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/v0.27.1/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/v0.27.1/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 '
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: 0.1s
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-jrksg274.lp -solve -solu /tmp/linopy-solve-av3_q3lc.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 0.02
Total time (CPU seconds): 0.16 (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-ec6t80_1.lp -solve -solu /tmp/linopy-solve-chrl14jp.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 0.002, Presolve 0.00
Total time (CPU seconds): 0.05 (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: 0.13s
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-rkf79nra.lp -solve -solu /tmp/linopy-solve-10an_j39.sol (default strategy 1)
Option for printingOptions changed from normal to all
Presolve 628 (-11021) rows, 1318 (-4013) columns and 4014 (-15375) elements
Perturbing problem by 0.001% of 2769.2736 - largest nonzero change 0.00099370588 ( 0.0068145073%) - largest zero change 0.0009911424
0 Obj 195156.62 Primal inf 1442369.2 (579) Dual inf 9173.8355 (158)
87 Obj -9.8027016 Primal inf 738598.23 (543)
169 Obj -9.5907459 Primal inf 1183266.9 (528)
245 Obj -8.7911062 Primal inf 641578.99 (478)
332 Obj -7.2620767 Primal inf 651657.27 (441)
419 Obj -5.3996339 Primal inf 500331.94 (340)
500 Obj 3998.6159 Primal inf 283169.7 (278)
569 Obj 4033.6593 Primal inf 479950.42 (260)
650 Obj 60337.23 Primal inf 125906.43 (186)
737 Obj 179405.15 Primal inf 215205.02 (159)
807 Obj 301210.66
807 Obj 301209.38 Dual inf 7.614291e-05 (4)
811 Obj 301209.38
Optimal - objective value 301209.38
After Postsolve, objective 301209.38, infeasibilities - dual 1544.6829 (105), primal 2.3057434e-05 (98)
Presolved model was optimal, full model needs cleaning up
0 Obj 301209.38 Primal inf 1.094664e-06 (7) Dual inf 7.0000001e+08 (112)
End of values pass after 113 iterations
113 Obj 301209.38
Optimal - objective value 301209.38
Optimal objective 301209.3811 - 924 iterations time 0.112, Presolve 0.03
Total time (CPU seconds): 0.20 (Wallclock seconds): 0.16
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/v0.27.1/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 '
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_4987/2204001103.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: 0.13s
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-ik1jx4mn.lp -solve -solu /tmp/linopy-solve-shwjbpvw.sol (default strategy 1)
Option for printingOptions changed from normal to all
Presolve 628 (-11021) rows, 1318 (-4013) columns and 4014 (-15375) elements
Perturbing problem by 0.001% of 5538.5472 - largest nonzero change 0.00072205682 ( 0.0021533677%) - largest zero change 0.00066021858
0 Obj 223389.67 Primal inf 1442369.2 (579)
87 Obj 223390.08 Primal inf 746208.68 (542)
174 Obj 223390.58 Primal inf 586052.62 (492)
256 Obj 223392.87 Primal inf 572289.43 (456)
343 Obj 223424.35 Primal inf 385360.71 (380)
408 Obj 223425.95 Primal inf 1187674.6 (366)
484 Obj 230810.63 Primal inf 1256511.4 (298)
571 Obj 230814.89 Primal inf 1260910.9 (334)
640 Obj 230856.66 Primal inf 411349.68 (307)
727 Obj 305316.45 Primal inf 8008.911 (59)
811 Obj 479005.52
811 Obj 479003.13 Dual inf 0.00042533515 (10)
822 Obj 479003.12
Optimal - objective value 479003.12
After Postsolve, objective 479003.12, infeasibilities - dual 2875.6307 (94), primal 2.032744e-05 (88)
Presolved model was optimal, full model needs cleaning up
0 Obj 479003.12 Primal inf 1.0946654e-06 (7) Dual inf 7.0000003e+08 (101)
End of values pass after 101 iterations
101 Obj 479003.12
Optimal - objective value 479003.12
Optimal objective 479003.1219 - 923 iterations time 0.112, Presolve 0.03
Total time (CPU seconds): 0.21 (Wallclock seconds): 0.16
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€.