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Redispatch Example with SciGRID network

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 pypsa
import matplotlib.pyplot as plt
import cartopy.crs as ccrs
from pypsa.descriptors import get_switchable_as_dense as as_dense

ERROR 1: PROJ: proj_create_from_database: Open of /home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/stable/share/proj failed

[2]:

solver = "cbc"

Load example network#

[3]:

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 v0.27.1. 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

[4]:

n = o.copy()  # for redispatch model
m = o.copy()  # for market model

[5]:

o.plot();

/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/stable/lib/python3.11/site-packages/cartopy/mpl/style.py:76: UserWarning: facecolor will have no effect as it has been defined as "never".
  warnings.warn('facecolor will have no effect as it has been '
../_images/examples_scigrid-redispatch_6_1.png

Solve original nodal market model o#

First, let us solve a nodal market using the original model o:

[6]:

o.optimize(solver_name=solver)

WARNING:pypsa.components: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')

WARNING:pypsa.components: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 Cbc solver

INFO:linopy.io: Writing time: 0.09s

INFO:linopy.solvers:Welcome to the CBC MILP Solver
Version: 2.10.10
Build Date: Apr 19 2023

command line - cbc -printingOptions all -import /tmp/linopy-problem-8x3_s1ef.lp -solve -solu /tmp/linopy-solve-qfpwjf77.sol (default strategy 1)
Option for printingOptions changed from normal to all
Presolve 625 (-5332) rows, 1084 (-1401) columns and 3764 (-7087) elements
Perturbing problem by 0.001% of 2769.2736 - largest nonzero change 0.0009679296 ( 0.0062544522%) - largest zero change 0.00094707222
0  Obj -10.397643 Primal inf 1419051.3 (577)
87  Obj -10.10201 Primal inf 708489.57 (542)
163  Obj -9.8784203 Primal inf 1206523.7 (522)
250  Obj -8.8949376 Primal inf 534905.44 (455)
323  Obj -7.3351024 Primal inf 541507.17 (418)
390  Obj -6.362348 Primal inf 1383812.5 (405)
466  Obj 3997.9403 Primal inf 657404.37 (359)
540  Obj 4033.5302 Primal inf 1136566.5 (286)
603  Obj 4035.7454 Primal inf 126582.34 (158)
690  Obj 186597.76 Primal inf 10289.876 (88)
777  Obj 300862.74 Primal inf 219.19098 (9)
786  Obj 301211.14
Optimal - objective value 301209.38
After Postsolve, objective 301209.38, infeasibilities - dual 24.116221 (1), primal 6.043627e-07 (1)
Presolved model was optimal, full model needs cleaning up
0  Obj 301209.38 Dual inf 0.24116211 (1)
End of values pass after 1 iterations
1  Obj 301209.38
Optimal - objective value 301209.38
Optimal objective 301209.3823 - 787 iterations time 0.112, Presolve 0.01
Total time (CPU seconds):       0.15   (Wallclock seconds):       0.13



INFO:linopy.constants: Optimization successful:
Status: ok
Termination condition: optimal
Solution: 2485 primals, 5957 duals
Objective: 3.01e+05
Solver model: not available
Solver message: Optimal - objective value 301209.38232509



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.

[6]:

('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.

[7]:

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.

[8]:

for c in m.iterate_components(m.one_port_components):
    c.df.bus = c.df.bus.map(zones)

for c in m.iterate_components(m.branch_components):
    c.df.bus0 = c.df.bus0.map(zones)
    c.df.bus1 = c.df.bus1.map(zones)
    internal = c.df.bus0 == c.df.bus1
    m.mremove(c.name, c.df.loc[internal].index)

m.mremove("Bus", m.buses.index)
m.madd("Bus", ["North", "South"]);

Now, we can solve the coupled market with two bidding zones.

[9]:

m.optimize(solver_name=solver)

INFO:linopy.model: Solve problem using Cbc solver

INFO:linopy.io: Writing time: 0.07s

INFO:linopy.solvers:Welcome to the CBC MILP Solver
Version: 2.10.10
Build Date: Apr 19 2023

command line - cbc -printingOptions all -import /tmp/linopy-problem-q8qmax_m.lp -solve -solu /tmp/linopy-solve-7ahzsllj.sol (default strategy 1)
Option for printingOptions changed from normal to all
Presolve 40 (-3145) rows, 410 (-1151) columns and 487 (-4342) elements
Perturbing problem by 0.001% of 212.59539 - largest nonzero change 0.00017578427 ( 0.0036987348%) - largest zero change 0.00015445146
0  Obj 0 Primal inf 11285.222 (1)
48  Obj 184184.9 Primal inf 1700.1029 (24)
86  Obj 213988.73
Optimal - objective value 213988.69
After Postsolve, objective 213988.69, infeasibilities - dual 0 (0), primal 0 (0)
Optimal objective 213988.686 - 86 iterations time 0.012, Presolve 0.00
Total time (CPU seconds):       0.03   (Wallclock seconds):       0.03



INFO:linopy.constants: Optimization successful:
Status: ok
Termination condition: optimal
Solution: 1561 primals, 3185 duals
Objective: 2.14e+05
Solver model: not available
Solver message: Optimal - objective value 213988.68595810



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.

[9]:

('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:

[10]:

m.buses_t.marginal_price

[10]:
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.)

[11]:

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.

[12]:

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.madd("Generator", g_up.index, p_max_pu=up, **g_up.drop("p_max_pu", axis=1))

n.madd(
    "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:

[13]:

n.optimize(solver_name=solver)

WARNING:pypsa.components: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')

WARNING:pypsa.components: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 Cbc solver

INFO:linopy.io: Writing time: 0.12s

INFO:linopy.solvers:Welcome to the CBC MILP Solver
Version: 2.10.10
Build Date: Apr 19 2023

command line - cbc -printingOptions all -import /tmp/linopy-problem-g0njeiva.lp -solve -solu /tmp/linopy-solve-mymgcr33.sol (default strategy 1)
Option for printingOptions changed from normal to all
Presolve 628 (-11021) rows, 1323 (-4008) columns and 4019 (-15370) elements
Perturbing problem by 0.001% of 2769.2736 - largest nonzero change 0.00099864482 ( 0.0069710271%) - largest zero change 0.00099527462
0  Obj 195156.47 Primal inf 1442369.2 (579) Dual inf 9173.8355 (158)
87  Obj -9.9640933 Primal inf 743063.34 (543)
172  Obj -9.6527524 Primal inf 886165.45 (512)
251  Obj -9.0914629 Primal inf 1216289.6 (484)
338  Obj -7.5861179 Primal inf 2278115.9 (448)
425  Obj 3997.4979 Primal inf 20922493 (384)
489  Obj 3998.9378 Primal inf 820337.05 (305)
563  Obj 4034.4114 Primal inf 2233760 (251)
624  Obj 4036.6913 Primal inf 111976.57 (101)
711  Obj 161081.73 Primal inf 16356.209 (81)
795  Obj 301210.73
795  Obj 301209.38 Dual inf 6.0152273e-05 (3)
798  Obj 301209.38
Optimal - objective value 301209.38
After Postsolve, objective 301209.38, infeasibilities - dual 1508.3963 (101), primal 2.2913148e-05 (96)
Presolved model was optimal, full model needs cleaning up
0  Obj 301209.38 Primal inf 7.8549923e-07 (4) Dual inf 4.0000001e+08 (105)
End of values pass after 105 iterations
105  Obj 301209.38
Optimal - objective value 301209.38
Optimal objective 301209.3811 - 903 iterations time 0.102, Presolve 0.03
Total time (CPU seconds):       0.20   (Wallclock seconds):       0.17



INFO:linopy.constants: Optimization successful:
Status: ok
Termination condition: optimal
Solution: 5331 primals, 11649 duals
Objective: 3.01e+05
Solver model: not available
Solver message: Optimal - objective value 301209.38114435



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.

[13]:

('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:

[14]:

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/conda/stable/lib/python3.11/site-packages/cartopy/mpl/style.py:76: UserWarning: facecolor will have no effect as it has been defined as "never".
  warnings.warn('facecolor will have no effect as it has been '
../_images/examples_scigrid-redispatch_30_1.png

We can also read out the final dispatch of each generator:

[15]:

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_4984/2204001103.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()

[15]:

1 Gas                     0.000000
1 Hard Coal               0.000000
1 Solar                  11.326192
1 Wind Onshore            1.754375
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.

[16]:

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.

[17]:

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:

[18]:

n.optimize(solver_name=solver)

WARNING:pypsa.components: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')

WARNING:pypsa.components: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 Cbc solver

INFO:linopy.io: Writing time: 0.12s

INFO:linopy.solvers:Welcome to the CBC MILP Solver
Version: 2.10.10
Build Date: Apr 19 2023

command line - cbc -printingOptions all -import /tmp/linopy-problem-5pnnr59_.lp -solve -solu /tmp/linopy-solve-nxmms5vd.sol (default strategy 1)
Option for printingOptions changed from normal to all
Presolve 628 (-11021) rows, 1323 (-4008) columns and 4019 (-15370) elements
Perturbing problem by 0.001% of 5538.5472 - largest nonzero change 0.00072205682 ( 0.0022475848%) - largest zero change 0.00072046897
0  Obj 223389.27 Primal inf 1442369.2 (579)
87  Obj 223389.75 Primal inf 743985.17 (543)
164  Obj 223389.94 Primal inf 1118826.3 (531)
251  Obj 223392.06 Primal inf 1145756 (492)
326  Obj 223393.59 Primal inf 600728.19 (398)
398  Obj 223394.61 Primal inf 10054517 (468)
465  Obj 230852.15 Primal inf 999511.89 (334)
536  Obj 231304.24 Primal inf 132137.17 (231)
599  Obj 231345.83 Primal inf 433818.2 (323)
673  Obj 231755.17 Primal inf 65392.774 (135)
760  Obj 421715.2 Primal inf 1662.3158 (42)
815  Obj 479005.31
815  Obj 479003.13 Dual inf 0.00037998467 (8)
823  Obj 479003.12
Optimal - objective value 479003.12
After Postsolve, objective 479003.12, infeasibilities - dual 2801.4497 (90), primal 1.9814769e-05 (85)
Presolved model was optimal, full model needs cleaning up
0  Obj 479003.12 Primal inf 7.8549877e-07 (4) Dual inf 4.0000003e+08 (94)
End of values pass after 94 iterations
94  Obj 479003.12
Optimal - objective value 479003.12
Optimal objective 479003.1219 - 917 iterations time 0.112, Presolve 0.02
Total time (CPU seconds):       0.21   (Wallclock seconds):       0.17



INFO:linopy.constants: Optimization successful:
Status: ok
Termination condition: optimal
Solution: 5331 primals, 11649 duals
Objective: 4.79e+05
Solver model: not available
Solver message: Optimal - objective value 479003.12190570



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.

[18]:

('ok', 'optimal')

Costs are now 502 k€ compared to 301 k€.

Contents