generators.bus)
.sum()
.div(2e4)
)
n.plot(ax=axs[0], bus_sizes=market, title="2 bidding zones market simulation")
redispatch_up = (
n.generators_t.p.filter(like="ramp up")
.T.squeeze()
.groupby(n.generators.bus)
.sum()
.div(2e4)
)
n.plot(
ax=axs[1], bus_sizes=redispatch_up, bus_colors="blue", title="Redispatch: ramp up"
)
redispatch_down = (
n.generators_t.p.filter(like="ramp down")
.T.squeeze()
.groupby(n.generators.bus)
.sum()
.div(-2e4)
)
n.plot(
ax=axs[2],
bus_sizes=redispatch_down,
bus_colors="red",
title="Redispatch: ramp down / curtail",
);
/tmp/ipykernel_3743/1476626274.py:12: DeprecatedWarning: plot is deprecated. Use `n.plot.map()` as a drop-in replacement instead.
n.plot(ax=axs[0], bus_sizes=market, title="2 bidding zones market simulation")
/tmp/ipykernel_3743/1476626274.py:21: DeprecatedWarning: plot is deprecated. Use `n.plot.map()` as a drop-in replacement instead.
n.plot(
/tmp/ipykernel_3743/1476626274.py:32: DeprecatedWarning: plot is deprecated. Use `n.plot.map()` as a drop-in replacement instead.
n.plot(
We can also read out the final dispatch of each generator:
[14]:
grouper = n.generators.index.str.split(" ramp", expand=True).get_level_values(0)
n.generators_t.p.groupby(grouper, axis=1).sum().squeeze()
/tmp/ipykernel_3743/2204001103.py:3: FutureWarning: DataFrame.groupby with axis=1 is deprecated. Do `frame.T.groupby(...)` without axis instead.
n.generators_t.p.groupby(grouper, axis=1).sum().squeeze()
[14]:
1 Gas 0.000000
1 Hard Coal 0.000000
1 Solar 11.326192
1 Wind Onshore 1.754382
100_220kV Solar 14.913326
...
98 Wind Onshore 71.451646
99_220kV Gas 0.000000
99_220kV Hard Coal 0.000000
99_220kV Solar 8.246606
99_220kV Wind Onshore 3.432939
Name: 2011-01-01 12:00:00, Length: 1423, dtype: float64
Changing bidding strategies in redispatch market#
We can also formulate other bidding strategies or compensation mechanisms for the redispatch market.
For example, that ramping up a generator is twice as expensive.
[15]:
n.generators.loc[n.generators.index.str.contains("ramp up"), "marginal_cost"] *= 2
Or that generators need to be compensated for curtailing them or ramping them down at 50% of their marginal cost.
[16]:
n.generators.loc[n.generators.index.str.contains("ramp down"), "marginal_cost"] *= -0.5
In this way, the outcome should be more expensive than the ideal nodal market:
[17]:
n.optimize()
WARNING:pypsa.consistency:The following transformers have zero r, which could break the linear load flow:
Index(['2', '5', '10', '12', '13', '15', '18', '20', '22', '24', '26', '30',
'32', '37', '42', '46', '52', '56', '61', '68', '69', '74', '78', '86',
'87', '94', '95', '96', '99', '100', '104', '105', '106', '107', '117',
'120', '123', '124', '125', '128', '129', '138', '143', '156', '157',
'159', '160', '165', '184', '191', '195', '201', '220', '231', '232',
'233', '236', '247', '248', '250', '251', '252', '261', '263', '264',
'267', '272', '279', '281', '282', '292', '303', '307', '308', '312',
'315', '317', '322', '332', '334', '336', '338', '351', '353', '360',
'362', '382', '384', '385', '391', '403', '404', '413', '421', '450',
'458'],
dtype='object', name='Transformer')
INFO:linopy.model: Solve problem using Highs solver
INFO:linopy.io: Writing time: 0.12s
INFO:linopy.constants: Optimization successful:
Status: ok
Termination condition: optimal
Solution: 5331 primals, 11649 duals
Objective: 4.99e+05
Solver model: available
Solver message: optimal
INFO:pypsa.optimization.optimize:The shadow-prices of the constraints Generator-fix-p-lower, Generator-fix-p-upper, Line-fix-s-lower, Line-fix-s-upper, Transformer-fix-s-lower, Transformer-fix-s-upper, StorageUnit-fix-p_dispatch-lower, StorageUnit-fix-p_dispatch-upper, StorageUnit-fix-p_store-lower, StorageUnit-fix-p_store-upper, StorageUnit-fix-state_of_charge-lower, StorageUnit-fix-state_of_charge-upper, Kirchhoff-Voltage-Law, StorageUnit-energy_balance were not assigned to the network.
Running HiGHS 1.10.0 (git hash: fd86653): Copyright (c) 2025 HiGHS under MIT licence terms
LP linopy-problem-ucgr9vds has 11649 rows; 5331 cols; 19486 nonzeros
Coefficient ranges:
Matrix [1e-02, 2e+02]
Cost [2e+00, 2e+02]
Bound [0e+00, 0e+00]
RHS [2e-19, 6e+03]
Presolving model
817 rows, 2277 cols, 5243 nonzeros 0s
558 rows, 2004 cols, 4855 nonzeros 0s
536 rows, 1350 cols, 4138 nonzeros 0s
Dependent equations search running on 524 equations with time limit of 1000.00s
Dependent equations search removed 0 rows and 0 nonzeros in 0.00s (limit = 1000.00s)
524 rows, 1333 cols, 4181 nonzeros 0s
Presolve : Reductions: rows 524(-11125); columns 1333(-3998); elements 4181(-15305)
Solving the presolved LP
Using EKK dual simplex solver - serial
Iteration Objective Infeasibilities num(sum)
0 0.0000000000e+00 Ph1: 0(0) 0s
628 4.9929741194e+05 Pr: 0(0) 0s
Solving the original LP from the solution after postsolve
Model name : linopy-problem-ucgr9vds
Model status : Optimal
Simplex iterations: 628
Objective value : 4.9929741194e+05
Relative P-D gap : 1.6402684441e-13
HiGHS run time : 0.04
Writing the solution to /tmp/linopy-solve-bllpexiu.sol
[17]:
('ok', 'optimal')
Costs are now 502 k€ compared to 301 k€.