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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]:

import pypsa
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns

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

[2]:

network = pypsa.Network()

Add three buses of AC and heat carrier each

[3]:

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

[3]:
attribute v_nom type x y carrier unit v_mag_pu_set v_mag_pu_min v_mag_pu_max control 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 
[4]:

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

[4]:

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

Add three lines in a ring

[5]:

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

[5]:
attribute bus0 bus1 type x r g b s_nom s_nom_extendable s_nom_min ... 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 False 0.0 ... -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 False 0.0 ... -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 False 0.0 ... -inf inf 0.0 0.0 0.0 0.0 0.0 0.0 0.0

3 rows × 29 columns

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

[6]:

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

[6]:
attribute bus0 bus1 type carrier efficiency build_year lifetime p_nom p_nom_extendable p_nom_min ... 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 0 inf 100.0 False 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 0 inf 100.0 False 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 0 inf 100.0 False 0.0 ... 0.0 0 0 1 0 NaN NaN 1.0 1.0 0.0

3 rows × 32 columns

Add carriers

[7]:

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

[7]:
attribute 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

[8]:

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",
        "boiler {}".format(i),
        bus="heat bus {}".format(i),
        p_nom=1000,
        efficiency=0.9,
        marginal_cost=20.0,
        carrier="gas",
    )

network.generators

[8]:
attribute bus control type p_nom p_nom_extendable p_nom_min p_nom_max p_min_pu p_max_pu p_set ... 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 False 0.0 inf 0.0 1.0 0.0 ... 0 0 1 0 NaN NaN 1.0 1.0 1.0 0.0
biomass generator electric bus 1 PQ 100.0 False 0.0 inf 0.0 1.0 0.0 ... 0 0 1 0 NaN NaN 1.0 1.0 1.0 0.0
boiler 0 heat bus 0 PQ 1000.0 False 0.0 inf 0.0 1.0 0.0 ... 0 0 1 0 NaN NaN 1.0 1.0 1.0 0.0
boiler 1 heat bus 1 PQ 1000.0 False 0.0 inf 0.0 1.0 0.0 ... 0 0 1 0 NaN NaN 1.0 1.0 1.0 0.0
boiler 2 heat bus 2 PQ 1000.0 False 0.0 inf 0.0 1.0 0.0 ... 0 0 1 0 NaN NaN 1.0 1.0 1.0 0.0

5 rows × 33 columns

Add electric loads and heat loads.

[9]:

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

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

network.loads

[9]:
attribute bus carrier type p_set q_set sign
Load
electric load 0 electric bus 0 0.0 0.0 -1.0
electric load 1 electric bus 1 10.0 0.0 -1.0
electric load 2 electric bus 2 20.0 0.0 -1.0
heat load 0 heat bus 0 30.0 0.0 -1.0
heat load 1 heat bus 1 20.0 0.0 -1.0
heat load 2 heat bus 2 10.0 0.0 -1.0

We define a function for the LOPF

[10]:

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()

[11]:

run_lopf()

WARNING:pypsa.components: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.components:The following lines have zero r, which could break the linear load flow:
Index(['line 0', 'line 1', 'line 2'], dtype='object', name='Line')
INFO:linopy.model: Solve problem using Glpk solver
INFO:linopy.io: Writing time: 0.06s
INFO:linopy.constants: Optimization successful:
Status: ok
Termination condition: optimal
Solution: 11 primals, 29 duals
Objective: 2.50e+03
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, Link-fix-p-lower, Link-fix-p-upper, Kirchhoff-Voltage-Law were not assigned to the network.

GLPSOL--GLPK LP/MIP Solver 5.0
Parameter(s) specified in the command line:
 --lp /tmp/linopy-problem-xkyl1int.lp --output /tmp/linopy-solve-wwyoj5li.sol
Reading problem data from '/tmp/linopy-problem-xkyl1int.lp'...
29 rows, 11 columns, 42 non-zeros
150 lines were read
GLPK Simplex Optimizer 5.0
29 rows, 11 columns, 42 non-zeros
Preprocessing...
4 rows, 5 columns, 11 non-zeros
Scaling...
 A: min|aij| =  1.000e+00  max|aij| =  2.500e+01  ratio =  2.500e+01
GM: min|aij| =  1.000e+00  max|aij| =  1.000e+00  ratio =  1.000e+00
EQ: min|aij| =  1.000e+00  max|aij| =  1.000e+00  ratio =  1.000e+00
Constructing initial basis...
Size of triangular part is 4
      0: obj =   3.340000000e+04 inf =   7.020e+03 (3)
      4: obj =   2.700000000e+03 inf =   0.000e+00 (0)
*     7: obj =   2.500000000e+03 inf =   0.000e+00 (0)
OPTIMAL LP SOLUTION FOUND
Time used:   0.0 secs
Memory used: 0.0 Mb (40436 bytes)
Writing basic solution to '/tmp/linopy-solve-wwyoj5li.sol'...
../_images/examples_lopf-with-heating_18_2.png

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

[12]:

network.links.marginal_cost = 10
run_lopf()

WARNING:pypsa.components: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.components:The following lines have zero r, which could break the linear load flow:
Index(['line 0', 'line 1', 'line 2'], dtype='object', name='Line')
INFO:linopy.model: Solve problem using Glpk solver
INFO:linopy.io: Writing time: 0.06s
INFO:linopy.constants: Optimization successful:
Status: ok
Termination condition: optimal
Solution: 11 primals, 29 duals
Objective: 2.70e+03
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, Link-fix-p-lower, Link-fix-p-upper, Kirchhoff-Voltage-Law were not assigned to the network.

GLPSOL--GLPK LP/MIP Solver 5.0
Parameter(s) specified in the command line:
 --lp /tmp/linopy-problem-bjdbjyye.lp --output /tmp/linopy-solve-zb6ou60q.sol
Reading problem data from '/tmp/linopy-problem-bjdbjyye.lp'...
29 rows, 11 columns, 42 non-zeros
153 lines were read
GLPK Simplex Optimizer 5.0
29 rows, 11 columns, 42 non-zeros
Preprocessing...
4 rows, 5 columns, 11 non-zeros
Scaling...
 A: min|aij| =  1.000e+00  max|aij| =  2.500e+01  ratio =  2.500e+01
GM: min|aij| =  1.000e+00  max|aij| =  1.000e+00  ratio =  1.000e+00
EQ: min|aij| =  1.000e+00  max|aij| =  1.000e+00  ratio =  1.000e+00
Constructing initial basis...
Size of triangular part is 4
      0: obj =   3.200000000e+03 inf =   7.020e+03 (3)
      4: obj =   2.700000000e+03 inf =   0.000e+00 (0)
OPTIMAL LP SOLUTION FOUND
Time used:   0.0 secs
Memory used: 0.0 Mb (40436 bytes)
Writing basic solution to '/tmp/linopy-solve-zb6ou60q.sol'...
../_images/examples_lopf-with-heating_20_2.png

Finally, rerun with no CO2 emissions.

[13]:

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

run_lopf()

WARNING:pypsa.components: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.components:The following lines have zero r, which could break the linear load flow:
Index(['line 0', 'line 1', 'line 2'], dtype='object', name='Line')
INFO:linopy.model: Solve problem using Glpk solver
INFO:linopy.io: Writing time: 0.06s
INFO:linopy.constants: Optimization successful:
Status: ok
Termination condition: optimal
Solution: 11 primals, 30 duals
Objective: 5.20e+03
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, Link-fix-p-lower, Link-fix-p-upper, Kirchhoff-Voltage-Law were not assigned to the network.

GLPSOL--GLPK LP/MIP Solver 5.0
Parameter(s) specified in the command line:
 --lp /tmp/linopy-problem-jgq0xgyj.lp --output /tmp/linopy-solve-5waktq_3.sol
Reading problem data from '/tmp/linopy-problem-jgq0xgyj.lp'...
30 rows, 11 columns, 46 non-zeros
159 lines were read
GLPK Simplex Optimizer 5.0
30 rows, 11 columns, 46 non-zeros
Preprocessing...
4 rows, 3 columns, 9 non-zeros
Scaling...
 A: min|aij| =  1.000e+00  max|aij| =  2.500e+01  ratio =  2.500e+01
GM: min|aij| =  1.000e+00  max|aij| =  1.000e+00  ratio =  1.000e+00
EQ: min|aij| =  1.000e+00  max|aij| =  1.000e+00  ratio =  1.000e+00
Constructing initial basis...
Size of triangular part is 3
      0: obj =   5.200000000e+03 inf =   2.997e+03 (2)
      2: obj =   5.200000000e+03 inf =   0.000e+00 (0)
OPTIMAL LP SOLUTION FOUND
Time used:   0.0 secs
Memory used: 0.0 Mb (40436 bytes)
Writing basic solution to '/tmp/linopy-solve-5waktq_3.sol'...
../_images/examples_lopf-with-heating_22_2.png