Note

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

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.optimize()

INFO:linopy.model: Solve problem using Glpk solver
INFO:linopy.io: Writing time: 0.1s
INFO:linopy.constants: Optimization successful:
Status: ok
Termination condition: optimal
Solution: 19 primals, 39 duals
Objective: 2.35e+04
Solver model: not 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-ext-e-lower, Store-ext-e-upper, Store-energy_balance were not assigned to the network.

GLPSOL--GLPK LP/MIP Solver 5.0
Parameter(s) specified in the command line:
 --lp /tmp/linopy-problem-yb7cd3u3.lp --output /tmp/linopy-solve-nrsdj_02.sol
Reading problem data from '/tmp/linopy-problem-yb7cd3u3.lp'...
39 rows, 19 columns, 66 non-zeros
206 lines were read
GLPK Simplex Optimizer 5.0
39 rows, 19 columns, 66 non-zeros
Preprocessing...
20 rows, 16 columns, 43 non-zeros
Scaling...
 A: min|aij| =  2.000e-01  max|aij| =  3.200e+00  ratio =  1.600e+01
Problem data seem to be well scaled
Constructing initial basis...
Size of triangular part is 19
      0: obj =   0.000000000e+00 inf =   1.980e+02 (4)
      9: obj =   2.549967375e+04 inf =   0.000e+00 (0)
*    11: obj =   2.350058582e+04 inf =   0.000e+00 (0)
OPTIMAL LP SOLUTION FOUND
Time used:   0.0 secs
Memory used: 0.1 Mb (56692 bytes)
Writing basic solution to '/tmp/linopy-solve-nrsdj_02.sol'...

[3]:

('ok', '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	20.00000	4.37671
2016-01-01 01:00:00	4.33294	0.00000
2016-01-01 02:00:00	-13.42310	13.42310
2016-01-01 03:00:00	-11.33410	24.62290

[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	0.00000	-0.00000
2016-01-01 01:00:00	5.22235	-15.66705
2016-01-01 02:00:00	10.44470	-33.42304
2016-01-01 03:00:00	10.44470	-31.33410

[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
marginal_cost_quadratic	0.0
capital_cost	0.0
standing_loss	0.01
build_year	0
lifetime	inf
e_nom_opt	24.6229

[7]:

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

[7]:

Generator	wind turbine
attribute
bus	0
control	PQ
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
marginal_cost_quadratic	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
stand_by_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
weight	1.0
p_nom_opt	26.1118