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

[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 v0.25.1. 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/latest/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: 0.14s
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.

Welcome to the CBC MILP Solver
Version: 2.10.10
Build Date: Apr 19 2023

command line - cbc -printingOptions all -import /tmp/linopy-problem-vrs0tvpm.lp -solve -solu /tmp/linopy-solve-u74uj7m4.sol (default strategy 1)
Option for printingOptions changed from normal to all
Presolve 624 (-5333) rows, 1086 (-1399) columns and 3986 (-7065) elements
Perturbing problem by 0.001% of 2348.6084 - largest nonzero change 0.00098110969 ( 0.0055657572%) - largest zero change 0.00097928235
0  Obj -11.980079 Primal inf 1414890.7 (576)
87  Obj -11.980079 Primal inf 864423.34 (545)
173  Obj -11.444823 Primal inf 854671.97 (509)
249  Obj -10.197853 Primal inf 561782.07 (468)
334  Obj -7.637002 Primal inf 760484.32 (423)
400  Obj -6.6157026 Primal inf 2895456.2 (438)
470  Obj -5.1372559 Primal inf 2880809 (402)
551  Obj 30.153704 Primal inf 994133.95 (260)
616  Obj 35.017327 Primal inf 82089.245 (140)
703  Obj 237073.58 Primal inf 4641.7063 (67)
772  Obj 301211.94
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 - 773 iterations time 0.112, Presolve 0.02
Total time (CPU seconds):       0.15   (Wallclock seconds):       0.12


[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: 0.11s
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.

Welcome to the CBC MILP Solver
Version: 2.10.10
Build Date: Apr 19 2023

command line - cbc -printingOptions all -import /tmp/linopy-problem-bt_9gbn3.lp -solve -solu /tmp/linopy-solve-qmvc4qn_.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


[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: 0.17s
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.

Welcome to the CBC MILP Solver
Version: 2.10.10
Build Date: Apr 19 2023

command line - cbc -printingOptions all -import /tmp/linopy-problem-1vpr64sd.lp -solve -solu /tmp/linopy-solve-a_8mbjq8.sol (default strategy 1)
Option for printingOptions changed from normal to all
Presolve 629 (-11020) rows, 1325 (-4006) columns and 4240 (-15349) elements
Perturbing problem by 0.001% of 2381.906 - largest nonzero change 0.00099500838 ( 0.0081366303%) - largest zero change 0.00099445828
0  Obj 195155.89 Primal inf 1435837.5 (579) Dual inf 7358.5276 (158)
87  Obj -10.942013 Primal inf 869638.52 (551)
161  Obj -10.555108 Primal inf 1724066 (529)
248  Obj -9.3245471 Primal inf 1537085.1 (485)
335  Obj -8.3194314 Primal inf 856260.27 (461)
416  Obj -6.8537049 Primal inf 1010080.3 (416)
484  Obj 3998.335 Primal inf 3214286.5 (415)
564  Obj 4032.7257 Primal inf 1020760.2 (334)
644  Obj 4036.0121 Primal inf 126326.62 (141)
730  Obj 181744.37 Primal inf 14566.091 (90)
817  Obj 301165.01 Primal inf 2.708495 (7)
824  Obj 301211.34
824  Obj 301209.38 Dual inf 1.4139822e-05 (3)
827  Obj 301209.38
Optimal - objective value 301209.38
After Postsolve, objective 301209.38, infeasibilities - dual 1459.5747 (98), primal 2.1848586e-05 (90)
Presolved model was optimal, full model needs cleaning up
0  Obj 301209.38 Primal inf 1.659609e-07 (1) Dual inf 1.0000001e+08 (99)
End of values pass after 100 iterations
100  Obj 301209.38
Optimal - objective value 301209.38
Optimal objective 301209.3811 - 927 iterations time 0.092, Presolve 0.02
Total time (CPU seconds):       0.18   (Wallclock seconds):       0.17


[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/latest/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()

[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: 0.17s
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



Welcome to the CBC MILP Solver
Version: 2.10.10
Build Date: Apr 19 2023

command line - cbc -printingOptions all -import /tmp/linopy-problem-ci2oom35.lp -solve -solu /tmp/linopy-solve-tcdfbab7.sol (default strategy 1)
Option for printingOptions changed from normal to all
Presolve 629 (-11020) rows, 1325 (-4006) columns and 4240 (-15349) elements
Perturbing problem by 0.001% of 4763.8119 - largest nonzero change 0.000755846 ( 0.0022183461%) - largest zero change 0.00075574518
0  Obj 223384.26 Primal inf 1435837.5 (579)
87  Obj 223384.26 Primal inf 879409.87 (548)
159  Obj 223384.26 Primal inf 1728473.1 (525)
246  Obj 223386.04 Primal inf 1489346.3 (486)
327  Obj 223388.49 Primal inf 1586340.5 (484)
410  Obj 223391.4 Primal inf 885474.18 (419)
490  Obj 230849.32 Primal inf 468938.53 (306)
562  Obj 230894.8 Primal inf 1785240.6 (324)
641  Obj 230898.44 Primal inf 23223.643 (86)
728  Obj 378146.89 Primal inf 12217.673 (61)
798  Obj 479006.12
798  Obj 479003.13 Dual inf 8.9418704e-05 (4)
806  Obj 479003.12
Optimal - objective value 479003.12
After Postsolve, objective 479003.12, infeasibilities - dual 2705.9552 (87), primal 1.921637e-05 (80)
Presolved model was optimal, full model needs cleaning up
0  Obj 479003.12 Primal inf 1.659609e-07 (1) Dual inf 1.0000003e+08 (88)
End of values pass after 89 iterations
89  Obj 479003.12
Optimal - objective value 479003.12
Optimal objective 479003.1219 - 895 iterations time 0.112, Presolve 0.02
Total time (CPU seconds):       0.19   (Wallclock seconds):       0.16


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€.