Wind Turbine combined with Heat Pump and Water Tank

In this example the 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.

[1]:

import pypsa
import pandas as pd
from pyomo.environ import Constraint

[2]:

network = pypsa.Network()
network.set_snapshots(pd.date_range("2016-01-01 00:00", "2016-01-01 03:00", freq="H"))

network.add("Bus", "0", carrier="AC")
network.add("Bus", "0 heat", carrier="heat")

network.add("Carrier", "wind")
network.add("Carrier", "heat")

network.add(
    "Generator",
    "wind turbine",
    bus="0",
    carrier="wind",
    p_nom_extendable=True,
    p_max_pu=[0.0, 0.2, 0.7, 0.4],
    capital_cost=500,
)

network.add("Load", "heat demand", bus="0 heat", p_set=20.0)

# NB: Heat pump has changing efficiency (properly the Coefficient of Performance, COP)
# due to changing ambient temperature
network.add(
    "Link",
    "heat pump",
    bus0="0",
    bus1="0 heat",
    efficiency=[2.5, 3.0, 3.2, 3.0],
    capital_cost=1000,
    p_nom_extendable=True,
)

network.add(
    "Store",
    "water tank",
    bus="0 heat",
    e_cyclic=True,
    e_nom_extendable=True,
    standing_loss=0.01,
)

[3]:

network.lopf(network.snapshots)

WARNING:pypsa.components:Solving optimisation problem with pyomo.In PyPSA version 0.21 the default will change to ``n.lopf(pyomo=False)``.Explicitly set ``n.lopf(pyomo=True)`` to retain current behaviour.
INFO:pypsa.opf:Performed preliminary steps
INFO:pypsa.opf:Building pyomo model using `kirchhoff` formulation
INFO:pypsa.opf:Solving model using glpk
INFO:pypsa.opf:Optimization successful

# ==========================================================
# = Solver Results                                         =
# ==========================================================
# ----------------------------------------------------------
#   Problem Information
# ----------------------------------------------------------
Problem:
- Name: unknown
  Lower bound: 23500.5858249914
  Upper bound: 23500.5858249914
  Number of objectives: 1
  Number of constraints: 37
  Number of variables: 20
  Number of nonzeros: 64
  Sense: minimize
# ----------------------------------------------------------
#   Solver Information
# ----------------------------------------------------------
Solver:
- Status: ok
  Termination condition: optimal
  Statistics:
    Branch and bound:
      Number of bounded subproblems: 0
      Number of created subproblems: 0
  Error rc: 0
  Time: 0.0025746822357177734
# ----------------------------------------------------------
#   Solution Information
# ----------------------------------------------------------
Solution:
- number of solutions: 0
  number of solutions displayed: 0

[3]:

(<SolverStatus.ok: 'ok'>, <TerminationCondition.optimal: 'optimal'>)

[4]:

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

[4]:

	p	e
snapshot
2016-01-01 00:00:00	20.000000	4.376710
2016-01-01 01:00:00	4.332943	0.000000
2016-01-01 02:00:00	-13.423055	13.423055
2016-01-01 03:00:00	-11.334114	24.622939

[5]:

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

[5]:

	p0	p1
snapshot
2016-01-01 00:00:00	0.000000	-0.000000
2016-01-01 01:00:00	5.222352	-15.667057
2016-01-01 02:00:00	10.444705	-33.423055
2016-01-01 03:00:00	10.444705	-31.334114

[6]:

network.stores.loc[["water tank"]].T

[6]:

Store	water tank
attribute
bus	0 heat
type
carrier	heat
e_nom	0.0
e_nom_extendable	True
e_nom_min	0.0
e_nom_max	inf
e_min_pu	0.0
e_max_pu	1.0
e_initial	0.0
e_initial_per_period	False
e_cyclic	True
e_cyclic_per_period	True
p_set	0.0
q_set	0.0
sign	1.0
marginal_cost	0.0
capital_cost	0.0
standing_loss	0.01
build_year	0
lifetime	inf
e_nom_opt	24.622939

[7]:

network.generators.loc[["wind turbine"]].T

[7]:

Generator	wind turbine
attribute
bus	0
control	Slack
type
p_nom	0.0
p_nom_extendable	True
p_nom_min	0.0
p_nom_max	inf
p_min_pu	0.0
p_max_pu	1.0
p_set	0.0
q_set	0.0
sign	1.0
carrier	wind
marginal_cost	0.0
build_year	0
lifetime	inf
capital_cost	500.0
efficiency	1.0
committable	False
start_up_cost	0.0
shut_down_cost	0.0
min_up_time	0
min_down_time	0
up_time_before	1
down_time_before	0
ramp_limit_up	NaN
ramp_limit_down	NaN
ramp_limit_start_up	1.0
ramp_limit_shut_down	1.0
p_nom_opt	26.111762