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: https://github.com/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))
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Cell In [1], line 1
----> 1 import pypsa
2 import numpy as np
3 import pandas as pd
File ~/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.21.2/lib/python3.11/site-packages/pypsa/__init__.py:10
1 # -*- coding: utf-8 -*-
4 """
5 Python for Power Systems Analysis (PyPSA)
6
7 Grid calculation library.
8 """
---> 10 from pypsa import (
11 components,
12 contingency,
13 descriptors,
14 examples,
15 geo,
16 io,
17 linopf,
18 linopt,
19 networkclustering,
20 opf,
21 opt,
22 optimization,
23 pf,
24 plot,
25 )
26 from pypsa.components import Network, SubNetwork
28 __version__ = "0.21.2"
File ~/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.21.2/lib/python3.11/site-packages/pypsa/components.py:50
37 from pypsa.io import (
38 export_to_csv_folder,
39 export_to_hdf5,
(...)
47 import_series_from_dataframe,
48 )
49 from pypsa.opf import network_lopf, network_opf
---> 50 from pypsa.optimization.optimize import OptimizationAccessor
51 from pypsa.pf import (
52 calculate_B_H,
53 calculate_dependent_values,
(...)
62 sub_network_pf,
63 )
64 from pypsa.plot import iplot, plot
File ~/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.21.2/lib/python3.11/site-packages/pypsa/optimization/__init__.py:7
1 #!/usr/bin/env python3
2 # -*- coding: utf-8 -*-
3 """
4 Build optimisation problems from PyPSA networks with Linopy.
5 """
----> 7 from pypsa.optimization import abstract, constraints, optimize, variables
8 from pypsa.optimization.optimize import create_model
File ~/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.21.2/lib/python3.11/site-packages/pypsa/optimization/constraints.py:9
6 import logging
8 import pandas as pd
----> 9 from linopy.expressions import LinearExpression, merge
10 from numpy import arange, cumsum, inf, nan, roll
11 from scipy import sparse
File ~/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.21.2/lib/python3.11/site-packages/linopy/__init__.py:9
1 #!/usr/bin/env python3
2 # -*- coding: utf-8 -*-
3 """
4 Created on Wed Mar 10 11:03:06 2021.
5
6 @author: fabulous
7 """
----> 9 from linopy import model, remote
10 from linopy.expressions import merge
11 from linopy.io import read_netcdf
File ~/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.21.2/lib/python3.11/site-packages/linopy/model.py:22
20 from linopy import solvers
21 from linopy.common import best_int, replace_by_map
---> 22 from linopy.constraints import (
23 AnonymousConstraint,
24 AnonymousScalarConstraint,
25 Constraints,
26 )
27 from linopy.eval import Expr
28 from linopy.expressions import LinearExpression, ScalarLinearExpression
File ~/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.21.2/lib/python3.11/site-packages/linopy/constraints.py:21
18 from scipy.sparse import coo_matrix
19 from xarray import DataArray, Dataset
---> 21 from linopy import expressions, variables
22 from linopy.common import (
23 _merge_inplace,
24 has_assigned_model,
(...)
27 replace_by_map,
28 )
31 class Constraint(DataArray):
File ~/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.21.2/lib/python3.11/site-packages/linopy/expressions.py:23
20 from xarray.core.dataarray import DataArrayCoordinates
21 from xarray.core.groupby import _maybe_reorder, peek_at
---> 23 from linopy import constraints, variables
24 from linopy.common import as_dataarray
27 def exprwrap(method, *default_args, **new_default_kwargs):
File ~/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.21.2/lib/python3.11/site-packages/linopy/variables.py:398
393 roll = varwrap(DataArray.roll)
395 rolling = varwrap(DataArray.rolling)
--> 398 @dataclass(repr=False)
399 class Variables:
400 """
401 A variables container used for storing multiple variable arrays.
402 """
404 labels: Dataset = Dataset()
File ~/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.21.2/lib/python3.11/dataclasses.py:1211, in dataclass.<locals>.wrap(cls)
1210 def wrap(cls):
-> 1211 return _process_class(cls, init, repr, eq, order, unsafe_hash,
1212 frozen, match_args, kw_only, slots,
1213 weakref_slot)
File ~/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.21.2/lib/python3.11/dataclasses.py:959, in _process_class(cls, init, repr, eq, order, unsafe_hash, frozen, match_args, kw_only, slots, weakref_slot)
956 kw_only = True
957 else:
958 # Otherwise it's a field of some type.
--> 959 cls_fields.append(_get_field(cls, name, type, kw_only))
961 for f in cls_fields:
962 fields[f.name] = f
File ~/checkouts/readthedocs.org/user_builds/pypsa/conda/v0.21.2/lib/python3.11/dataclasses.py:816, in _get_field(cls, a_name, a_type, default_kw_only)
812 # For real fields, disallow mutable defaults. Use unhashable as a proxy
813 # indicator for mutability. Read the __hash__ attribute from the class,
814 # not the instance.
815 if f._field_type is _FIELD and f.default.__class__.__hash__ is None:
--> 816 raise ValueError(f'mutable default {type(f.default)} for field '
817 f'{f.name} is not allowed: use default_factory')
819 return f
ValueError: mutable default <class 'xarray.core.dataset.Dataset'> for field labels is not allowed: use default_factory
[2]:
network = pypsa.examples.ac_dc_meshed(from_master=True)
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Cell In [2], line 1
----> 1 network = pypsa.examples.ac_dc_meshed(from_master=True)
NameError: name 'pypsa' is not defined
[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
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Cell In [3], line 2
1 # get current type (AC or DC) of the lines from the buses
----> 2 lines_current_type = network.lines.bus0.map(network.buses.carrier)
3 lines_current_type
NameError: name 'network' is not defined
[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()
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Cell In [4], line 1
----> 1 network.plot(
2 line_colors=lines_current_type.map(lambda ct: "r" if ct == "DC" else "b"),
3 title="Mixed AC (blue) - DC (red) network - DC (cyan)",
4 color_geomap=True,
5 jitter=0.3,
6 )
7 plt.tight_layout()
NameError: name 'network' is not defined
[5]:
network.links.loc["Norwich Converter", "p_nom_extendable"] = False
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Cell In [5], line 1
----> 1 network.links.loc["Norwich Converter", "p_nom_extendable"] = False
NameError: name 'network' is not defined
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
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Cell In [6], line 1
----> 1 network.determine_network_topology()
2 network.sub_networks["n_branches"] = [
3 len(sn.branches()) for sn in network.sub_networks.obj
4 ]
5 network.sub_networks["n_buses"] = [len(sn.buses()) for sn in network.sub_networks.obj]
NameError: name 'network' is not defined
The network covers 10 time steps. These are given by the snapshots attribute.
[7]:
network.snapshots
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Cell In [7], line 1
----> 1 network.snapshots
NameError: name 'network' is not defined
There are 6 generators in the network, 3 wind and 3 gas. All are attached to buses:
[8]:
network.generators
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Cell In [8], line 1
----> 1 network.generators
NameError: name 'network' is not defined
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()
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Cell In [9], line 1
----> 1 network.generators_t.p_max_pu.plot.area(subplots=True)
2 plt.tight_layout()
NameError: name 'network' is not defined
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);
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Cell In [10], line 1
----> 1 network.lopf(pyomo=False);
NameError: name 'network' is not defined
The objective is given by:
[11]:
network.objective
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Cell In [11], line 1
----> 1 network.objective
NameError: name 'network' is not defined
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
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Cell In [12], line 1
----> 1 network.objective + network.objective_constant
NameError: name 'network' is not defined
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()
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Cell In [13], line 1
----> 1 network.generators.p_nom_opt.div(1e3).plot.bar(ylabel="GW", figsize=(8, 3))
2 plt.tight_layout()
NameError: name 'network' is not defined
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()
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Cell In [14], line 1
----> 1 network.generators_t.p.div(1e3).plot.area(subplots=True, ylabel="GW")
2 plt.tight_layout()
NameError: name 'network' is not defined
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()
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Cell In [15], line 1
----> 1 network.buses_t.marginal_price.mean(1).plot.area(figsize=(8, 3), ylabel="Euro per MWh")
2 plt.tight_layout()
NameError: name 'network' is not defined
We can inspect futher quantities as the active power of AC-DC converters and HVDC link.
[16]:
network.links_t.p0
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Cell In [16], line 1
----> 1 network.links_t.p0
NameError: name 'network' is not defined
[17]:
network.lines_t.p0
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Cell In [17], line 1
----> 1 network.lines_t.p0
NameError: name 'network' is not defined
…or the active power injection per bus.
[18]:
network.buses_t.p
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Cell In [18], line 1
----> 1 network.buses_t.p
NameError: name 'network' is not defined