LOPF with coupling to heating sector

Note

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

LOPF with coupling to heating sector#

In this example three locations are optimised, each with an electric bus and a heating bus and corresponding loads. At each location the electric and heating buses are connected with heat pumps; heat can also be supplied to the heat bus with a boiler. The electric buses are connected with transmission lines and there are electrical generators at two of the nodes.

[1]:

%pip install seaborn

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[2]:

import matplotlib.pyplot as plt
import pandas as pd
import seaborn as sns

import pypsa

sns.set(rc={"figure.figsize": (9, 5)})

[3]:

network = pypsa.Network()

Add three buses of AC and heat carrier each

[4]:

for i in range(3):
    network.add("Bus", f"electric bus {i}", v_nom=20.0)
    network.add("Bus", f"heat bus {i}", carrier="heat")
network.buses

[4]:
v_nom type x y carrier unit v_mag_pu_set v_mag_pu_min v_mag_pu_max control generator sub_network
Bus
electric bus 0 20.0 0.0 0.0 AC 1.0 0.0 inf PQ
heat bus 0 1.0 0.0 0.0 heat 1.0 0.0 inf PQ
electric bus 1 20.0 0.0 0.0 AC 1.0 0.0 inf PQ
heat bus 1 1.0 0.0 0.0 heat 1.0 0.0 inf PQ
electric bus 2 20.0 0.0 0.0 AC 1.0 0.0 inf PQ
heat bus 2 1.0 0.0 0.0 heat 1.0 0.0 inf PQ 
[5]:

network.buses["carrier"].value_counts()

[5]:

carrier
AC      3
heat    3
Name: count, dtype: int64

Add three lines in a ring

[6]:

for i in range(3):
    network.add(
        "Line",
        f"line {i}",
        bus0=f"electric bus {i}",
        bus1=f"electric bus {(i + 1) % 3}",
        x=0.1,
        s_nom=1000,
    )
network.lines

[6]:
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
Line
line 0 electric bus 0 electric bus 1 0.1 0.0 0.0 0.0 1000.0 0.0 False ... -inf inf 0.0 0.0 0.0 0.0 0.0 0.0 0.0
line 1 electric bus 1 electric bus 2 0.1 0.0 0.0 0.0 1000.0 0.0 False ... -inf inf 0.0 0.0 0.0 0.0 0.0 0.0 0.0
line 2 electric bus 2 electric bus 0 0.1 0.0 0.0 0.0 1000.0 0.0 False ... -inf inf 0.0 0.0 0.0 0.0 0.0 0.0 0.0

3 rows × 31 columns

Connect the electric to the heat buses with heat pumps with COP 3

[7]:

for i in range(3):
    network.add(
        "Link",
        f"heat pump {i}",
        bus0=f"electric bus {i}",
        bus1=f"heat bus {i}",
        p_nom=100,
        efficiency=3.0,
    )
network.links

[7]:
bus0 bus1 type carrier efficiency active build_year lifetime p_nom p_nom_mod ... 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
Link
heat pump 0 electric bus 0 heat bus 0 3.0 True 0 inf 100.0 0.0 ... 0.0 0 0 1 0 NaN NaN 1.0 1.0 0.0
heat pump 1 electric bus 1 heat bus 1 3.0 True 0 inf 100.0 0.0 ... 0.0 0 0 1 0 NaN NaN 1.0 1.0 0.0
heat pump 2 electric bus 2 heat bus 2 3.0 True 0 inf 100.0 0.0 ... 0.0 0 0 1 0 NaN NaN 1.0 1.0 0.0

3 rows × 34 columns

Add carriers

[8]:

network.add("Carrier", "gas", co2_emissions=0.27)
network.add("Carrier", "biomass", co2_emissions=0.0)
network.carriers

[8]:
co2_emissions color nice_name max_growth max_relative_growth
Carrier
gas 0.27 inf 0.0
biomass 0.00 inf 0.0

Add a gas generator at bus 0, a biomass generator at bus 1 and a boiler at all heat buses

[9]:

network.add(
    "Generator",
    "gas generator",
    bus="electric bus 0",
    p_nom=100,
    marginal_cost=50,
    carrier="gas",
    efficiency=0.3,
)

network.add(
    "Generator",
    "biomass generator",
    bus="electric bus 1",
    p_nom=100,
    marginal_cost=100,
    efficiency=0.3,
    carrier="biomass",
)

for i in range(3):
    network.add(
        "Generator",
        f"boiler {i}",
        bus=f"heat bus {i}",
        p_nom=1000,
        efficiency=0.9,
        marginal_cost=20.0,
        carrier="gas",
    )

network.generators

[9]:
bus control type p_nom p_nom_mod p_nom_extendable p_nom_min p_nom_max p_min_pu p_max_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
Generator
gas generator electric bus 0 PQ 100.0 0.0 False 0.0 inf 0.0 1.0 ... 0 0 1 0 NaN NaN 1.0 1.0 1.0 0.0
biomass generator electric bus 1 PQ 100.0 0.0 False 0.0 inf 0.0 1.0 ... 0 0 1 0 NaN NaN 1.0 1.0 1.0 0.0
boiler 0 heat bus 0 PQ 1000.0 0.0 False 0.0 inf 0.0 1.0 ... 0 0 1 0 NaN NaN 1.0 1.0 1.0 0.0
boiler 1 heat bus 1 PQ 1000.0 0.0 False 0.0 inf 0.0 1.0 ... 0 0 1 0 NaN NaN 1.0 1.0 1.0 0.0
boiler 2 heat bus 2 PQ 1000.0 0.0 False 0.0 inf 0.0 1.0 ... 0 0 1 0 NaN NaN 1.0 1.0 1.0 0.0

5 rows × 37 columns

Add electric loads and heat loads.

[10]:

for i in range(3):
    network.add(
        "Load",
        f"electric load {i}",
        bus=f"electric bus {i}",
        p_set=i * 10,
    )

for i in range(3):
    network.add(
        "Load",
        f"heat load {i}",
        bus=f"heat bus {i}",
        p_set=(3 - i) * 10,
    )

network.loads

[10]:
bus carrier type p_set q_set sign active
Load
electric load 0 electric bus 0 0.0 0.0 -1.0 True
electric load 1 electric bus 1 10.0 0.0 -1.0 True
electric load 2 electric bus 2 20.0 0.0 -1.0 True
heat load 0 heat bus 0 30.0 0.0 -1.0 True
heat load 1 heat bus 1 20.0 0.0 -1.0 True
heat load 2 heat bus 2 10.0 0.0 -1.0 True

We define a function for the LOPF

[11]:

def run_lopf():
    network.optimize()
    df = pd.concat(
        [
            network.generators_t.p.loc["now"],
            network.links_t.p0.loc["now"],
            network.loads_t.p.loc["now"],
        ],
        keys=["Generators", "Links", "Line"],
        names=["Component", "index"],
    ).reset_index(name="Production")

    sns.barplot(data=df, x="index", y="Production", hue="Component")
    plt.title(f"Objective: {network.objective}")
    plt.xticks(rotation=90)
    plt.tight_layout()

[12]:

run_lopf()

WARNING:pypsa.consistency:The following lines have carriers which are not defined:
Index(['line 0', 'line 1', 'line 2'], dtype='object', name='Line')
WARNING:pypsa.consistency:The following lines have zero r, which could break the linear load flow:
Index(['line 0', 'line 1', 'line 2'], dtype='object', name='Line')
WARNING:pypsa.consistency:The following buses have carriers which are not defined:
Index(['electric bus 0', 'heat bus 0', 'electric bus 1', 'heat bus 1',
       'electric bus 2', 'heat bus 2'],
      dtype='object', name='Bus')
WARNING:pypsa.consistency:The following links have carriers which are not defined:
Index(['heat pump 0', 'heat pump 1', 'heat pump 2'], dtype='object', name='Link')
WARNING:pypsa.consistency:The following lines have carriers which are not defined:
Index(['line 0', 'line 1', 'line 2'], dtype='object', name='Line')
WARNING:pypsa.consistency:The following lines have zero r, which could break the linear load flow:
Index(['line 0', 'line 1', 'line 2'], dtype='object', name='Line')
WARNING:pypsa.consistency:The following buses have carriers which are not defined:
Index(['electric bus 0', 'heat bus 0', 'electric bus 1', 'heat bus 1',
       'electric bus 2', 'heat bus 2'],
      dtype='object', name='Bus')
WARNING:pypsa.consistency:The following links have carriers which are not defined:
Index(['heat pump 0', 'heat pump 1', 'heat pump 2'], dtype='object', name='Link')
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/envs/latest/lib/python3.12/site-packages/linopy/common.py:147: UserWarning: coords for dimension(s) ['Generator'] is not aligned with the pandas object. Previously, the indexes of the pandas were ignored and overwritten in these cases. Now, the pandas object's coordinates are taken considered for alignment.
  warn(
INFO:linopy.model: Solve problem using Highs solver
INFO:linopy.io: Writing time: 0.04s
INFO:linopy.solvers:Log file at /tmp/highs.log
INFO:linopy.constants: Optimization successful:
Status: ok
Termination condition: optimal
Solution: 11 primals, 34 duals
Objective: 2.50e+03
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, Link-fix-p-lower, Link-fix-p-upper, Kirchhoff-Voltage-Law were not assigned to the network.

Running HiGHS 1.7.2 (git hash: 184e327): Copyright (c) 2024 HiGHS under MIT licence terms
Coefficient ranges:
  Matrix [1e+00, 2e+01]
  Cost   [2e+01, 1e+02]
  Bound  [0e+00, 0e+00]
  RHS    [1e+01, 1e+03]
Presolving model
4 rows, 8 cols, 14 nonzeros  0s
4 rows, 8 cols, 14 nonzeros  0s
Presolve : Reductions: rows 4(-30); columns 8(-3); elements 14(-33)
Solving the presolved LP
Using EKK dual simplex solver - serial
  Iteration        Objective     Infeasibilities num(sum)
          0    -1.8728037080e-03 Pr: 4(9575) 0s
          4     2.5000000000e+03 Pr: 0(0) 0s
Solving the original LP from the solution after postsolve
Model   status      : Optimal
Simplex   iterations: 4
Objective value     :  2.5000000000e+03
HiGHS run time      :          0.00
Writing the solution to /tmp/linopy-solve-y61l_eqc.sol
../_images/examples_lopf-with-heating_19_2.png

Now, rerun with marginal costs for the heat pump operation.

[13]:

network.links.marginal_cost = 10
run_lopf()

WARNING:pypsa.consistency:The following lines have carriers which are not defined:
Index(['line 0', 'line 1', 'line 2'], dtype='object', name='Line')
WARNING:pypsa.consistency:The following lines have zero r, which could break the linear load flow:
Index(['line 0', 'line 1', 'line 2'], dtype='object', name='Line')
WARNING:pypsa.consistency:The following buses have carriers which are not defined:
Index(['electric bus 0', 'heat bus 0', 'electric bus 1', 'heat bus 1',
       'electric bus 2', 'heat bus 2'],
      dtype='object', name='Bus')
WARNING:pypsa.consistency:The following links have carriers which are not defined:
Index(['heat pump 0', 'heat pump 1', 'heat pump 2'], dtype='object', name='Link')
WARNING:pypsa.consistency:The following sub_networks have carriers which are not defined:
Index(['0'], dtype='object', name='SubNetwork')
WARNING:pypsa.consistency:The following lines have carriers which are not defined:
Index(['line 0', 'line 1', 'line 2'], dtype='object', name='Line')
WARNING:pypsa.consistency:The following lines have zero r, which could break the linear load flow:
Index(['line 0', 'line 1', 'line 2'], dtype='object', name='Line')
WARNING:pypsa.consistency:The following buses have carriers which are not defined:
Index(['electric bus 0', 'heat bus 0', 'electric bus 1', 'heat bus 1',
       'electric bus 2', 'heat bus 2'],
      dtype='object', name='Bus')
WARNING:pypsa.consistency:The following links have carriers which are not defined:
Index(['heat pump 0', 'heat pump 1', 'heat pump 2'], dtype='object', name='Link')
WARNING:pypsa.consistency:The following sub_networks have carriers which are not defined:
Index(['0'], dtype='object', name='SubNetwork')
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/envs/latest/lib/python3.12/site-packages/linopy/common.py:147: UserWarning: coords for dimension(s) ['Generator'] is not aligned with the pandas object. Previously, the indexes of the pandas were ignored and overwritten in these cases. Now, the pandas object's coordinates are taken considered for alignment.
  warn(
INFO:linopy.model: Solve problem using Highs solver
INFO:linopy.io: Writing time: 0.04s
INFO:linopy.solvers:Log file at /tmp/highs.log
INFO:linopy.constants: Optimization successful:
Status: ok
Termination condition: optimal
Solution: 11 primals, 34 duals
Objective: 2.70e+03
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, Link-fix-p-lower, Link-fix-p-upper, Kirchhoff-Voltage-Law were not assigned to the network.

Running HiGHS 1.7.2 (git hash: 184e327): Copyright (c) 2024 HiGHS under MIT licence terms
Coefficient ranges:
  Matrix [1e+00, 2e+01]
  Cost   [1e+01, 1e+02]
  Bound  [0e+00, 0e+00]
  RHS    [1e+01, 1e+03]
Presolving model
4 rows, 8 cols, 14 nonzeros  0s
4 rows, 7 cols, 13 nonzeros  0s
Presolve : Reductions: rows 4(-30); columns 7(-4); elements 13(-34)
Solving the presolved LP
Using EKK dual simplex solver - serial
  Iteration        Objective     Infeasibilities num(sum)
          0     1.9999802937e+02 Pr: 4(9575) 0s
          4     2.7000000000e+03 Pr: 0(0); Du: 0(3.55271e-15) 0s
Solving the original LP from the solution after postsolve
Model   status      : Optimal
Simplex   iterations: 4
Objective value     :  2.7000000000e+03
HiGHS run time      :          0.00
Writing the solution to /tmp/linopy-solve-84cs1i1a.sol
../_images/examples_lopf-with-heating_21_2.png

Finally, rerun with no CO2 emissions.

[14]:

network.add("GlobalConstraint", "co2_limit", sense="<=", constant=0.0)

run_lopf()

WARNING:pypsa.consistency:The following lines have carriers which are not defined:
Index(['line 0', 'line 1', 'line 2'], dtype='object', name='Line')
WARNING:pypsa.consistency:The following lines have zero r, which could break the linear load flow:
Index(['line 0', 'line 1', 'line 2'], dtype='object', name='Line')
WARNING:pypsa.consistency:The following buses have carriers which are not defined:
Index(['electric bus 0', 'heat bus 0', 'electric bus 1', 'heat bus 1',
       'electric bus 2', 'heat bus 2'],
      dtype='object', name='Bus')
WARNING:pypsa.consistency:The following links have carriers which are not defined:
Index(['heat pump 0', 'heat pump 1', 'heat pump 2'], dtype='object', name='Link')
WARNING:pypsa.consistency:The following sub_networks have carriers which are not defined:
Index(['0'], dtype='object', name='SubNetwork')
WARNING:pypsa.consistency:The following lines have carriers which are not defined:
Index(['line 0', 'line 1', 'line 2'], dtype='object', name='Line')
WARNING:pypsa.consistency:The following lines have zero r, which could break the linear load flow:
Index(['line 0', 'line 1', 'line 2'], dtype='object', name='Line')
WARNING:pypsa.consistency:The following buses have carriers which are not defined:
Index(['electric bus 0', 'heat bus 0', 'electric bus 1', 'heat bus 1',
       'electric bus 2', 'heat bus 2'],
      dtype='object', name='Bus')
WARNING:pypsa.consistency:The following links have carriers which are not defined:
Index(['heat pump 0', 'heat pump 1', 'heat pump 2'], dtype='object', name='Link')
WARNING:pypsa.consistency:The following sub_networks have carriers which are not defined:
Index(['0'], dtype='object', name='SubNetwork')
/home/docs/checkouts/readthedocs.org/user_builds/pypsa/envs/latest/lib/python3.12/site-packages/linopy/common.py:147: UserWarning: coords for dimension(s) ['Generator'] is not aligned with the pandas object. Previously, the indexes of the pandas were ignored and overwritten in these cases. Now, the pandas object's coordinates are taken considered for alignment.
  warn(
INFO:linopy.model: Solve problem using Highs solver
INFO:linopy.io: Writing time: 0.05s
INFO:linopy.solvers:Log file at /tmp/highs.log
INFO:linopy.constants: Optimization successful:
Status: ok
Termination condition: optimal
Solution: 11 primals, 35 duals
Objective: 5.20e+03
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, Link-fix-p-lower, Link-fix-p-upper, Kirchhoff-Voltage-Law were not assigned to the network.

Running HiGHS 1.7.2 (git hash: 184e327): Copyright (c) 2024 HiGHS under MIT licence terms
Coefficient ranges:
  Matrix [3e-01, 2e+01]
  Cost   [1e+01, 1e+02]
  Bound  [0e+00, 0e+00]
  RHS    [1e+01, 1e+03]
Presolving model
4 rows, 4 cols, 10 nonzeros  0s
0 rows, 0 cols, 0 nonzeros  0s
Presolve : Reductions: rows 0(-35); columns 0(-11); elements 0(-51) - Reduced to empty
Solving the original LP from the solution after postsolve
Model   status      : Optimal
Objective value     :  5.2000000000e+03
HiGHS run time      :          0.00
Writing the solution to /tmp/linopy-solve-082k_wjh.sol
../_images/examples_lopf-with-heating_23_2.png