Note
You can download this example as a Jupyter notebook or start it in interactive mode.
Meshed AC-DC example#
This example has a 3-node AC network coupled via AC-DC converters to a 3-node DC network. There is also a single point-to-point DC using the Link component.
The data files for this example are in the examples folder of the github repository: PyPSA/PyPSA.
[1]:
import matplotlib.pyplot as plt
import pypsa
%matplotlib inline
plt.rc("figure", figsize=(8, 8))
[2]:
network = pypsa.examples.ac_dc_meshed(from_master=True)
WARNING:pypsa.io:Importing network from PyPSA version v0.17.1 while current version is v0.32.0. Read the release notes at https://pypsa.readthedocs.io/en/latest/release_notes.html to prepare your network for import.
INFO:pypsa.io:Imported network ac-dc-meshed.nc has buses, carriers, generators, global_constraints, lines, links, loads
[3]:
# get current type (AC or DC) of the lines from the buses
lines_current_type = network.lines.bus0.map(network.buses.carrier)
lines_current_type
[3]:
Line
0 AC
1 AC
2 DC
3 DC
4 DC
5 AC
6 AC
Name: bus0, dtype: object
[4]:
network.plot(
line_colors=lines_current_type.map(lambda ct: "r" if ct == "DC" else "b"),
title="Mixed AC (blue) - DC (red) network - DC (cyan)",
color_geomap=True,
jitter=0.3,
)
plt.tight_layout()
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/envs/latest/lib/python3.13/site-packages/cartopy/mpl/feature_artist.py:144: UserWarning: facecolor will have no effect as it has been defined as "never".
warnings.warn('facecolor will have no effect as it has been '
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/envs/latest/lib/python3.13/site-packages/cartopy/io/__init__.py:241: DownloadWarning: Downloading: https://naturalearth.s3.amazonaws.com/50m_physical/ne_50m_land.zip
warnings.warn(f'Downloading: {url}', DownloadWarning)
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/envs/latest/lib/python3.13/site-packages/cartopy/io/__init__.py:241: DownloadWarning: Downloading: https://naturalearth.s3.amazonaws.com/50m_physical/ne_50m_ocean.zip
warnings.warn(f'Downloading: {url}', DownloadWarning)
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/envs/latest/lib/python3.13/site-packages/cartopy/io/__init__.py:241: DownloadWarning: Downloading: https://naturalearth.s3.amazonaws.com/50m_cultural/ne_50m_admin_0_boundary_lines_land.zip
warnings.warn(f'Downloading: {url}', DownloadWarning)
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/envs/latest/lib/python3.13/site-packages/cartopy/io/__init__.py:241: DownloadWarning: Downloading: https://naturalearth.s3.amazonaws.com/50m_physical/ne_50m_coastline.zip
warnings.warn(f'Downloading: {url}', DownloadWarning)
[5]:
network.links.loc["Norwich Converter", "p_nom_extendable"] = False
We inspect the topology of the network. Therefore use the function determine_network_topology and inspect the subnetworks in network.sub_networks.
[6]:
network.determine_network_topology()
network.sub_networks["n_branches"] = [
len(sn.branches()) for sn in network.sub_networks.obj
]
network.sub_networks["n_buses"] = [len(sn.buses()) for sn in network.sub_networks.obj]
network.sub_networks
[6]:
| carrier | slack_bus | obj | n_branches | n_buses | |
|---|---|---|---|---|---|
| SubNetwork | |||||
| 0 | AC | Manchester | <pypsa.networks.SubNetwork object at 0x7fb11f1... | 3 | 3 |
| 1 | DC | Norwich DC | <pypsa.networks.SubNetwork object at 0x7fb11dc... | 3 | 3 |
| 2 | AC | Frankfurt | <pypsa.networks.SubNetwork object at 0x7fb11dc... | 1 | 2 |
| 3 | AC | Norway | <pypsa.networks.SubNetwork object at 0x7fb11dd... | 0 | 1 |
The network covers 10 time steps. These are given by the snapshots attribute.
[7]:
network.snapshots
[7]:
DatetimeIndex(['2015-01-01 00:00:00', '2015-01-01 01:00:00',
'2015-01-01 02:00:00', '2015-01-01 03:00:00',
'2015-01-01 04:00:00', '2015-01-01 05:00:00',
'2015-01-01 06:00:00', '2015-01-01 07:00:00',
'2015-01-01 08:00:00', '2015-01-01 09:00:00'],
dtype='datetime64[ns]', name='snapshot', freq=None)
There are 6 generators in the network, 3 wind and 3 gas. All are attached to buses:
[8]:
network.generators
[8]:
| bus | control | type | p_nom | p_nom_mod | p_nom_extendable | p_nom_min | p_nom_max | p_min_pu | p_max_pu | ... | min_up_time | min_down_time | up_time_before | down_time_before | ramp_limit_up | ramp_limit_down | ramp_limit_start_up | ramp_limit_shut_down | weight | p_nom_opt | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Generator | |||||||||||||||||||||
| Manchester Wind | Manchester | Slack | 80.0 | 0.0 | True | 100.0 | inf | 0.0 | 1.0 | ... | 0 | 0 | 1 | 0 | NaN | NaN | 1.0 | 1.0 | 1.0 | 0.0 | |
| Manchester Gas | Manchester | PQ | 50000.0 | 0.0 | True | 0.0 | inf | 0.0 | 1.0 | ... | 0 | 0 | 1 | 0 | NaN | NaN | 1.0 | 1.0 | 1.0 | 0.0 | |
| Norway Wind | Norway | Slack | 100.0 | 0.0 | True | 100.0 | inf | 0.0 | 1.0 | ... | 0 | 0 | 1 | 0 | NaN | NaN | 1.0 | 1.0 | 1.0 | 0.0 | |
| Norway Gas | Norway | PQ | 20000.0 | 0.0 | True | 0.0 | inf | 0.0 | 1.0 | ... | 0 | 0 | 1 | 0 | NaN | NaN | 1.0 | 1.0 | 1.0 | 0.0 | |
| Frankfurt Wind | Frankfurt | Slack | 110.0 | 0.0 | True | 100.0 | inf | 0.0 | 1.0 | ... | 0 | 0 | 1 | 0 | NaN | NaN | 1.0 | 1.0 | 1.0 | 0.0 | |
| Frankfurt Gas | Frankfurt | PQ | 80000.0 | 0.0 | True | 0.0 | inf | 0.0 | 1.0 | ... | 0 | 0 | 1 | 0 | NaN | NaN | 1.0 | 1.0 | 1.0 | 0.0 |
6 rows × 37 columns
We see that the generators have different capital and marginal costs. All of them have a p_nom_extendable set to True, meaning that capacities can be extended in the optimization.
The wind generators have a per unit limit for each time step, given by the weather potentials at the site.
[9]:
network.generators_t.p_max_pu.plot.area(subplots=True)
plt.tight_layout()
Alright now we know how the network looks like, where the generators and lines are. Now, let’s perform a optimization of the operation and capacities.
[10]:
network.optimize();
WARNING:pypsa.consistency:The following lines have carriers which are not defined:
Index(['0', '1', '2', '3', '4', '5', '6'], dtype='object', name='Line')
WARNING:pypsa.consistency:The following lines have zero x, which could break the linear load flow:
Index(['2', '3', '4'], dtype='object', name='Line')
WARNING:pypsa.consistency:The following lines have zero r, which could break the linear load flow:
Index(['0', '1', '5', '6'], dtype='object', name='Line')
WARNING:pypsa.consistency:The following sub_networks have carriers which are not defined:
Index(['0', '1', '2', '3'], dtype='object', name='SubNetwork')
WARNING:pypsa.consistency:The following buses have carriers which are not defined:
Index(['London', 'Norwich', 'Norwich DC', 'Manchester', 'Bremen', 'Bremen DC',
'Frankfurt', 'Norway', 'Norway DC'],
dtype='object', name='Bus')
WARNING:pypsa.consistency:The following links have carriers which are not defined:
Index(['Norwich Converter', 'Norway Converter', 'Bremen Converter', 'DC link'], dtype='object', name='Link')
INFO:linopy.model: Solve problem using Highs solver
INFO:linopy.io: Writing time: 0.06s
INFO:linopy.constants: Optimization successful:
Status: ok
Termination condition: optimal
Solution: 187 primals, 467 duals
Objective: -3.47e+06
Solver model: available
Solver message: optimal
INFO:pypsa.optimization.optimize:The shadow-prices of the constraints Generator-ext-p-lower, Generator-ext-p-upper, Line-ext-s-lower, Line-ext-s-upper, Link-fix-p-lower, Link-fix-p-upper, Link-ext-p-lower, Link-ext-p-upper, Kirchhoff-Voltage-Law were not assigned to the network.
Running HiGHS 1.9.0 (git hash: fa40bdf): Copyright (c) 2024 HiGHS under MIT licence terms
Coefficient ranges:
Matrix [1e-02, 1e+00]
Cost [9e-03, 3e+03]
Bound [2e+07, 2e+07]
RHS [9e-01, 1e+03]
Presolving model
371 rows, 186 cols, 890 nonzeros 0s
283 rows, 98 cols, 948 nonzeros 0s
283 rows, 98 cols, 948 nonzeros 0s
Presolve : Reductions: rows 283(-184); columns 98(-89); elements 948(-38)
Solving the presolved LP
Using EKK dual simplex solver - serial
Iteration Objective Infeasibilities num(sum)
0 -2.1204300613e+07 Pr: 110(90228.6); Du: 0(1.47603e-11) 0s
96 -3.4740941308e+06 Pr: 0(0); Du: 0(1.57124e-13) 0s
Solving the original LP from the solution after postsolve
Model name : linopy-problem-xmfd43g1
Model status : Optimal
Simplex iterations: 96
Objective value : -3.4740941308e+06
Relative P-D gap : 2.6807637892e-15
HiGHS run time : 0.00
Writing the solution to /tmp/linopy-solve-37x9ecwd.sol
The objective is given by:
[11]:
network.objective
[11]:
-3474094.1308449395
Why is this number negative? It considers the starting point of the optimization, thus the existent capacities given by network.generators.p_nom are taken into account.
The real system cost are given by
[12]:
network.objective + network.objective_constant
[12]:
18440973.387434203
The optimal capacities are given by p_nom_opt for generators, links and storages and s_nom_opt for lines.
Let’s look how the optimal capacities for the generators look like.
[13]:
network.generators.p_nom_opt.div(1e3).plot.bar(ylabel="GW", figsize=(8, 3))
plt.tight_layout()
Their production is again given as a time-series in network.generators_t.
[14]:
network.generators_t.p.div(1e3).plot.area(subplots=True, ylabel="GW")
plt.tight_layout()
What are the Locational Marginal Prices in the network. From the optimization these are given for each bus and snapshot.
[15]:
network.buses_t.marginal_price.mean(1).plot.area(figsize=(8, 3), ylabel="Euro per MWh")
plt.tight_layout()
We can inspect further quantities as the active power of AC-DC converters and HVDC link.
[16]:
network.links_t.p0
[16]:
| Link | Norwich Converter | Norway Converter | Bremen Converter | DC link |
|---|---|---|---|---|
| snapshot | ||||
| 2015-01-01 00:00:00 | -250.841318 | 674.584826 | -423.743508 | -317.997991 |
| 2015-01-01 01:00:00 | 315.068611 | -116.727192 | -198.341419 | -317.997991 |
| 2015-01-01 02:00:00 | 350.761618 | 581.970687 | -932.732306 | -317.997991 |
| 2015-01-01 03:00:00 | -85.772148 | 272.557949 | -186.785801 | -317.997991 |
| 2015-01-01 04:00:00 | 317.366721 | -79.749487 | -237.617234 | -317.997991 |
| 2015-01-01 05:00:00 | 386.747627 | -494.197717 | 107.450090 | -317.997991 |
| 2015-01-01 06:00:00 | 900.000000 | -257.520720 | -642.479280 | 317.997991 |
| 2015-01-01 07:00:00 | 123.677319 | 971.918845 | -1095.596165 | -86.858742 |
| 2015-01-01 08:00:00 | 244.715828 | 850.880337 | -1095.596165 | 317.997991 |
| 2015-01-01 09:00:00 | 820.022865 | -86.851803 | -733.171062 | -83.684817 |
[17]:
network.lines_t.p0
[17]:
| Line | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| snapshot | |||||||
| 2015-01-01 00:00:00 | 79.474931 | -38.105568 | -52.967153 | -303.808471 | 370.776355 | -202.726815 | -534.340860 |
| 2015-01-01 01:00:00 | -449.464018 | 787.037310 | -211.273022 | 103.795589 | -12.931603 | 209.362553 | -823.210906 |
| 2015-01-01 02:00:00 | -181.265945 | 520.561348 | -505.913540 | -155.151921 | 426.818766 | -248.676623 | 173.898185 |
| 2015-01-01 03:00:00 | -45.472529 | 234.470017 | -34.040733 | -119.812880 | 152.745069 | -232.717375 | -743.788495 |
| 2015-01-01 04:00:00 | -73.207796 | 295.420961 | -227.198461 | 90.168260 | 10.418773 | -240.105618 | -883.817538 |
| 2015-01-01 05:00:00 | -594.500052 | 1198.082901 | -125.903894 | 260.843733 | -233.353984 | 19.359009 | -1030.848768 |
| 2015-01-01 06:00:00 | -661.294714 | 1378.422245 | -632.371427 | 267.628573 | 10.107853 | -53.448436 | 319.386680 |
| 2015-01-01 07:00:00 | -383.768641 | 540.906725 | -469.925715 | -346.248396 | 625.670450 | 393.715939 | 600.728881 |
| 2015-01-01 08:00:00 | -778.280943 | 1444.069207 | -522.116240 | -277.400413 | 573.479924 | 229.294311 | 501.346379 |
| 2015-01-01 09:00:00 | -465.576406 | 899.565461 | -632.371427 | 187.651438 | 100.799635 | 78.617762 | -248.566847 |
…or the active power injection per bus.
[18]:
network.buses_t.p
[18]:
| Bus | London | Norwich | Norwich DC | Manchester | Bremen | Bremen DC | Frankfurt | Norway | Norway DC |
|---|---|---|---|---|---|---|---|---|---|
| snapshot | |||||||||
| 2015-01-01 00:00:00 | 282.201747 | -164.621247 | -250.841318 | -117.580500 | -534.340860 | -423.743508 | 534.340860 | 0.000000e+00 | 674.584826 |
| 2015-01-01 01:00:00 | -658.826571 | -577.674757 | 315.068611 | 1236.501328 | -823.210906 | -198.341419 | 823.210906 | 2.000888e-10 | -116.727192 |
| 2015-01-01 02:00:00 | 67.410679 | -769.237972 | 350.761618 | 701.827293 | 173.898185 | -932.732306 | -173.898185 | 0.000000e+00 | 581.970687 |
| 2015-01-01 03:00:00 | 187.244846 | -467.187392 | -85.772148 | 279.942546 | -743.788495 | -186.785801 | 743.788495 | -1.000444e-10 | 272.557949 |
| 2015-01-01 04:00:00 | 166.897822 | -535.526579 | 317.366721 | 368.628757 | -883.817538 | -237.617234 | 883.817538 | 3.999503e-10 | -79.749487 |
| 2015-01-01 05:00:00 | -613.859061 | -1178.723892 | 386.747627 | 1792.582954 | -1030.848768 | 107.450090 | 1030.848768 | 3.999503e-10 | -494.197717 |
| 2015-01-01 06:00:00 | -607.846278 | -1431.870681 | 900.000000 | 2039.716959 | 319.386680 | -642.479280 | -319.386680 | 2.999059e-10 | -257.520720 |
| 2015-01-01 07:00:00 | -777.484580 | -147.190786 | 123.677319 | 924.675366 | 600.728881 | -1095.596165 | -600.728881 | -3.999503e-10 | 971.918845 |
| 2015-01-01 08:00:00 | -1007.575254 | -1214.774896 | 244.715828 | 2222.350150 | 501.346379 | -1095.596165 | -501.346379 | 0.000000e+00 | 850.880337 |
| 2015-01-01 09:00:00 | -544.194169 | -820.947699 | 820.022865 | 1365.141868 | -248.566847 | -733.171062 | 248.566847 | 2.000888e-10 | -86.851803 |