Backpressure CHP¶

This example demonstrates how to model a Combined Heat and Power (CHP) plant with a fixed heat-power ratio, assuming that the plant is operated in backpressure mode. For an example of a CHP plant with a more complicated heat-power feasible operational area, see the extraction-condensing CHP example. In this example, the CHP is modelled as a Link component with two output buses: one for electricity and one for heat. The CHP unit must be heat-following since there is no other supply of heat to the "Frankfurt heat" bus.

In [2]:

import pypsa

n = pypsa.Network()

n.add("Bus", "Frankfurt", carrier="AC")
n.add("Load", "Frankfurt", bus="Frankfurt", p_set=5)

n.add("Bus", "Frankfurt heat", carrier="heat")
n.add("Load", "Frankfurt heat", bus="Frankfurt heat", p_set=3)

n.add("Bus", "Frankfurt gas", carrier="gas")
n.add("Generator", "Frankfurt gas", bus="Frankfurt gas", marginal_cost=100, p_nom=100)

n.add(
    "Link",
    "OCGT",
    bus0="Frankfurt gas",
    bus1="Frankfurt",
    p_nom_extendable=True,
    capital_cost=600,
    efficiency=0.4,  # electricity per unit of gas
)

n.add(
    "Link",
    "CHP",
    bus0="Frankfurt gas",
    bus1="Frankfurt",
    bus2="Frankfurt heat",
    p_nom_extendable=True,
    capital_cost=1400,
    efficiency=0.3,  # electricity per unit of gas
    efficiency2=0.3,  # heat per unit of gas
)

n.optimize();

import pypsa n = pypsa.Network() n.add("Bus", "Frankfurt", carrier="AC") n.add("Load", "Frankfurt", bus="Frankfurt", p_set=5) n.add("Bus", "Frankfurt heat", carrier="heat") n.add("Load", "Frankfurt heat", bus="Frankfurt heat", p_set=3) n.add("Bus", "Frankfurt gas", carrier="gas") n.add("Generator", "Frankfurt gas", bus="Frankfurt gas", marginal_cost=100, p_nom=100) n.add( "Link", "OCGT", bus0="Frankfurt gas", bus1="Frankfurt", p_nom_extendable=True, capital_cost=600, efficiency=0.4, # electricity per unit of gas ) n.add( "Link", "CHP", bus0="Frankfurt gas", bus1="Frankfurt", bus2="Frankfurt heat", p_nom_extendable=True, capital_cost=1400, efficiency=0.3, # electricity per unit of gas efficiency2=0.3, # heat per unit of gas ) n.optimize();

/tmp/ipykernel_3595/1890019209.py:36: 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(['Frankfurt', 'Frankfurt heat', 'Frankfurt gas'], 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(['OCGT', 'CHP'], dtype='object', name='name')

WARNING:pypsa.consistency:Encountered nan's in static data for columns ['efficiency2'] of component 'Link'.

INFO:linopy.model: Solve problem using Highs solver

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

INFO:linopy.io: Writing time: 0.04s

INFO:linopy.constants: Optimization successful: 
Status: ok
Termination condition: optimal
Solution: 5 primals, 11 duals
Objective: 1.85e+04
Solver model: available
Solver message: Optimal

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

In [3]:

n.loads_t.p

n.loads_t.p

Out[3]:

name	Frankfurt	Frankfurt heat
snapshot
now	5.0	3.0

In [4]:

n.links_t.p0

n.links_t.p0

Out[4]:

name	OCGT	CHP
snapshot
now	5.0	10.0

In [5]:

n.links_t.p1

n.links_t.p1

Out[5]:

name	OCGT	CHP
snapshot
now	-2.0	-3.0

In [6]:

n.links_t.p2

n.links_t.p2

Out[6]:

name	OCGT	CHP
snapshot
now	0.0	-3.0