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/v0.26.2/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 v0.26.2. 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/v0.26.2/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')
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
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-82enqrq5.lp -solve -solu /tmp/linopy-solve-3fyau868.sol (default strategy 1)
Option for printingOptions changed from normal to all
Presolve 629 (-5328) rows, 1091 (-1394) columns and 3871 (-7077) elements
Perturbing problem by 0.001% of 2769.2736 - largest nonzero change 0.00099220524 ( 0.0061979697%) - largest zero change 0.00098939989
0 Obj -9.5083027 Primal inf 1298365.2 (581)
87 Obj -9.2453851 Primal inf 736836.08 (538)
174 Obj -9.1687351 Primal inf 885985.69 (529)
232 Obj -8.9230987 Primal inf 890466.24 (502)
300 Obj -7.9224648 Primal inf 643744.18 (467)
371 Obj -5.8404701 Primal inf 731238.9 (429)
444 Obj 3998.1369 Primal inf 777939.54 (327)
507 Obj 4000.1194 Primal inf 1823422.9 (359)
580 Obj 4389.4002 Primal inf 808502.75 (233)
659 Obj 151151.3 Primal inf 14901.518 (87)
746 Obj 297651.07 Primal inf 22921.947 (99)
773 Obj 301211.09
Optimal - objective value 301209.38
After Postsolve, objective 301209.38, infeasibilities - dual 0 (0), primal 0 (0)
Optimal objective 301209.3823 - 773 iterations time 0.092, Presolve 0.01
Total time (CPU seconds): 0.13 (Wallclock seconds): 0.13
[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)
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
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-3pb6q1km.lp -solve -solu /tmp/linopy-solve-3lawfelk.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 0.01
Total time (CPU seconds): 0.04 (Wallclock seconds): 0.04
[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')
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
INFO:linopy.model: Solve problem using Cbc solver
INFO:linopy.io: Writing time: 0.21s
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-5b_hzsgj.lp -solve -solu /tmp/linopy-solve-59gy0d7e.sol (default strategy 1)
Option for printingOptions changed from normal to all
Presolve 633 (-11016) rows, 1315 (-4016) columns and 4108 (-15378) elements
Perturbing problem by 0.001% of 2769.2736 - largest nonzero change 0.00096825899 ( 0.007452601%) - largest zero change 0.00096822029
0 Obj 195157.09 Primal inf 1314652.2 (583) Dual inf 9200.1216 (158)
87 Obj -9.7394613 Primal inf 769507.01 (549)
174 Obj -9.4561476 Primal inf 2469275.6 (525)
250 Obj -8.3893865 Primal inf 597062.41 (468)
337 Obj -6.6006646 Primal inf 486334.47 (398)
416 Obj 3996.7422 Primal inf 807858.84 (379)
498 Obj 4031.5058 Primal inf 230443.17 (253)
569 Obj 4033.2926 Primal inf 310267.74 (243)
639 Obj 14973.122 Primal inf 5825468.9 (327)
722 Obj 70659.306 Primal inf 2.8081791e+08 (158)
809 Obj 295159.29 Primal inf 2279.7702 (23)
838 Obj 301210.85
838 Obj 301209.38 Dual inf 3.0130458e-05 (4)
842 Obj 301209.38
Optimal - objective value 301209.38
After Postsolve, objective 301209.38, infeasibilities - dual 1520.2117 (103), primal 2.3109177e-05 (98)
Presolved model was optimal, full model needs cleaning up
0 Obj 301209.38 Primal inf 9.0634195e-07 (5) Dual inf 5.0000001e+08 (108)
End of values pass after 109 iterations
109 Obj 301209.38
Optimal - objective value 301209.38
Optimal objective 301209.3811 - 951 iterations time 0.122, Presolve 0.02
Total time (CPU seconds): 0.21 (Wallclock seconds): 0.26
[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/v0.26.2/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_4625/2204001103.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')
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.26.2/lib/python3.11/site-packages/xarray/core/utils.py:494: FutureWarning: The return type of `Dataset.dims` will be changed to return a set of dimension names in future, in order to be more consistent with `DataArray.dims`. To access a mapping from dimension names to lengths, please use `Dataset.sizes`.
warnings.warn(
INFO:linopy.model: Solve problem using Cbc solver
INFO:linopy.io: Writing time: 0.21s
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-2bvlxpdv.lp -solve -solu /tmp/linopy-solve-1jbxybw2.sol (default strategy 1)
Option for printingOptions changed from normal to all
Presolve 633 (-11016) rows, 1315 (-4016) columns and 4108 (-15378) elements
Perturbing problem by 0.001% of 5538.5472 - largest nonzero change 0.00056339837 ( 0.0022781192%) - largest zero change 0.00056201469
0 Obj 223389.6 Primal inf 1314652.2 (583)
87 Obj 223389.82 Primal inf 795599.81 (549)
174 Obj 223390.15 Primal inf 1476438 (528)
261 Obj 223392.49 Primal inf 5275117.6 (500)
328 Obj 223393.1 Primal inf 783413.83 (430)
414 Obj 230850.19 Primal inf 556826.21 (355)
493 Obj 231302.2 Primal inf 232154.96 (294)
559 Obj 231305.79 Primal inf 428362.91 (242)
630 Obj 231347.91 Primal inf 158291.47 (265)
717 Obj 234768.07 Primal inf 39148.79 (73)
804 Obj 423428.4 Primal inf 25017.61 (37)
856 Obj 479004.92
856 Obj 479003.13 Dual inf 0.00050851625 (6)
862 Obj 479003.12
Optimal - objective value 479003.12
After Postsolve, objective 479003.12, infeasibilities - dual 2806.5353 (92), primal 2.0127517e-05 (87)
Presolved model was optimal, full model needs cleaning up
0 Obj 479003.12 Primal inf 9.3552662e-07 (5) Dual inf 5.0000003e+08 (97)
End of values pass after 97 iterations
97 Obj 479003.12
Optimal - objective value 479003.12
Optimal objective 479003.1219 - 959 iterations time 0.122, Presolve 0.02
Total time (CPU seconds): 0.23 (Wallclock seconds): 0.26
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€.