Heat Pumps and Thermal Storage¶

In this example, a heat demand is supplied by a wind turbine in combination with a heat pump and a water tank that stores hot water with a standing loss.

In [2]:

import pandas as pd

import pypsa

n = pypsa.Network()
n.set_snapshots(pd.date_range("2025-01-01 00:00", "2025-01-01 03:00", freq="H"))

n.add("Bus", "power", carrier="AC")
n.add("Bus", "heat", carrier="heat")

n.add(
    "Generator",
    "wind turbine",
    bus="power",
    carrier="wind",
    p_nom_extendable=True,
    p_max_pu=[0.0, 0.2, 0.7, 0.4],
    capital_cost=500,
)

n.add("Load", "heat demand", bus="heat", p_set=20);

import pandas as pd import pypsa n = pypsa.Network() n.set_snapshots(pd.date_range("2025-01-01 00:00", "2025-01-01 03:00", freq="H")) n.add("Bus", "power", carrier="AC") n.add("Bus", "heat", carrier="heat") n.add( "Generator", "wind turbine", bus="power", carrier="wind", p_nom_extendable=True, p_max_pu=[0.0, 0.2, 0.7, 0.4], capital_cost=500, ) n.add("Load", "heat demand", bus="heat", p_set=20);

/tmp/ipykernel_7742/3242665978.py:6: FutureWarning: 'H' is deprecated and will be removed in a future version, please use 'h' instead.
  n.set_snapshots(pd.date_range("2025-01-01 00:00", "2025-01-01 03:00", freq="H"))

The heat pump has time-varying efficiency (i.e. its coefficient of performance, COP) due to changing ambient temperatures.

In [3]:

n.add(
    "Link",
    "heat pump",
    bus0="power",
    bus1="heat",
    efficiency=[2.5, 3.0, 3.2, 3.0],
    capital_cost=1000,
    p_nom_extendable=True,
);

n.add( "Link", "heat pump", bus0="power", bus1="heat", efficiency=[2.5, 3.0, 3.2, 3.0], capital_cost=1000, p_nom_extendable=True, );

The hot water tank has a standing loss of 1% of its state of charge per hour.

In [4]:

n.add(
    "Store",
    "water tank",
    bus="heat",
    e_cyclic=True,
    e_nom=100,
    standing_loss=0.01,
);

n.add( "Store", "water tank", bus="heat", e_cyclic=True, e_nom=100, standing_loss=0.01, );

The wind turbine and the heat pump can be sized by the optimisation, while the water tank has a fixed size of 100 MWh.

In [5]:

n.optimize();

n.optimize();

/tmp/ipykernel_7742/1450685117.py:1: FutureWarning: The default value of `include_objective_constant` will change from True to False in version 2.0. Set `include_objective_constant` explicitly to suppress this warning. Using False improves LP numerical conditioning by not including the objective constant as a variable.
  n.optimize();
WARNING:pypsa.consistency:The following buses have carriers which are not defined. Run n.sanitize() to add them. Components with undefined carriers:
Index(['power', 'heat'], dtype='object', name='name')

WARNING:pypsa.consistency:The following generators have carriers which are not defined. Run n.sanitize() to add them. Components with undefined carriers:
Index(['wind turbine'], dtype='object', name='name')

WARNING:pypsa.consistency:The following links have carriers which are not defined. Run n.sanitize() to add them. Components with undefined carriers:
Index(['heat pump'], dtype='object', name='name')

WARNING:pypsa.consistency:The following stores have carriers which are not defined. Run n.sanitize() to add them. Components with undefined carriers:
Index(['water tank'], dtype='object', name='name')

INFO:linopy.model: Solve problem using Highs solver

INFO:linopy.model:Solver options:
 - log_to_console: False

INFO:linopy.io: Writing time: 0.06s

INFO:linopy.constants: Optimization successful: 
Status: ok
Termination condition: optimal
Solution: 18 primals, 38 duals
Objective: 2.35e+04
Solver model: available
Solver message: Optimal

INFO:pypsa.optimization.optimize:The shadow-prices of the constraints Generator-ext-p-lower, Generator-ext-p-upper, Link-ext-p-lower, Link-ext-p-upper, Store-fix-e-lower, Store-fix-e-upper, Store-energy_balance were not assigned to the network.

In [6]:

pd.DataFrame({attr: n.stores_t[attr]["water tank"] for attr in ["p", "e"]}).round(3)

pd.DataFrame({attr: n.stores_t[attr]["water tank"] for attr in ["p", "e"]}).round(3)

Out[6]:

	p	e
snapshot
2025-01-01 00:00:00	20.000	4.377
2025-01-01 01:00:00	4.333	-0.000
2025-01-01 02:00:00	-13.423	13.423
2025-01-01 03:00:00	-11.334	24.623

In [7]:

pd.DataFrame({attr: n.links_t[attr]["heat pump"] for attr in ["p0", "p1"]}).round(3)

pd.DataFrame({attr: n.links_t[attr]["heat pump"] for attr in ["p0", "p1"]}).round(3)

Out[7]:

	p0	p1
snapshot
2025-01-01 00:00:00	-0.000	0.000
2025-01-01 01:00:00	5.222	-15.667
2025-01-01 02:00:00	10.445	-33.423
2025-01-01 03:00:00	10.445	-31.334