Note
You can download this example as a Jupyter notebook or start it in interactive mode.
Two chained reservoirs
Two disconnected electrical loads are fed from two reservoirs linked by a river; the first reservoir has inflow from rain onto a water basin.
Note that the two reservoirs are tightly coupled, meaning there is no time delay between the first one emptying and the second one filling, as there would be if there were a long stretch of river between the reservoirs. The reservoirs are essentially assumed to be close to each other. A time delay would require a “Link” element between different snapshots, which is not yet supported by PyPSA (but could be enabled by passing network.lopf() an extra_functionality function).
[1]:
import pypsa
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from pyomo.environ import Constraint
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Cell In [1], line 1
----> 1 import pypsa
2 import pandas as pd
3 import numpy as np
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
First tell PyPSA that links will have a 2nd bus by overriding the component_attrs. This is needed so that water can both go through a turbine AND feed the next reservoir
[2]:
override_component_attrs = pypsa.descriptors.Dict(
{k: v.copy() for k, v in pypsa.components.component_attrs.items()}
)
override_component_attrs["Link"].loc["bus2"] = [
"string",
np.nan,
np.nan,
"2nd bus",
"Input (optional)",
]
override_component_attrs["Link"].loc["efficiency2"] = [
"static or series",
"per unit",
1.0,
"2nd bus efficiency",
"Input (optional)",
]
override_component_attrs["Link"].loc["p2"] = [
"series",
"MW",
0.0,
"2nd bus output",
"Output",
]
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Cell In [2], line 1
----> 1 override_component_attrs = pypsa.descriptors.Dict(
2 {k: v.copy() for k, v in pypsa.components.component_attrs.items()}
3 )
4 override_component_attrs["Link"].loc["bus2"] = [
5 "string",
6 np.nan,
(...)
9 "Input (optional)",
10 ]
11 override_component_attrs["Link"].loc["efficiency2"] = [
12 "static or series",
13 "per unit",
(...)
16 "Input (optional)",
17 ]
NameError: name 'pypsa' is not defined
[3]:
network = pypsa.Network(override_component_attrs=override_component_attrs)
network.set_snapshots(pd.date_range("2016-01-01 00:00", "2016-01-01 03:00", freq="H"))
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Cell In [3], line 1
----> 1 network = pypsa.Network(override_component_attrs=override_component_attrs)
2 network.set_snapshots(pd.date_range("2016-01-01 00:00", "2016-01-01 03:00", freq="H"))
NameError: name 'pypsa' is not defined
Add assets to the network.
[4]:
network.add("Carrier", "reservoir")
network.add("Carrier", "rain")
network.add("Bus", "0", carrier="AC")
network.add("Bus", "1", carrier="AC")
network.add("Bus", "0 reservoir", carrier="reservoir")
network.add("Bus", "1 reservoir", carrier="reservoir")
network.add(
"Generator",
"rain",
bus="0 reservoir",
carrier="rain",
p_nom=1000,
p_max_pu=[0.0, 0.2, 0.7, 0.4],
)
network.add("Load", "0 load", bus="0", p_set=20.0)
network.add("Load", "1 load", bus="1", p_set=30.0)
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Cell In [4], line 1
----> 1 network.add("Carrier", "reservoir")
2 network.add("Carrier", "rain")
4 network.add("Bus", "0", carrier="AC")
NameError: name 'network' is not defined
The efficiency of a river is the relation between the gravitational potential energy of 1 m^3 of water in reservoir 0 relative to its turbine versus the potential energy of 1 m^3 of water in reservoir 1 relative to its turbine
[5]:
network.add(
"Link",
"spillage",
bus0="0 reservoir",
bus1="1 reservoir",
efficiency=0.5,
p_nom_extendable=True,
)
# water from turbine also goes into next reservoir
network.add(
"Link",
"0 turbine",
bus0="0 reservoir",
bus1="0",
bus2="1 reservoir",
efficiency=0.9,
efficiency2=0.5,
capital_cost=1000,
p_nom_extendable=True,
)
network.add(
"Link",
"1 turbine",
bus0="1 reservoir",
bus1="1",
efficiency=0.9,
capital_cost=1000,
p_nom_extendable=True,
)
network.add(
"Store", "0 reservoir", bus="0 reservoir", e_cyclic=True, e_nom_extendable=True
)
network.add(
"Store", "1 reservoir", bus="1 reservoir", e_cyclic=True, e_nom_extendable=True
)
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Cell In [5], line 1
----> 1 network.add(
2 "Link",
3 "spillage",
4 bus0="0 reservoir",
5 bus1="1 reservoir",
6 efficiency=0.5,
7 p_nom_extendable=True,
8 )
11 # water from turbine also goes into next reservoir
12 network.add(
13 "Link",
14 "0 turbine",
(...)
21 p_nom_extendable=True,
22 )
NameError: name 'network' is not defined
[6]:
network.lopf(network.snapshots)
print("Objective:", network.objective)
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Cell In [6], line 1
----> 1 network.lopf(network.snapshots)
2 print("Objective:", network.objective)
NameError: name 'network' is not defined
[7]:
network.generators_t.p.plot.area(figsize=(9, 4))
plt.tight_layout()
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Cell In [7], line 1
----> 1 network.generators_t.p.plot.area(figsize=(9, 4))
2 plt.tight_layout()
NameError: name 'network' is not defined
Now, let’s have look at the different outputs of the links.
[8]:
network.links_t.p0.plot(figsize=(9, 4), lw=3)
plt.tight_layout()
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Cell In [8], line 1
----> 1 network.links_t.p0.plot(figsize=(9, 4), lw=3)
2 plt.tight_layout()
NameError: name 'network' is not defined
[9]:
network.links_t.p1.plot(figsize=(9, 4), lw=3)
plt.tight_layout()
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Cell In [9], line 1
----> 1 network.links_t.p1.plot(figsize=(9, 4), lw=3)
2 plt.tight_layout()
NameError: name 'network' is not defined
[10]:
network.links_t.p2.plot(figsize=(9, 4), lw=3)
plt.tight_layout()
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Cell In [10], line 1
----> 1 network.links_t.p2.plot(figsize=(9, 4), lw=3)
2 plt.tight_layout()
NameError: name 'network' is not defined
What are the energy outputs and energy levels at the reservoirs?
[11]:
pd.DataFrame({attr: network.stores_t[attr]["0 reservoir"] for attr in ["p", "e"]})
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Cell In [11], line 1
----> 1 pd.DataFrame({attr: network.stores_t[attr]["0 reservoir"] for attr in ["p", "e"]})
NameError: name 'pd' is not defined
[12]:
pd.DataFrame({attr: network.stores_t[attr]["1 reservoir"] for attr in ["p", "e"]})
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
Cell In [12], line 1
----> 1 pd.DataFrame({attr: network.stores_t[attr]["1 reservoir"] for attr in ["p", "e"]})
NameError: name 'pd' is not defined