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]:

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)})

---------------------------------------------------------------------------
ModuleNotFoundError                       Traceback (most recent call last)
/tmp/ipykernel_471/634408091.py in <module>
      3 import pandas as pd
      4 import matplotlib.pyplot as plt
----> 5 import seaborn as sns
      6 sns.set(rc={"figure.figsize":(9, 5)})

ModuleNotFoundError: No module named 'seaborn'

[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.)
    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
electric bus 0 20.0 0.0 0.0 AC None 1.0 0.0 inf PQ
heat bus 0 1.0 0.0 0.0 heat None 1.0 0.0 inf PQ
electric bus 1 20.0 0.0 0.0 AC None 1.0 0.0 inf PQ
heat bus 1 1.0 0.0 0.0 heat None 1.0 0.0 inf PQ
electric bus 2 20.0 0.0 0.0 AC None 1.0 0.0 inf PQ
heat bus 2 1.0 0.0 0.0 heat None 1.0 0.0 inf PQ 
[4]:

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

[4]:

AC      3
heat    3
Name: carrier, 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 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.)
network.links

[6]:
attribute bus0 bus1 type carrier efficiency build_year lifetime p_nom p_nom_extendable p_nom_min p_nom_max p_set p_min_pu p_max_pu capital_cost marginal_cost length terrain_factor p_nom_opt
heat pump 0 electric bus 0 heat bus 0 3.0 0 inf 100.0 False 0.0 inf 0.0 0.0 1.0 0.0 0.0 0.0 1.0 0.0
heat pump 1 electric bus 1 heat bus 1 3.0 0 inf 100.0 False 0.0 inf 0.0 0.0 1.0 0.0 0.0 0.0 1.0 0.0
heat pump 2 electric bus 2 heat bus 2 3.0 0 inf 100.0 False 0.0 inf 0.0 0.0 1.0 0.0 0.0 0.0 1.0 0.0

Add carriers

[7]:

network.add("Carrier","gas", co2_emissions=0.27)
network.add("Carrier","biomass", co2_emissions=0.)
network.carriers

[7]:
attribute co2_emissions color nice_name max_growth
gas 0.27 inf
biomass 0.00 inf

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.,
            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 ... 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
gas generator electric bus 0 PQ 100.0 False 0.0 inf 0.0 1.0 0.0 ... 0.0 0 0 1 0 NaN NaN 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 0 0 1 0 NaN NaN 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 0 0 1 0 NaN NaN 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 0 0 1 0 NaN NaN 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 0 0 1 0 NaN NaN 1.0 1.0 0.0

5 rows × 30 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
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.lopf()
    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()

INFO:pypsa.opf:Performed preliminary steps
INFO:pypsa.opf:Building pyomo model using `kirchhoff` formulation
INFO:pypsa.opf:Solving model using glpk
WARNING:pyomo.solvers:Could not locate the 'glpsol' executable, which is required for solver 'glpk'

---------------------------------------------------------------------------
ApplicationError                          Traceback (most recent call last)
/tmp/ipykernel_471/262315099.py in <module>
----> 1 run_lopf()

/tmp/ipykernel_471/3405664651.py in run_lopf()
      1 def run_lopf():
----> 2     network.lopf()
      3     df = pd.concat([network.generators_t.p.loc['now'],
      4                    network.links_t.p0.loc['now'],
      5                    network.loads_t.p.loc['now']],

~/checkouts/readthedocs.org/user_builds/pypsa-docs-staging/envs/latest/lib/python3.7/site-packages/pypsa/components.py in lopf(self, snapshots, pyomo, solver_name, solver_options, solver_logfile, formulation, keep_files, extra_functionality, multi_investment_periods, **kwargs)
    646
    647         if pyomo:
--> 648             return network_lopf(self, **args)
    649         else:
    650             return network_lopf_lowmem(self, **args)

~/checkouts/readthedocs.org/user_builds/pypsa-docs-staging/envs/latest/lib/python3.7/site-packages/pypsa/opf.py in network_lopf(network, snapshots, solver_name, solver_io, skip_pre, extra_functionality, multi_investment_periods, solver_logfile, solver_options, keep_files, formulation, ptdf_tolerance, free_memory, extra_postprocessing)
   1663                               solver_logfile=solver_logfile, solver_options=solver_options,
   1664                               keep_files=keep_files, free_memory=free_memory,
-> 1665                               extra_postprocessing=extra_postprocessing)

~/checkouts/readthedocs.org/user_builds/pypsa-docs-staging/envs/latest/lib/python3.7/site-packages/pypsa/opf.py in network_lopf_solve(network, snapshots, formulation, solver_options, solver_logfile, keep_files, free_memory, extra_postprocessing)
   1563             network.results = network.opt.solve(*args, suffixes=["dual"], keepfiles=keep_files, logfile=solver_logfile, options=solver_options)
   1564     else:
-> 1565         network.results = network.opt.solve(*args, suffixes=["dual"], keepfiles=keep_files, logfile=solver_logfile, options=solver_options)
   1566
   1567     if logger.isEnabledFor(logging.INFO):

~/checkouts/readthedocs.org/user_builds/pypsa-docs-staging/envs/latest/lib/python3.7/site-packages/pyomo/opt/base/solvers.py in solve(self, *args, **kwds)
    510         """ Solve the problem """
    511
--> 512         self.available(exception_flag=True)
    513         #
    514         # If the inputs are models, then validate that they have been

~/checkouts/readthedocs.org/user_builds/pypsa-docs-staging/envs/latest/lib/python3.7/site-packages/pyomo/opt/solver/shellcmd.py in available(self, exception_flag)
    123             if exception_flag:
    124                 msg = "No executable found for solver '%s'"
--> 125                 raise ApplicationError(msg % self.name)
    126             return False
    127         return True

ApplicationError: No executable found for solver 'glpk'

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

[12]:

network.links.marginal_cost = 10
run_lopf()

INFO:pypsa.opf:Performed preliminary steps
INFO:pypsa.opf:Building pyomo model using `kirchhoff` formulation
INFO:pypsa.opf:Solving model using glpk
WARNING:pyomo.solvers:Could not locate the 'glpsol' executable, which is required for solver 'glpk'

---------------------------------------------------------------------------
ApplicationError                          Traceback (most recent call last)
/tmp/ipykernel_471/4148435902.py in <module>
      1 network.links.marginal_cost = 10
----> 2 run_lopf()

/tmp/ipykernel_471/3405664651.py in run_lopf()
      1 def run_lopf():
----> 2     network.lopf()
      3     df = pd.concat([network.generators_t.p.loc['now'],
      4                    network.links_t.p0.loc['now'],
      5                    network.loads_t.p.loc['now']],

~/checkouts/readthedocs.org/user_builds/pypsa-docs-staging/envs/latest/lib/python3.7/site-packages/pypsa/components.py in lopf(self, snapshots, pyomo, solver_name, solver_options, solver_logfile, formulation, keep_files, extra_functionality, multi_investment_periods, **kwargs)
    646
    647         if pyomo:
--> 648             return network_lopf(self, **args)
    649         else:
    650             return network_lopf_lowmem(self, **args)

~/checkouts/readthedocs.org/user_builds/pypsa-docs-staging/envs/latest/lib/python3.7/site-packages/pypsa/opf.py in network_lopf(network, snapshots, solver_name, solver_io, skip_pre, extra_functionality, multi_investment_periods, solver_logfile, solver_options, keep_files, formulation, ptdf_tolerance, free_memory, extra_postprocessing)
   1663                               solver_logfile=solver_logfile, solver_options=solver_options,
   1664                               keep_files=keep_files, free_memory=free_memory,
-> 1665                               extra_postprocessing=extra_postprocessing)

~/checkouts/readthedocs.org/user_builds/pypsa-docs-staging/envs/latest/lib/python3.7/site-packages/pypsa/opf.py in network_lopf_solve(network, snapshots, formulation, solver_options, solver_logfile, keep_files, free_memory, extra_postprocessing)
   1563             network.results = network.opt.solve(*args, suffixes=["dual"], keepfiles=keep_files, logfile=solver_logfile, options=solver_options)
   1564     else:
-> 1565         network.results = network.opt.solve(*args, suffixes=["dual"], keepfiles=keep_files, logfile=solver_logfile, options=solver_options)
   1566
   1567     if logger.isEnabledFor(logging.INFO):

~/checkouts/readthedocs.org/user_builds/pypsa-docs-staging/envs/latest/lib/python3.7/site-packages/pyomo/opt/base/solvers.py in solve(self, *args, **kwds)
    510         """ Solve the problem """
    511
--> 512         self.available(exception_flag=True)
    513         #
    514         # If the inputs are models, then validate that they have been

~/checkouts/readthedocs.org/user_builds/pypsa-docs-staging/envs/latest/lib/python3.7/site-packages/pyomo/opt/solver/shellcmd.py in available(self, exception_flag)
    123             if exception_flag:
    124                 msg = "No executable found for solver '%s'"
--> 125                 raise ApplicationError(msg % self.name)
    126             return False
    127         return True

ApplicationError: No executable found for solver 'glpk'

Finally, rerun with no CO2 emissions.

[13]:

network.add("GlobalConstraint",
            "co2_limit",
            sense="<=",
            constant=0.)

run_lopf()

INFO:pypsa.opf:Performed preliminary steps
INFO:pypsa.opf:Building pyomo model using `kirchhoff` formulation
INFO:pypsa.opf:Solving model using glpk
WARNING:pyomo.solvers:Could not locate the 'glpsol' executable, which is required for solver 'glpk'

---------------------------------------------------------------------------
ApplicationError                          Traceback (most recent call last)
/tmp/ipykernel_471/2487073327.py in <module>
      4             constant=0.)
      5
----> 6 run_lopf()

/tmp/ipykernel_471/3405664651.py in run_lopf()
      1 def run_lopf():
----> 2     network.lopf()
      3     df = pd.concat([network.generators_t.p.loc['now'],
      4                    network.links_t.p0.loc['now'],
      5                    network.loads_t.p.loc['now']],

~/checkouts/readthedocs.org/user_builds/pypsa-docs-staging/envs/latest/lib/python3.7/site-packages/pypsa/components.py in lopf(self, snapshots, pyomo, solver_name, solver_options, solver_logfile, formulation, keep_files, extra_functionality, multi_investment_periods, **kwargs)
    646
    647         if pyomo:
--> 648             return network_lopf(self, **args)
    649         else:
    650             return network_lopf_lowmem(self, **args)

~/checkouts/readthedocs.org/user_builds/pypsa-docs-staging/envs/latest/lib/python3.7/site-packages/pypsa/opf.py in network_lopf(network, snapshots, solver_name, solver_io, skip_pre, extra_functionality, multi_investment_periods, solver_logfile, solver_options, keep_files, formulation, ptdf_tolerance, free_memory, extra_postprocessing)
   1663                               solver_logfile=solver_logfile, solver_options=solver_options,
   1664                               keep_files=keep_files, free_memory=free_memory,
-> 1665                               extra_postprocessing=extra_postprocessing)

~/checkouts/readthedocs.org/user_builds/pypsa-docs-staging/envs/latest/lib/python3.7/site-packages/pypsa/opf.py in network_lopf_solve(network, snapshots, formulation, solver_options, solver_logfile, keep_files, free_memory, extra_postprocessing)
   1563             network.results = network.opt.solve(*args, suffixes=["dual"], keepfiles=keep_files, logfile=solver_logfile, options=solver_options)
   1564     else:
-> 1565         network.results = network.opt.solve(*args, suffixes=["dual"], keepfiles=keep_files, logfile=solver_logfile, options=solver_options)
   1566
   1567     if logger.isEnabledFor(logging.INFO):

~/checkouts/readthedocs.org/user_builds/pypsa-docs-staging/envs/latest/lib/python3.7/site-packages/pyomo/opt/base/solvers.py in solve(self, *args, **kwds)
    510         """ Solve the problem """
    511
--> 512         self.available(exception_flag=True)
    513         #
    514         # If the inputs are models, then validate that they have been

~/checkouts/readthedocs.org/user_builds/pypsa-docs-staging/envs/latest/lib/python3.7/site-packages/pyomo/opt/solver/shellcmd.py in available(self, exception_flag)
    123             if exception_flag:
    124                 msg = "No executable found for solver '%s'"
--> 125                 raise ApplicationError(msg % self.name)
    126             return False
    127         return True

ApplicationError: No executable found for solver 'glpk'