Introduction to pypsa

Note

This material is mostly adapted from the following resources:

• Data Science for Energy System Modelling: Introduction to PyPSA

PyPSA stands for Python for Power System Analysis.

PyPSA is an open source Python package for simulating and optimising modern energy systems that include features such as

• conventional generators with unit commitment (ramp-up, ramp-down, start-up, shut-down),

• time-varying wind and solar generation,

• energy storage with efficiency losses and inflow/spillage for hydroelectricity

• coupling to other energy sectors (electricity, transport, heat, industry),

• conversion between energy carriers (e.g. electricity to hydrogen),

• transmission networks (AC, DC, other fuels)

PyPSA can be used for a variety of problem types (e.g. electricity market modelling, long-term investment planning, transmission network expansion planning), and is designed to scale well with large networks and long time series.

Compared to building power system by hand in linopy, PyPSA does the following things for you:

• manage data inputs

• build optimisation problem

• communicate with the solver

• retrieve and process optimisation results

• manage data outputs

Dependencies

• pandas for storing data about network components and time series

• numpy and scipy for linear algebra and sparse matrix calculations

• matplotlib and cartopy for plotting on a map

• networkx for network calculations

• linopy for handling optimisation problems

Note

Documentation for this package is available at https://pypsa.readthedocs.io.

Note

If you have not yet set up Python on your computer, you can execute this tutorial in your browser via Google Colab. Click on the rocket in the top right corner and launch “Colab”. If that doesn’t work download the .ipynb file and import it in Google Colab.

Then install the following packages by executing the following command in a Jupyter cell at the top of the notebook.

!pip install pypsa matplotlib cartopy highspy

Basic Structure

Component	Description
Network	Container for all components.
Bus	Node where components attach.
Carrier	Energy carrier or technology (e.g. electricity, hydrogen, gas, coal, oil, biomass, on-/offshore wind, solar). Can track properties such as specific carbon dioxide emissions or nice names and colors for plots.
Load	Energy consumer (e.g. electricity demand).
Generator	Generator (e.g. power plant, wind turbine, PV panel).
Line	Power distribution and transmission lines (overhead and cables).
Link	Links connect two buses with controllable energy flow, direction-control and losses. They can be used to model: HVDC links HVAC lines (neglecting KVL, only net transfer capacities (NTCs)) conversion between carriers (e.g. electricity to hydrogen in electrolysis)
StorageUnit	Storage with fixed nominal energy-to-power ratio.
Store	Storage with separately extendable energy capacity.
GlobalConstraint	Constraints affecting many components at once, such as emission limits.
	not used in this course
LineType	Standard line types.
Transformer	2-winding transformer.
TransformerType	Standard types of 2-winding transformer.
ShuntImpedance	Shunt.

Note

Links in the table lead to documentation for each component.

Warning

Per unit values of voltage and impedance are used internally for network calculations. It is assumed internally that the base power is 1 MW.

From structured data to optimisation

The design principle of PyPSA is that basically each component is associated with a set of variables and constraints that will be added to the optimisation model based on the input data stored for the components.

For an hourly electricity market simulation, PyPSA will solve an optimisation problem that looks like this

(1)\[\begin{equation} \min_{g_{i,s,t}; f_{\ell,t}; g_{i,r,t,\text{charge}}; g_{i,r,t,\text{discharge}}; e_{i,r,t}} \sum_s o_{s} g_{i,s,t} \end{equation}\]

such that

(2)\[\begin{align} 0 & \leq g_{i,s,t} \leq \hat{g}_{i,s,t} G_{i,s} & \text{generation limits : generator} \\ -P_\ell &\leq p_{\ell,t} \leq P_\ell & \text{transmission limits : line} \\ d_{i,t} &= \sum_s g_{i,s,t} + \sum_r g_{i,r,t,\text{discharge}} - \sum_r g_{i,r,t,\text{charge}} - \sum_\ell K_{i\ell} p_{\ell,t} & \text{KCL : bus} \\ 0 &=\sum_\ell C_{\ell c} x_\ell p_{\ell,t} & \text{KVL : cycles} \\ 0 & \leq g_{i,r,t,\text{discharge}} \leq G_{i,r,\text{discharge}}& \text{discharge limits : storage unit} \\ 0 & \leq g_{i,r,t,\text{charge}} \leq G_{i,r,\text{charge}} & \text{charge limits : storage unit} \\ 0 & \leq e_{i,r,t} \leq E_{i,r} & \text{energy limits : storage unit} \\ e_{i,r,t} &= \eta^0_{i,r,t} e_{i,r,t-1} + \eta^1_{i,r,t}g_{i,r,t,\text{charge}} - \frac{1}{\eta^2_{i,r,t}} g_{i,r,t,\text{discharge}} & \text{consistency : storage unit} \\ e_{i,r,0} & = e_{i,r,|T|-1} & \text{cyclicity : storage unit} \end{align}\]

Decision variables:

• \(g_{i,s,t}\) is the generator dispatch at bus \(i\), technology \(s\), time step \(t\),

• \(p_{\ell,t}\) is the power flow in line \(\ell\),

• \(g_{i,r,t,\text{dis-/charge}}\) denotes the charge and discharge of storage unit \(r\) at bus \(i\) and time step \(t\),

• \(e_{i,r,t}\) is the state of charge of storage \(r\) at bus \(i\) and time step \(t\).

Parameters:

• \(o_{i,s}\) is the marginal generation cost of technology \(s\) at bus \(i\),

• \(x_\ell\) is the reactance of transmission line \(\ell\),

• \(K_{i\ell}\) is the incidence matrix,

• \(C_{\ell c}\) is the cycle matrix,

• \(G_{i,s}\) is the nominal capacity of the generator of technology \(s\) at bus \(i\),

• \(P_{\ell}\) is the rating of the transmission line \(\ell\),

• \(E_{i,r}\) is the energy capacity of storage \(r\) at bus \(i\),

• \(\eta^{0/1/2}_{i,r,t}\) denote the standing (0), charging (1), and discharging (2) efficiencies.

Note

For a full reference to the optimisation problem description, see https://pypsa.readthedocs.io/en/latest/optimal_power_flow.html

Simple electricity market (economic dispatch) example

Let’s assume we want to minimise the operational cost of an electricity system representing South Africa and Mozambique subject to generator limits and meeting the loads:

(3)\[\begin{equation} \min_{g_s} \sum_s o_s g_s \end{equation}\]

such that

(4)\[\begin{align} \sum_s g_s &= d \\ g_s &\leq G_s \\ g_s &\geq 0 \end{align}\]

We have the following data:

• fuel costs in € / MWh\(_{th}\)

We are given the following information:

• marginal costs in EUR/MWh

marginal_cost = dict(
    wind=0,
    coal=30,
    gas=60,
    oil=80,
)

• power plant capacities in MW

power_plants = {
    "SA": {"coal": 35000, "wind": 3000, "gas": 8000, "oil": 2000},
    "MZ": {"hydro": 1200},
}

• electrical load in MW

loads = {
    "SA": 42000,
    "MZ": 650,
}

Building a basic network

By convention, PyPSA is imported without an alias:

import pypsa

Set parameter Username
Set parameter LicenseID to value 2767832
Academic license - for non-commercial use only - expires 2027-01-20

First, we create a new network object which serves as the overall container for all components.

n = pypsa.Network()

The second component we need are buses. Buses are the fundamental nodes of the network, to which all other components like loads, generators and transmission lines attach. They enforce energy conservation for all elements feeding in and out of it (i.e. Kirchhoff’s Current Law).

Components can be added to the network n using the n.add() function. It takes the component name as a first argument, the name of the component as a second argument and possibly further parameters as keyword arguments. Let’s use this function, to add buses for each country to our network:

n.add("Bus", "SA", y=-30.5, x=25, v_nom=400, carrier="AC")
n.add("Bus", "MZ", y=-18.5, x=35.5, v_nom=400, carrier="AC")

For each class of components, the data describing the components is stored in a pandas.DataFrame. For example, all static data for buses is stored in n.buses

n.buses

	v_nom	type	x	y	carrier	unit	location	v_mag_pu_set	v_mag_pu_min	v_mag_pu_max	control	generator	sub_network
name
SA	400.0		25.0	-30.5	AC			1.0	0.0	inf	PQ
MZ	400.0		35.5	-18.5	AC			1.0	0.0	inf	PQ

You see there are many more attributes than we specified while adding the buses; many of them are filled with default parameters which were added. You can look up the field description, defaults and status (required input, optional input, output) for buses here https://pypsa.readthedocs.io/en/latest/components.html#bus, and analogous for all other components.

The method n.add() also allows you to add multiple components at once. For instance, multiple carriers for the fuels with information on specific carbon dioxide emissions, a nice name, and colors for plotting. For this, the function takes the component name as the first argument and then a list of component names and then optional arguments for the parameters. Here, scalar values, lists, dictionary or pandas.Series are allowed. The latter two needs keys or indices with the component names.

n.add(
    "Carrier",
    ["coal", "gas", "oil", "hydro", "wind"],
    nice_name=["Coal", "Gas", "Oil", "Hydro", "Onshore Wind"],
    color=["grey", "indianred", "black", "aquamarine", "dodgerblue"],
)

n.add("Carrier", ["electricity", "AC"])

The n.add() function is very general. It lets you add any component to the network object n. For instance, in the next step we add generators for all the different power plants.

In Mozambique:

n.add(
    "Generator",
    "MZ hydro",
    bus="MZ",
    carrier="hydro",
    p_nom=1200,  # MW
    marginal_cost=0,  # default
)

In South Africa (in a loop):

for tech, p_nom in power_plants["SA"].items():
    n.add(
        "Generator",
        f"SA {tech}",
        bus="SA",
        carrier=tech,
        p_nom=p_nom,
        marginal_cost=marginal_cost.get(tech,0),#fuel_cost.get(tech, 0) / efficiency.get(tech, 1),
    )

As a result, the n.generators DataFrame looks like this:

n.generators

	bus	control	type	p_nom	p_nom_mod	p_nom_extendable	p_nom_min	p_nom_max	p_nom_set	p_min_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
name
MZ hydro	MZ	PQ		1200.0	0.0	False	0.0	inf	NaN	0.0	...	0	0	1	0	NaN	NaN	1.0	1.0	1.0	0.0
SA coal	SA	PQ		35000.0	0.0	False	0.0	inf	NaN	0.0	...	0	0	1	0	NaN	NaN	1.0	1.0	1.0	0.0
SA wind	SA	PQ		3000.0	0.0	False	0.0	inf	NaN	0.0	...	0	0	1	0	NaN	NaN	1.0	1.0	1.0	0.0
SA gas	SA	PQ		8000.0	0.0	False	0.0	inf	NaN	0.0	...	0	0	1	0	NaN	NaN	1.0	1.0	1.0	0.0
SA oil	SA	PQ		2000.0	0.0	False	0.0	inf	NaN	0.0	...	0	0	1	0	NaN	NaN	1.0	1.0	1.0	0.0

5 rows × 38 columns

Next, we’re going to add the electricity demand.

A positive value for p_set means consumption of power from the bus.

n.add(
    "Load",
    "SA electricity demand",
    bus="SA",
    p_set=loads["SA"],
    carrier="electricity",
)

n.add(
    "Load",
    "MZ electricity demand",
    bus="MZ",
    p_set=loads["MZ"],
    carrier="electricity",
)

n.loads

	bus	carrier	type	p_set	q_set	sign	active
name
SA electricity demand	SA	electricity		42000.0	0.0	-1.0	True
MZ electricity demand	MZ	electricity		650.0	0.0	-1.0	True

Finally, we add the connection between Mozambique and South Africa with a 500 MW line:

n.add(
    "Line",
    "SA-MZ",
    bus0="SA",
    bus1="MZ",
    s_nom=500,
    x=1,
    r=1,
)

n.lines

	bus0	bus1	type	x	r	g	b	s_nom	s_nom_mod	s_nom_extendable	...	v_ang_min	v_ang_max	sub_network	x_pu	r_pu	g_pu	b_pu	x_pu_eff	r_pu_eff	s_nom_opt
name
SA-MZ	SA	MZ		1.0	1.0	0.0	0.0	500.0	0.0	False	...	-inf	inf		0.0	0.0	0.0	0.0	0.0	0.0	0.0

1 rows × 32 columns

We can have a sneak peek at the network we built with the n.plot() function. More details on this in a bit.

n.plot(bus_sizes=1, margin=1);

Optimisation

With all input data transferred into PyPSA’s data structure, we can now build and run the resulting optimisation problem. In PyPSA, building, solving and retrieving results from the optimisation model is contained in a single function call n.optimize(). This function optimises dispatch and investment decisions for least cost.

The n.optimize() function can take a variety of arguments. The most relevant for the moment is the choice of the solver. We already know some solvers from the introduction to linopy (e.g. “highs” and “gurobi”). They need to be installed on your computer, to use them here!

n.optimize(solver_name="highs")

Show code cell output

Hide code cell output

INFO:linopy.model: Solve problem using Highs solver
INFO:linopy.io: Writing time: 0.13s
INFO:linopy.constants: Optimization successful: 
Status: ok
Termination condition: optimal
Solution: 6 primals, 14 duals
Objective: 1.26e+06
Solver model: available
Solver message: Optimal

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 were not assigned to the network.

Running HiGHS 1.12.0 (git hash: n/a): Copyright (c) 2025 HiGHS under MIT licence terms
LP linopy-problem-oe4l426c has 14 rows; 6 cols; 19 nonzeros
Coefficient ranges:
  Matrix  [1e+00, 1e+00]
  Cost    [3e+01, 8e+01]
  Bound   [0e+00, 0e+00]
  RHS     [5e+02, 4e+04]
Presolving model
1 rows, 3 cols, 3 nonzeros  0s
0 rows, 0 cols, 0 nonzeros  0s
Presolve reductions: rows 0(-14); columns 0(-6); nonzeros 0(-19) - Reduced to empty
Performed postsolve
Solving the original LP from the solution after postsolve

Model name          : linopy-problem-oe4l426c
Model status        : Optimal
Objective value     :  1.2600000000e+06
P-D objective error :  0.0000000000e+00
HiGHS run time      :          0.00

('ok', 'optimal')

Let’s have a look at the results.

Since the power flow and dispatch are generally time-varying quantities, these are stored in a different location than e.g. n.generators. They are stored in n.generators_t. Thus, to find out the dispatch of the generators, run

n.generators_t.p

name	MZ hydro	SA coal	SA wind	SA gas	SA oil
snapshot
now	1150.0	35000.0	3000.0	3500.0	-0.0

or if you prefer it in relation to the generators nominal capacity

n.generators_t.p / n.generators.p_nom

name	MZ hydro	SA coal	SA wind	SA gas	SA oil
snapshot
now	0.958333	1.0	1.0	0.4375	-0.0

You see that the time index has the value ‘now’. This is the default index when no time series data has been specified and the network only covers a single state (e.g. a particular hour).

Similarly you will find the power flow in transmission lines at

n.lines_t.p0

name	SA-MZ
snapshot
now	-500.0

n.lines_t.p1

name	SA-MZ
snapshot
now	500.0

The p0 will tell you the flow from bus0 to bus1. p1 will tell you the flow from bus1 to bus0.

What about the shadow prices?

n.buses_t.marginal_price

name	SA	MZ
snapshot
now	60.0	-0.0

Basic network plotting

For plotting PyPSA network, we’re going use matplotlib and cartopy to plot the maps.

import matplotlib.pyplot as plt
import cartopy.crs as ccrs

PyPSA has a built-in plotting function based on matplotlib, ….

n.plot(margin=1, bus_sizes=2)

{'nodes': {'Bus': <matplotlib.collections.PatchCollection at 0x177c9f390>},
 'branches': {'Line': <matplotlib.collections.LineCollection at 0x177c9f4d0>},
 'flows': {}}

Since we have provided x and y coordinates for our buses, n.plot() will try to plot the network on a map by default. Of course, there’s an option to deactivate this behaviour:

n.plot(geomap=False);

The n.plot() function has a variety of styling arguments to tweak the appearance of the buses, the lines and the map in the background:

n.plot(
    margin=1,
    bus_sizes=2,
    bus_colors="orange",
    bus_alpha=0.7,
    geomap_color=True,
    line_colors="orchid",
    line_widths=3,
    title="Test",
);

Just like with geopandas we can also control the projection of the network plot:

fig = plt.figure(figsize=(5, 5))
ax = plt.axes(projection=ccrs.EqualEarth())

n.plot(ax=ax, margin=1, bus_sizes=2);

We can use the bus_sizes argument of n.plot() to display the regional distribution of load. First, we calculate the total load per bus:

s = n.loads.groupby("bus").p_set.sum() / 1e4

s

bus
MZ    0.065
SA    4.200
Name: p_set, dtype: float64

The resulting pandas.Series we can pass to n.plot(bus_sizes=...):

n.plot(margin=1, bus_sizes=s);

The important point here is, that s needs to have entries for all buses, i.e. its index needs to match n.buses.index.

The bus_sizes argument of n.plot() can be even more powerful. It can produce pie charts, e.g. for the mix of electricity generation at each bus.

The dispatch of each generator, we can find at:

n.generators_t.p.loc["now"]

name
MZ hydro     1150.0
SA coal     35000.0
SA wind      3000.0
SA gas       3500.0
SA oil         -0.0
Name: now, dtype: float64

If we group this by the bus and carrier…

s = n.generators_t.p.loc["now"].groupby([n.generators.bus, n.generators.carrier]).sum()

… we get a multi-indexed pandas.Series …

s

bus  carrier
MZ   hydro       1150.0
SA   coal       35000.0
     gas         3500.0
     oil            0.0
     wind        3000.0
Name: now, dtype: float64

… which we can pass to n.plot(bus_sizes=...):

n.plot(margin=1, bus_sizes=s / 3000);

How does this magic work? The plotting function will look up the colors specified in n.carriers for each carrier and match it with the second index-level of s.

Modifying networks

Modifying data of components in an existing PyPSA network is as easy as modifying the entries of a pandas.DataFrame. For instance, if we want to reduce the cross-border transmission capacity between South Africa and Mozambique, we’d run:

n.lines.loc["SA-MZ", "s_nom"] = 400

n.lines

	bus0	bus1	type	x	r	g	b	s_nom	s_nom_mod	s_nom_extendable	...	v_ang_max	sub_network	x_pu	r_pu	g_pu	b_pu	x_pu_eff	r_pu_eff	s_nom_opt	v_nom
name
SA-MZ	SA	MZ		1.0	1.0	0.0	0.0	400.0	0.0	False	...	inf	0	0.000006	0.000006	0.0	0.0	0.000006	0.000006	500.0	400.0

1 rows × 33 columns

n.optimize(solver_name="highs")

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INFO:linopy.model: Solve problem using Highs solver
INFO:linopy.io: Writing time: 0.01s
INFO:linopy.constants: Optimization successful: 
Status: ok
Termination condition: optimal
Solution: 6 primals, 14 duals
Objective: 1.27e+06
Solver model: available
Solver message: Optimal

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 were not assigned to the network.

Running HiGHS 1.12.0 (git hash: n/a): Copyright (c) 2025 HiGHS under MIT licence terms
LP linopy-problem-bj95r_jr has 14 rows; 6 cols; 19 nonzeros
Coefficient ranges:
  Matrix  [1e+00, 1e+00]
  Cost    [3e+01, 8e+01]
  Bound   [0e+00, 0e+00]
  RHS     [4e+02, 4e+04]
Presolving model
1 rows, 3 cols, 3 nonzeros  0s
0 rows, 0 cols, 0 nonzeros  0s
Presolve reductions: rows 0(-14); columns 0(-6); nonzeros 0(-19) - Reduced to empty
Performed postsolve
Solving the original LP from the solution after postsolve

Model name          : linopy-problem-bj95r_jr
Model status        : Optimal
Objective value     :  1.2660000000e+06
P-D objective error :  0.0000000000e+00
HiGHS run time      :          0.00

('ok', 'optimal')

You can see that the production of the hydro power plant was reduced and that of the gas power plant increased owing to the reduced transmission capacity.

n.generators_t.p

name	MZ hydro	SA coal	SA wind	SA gas	SA oil
snapshot
now	1050.0	35000.0	3000.0	3600.0	-0.0

Data import and export

Note

Documentation: https://pypsa.readthedocs.io/en/latest/import_export.html.

You may find yourself in a need to store PyPSA networks for later use. Or, maybe you want to import the genius PyPSA example that someone else uploaded to the web to explore.

PyPSA can be stored as netCDF (.nc) file or as a folder of CSV files.

• netCDF files have the advantage that they take up less space than CSV files and are faster to load.

• CSV might be easier to use with Excel.

n.export_to_csv_folder("tmp")

WARNING:pypsa.network.io:Directory tmp does not exist, creating it
INFO:pypsa.network.io:Exported network 'Unnamed Network' saved to 'tmp contains: generators, carriers, loads, lines, buses, sub_networks

n_csv = pypsa.Network("tmp")

INFO:pypsa.network.io:Imported network 'Unnamed Network' has buses, carriers, generators, lines, loads, sub_networks

n.export_to_netcdf("tmp.nc");

INFO:pypsa.network.io:Exported network 'Unnamed Network' saved to 'tmp.nc contains: generators, carriers, loads, lines, buses, sub_networks

n_nc = pypsa.Network("tmp.nc")

INFO:pypsa.network.io:Imported network 'Unnamed Network' has buses, carriers, generators, lines, loads, sub_networks

The following example is optional and not cover in the course “Integrated Energy Grids”

Dispatch problem with German SciGRID network

SciGRID is a project that provides an open reference model of the European transmission network. The network comprises time series for loads and the availability of renewable generation at an hourly resolution for January 1, 2011 as well as approximate generation capacities in 2014. This dataset is a little out of date and only intended to demonstrate the capabilities of PyPSA.

n = pypsa.examples.scigrid_de()

INFO:pypsa.network.io:Retrieving network data from https://github.com/PyPSA/PyPSA/raw/v1.0.7/examples/networks/scigrid-de/scigrid-de.nc.
INFO:pypsa.network.io:Imported network 'SciGrid-DE' has buses, carriers, generators, lines, loads, storage_units, transformers

There are some infeasibilities without allowing extension. Moreover, to approximate so-called \(N-1\) security, we don’t allow any line to be loaded above 70% of their thermal rating. \(N-1\) security is a constraint that states that no single transmission line may be overloaded by the failure of another transmission line (e.g. through a tripped connection).

n.lines.s_max_pu = 0.7
n.lines.loc[["316", "527", "602"], "s_nom"] = 1715

Because this network includes time-varying data, now is the time to look at another attribute of n: n.snapshots. Snapshots is the PyPSA terminology for time steps. In most cases, they represent a particular hour. They can be a pandas.DatetimeIndex or any other list-like attributes.

n.snapshots

DatetimeIndex(['2011-01-01 00:00:00', '2011-01-01 01:00:00',
               '2011-01-01 02:00:00', '2011-01-01 03:00:00',
               '2011-01-01 04:00:00', '2011-01-01 05:00:00',
               '2011-01-01 06:00:00', '2011-01-01 07:00:00',
               '2011-01-01 08:00:00', '2011-01-01 09:00:00',
               '2011-01-01 10:00:00', '2011-01-01 11:00:00',
               '2011-01-01 12:00:00', '2011-01-01 13:00:00',
               '2011-01-01 14:00:00', '2011-01-01 15:00:00',
               '2011-01-01 16:00:00', '2011-01-01 17:00:00',
               '2011-01-01 18:00:00', '2011-01-01 19:00:00',
               '2011-01-01 20:00:00', '2011-01-01 21:00:00',
               '2011-01-01 22:00:00', '2011-01-01 23:00:00'],
              dtype='datetime64[ns]', name='snapshot', freq=None)

This index will match with any time-varying attributes of components:

n.loads_t.p_set.head(3)

name	1	3	4	6	7	8	9	11	14	16	...	382_220kV	384_220kV	385_220kV	391_220kV	403_220kV	404_220kV	413_220kV	421_220kV	450_220kV	458_220kV
snapshot
2011-01-01 00:00:00	231.716206	40.613618	66.790442	196.124424	147.804142	123.671946	83.637404	73.280624	175.260369	298.900165	...	202.010114	222.695091	212.621816	77.570241	16.148970	0.092794	58.427056	67.013686	38.449243	66.752618
2011-01-01 01:00:00	221.822547	38.879526	63.938670	187.750439	141.493303	118.391487	80.066312	70.151738	167.777223	286.137932	...	193.384825	213.186609	203.543436	74.258201	15.459452	0.088831	55.932378	64.152382	36.807564	63.902460
2011-01-01 02:00:00	213.127360	37.355494	61.432348	180.390839	135.946929	113.750678	76.927805	67.401871	161.200550	274.921657	...	185.804364	204.829941	195.564769	71.347365	14.853460	0.085349	53.739893	61.637683	35.364750	61.397558

3 rows × 485 columns

We can use simple pandas syntax, to create an overview of the load time series…

n.loads_t.p_set.sum(axis=1).div(1e3).plot(ylim=[0, 60], ylabel="MW")

<Axes: xlabel='snapshot', ylabel='MW'>

… and the capacity factor time series:

n.generators_t.p_max_pu.T.groupby(n.generators.carrier).mean().T.plot(ylabel="p.u.")

<Axes: xlabel='snapshot', ylabel='p.u.'>

We can also inspect the total power plant capacities per technology…

n.generators.groupby("carrier").p_nom.sum().div(1e3).plot.barh()
plt.xlabel("GW")

Text(0.5, 0, 'GW')

… and plot the regional distribution of loads…

load = n.loads_t.p_set.sum(axis=0).groupby(n.loads.bus).sum()

fig = plt.figure()
ax = plt.axes(projection=ccrs.EqualEarth())

n.plot(
    ax=ax,
    bus_sizes=load / 2e5,
);

… and power plant capacities:

capacities = n.generators.groupby(["bus", "carrier"]).p_nom.sum()

For plotting we need to assign some colors to the technologies.

import random

carriers = list(n.generators.carrier.unique()) + list(n.storage_units.carrier.unique())
colors = ["#%06x" % random.randint(0, 0xFFFFFF) for _ in carriers]
n.add("Carrier", carriers, color=colors, overwrite=True)

Because we want to see which color represents which technology, we cann add a legend using the add_legend_patches function of PyPSA.

from pypsa.plot import add_legend_patches

fig = plt.figure()
ax = plt.axes(projection=ccrs.EqualEarth())

n.plot(
    ax=ax,
    bus_sizes=capacities / 2e4,
)

add_legend_patches(
    ax, colors, carriers, legend_kw=dict(frameon=False, bbox_to_anchor=(0, 1))
)

<matplotlib.legend.Legend at 0x31383a990>

This dataset also includes a few hydro storage units:

n.storage_units.head(3)

	bus	control	type	p_nom	p_nom_mod	p_nom_extendable	p_nom_min	p_nom_max	p_nom_set	p_min_pu	...	state_of_charge_initial_per_period	state_of_charge_set	cyclic_state_of_charge	cyclic_state_of_charge_per_period	max_hours	efficiency_store	efficiency_dispatch	standing_loss	inflow	p_nom_opt
name
100_220kV Pumped Hydro	100_220kV	PQ		144.5	0.0	False	0.0	inf	NaN	-1.0	...	False	NaN	False	False	6.0	0.95	0.95	0.0	0.0	0.0
114 Pumped Hydro	114	PQ		138.0	0.0	False	0.0	inf	NaN	-1.0	...	False	NaN	False	False	6.0	0.95	0.95	0.0	0.0	0.0
121 Pumped Hydro	121	PQ		238.0	0.0	False	0.0	inf	NaN	-1.0	...	False	NaN	False	False	6.0	0.95	0.95	0.0	0.0	0.0

3 rows × 36 columns

So let’s solve the electricity market simulation for January 1, 2011. It’ll take a short moment.

n.optimize(solver_name="highs")

Show code cell output

Hide code cell output

WARNING:pypsa.consistency: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='name')
INFO:linopy.model: Solve problem using Highs solver
INFO:linopy.io:Writing objective.
Writing constraints.: 100%|██████████| 15/15 [00:00<00:00, 72.59it/s]
Writing continuous variables.: 100%|██████████| 6/6 [00:00<00:00, 432.09it/s]
INFO:linopy.io: Writing time: 0.32s

Running HiGHS 1.12.0 (git hash: n/a): Copyright (c) 2025 HiGHS under MIT licence terms
LP linopy-problem-2pjl5c38 has 142968 rows; 59640 cols; 261298 nonzeros
Coefficient ranges:
  Matrix  [1e-02, 2e+02]
  Cost    [3e+00, 1e+02]
  Bound   [0e+00, 0e+00]
  RHS     [2e-11, 6e+03]
WARNING: Problem has some excessively small row bounds
Presolving model
18737 rows, 44750 cols, 113266 nonzeros  0s
13253 rows, 39072 cols, 104687 nonzeros  0s
12725 rows, 31714 cols, 97262 nonzeros  0s
Dependent equations search running on 12697 equations with time limit of 1000.00s
Dependent equations search removed 0 rows and 0 nonzeros in 0.00s (limit = 1000.00s)
12697 rows, 31673 cols, 97185 nonzeros  0s
Presolve reductions: rows 12697(-130271); columns 31673(-27967); nonzeros 97185(-164113) 
Solving the presolved LP
Using EKK dual simplex solver - serial
  Iteration        Objective     Infeasibilities num(sum)
          0     0.0000000000e+00 Ph1: 0(0) 0s

INFO:linopy.constants: Optimization successful: 
Status: ok
Termination condition: optimal
Solution: 59640 primals, 142968 duals
Objective: 9.20e+06
Solver model: available
Solver message: Optimal

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.

      17237     9.1992880405e+06 Pr: 0(0); Du: 0(9.94274e-13) 3s
      17237     9.1992880405e+06 Pr: 0(0); Du: 0(9.94274e-13) 3s

Performed postsolve
Solving the original LP from the solution after postsolve

Model name          : linopy-problem-2pjl5c38
Model status        : Optimal
Simplex   iterations: 17237
Objective value     :  9.1992880405e+06
P-D objective error :  2.3284865043e-15
HiGHS run time      :          2.90

('ok', 'optimal')

Now, we can also plot model outputs, like the calculated power flows on the network map.

line_loading = n.lines_t.p0.iloc[0].abs() / n.lines.s_nom / n.lines.s_max_pu * 100  # %

norm = plt.Normalize(vmin=0, vmax=100)

fig = plt.figure(figsize=(7, 7))
ax = plt.axes(projection=ccrs.EqualEarth())

n.plot(
    ax=ax,
    bus_sizes=0,
    line_colors=line_loading,
    line_cmap_norm=norm,
    line_cmap="plasma",
    line_widths=n.lines.s_nom / 1000,
)

plt.colorbar(
    plt.cm.ScalarMappable(cmap="plasma", norm=norm),
    ax=ax,
    label="Relative line loading [%]",
    shrink=0.6,
)

<matplotlib.colorbar.Colorbar at 0x176ab9a90>

Or plot the hourly dispatch grouped by carrier:

p_by_carrier = n.generators_t.p.T.groupby(n.generators.carrier).sum().T.div(1e3)

fig, ax = plt.subplots(figsize=(11, 4))

p_by_carrier.plot(
    kind="area",
    ax=ax,
    linewidth=0,
    cmap="tab20b",
)

ax.legend(ncol=5, loc="upper left", frameon=False)

ax.set_ylabel("GW")

ax.set_ylim(0, 80);

Or plot the aggregate dispatch of the pumped hydro storage units and the state of charge throughout the day:

fig, ax = plt.subplots()

p_storage = n.storage_units_t.p.sum(axis=1).div(1e3)
state_of_charge = n.storage_units_t.state_of_charge.sum(axis=1).div(1e3)

p_storage.plot(label="Pumped hydro dispatch [GW]", ax=ax)
state_of_charge.plot(label="State of charge [GWh]", ax=ax)

ax.grid()
ax.legend()
ax.set_ylabel("MWh or MW")

Text(0, 0.5, 'MWh or MW')

Or plot the locational marginal prices (LMPs):

fig = plt.figure(figsize=(7, 7))
ax = plt.axes(projection=ccrs.EqualEarth())

norm = plt.Normalize(vmin=0, vmax=100)  # €/MWh

n.plot(
    ax=ax,
    bus_colors=n.buses_t.marginal_price.mean(),
    bus_cmap="plasma",
    bus_cmap_norm=norm,
    bus_alpha=0.7,
)

plt.colorbar(
    plt.cm.ScalarMappable(cmap="plasma", norm=norm),
    ax=ax,
    label="LMP [€/MWh]",
    shrink=0.6,
)

<matplotlib.colorbar.Colorbar at 0x344038f50>