Note

You can download this example as a Jupyter notebook or start it in interactive mode.

Using the statistics module in PyPSA#

The statistics module is used to easily extract information from your networks. This is useful when inspecting your solved networks and creating first visualizations of your results.

With the statistics module, you can look at different metrics of your network. A list of the implemented metrics are:

  • Capital expenditure

  • Operational expenditure

  • Installed capacities

  • Optimal capacities

  • Supply

  • Withdrawal

  • Curtailment

  • Capacity Factor

  • Revenue

  • Market value

  • Energy balance

Now lets look at an example.

[1]:

import pypsa
import matplotlib.pyplot as plt
import numpy as np

First, we open an example network we want to investigate.

[2]:

n = pypsa.examples.scigrid_de()

WARNING:pypsa.io:Importing network from PyPSA version v0.17.1 while current version is v0.25.2. 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

Lets run an overview of all statistics by calling:

[3]:

n.statistics().dropna()

[3]:
Capacity Factor Capital Expenditure Curtailment Dispatch Installed Capacity Market Value Operational Expenditure Optimal Capacity Revenue Supply Withdrawal
carrier

So far the statistics are not so interesting, because we have not solved the network yet. We can only see that the network already has some installed capacities for different components.

You can see that statistics returns a pandas.DataFrame. The MultiIndex of the DataFrame provides the name of the network component (i.e. first entry of the MultiIndex, like Generator, Line,…) on the first index level. The carrier index level provides the carrier name of the given component. For example, in n.generators, we have the carriers Brown Coal, Gas and so on.

Now lets solve the network.

[4]:

n.optimize(n.snapshots[:4])

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/v0.25.2/lib/python3.11/site-packages/linopy/expressions.py:176: FutureWarning: the `pandas.MultiIndex` object(s) passed as 'Generator' coordinate(s) or data variable(s) will no longer be implicitly promoted and wrapped into multiple indexed coordinates in the future (i.e., one coordinate for each multi-index level + one dimension coordinate). If you want to keep this behavior, you need to first wrap it explicitly using `mindex_coords = xarray.Coordinates.from_pandas_multiindex(mindex_obj, 'dim')` and pass it as coordinates, e.g., `xarray.Dataset(coords=mindex_coords)`, `dataset.assign_coords(mindex_coords)` or `dataarray.assign_coords(mindex_coords)`.
  ds = self.data.assign_coords({group_dim: idx})
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.25.2/lib/python3.11/site-packages/linopy/expressions.py:176: FutureWarning: the `pandas.MultiIndex` object(s) passed as 'StorageUnit' coordinate(s) or data variable(s) will no longer be implicitly promoted and wrapped into multiple indexed coordinates in the future (i.e., one coordinate for each multi-index level + one dimension coordinate). If you want to keep this behavior, you need to first wrap it explicitly using `mindex_coords = xarray.Coordinates.from_pandas_multiindex(mindex_obj, 'dim')` and pass it as coordinates, e.g., `xarray.Dataset(coords=mindex_coords)`, `dataset.assign_coords(mindex_coords)` or `dataarray.assign_coords(mindex_coords)`.
  ds = self.data.assign_coords({group_dim: idx})
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.25.2/lib/python3.11/site-packages/linopy/expressions.py:176: FutureWarning: the `pandas.MultiIndex` object(s) passed as 'StorageUnit' coordinate(s) or data variable(s) will no longer be implicitly promoted and wrapped into multiple indexed coordinates in the future (i.e., one coordinate for each multi-index level + one dimension coordinate). If you want to keep this behavior, you need to first wrap it explicitly using `mindex_coords = xarray.Coordinates.from_pandas_multiindex(mindex_obj, 'dim')` and pass it as coordinates, e.g., `xarray.Dataset(coords=mindex_coords)`, `dataset.assign_coords(mindex_coords)` or `dataarray.assign_coords(mindex_coords)`.
  ds = self.data.assign_coords({group_dim: idx})
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.25.2/lib/python3.11/site-packages/linopy/expressions.py:176: FutureWarning: the `pandas.MultiIndex` object(s) passed as 'Line' coordinate(s) or data variable(s) will no longer be implicitly promoted and wrapped into multiple indexed coordinates in the future (i.e., one coordinate for each multi-index level + one dimension coordinate). If you want to keep this behavior, you need to first wrap it explicitly using `mindex_coords = xarray.Coordinates.from_pandas_multiindex(mindex_obj, 'dim')` and pass it as coordinates, e.g., `xarray.Dataset(coords=mindex_coords)`, `dataset.assign_coords(mindex_coords)` or `dataarray.assign_coords(mindex_coords)`.
  ds = self.data.assign_coords({group_dim: idx})
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.25.2/lib/python3.11/site-packages/linopy/expressions.py:176: FutureWarning: the `pandas.MultiIndex` object(s) passed as 'Line' coordinate(s) or data variable(s) will no longer be implicitly promoted and wrapped into multiple indexed coordinates in the future (i.e., one coordinate for each multi-index level + one dimension coordinate). If you want to keep this behavior, you need to first wrap it explicitly using `mindex_coords = xarray.Coordinates.from_pandas_multiindex(mindex_obj, 'dim')` and pass it as coordinates, e.g., `xarray.Dataset(coords=mindex_coords)`, `dataset.assign_coords(mindex_coords)` or `dataarray.assign_coords(mindex_coords)`.
  ds = self.data.assign_coords({group_dim: idx})
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.25.2/lib/python3.11/site-packages/linopy/expressions.py:176: FutureWarning: the `pandas.MultiIndex` object(s) passed as 'Transformer' coordinate(s) or data variable(s) will no longer be implicitly promoted and wrapped into multiple indexed coordinates in the future (i.e., one coordinate for each multi-index level + one dimension coordinate). If you want to keep this behavior, you need to first wrap it explicitly using `mindex_coords = xarray.Coordinates.from_pandas_multiindex(mindex_obj, 'dim')` and pass it as coordinates, e.g., `xarray.Dataset(coords=mindex_coords)`, `dataset.assign_coords(mindex_coords)` or `dataarray.assign_coords(mindex_coords)`.
  ds = self.data.assign_coords({group_dim: idx})
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.25.2/lib/python3.11/site-packages/linopy/expressions.py:176: FutureWarning: the `pandas.MultiIndex` object(s) passed as 'Transformer' coordinate(s) or data variable(s) will no longer be implicitly promoted and wrapped into multiple indexed coordinates in the future (i.e., one coordinate for each multi-index level + one dimension coordinate). If you want to keep this behavior, you need to first wrap it explicitly using `mindex_coords = xarray.Coordinates.from_pandas_multiindex(mindex_obj, 'dim')` and pass it as coordinates, e.g., `xarray.Dataset(coords=mindex_coords)`, `dataset.assign_coords(mindex_coords)` or `dataarray.assign_coords(mindex_coords)`.
  ds = self.data.assign_coords({group_dim: idx})
INFO:linopy.model: Solve problem using Glpk solver
INFO:linopy.io:Writing objective.
Writing constraints.: 100%|██████████| 15/15 [00:00<00:00, 94.07it/s]
Writing continuous variables.: 100%|██████████| 7/7 [00:00<00:00, 262.13it/s]
INFO:linopy.io: Writing time: 0.2s

GLPSOL--GLPK LP/MIP Solver 5.0
Parameter(s) specified in the command line:
 --lp /tmp/linopy-problem-azm1pcnu.lp --output /tmp/linopy-solve-sj8h_4wx.sol
Reading problem data from '/tmp/linopy-problem-azm1pcnu.lp'...
23828 rows, 9940 columns, 43654 non-zeros
126992 lines were read
GLPK Simplex Optimizer 5.0
23828 rows, 9940 columns, 43654 non-zeros
Preprocessing...
3772 rows, 5708 columns, 19366 non-zeros
Scaling...
 A: min|aij| =  1.485e-02  max|aij| =  1.974e+02  ratio =  1.329e+04
GM: min|aij| =  1.907e-01  max|aij| =  5.245e+00  ratio =  2.751e+01
EQ: min|aij| =  3.688e-02  max|aij| =  1.000e+00  ratio =  2.711e+01
Constructing initial basis...
Size of triangular part is 3669
      0: obj =  -5.986899755e+08 inf =   1.551e+08 (2823)
   6642: obj =   4.445245001e+06 inf =   4.547e-13 (0) 39
*  9066: obj =   1.038959807e+06 inf =   0.000e+00 (0) 10
OPTIMAL LP SOLUTION FOUND
Time used:   2.1 secs
Memory used: 17.2 Mb (18079220 bytes)
Writing basic solution to '/tmp/linopy-solve-sj8h_4wx.sol'...

INFO:linopy.constants: Optimization successful:
Status: ok
Termination condition: optimal
Solution: 9940 primals, 23828 duals
Objective: 1.04e+06
Solver model: not 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.

[4]:

('ok', 'optimal')

Now we can look at the statistics of the solved network.

[5]:

n.statistics().round(1)

[5]:
Capacity Factor Capital Expenditure Curtailment Dispatch Installed Capacity Market Value Operational Expenditure Optimal Capacity Revenue Supply Withdrawal
carrier
Generator Brown Coal 0.1 0.0 0.0 42859.0 20879.5 13.7 428590.3 20879.5 588266.5 42859.0 0.0
Gas 0.0 0.0 0.0 79.4 23913.1 50.0 3971.9 23913.1 3971.9 79.4 0.0
Geothermal 0.0 0.0 0.0 0.0 31.7 NaN 0.0 31.7 0.0 0.0 0.0
Hard Coal 0.0 0.0 0.0 10535.7 25312.6 25.8 263391.6 25312.6 272172.0 10535.7 0.0
Multiple 0.0 0.0 0.0 0.0 152.7 NaN 0.0 152.7 0.0 0.0 0.0
Nuclear 0.1 0.0 0.0 31473.0 12068.0 16.7 251784.0 12068.0 527108.2 31473.0 0.0
Oil 0.0 0.0 0.0 0.0 2710.2 NaN 0.0 2710.2 0.0 0.0 0.0
Other 0.0 0.0 0.0 336.0 3027.8 34.2 10752.0 3027.8 11503.2 336.0 0.0
Run of River 0.1 0.0 0.0 13723.3 3999.1 22.0 41170.0 3999.1 301812.2 13723.3 0.0
Solar 0.0 0.0 47391.0 0.0 37041.5 NaN 0.0 37041.5 0.0 0.0 0.0
Storage Hydro 0.1 0.0 0.0 3580.0 1445.0 20.4 10740.0 1445.0 72904.4 3580.0 0.0
Waste 0.1 0.0 0.0 4760.0 1645.9 20.5 28560.0 1645.9 97621.8 4760.0 0.0
Wind Offshore 0.1 0.0 62904.9 6568.8 2973.5 2.1 0.0 2973.5 14034.2 6568.8 0.0
Wind Onshore 0.1 0.0 391045.1 82395.2 37339.9 4.9 0.0 37339.9 406030.6 82395.2 0.0
Line AC 0.0 0.0 NaN 17530.5 961101.1 59.6 NaN 961101.1 1045149.1 843709.7 -843709.7
Load - NaN NaN NaN -195357.1 NaN -17.4 NaN NaN 3396077.6 0.0 -195357.1
StorageUnit Pumped Hydro 0.0 0.0 0.0 -953.3 9179.5 -4.2 0.0 9179.5 4013.3 0.0 -953.3
Transformer - 0.0 0.0 NaN -14003.7 192000.0 -3.7 NaN 192000.0 51490.2 103414.7 -103414.7

As you can see there is now much more information available. There are still no capital expenditures in the network, because we only performed an operational optimization with this example network.

If you are interested in a specific metric, e.g. curtailment, you can run

[6]:

curtailment = n.statistics.curtailment()
curtailment[curtailment != 0]

[6]:

           carrier
Generator  Solar             47391.043207
           Wind Offshore     62904.857344
           Wind Onshore     391045.130624
dtype: float64

Note that when calling a specific metric the statistics module returns a pandas.Series. To find the unit of the data returned by statistics, you can call attrs on the DataFrame or Series.

[7]:

curtailment.attrs

[7]:

{'name': 'Curtailment', 'unit': 'MWh'}

So the unit of curtailment is given in MWh. You can also customize your request.

For this you have various options: 1. You can select the component from which you want to get the metric with the attribute comps. Careful, comps has to be a list of strings.

[8]:

n.statistics.supply(comps=["Generator"])

[8]:

           carrier
Generator  Brown Coal       42859.029000
           Gas                 79.437970
           Geothermal           0.000000
           Hard Coal        10535.663500
           Multiple             0.000000
           Nuclear          31472.994000
           Oil                  0.000000
           Other              336.000000
           Run of River     13723.318200
           Solar                0.000000
           Storage Hydro     3580.000000
           Waste             4760.000000
           Wind Offshore     6568.792000
           Wind Onshore     82395.152709
Name: generators, dtype: float64

  1. For metrics which have a time dimension, you can choose the aggregation method or decide to not aggregate them at all. Just use the aggregate_time attribute to specify what you want to do.

For example calculate the mean supply/generation per time step is

[9]:

n.statistics.supply(comps=["Generator"], aggregate_time="mean")

[9]:

           carrier
Generator  Brown Coal       1785.792875
           Gas                 3.309915
           Geothermal          0.000000
           Hard Coal         438.985979
           Multiple            0.000000
           Nuclear          1311.374750
           Oil                 0.000000
           Other              14.000000
           Run of River      571.804925
           Solar               0.000000
           Storage Hydro     149.166667
           Waste             198.333333
           Wind Offshore     273.699667
           Wind Onshore     3433.131363
dtype: float64

Or retrieve the supply time series by not aggregating the time series.

[10]:

n.statistics.supply(comps=["Generator"], aggregate_time=False).iloc[:, :4]

[10]:
snapshot 2011-01-01 00:00:00 2011-01-01 01:00:00 2011-01-01 02:00:00 2011-01-01 03:00:00
carrier
Generator Brown Coal 12563.897000 10848.560000 10006.395000 9440.17700
Gas 35.826800 23.721700 13.083000 6.80647
Geothermal 0.000000 0.000000 0.000000 0.00000
Hard Coal 4778.482000 3124.547000 1722.869000 909.76550
Multiple 0.000000 0.000000 0.000000 0.00000
Nuclear 7842.041000 7863.186000 7882.532000 7885.23500
Oil 0.000000 0.000000 0.000000 0.00000
Other 84.000000 84.000000 84.000000 84.00000
Run of River 3458.909000 3419.332800 3413.465800 3431.61060
Solar 0.000000 0.000000 0.000000 0.00000
Storage Hydro 895.000000 895.000000 895.000000 895.00000
Waste 1167.500000 1240.500000 1184.500000 1167.50000
Wind Offshore 2489.407000 1040.562000 1672.360000 1366.46300
Wind Onshore 18735.003302 21223.999338 20947.135229 21489.01484

  1. You can choose how you want to group the components of the network and how to aggregate the groups. By default the components are grouped by their carriers and summed. However, you can change this by providing different groupby and aggregate_groups attributes.

[11]:

n.statistics.supply(comps=["Generator"], groupby=["bus"], aggregate_groups="max")

[11]:

           bus
Generator  1               0.000000
           100_220kV       0.000000
           101          1392.589000
           102           970.750000
           103             0.127076
                           ...
           95_220kV      186.429300
           96_220kV       53.032800
           97              0.002514
           98            335.603700
           99_220kV        0.000000
Name: generators, Length: 489, dtype: float64

Now you obtained the maximal supply in one time step for every bus in the network.

Often it is better when inspecting your network to visualize the tables. Therefore, you can easily make plots to analyze your results. For example the supply of the generators.

[12]:

n.statistics.supply(comps=["Generator"]).droplevel(0).div(1e3).plot.bar(
    title="Generator in GWh"
)

[12]:

<Axes: title={'center': 'Generator in GWh'}, xlabel='carrier'>
../_images/examples_statistics_23_1.png

Or you could plot the generation time series of the generators.

[13]:

fig, ax = plt.subplots()
n.statistics.supply(comps=["Generator"], aggregate_time=False).droplevel(0).iloc[
    :, :4
].div(1e3).T.plot.area(
    title="Generation in GW",
    ax=ax,
    legend=False,
    linewidth=0,
)
ax.legend(bbox_to_anchor=(1, 0), loc="lower left", title=None, ncol=1)

[13]:

<matplotlib.legend.Legend at 0x7fe3497bd050>
../_images/examples_statistics_25_1.png

Finally, we want to look at the energy balance of the network. The energy balance is not included in the overview of the statistics module. To calculate the energy balance, you can do

[14]:

n.statistics.energy_balance()

[14]:

             carrier        bus_carrier
Transformer  -              AC            -5.684342e-13
Line         AC             AC            -6.821210e-13
StorageUnit  Pumped Hydro   AC            -9.533000e+02
Generator    Brown Coal     AC             4.285903e+04
             Gas            AC             7.943797e+01
             Geothermal     AC             0.000000e+00
             Hard Coal      AC             1.053566e+04
             Multiple       AC             0.000000e+00
             Nuclear        AC             3.147299e+04
             Oil            AC             0.000000e+00
             Other          AC             3.360000e+02
             Run of River   AC             1.372332e+04
             Solar          AC             0.000000e+00
             Storage Hydro  AC             3.580000e+03
             Waste          AC             4.760000e+03
             Wind Offshore  AC             6.568792e+03
             Wind Onshore   AC             8.239515e+04
Load         -              AC            -1.953571e+05
dtype: float64

Note that there is now an additional index level called bus carrier. This is because an energy balance is defined for every bus carrier. The bus carriers you have in your network you can find by looking at n.buses.carrier.unique(). For this network, there is only one bus carrier which is AC and corresponds to electricity. However, you can have further bus carriers for example when you have a sector coupled network. You could have heat or CO \(_2\) as bus carrier. Therefore, for many statistics functions you have to be careful about the units of the values and it is not always given by the attr object of the DataFrame or Series.

Finally, we want to plot the energy balance and the energy balance time series for electrcity which has the bus carrier AC. In a sector coupled network, you could also choose other bus carriers like H2 or heat. Note that in this example “-” represents the load in the system.

[15]:

fig, ax = plt.subplots()
n.statistics.energy_balance().loc[:, :, "AC"].groupby(
    "carrier"
).sum().to_frame().T.plot.bar(stacked=True, ax=ax, title="Energy Balance")
ax.legend(bbox_to_anchor=(1, 0), loc="lower left", title=None, ncol=1)

[15]:

<matplotlib.legend.Legend at 0x7fe349886f90>
../_images/examples_statistics_29_1.png 
[16]:

fig, ax = plt.subplots()
n.statistics.energy_balance(aggregate_time=False).loc[:, :, "AC"].droplevel(0).iloc[
    :, :4
].groupby("carrier").sum().where(lambda x: np.abs(x) > 1).fillna(0).T.plot.area(
    ax=ax, title="Energy Balance Timeseries"
)
ax.legend(bbox_to_anchor=(1, 0), loc="lower left", title=None, ncol=1)

[16]:

<matplotlib.legend.Legend at 0x7fe3499bbf10>
../_images/examples_statistics_30_1.png