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 pypsa
import numpy as np
import pandas as pd
import os
import matplotlib.pyplot as plt
import cartopy.crs as ccrs

%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 v0.22.1. 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 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/conda/latest/lib/python3.11/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/conda/latest/lib/python3.11/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/conda/latest/lib/python3.11/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/conda/latest/lib/python3.11/site-packages/cartopy/mpl/style.py:76: UserWarning: facecolor will have no effect as it has been defined as "never".
  warnings.warn('facecolor will have no effect as it has been '
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/latest/lib/python3.11/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)
../_images/examples_ac-dc-lopf_4_1.png
[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]:
attribute carrier slack_bus obj n_branches n_buses
SubNetwork
0 AC Manchester SubNetwork 0 3 3
1 DC Norwich DC SubNetwork 1 3 3
2 AC Frankfurt SubNetwork 2 1 2
3 AC Norway SubNetwork 3 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 capital_cost efficiency marginal_cost p_nom p_nom_extendable p_nom_min carrier control type ... shut_down_cost 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 p_nom_opt
Generator
Manchester Wind Manchester 2793.651603 1.000000 0.110000 80.0 True 100.0 wind Slack ... 0.0 0 0 1 0 NaN NaN 1.0 1.0 0.0
Manchester Gas Manchester 196.615168 0.350026 4.532368 50000.0 True 0.0 gas PQ ... 0.0 0 0 1 0 NaN NaN 1.0 1.0 0.0
Norway Wind Norway 2184.374796 1.000000 0.090000 100.0 True 100.0 wind Slack ... 0.0 0 0 1 0 NaN NaN 1.0 1.0 0.0
Norway Gas Norway 158.251250 0.356836 5.892845 20000.0 True 0.0 gas PQ ... 0.0 0 0 1 0 NaN NaN 1.0 1.0 0.0
Frankfurt Wind Frankfurt 2129.456122 1.000000 0.100000 110.0 True 100.0 wind Slack ... 0.0 0 0 1 0 NaN NaN 1.0 1.0 0.0
Frankfurt Gas Frankfurt 102.676953 0.351666 4.086322 80000.0 True 0.0 gas PQ ... 0.0 0 0 1 0 NaN NaN 1.0 1.0 0.0

6 rows × 30 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()
../_images/examples_ac-dc-lopf_13_0.png

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.lopf(pyomo=False);
INFO:pypsa.linopf:Prepare linear problem
INFO:pypsa.linopf:Total preparation time: 0.18s
INFO:pypsa.linopf:Solve linear problem using Glpk solver
INFO:pypsa.linopf:Optimization successful. Objective value: -3.47e+06

The objective is given by:

[11]:
network.objective
[11]:
-3474092.381

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]:
18440975.13727914

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()
../_images/examples_ac-dc-lopf_21_0.png

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()
../_images/examples_ac-dc-lopf_23_0.png

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()
../_images/examples_ac-dc-lopf_25_0.png

We can inspect futher 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 -250.8340 674.5810 -423.746 -317.9990
2015-01-01 01:00:00 315.0740 -116.7300 -198.344 -317.9990
2015-01-01 02:00:00 -285.2340 581.9690 -296.735 317.9990
2015-01-01 03:00:00 -85.7678 272.5560 -186.788 -317.9990
2015-01-01 04:00:00 317.3710 -79.7518 -237.619 -317.9990
2015-01-01 05:00:00 386.7500 -494.1970 107.447 -317.9990
2015-01-01 06:00:00 900.0000 -257.5220 -642.478 317.9990
2015-01-01 07:00:00 123.6790 971.9160 -1095.600 -86.8575
2015-01-01 08:00:00 244.7170 850.8790 -1095.600 317.9990
2015-01-01 09:00:00 820.0230 -86.8535 -733.169 -83.6841
[17]:
network.lines_t.p0
[17]:
Line 0 1 2 3 4 5 6
snapshot
2015-01-01 00:00:00 79.4736 -38.1015 -52.9713 -303.806 370.7750 -202.7300 -534.340
2015-01-01 01:00:00 -449.4640 787.0410 -211.2770 103.798 -12.9321 209.3610 -823.209
2015-01-01 02:00:00 -287.6790 414.1500 10.1573 -275.077 306.8920 280.9080 173.898
2015-01-01 03:00:00 -45.4730 234.4720 -34.0434 -119.811 152.7440 -232.7190 -743.788
2015-01-01 04:00:00 -73.2083 295.4240 -227.2010 90.170 10.4182 -240.1080 -883.817
2015-01-01 05:00:00 -594.4990 1198.0800 -125.9060 260.844 -233.3530 19.3581 -1030.850
2015-01-01 06:00:00 -661.2950 1378.4200 -632.3710 267.629 10.1069 -53.4469 319.387
2015-01-01 07:00:00 -383.7690 540.9090 -469.9270 -346.247 625.6690 393.7160 600.730
2015-01-01 08:00:00 -778.2810 1444.0700 -522.1170 -277.400 573.4790 229.2960 501.348
2015-01-01 09:00:00 -465.5760 899.5660 -632.3710 187.652 100.7980 78.6186 -248.568

…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 00:00:00 282.202756 -164.628564 -250.8340 -117.575440 -534.339378 -423.746 534.339153 0.003164 674.5810
2015-01-01 01:00:00 -658.825561 -577.680146 315.0740 1236.500376 -823.209334 -198.344 823.213894 -0.000047 -116.7300
2015-01-01 02:00:00 -568.586312 -133.242353 -285.2340 701.829124 173.897870 -296.735 -173.898928 0.000256 581.9690
2015-01-01 03:00:00 187.245855 -467.191739 -85.7678 279.945178 -743.787306 -186.788 743.788236 -0.000233 272.5560
2015-01-01 04:00:00 166.898831 -535.530858 317.3710 368.632241 -883.816781 -237.619 883.819245 -0.000073 -79.7518
2015-01-01 05:00:00 -613.858052 -1178.726266 386.7500 1792.586681 -1030.846687 107.447 1030.846757 -0.000349 -494.1970
2015-01-01 06:00:00 -607.847287 -1431.870681 900.0000 2039.722900 319.386410 -642.478 -319.386752 0.000035 -257.5220
2015-01-01 07:00:00 -777.485822 -147.192467 123.6790 924.675111 600.733959 -1095.600 -600.729766 0.001550 971.9160
2015-01-01 08:00:00 -1007.576264 -1214.776068 244.7170 2222.351918 501.351224 -1095.600 -501.347780 -0.000493 850.8790
2015-01-01 09:00:00 -544.194886 -820.947834 820.0230 1365.139414 -248.568192 -733.169 248.567354 0.000323 -86.8535