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 v0.33.0. 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();
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/envs/latest/lib/python3.13/site-packages/cartopy/mpl/feature_artist.py:144: UserWarning: facecolor will have no effect as it has been defined as "never".
warnings.warn('facecolor will have no effect as it has been '

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 1.9.0 (git hash: fa40bdf): Copyright (c) 2024 HiGHS under MIT licence terms
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
557 rows, 2015 cols, 4868 nonzeros 0s
533 rows, 1352 cols, 4130 nonzeros 0s
521 rows, 1335 cols, 4173 nonzeros 0s
Presolve : Reductions: rows 521(-5436); columns 1335(-1150); elements 4173(-6775)
Solving the presolved LP
Using EKK dual simplex solver - serial
Iteration Objective Infeasibilities num(sum)
0 -2.2066015286e-01 Pr: 483(2.82493e+06) 0s
621 3.0120938233e+05 Pr: 0(0) 0s
Solving the original LP from the solution after postsolve
Model name : linopy-problem-ldp8_8_l
Model status : Optimal
Simplex iterations: 621
Objective value : 3.0120938233e+05
Relative P-D gap : 1.9324650668e-16
HiGHS run time : 0.04
Writing the solution to /tmp/linopy-solve-4dx9yn59.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 1.9.0 (git hash: fa40bdf): Copyright (c) 2024 HiGHS under MIT licence terms
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
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-tdu5u2nu
Model status : Optimal
Simplex iterations: 42
Objective value : 2.1398868596e+05
Relative P-D gap : 6.2562943224e-15
HiGHS run time : 0.00
Writing the solution to /tmp/linopy-solve-yhdwv0mt.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 1.9.0 (git hash: fa40bdf): Copyright (c) 2024 HiGHS under MIT licence terms
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
558 rows, 2018 cols, 4874 nonzeros 0s
537 rows, 1356 cols, 4142 nonzeros 0s
525 rows, 1339 cols, 4185 nonzeros 0s
Presolve : Reductions: rows 525(-11124); columns 1339(-3992); elements 4185(-15301)
Solving the presolved LP
Using EKK dual simplex solver - serial
Iteration Objective Infeasibilities num(sum)
0 0.0000000000e+00 Ph1: 0(0) 0s
628 3.0120938233e+05 Pr: 0(0); Du: 0(8.88178e-16) 0s
Solving the original LP from the solution after postsolve
Model name : linopy-problem-erdngt9m
Model status : Optimal
Simplex iterations: 628
Objective value : 3.0120938232e+05
Relative P-D gap : 7.1501207472e-15
HiGHS run time : 0.04
Writing the solution to /tmp/linopy-solve-iyqf_hjw.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",
);
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/envs/latest/lib/python3.13/site-packages/cartopy/mpl/feature_artist.py:144: UserWarning: facecolor will have no effect as it has been defined as "never".
warnings.warn('facecolor will have no effect as it has been '
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/envs/latest/lib/python3.13/site-packages/cartopy/mpl/feature_artist.py:144: UserWarning: facecolor will have no effect as it has been defined as "never".
warnings.warn('facecolor will have no effect as it has been '
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/envs/latest/lib/python3.13/site-packages/cartopy/mpl/feature_artist.py:144: UserWarning: facecolor will have no effect as it has been defined as "never".
warnings.warn('facecolor will have no effect as it has been '

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_6364/2204001103.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 1.9.0 (git hash: fa40bdf): Copyright (c) 2024 HiGHS under MIT licence terms
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
556 rows, 2002 cols, 4856 nonzeros 0s
534 rows, 1348 cols, 4131 nonzeros 0s
522 rows, 1331 cols, 4174 nonzeros 0s
Presolve : Reductions: rows 522(-11127); columns 1331(-4000); elements 4174(-15312)
Solving the presolved LP
Using EKK dual simplex solver - serial
Iteration Objective Infeasibilities num(sum)
0 0.0000000000e+00 Ph1: 0(0) 0s
647 4.9929741194e+05 Pr: 0(0); Du: 0(9.9476e-14) 0s
Solving the original LP from the solution after postsolve
Model name : linopy-problem-6katkvxr
Model status : Optimal
Simplex iterations: 647
Objective value : 4.9929741194e+05
Relative P-D gap : 1.6402684441e-13
HiGHS run time : 0.04
Writing the solution to /tmp/linopy-solve-5c030s6i.sol
[17]:
('ok', 'optimal')
Costs are now 502 k€ compared to 301 k€.