Heat pump issue - Possiblie linear dependencies #503

rafaelmarqferreira · 2024-04-16T11:10:36Z

rafaelmarqferreira
Apr 16, 2024

Hi,

Been trying to learn TESPy (also getting introduced to Python itself) and tried building a heat pump model. Sadly, over the span of multiple tries, i havent been able to get rid of the following error

Singularity in jacobian matrix, calculation aborted! Make sure your network does not have any linear dependencies in the parametrisation. Other reasons might be
-> given temperature with given pressure in two phase region, try setting enthalpy instead or provide accurate starting value for pressure.
-> given logarithmic temperature differences or kA-values for heat exchangers,
-> support better starting values.
-> bad starting value for fuel mass flow of combustion chamber, provide small (near to zero, but not zero) starting value.

From what I ve read, it probably is an issue concerning linear dependencies or two phase region due to the expantion valve.

I ll leave my code bellow as well as an image of the cycle i ve been trying to implemet in my latest attempt, in case its useful.

from tespy.networks import Network
import CoolProp.CoolProp as CP
import math
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np

fluids = ["R1234yf"]
massFluidInlet = 0.04 #kg
coolingTempIn = -20 #C
pressureIn = 1e5 #Pa
pressureOut = 8e5 #Pa
compressionRatio = pressureOut / pressureIn
initialTempWF = -23 #C
coolingTempOut = 20 #C
coolingFluid = "Air"
coolingVolume = 500 / 3600 #m3/s
efficiencyCompressor = 0.85
efficiencyPump = 0.6
constantR = 8.314 / 1000 #kJ/mol.K
densityCooling = CP.PropsSI('D', 'T', 273.15 + coolingTempIn, 'P', 1e5, coolingFluid) #kg/m3
massRateCooling = densityCooling * coolingVolume #kg/s
condenserPressureLoss = pressureOut * 0.1 #Pa

heatPump = Network(T_unit='C', p_unit='Pa', h_unit='kJ / kg')

from tespy.components import (
    CycleCloser, Pump, Condenser, HeatExchanger, Source, Sink, Compressor, Valve, Drum
)

closer = CycleCloser("ciclo fechado principal")
valve = Valve("valvula expansao") #Valve representa uma válvula isenltálpica
compressor = Compressor("compressor")
pump = Pump("bomba fluído")
condenser = Condenser("condensador")
evaporator = HeatExchanger("evaporador")
superheater = HeatExchanger("sobreaquecedor")
ambCooling11 = Source("fonte fria 11")
ambCooling12 = Sink("fonte fria 12")
ambHeating21 = Source("fonte fria 21")
ambHeating23 = Sink("fonte fria 23")
drum = Drum("separador fases")


from tespy.connections import Connection, Bus

c1 = Connection(closer, 'out1', compressor, 'in1', label= '1')
c2 = Connection(compressor, 'out1', condenser, 'in1', label= '2')
c3 = Connection(condenser, 'out1', pump, 'in1', label='3')
c4 = Connection(pump, 'out1', valve, 'in1', label= '4')
c5 = Connection(valve, 'out1', drum, 'in1', label= '5')
c6 = Connection(drum, 'out2', superheater, 'in1', label= '6')
c7 = Connection(superheater, 'out1', closer, 'in1')

heatPump.add_conns(c1,c2,c3,c4,c5,c6,c7)

motor = Bus("potência compressor")
motor.add_comps(
    {"comp": compressor, "char": 1, "base": "bus"},
)
heatPump.add_busses(motor)

c11 = Connection(ambCooling11, 'out1', condenser, 'in2', label= '11')
c12 = Connection(condenser, 'out2', ambCooling12, 'in1', label= '12')

heatPump.add_conns(c11, c12)

c21 = Connection(ambHeating21, 'out1', evaporator, 'in1', label= '21')
c22 = Connection(evaporator, 'out1', superheater, 'in2', label= '22')
c23 = Connection(superheater, 'out2', ambHeating23, 'in1', label= '23')

heatPump.add_conns(c21, c22, c23)

c31 = Connection(drum, 'out1', evaporator, 'in2', label= '31')
c32 = Connection(evaporator, "out2", drum, "in2", label= "32")

heatPump.add_conns(c31, c32)

#Valores de compressor

h1_wf = CP.PropsSI("H", "P", pressureIn, "T", 273.15 + initialTempWF, "R1234yf") / 1000 # kJ/kg
s1_wf = CP.PropsSI("S", "P", pressureIn, "T", 273.15 + initialTempWF, "R1234yf") / 1000 # kJ/kg.K
h2s_wf = CP.PropsSI("H", "P", pressureOut, "S", s1_wf * 1000, "R1234yf") / 1000 #kJ/kg
h2a_wf = h1_wf + (h2s_wf - h1_wf) / efficiencyCompressor #kJ/kg
tcompressedWF = CP.PropsSI("T", "H", h2a_wf * 1000, "P", pressureOut, "R1234yf") - 273.15 #C

cp_cooling_average = CP.PropsSI("C", "T", 273.15 + (coolingTempIn + coolingTempOut) / 2, "P", 1e5, coolingFluid) / 1000 #kJ/kg.K
coolingPower = massRateCooling * cp_cooling_average * (coolingTempOut - coolingTempIn) #kW
h3_wf = h2a_wf - coolingPower / massFluidInlet #kJ/kg
t3WF = CP.PropsSI("T", "H", h3_wf * 1000, "P", (pressureOut - condenserPressureLoss), "R1234yf") - 273.15 #C
h4WF = CP.PropsSI("H", "T", 273.15 + t3WF, "P", pressureOut, "R1234yf") / 1000 #kJ/kg.K
h5WF = h4WF #kJ/kg.K

compressor.set_attr(pr = compressionRatio, eta_s = efficiencyCompressor)
pump.set_attr(eta_s = efficiencyPump)
condenser.set_attr(subcooling = True, Q = None, pr1= (pressureOut - condenserPressureLoss)/pressureOut)
evaporator.set_attr(pr1 = 0.9)
superheater.set_attr(pr2 = 0.9)


c1.set_attr(m = massFluidInlet, p = pressureIn, T = initialTempWF, fluid = {"R1234yf": 1})
c3.set_attr(T = t3WF)
c4.set_attr(p = pressureOut)
c5.set_attr(p = pressureIn, h = h5WF)


c11.set_attr(m = massRateCooling, p = 1e5, T = coolingTempIn, fluid = {coolingFluid: 1})
c12.set_attr(T = coolingTempOut)

c21.set_attr(m = massRateCooling, p = 1e5, T = coolingTempIn, fluid = {coolingFluid: 1})
heatPump.solve('design')
# heatPump.print_results()

Thanks in advance!

fwitte · 2024-04-16T17:04:36Z

fwitte
Apr 16, 2024
Maintainer

Hi @rafaelmarqferreira,

I'd strongly advise you, to set up your system component by component. This way, you will be able to identify, what specifications lead to the linear dependency. In this case, it has nothing to do with the starting values. I can see at first glance, that your streams 21 to 23 are underdetermined in pressure:

pressure 21 is known
pressure 22 is unknown but can be determined via pressure 21 and evaporator pressure ration
pressure 23 is unknown and cannot be determined from your specifications.

Same goes for the condensing side:

pressure 11 is known
pressure 12 is unknown and cannot be determined from your specifications (condenser pressure ration only states the condensing side pressure ratio).

I can provide a working version of that model, but I think it would be wise to refactor your model first :).

Have a nice day, best

Francesco

3 replies

rafaelmarqferreira Apr 17, 2024
Author

Hi Francesco,

Firstly, thanks for the quick response. I ll try setting up the model component by component and give some feedback later on.

Best wishes,

Rafael

rafaelmarqferreira Apr 17, 2024
Author

Hello again.

After trying again, i managed to figure out how to set the model up so that the end results are indeed the intended one. The only issue I'm facing is on how to introduce the CycleCloser as in to make this a closed cycle. I've left the newer code down bellow.

from tespy.networks import Network
from CoolProp.CoolProp import PropsSI as PSI
import math
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np

heatPump = Network(
    T_unit="C", p_unit="Pa", h_unit="kJ / kg", m_unit="kg / s", iterinfo=False
)

WF = "R1234yf"
massRateWF = 0.04
condenserPressureLossRatioHot = 0.95 
evaporatorPressureLossRatioCold = 0.95 
efficiencyPump = 0.60
efficiencyCompressor = 0.85
T_wf_in = -23
T_exterior = -20
coolingHeated = 15
average_temp_cooling = (T_exterior + coolingHeated) / 2 
coolingVolumeRate = 500 / 3600 #m3/s
coolingFluid = "Air"
pressureIn = 100000
pressureOut = 800000

coolingDensity = PSI("D", "T", 273.15 + T_exterior, "P", 1.01325e5, coolingFluid)
massRateCooling = coolingVolumeRate * coolingDensity

from tespy.components import (
    Source, Compressor, Condenser, Pump, Sink, HeatExchanger, Valve, CycleCloser
)

wf_in = Source('Fluído de trabalho')
compressor = Compressor('Compressor')
condenser = Sink('Condensador')


from tespy.connections import Connection, Bus

c0 = Connection(wf_in, 'out1', compressor, 'in1', label= '0')
c1 = Connection(compressor, 'out1', condenser, 'in1', label= '1')

heatPump.add_conns(c0,c1)

compressor.set_attr(eta_s = efficiencyCompressor, pr = (pressureOut / pressureIn))


c0.set_attr(T = T_wf_in, fluid={WF: 1}, m = massRateWF)
c1.set_attr(p = pressureOut)

heatPump.solve("design")

amb_in1 = Source("Ar exterior frio 1")
amb_out1 = Sink("Ar exterior aquecido 1")
condenser = Condenser("Condensador")
pump = Sink("Bomba de recirculação")

heatPump.del_conns(c1)

c1 = Connection(compressor, 'out1', condenser, "in1", label= "1")
c2 = Connection(condenser, "out1", pump, "in1", label= "2")

c10 = Connection(amb_in1, "out1", condenser, "in2", label= "10")
c11 = Connection(condenser, "out2", amb_out1, "in1", label= "11")

heatPump.add_conns(c1,c2,c10,c11)

compressorPower = Bus("Potência do compressor")

compressorPower.add_comps(
    {"comp": compressor, "char": 1, "base": "bus"},
)


condenser.set_attr(pr1 = condenserPressureLossRatioHot, pr2 = 1, subcooling = True)

c1.set_attr(p = pressureOut)

c10.set_attr(T = T_exterior, p = 1.01325e5, m = massRateCooling, fluid={coolingFluid: 1})
c11.set_attr(T = coolingHeated)

heatPump.solve("design")

heatPump.del_conns(c2)

pump = Pump("Bomba de recirculação")
valve = Sink("Válvula de expansão")

c2 = Connection(condenser, "out1", pump, "in1", label= "2")
c3 = Connection(pump, "out1", valve, "in1", label= "3")

heatPump.add_conns(c2, c3)

pump.set_attr(eta_s = efficiencyPump, pr = 1 / condenserPressureLossRatioHot)

heatPump.solve("design")


heatPump.del_conns(c3)

valve = Valve("Válvula de expansão")
evaporator = Sink("Separador de fases")

c3 = Connection(pump, "out1", valve, "in1", label= "3")
c4 = Connection(valve, "out1", evaporator, "in1", label= "4")

heatPump.add_conns(c3, c4)

valve.set_attr(pr = pressureIn / pressureOut)

heatPump.solve("design")

heatPump.del_conns(c4)

evaporator = HeatExchanger("Evaporador")
closer = Sink("Fim de circuito")
amb_in2 = Source("Ar exterior frio 2")
amb_out2 = Sink("Ar exterior aquecido 2")

c4 = Connection(valve, "out1", evaporator, "in2", label= "4")
c5 = Connection(evaporator, "out2", closer, "in1", label= "5")

c20 = Connection(amb_in2, "out1", evaporator, "in1", label= "20")
c21 = Connection(evaporator, "out1", amb_out2, "in1", label= "21")

heatPump.add_conns(c4, c5, c20, c21)
h5 = PSI("H", "P", pressureIn, "T", 273.15 - 23, "R1234yf") / 1000

evaporator.set_attr(pr1 = 1, pr2 = 1)

c20.set_attr(T = T_exterior, m = massRateCooling * 20, p = 1.01325e5, fluid={coolingFluid: 1})
c5.set_attr(h = h5)

heatPump.solve("design")
heatPump.print_results()

# heatPump.del_conns(c0, c5)

# closer = CycleCloser("Fim de circuito")

# c0 = Connection(closer, 'out1', compressor, 'in1', label= '0')
# c5 = Connection(evaporator, "out2", closer, "in1", label= "5")

# heatPump.add_conns(c0, c5)

# c0.set_attr(T = T_wf_in, fluid={WF: 1}, m = massRateWF)

# heatPump.solve("design")
# heatPump.print_results()

rafaelmarqferreira Apr 17, 2024
Author

Once again, thank you in advance for the help!

Cheers

rafaelmarqferreira · 2024-04-19T08:59:04Z

rafaelmarqferreira
Apr 19, 2024
Author

Hi there,

I've managed to redesign my model but while running and offdesign attempt, I can't figure out what parameters I'm adding that I shouldn't

from tespy.networks import Network
from CoolProp.CoolProp import PropsSI as PSI
import matplotlib.pyplot as plt
import numpy as np

heatPump = Network()
heatPump.set_attr(T_unit='C', p_unit='Pa', h_unit='kJ / kg', iterinfo=False)

from tespy.components import (
    CycleCloser, Compressor, Valve, Pump, HeatExchanger, Source, Sink
)

closer = CycleCloser('cycle closer')
condenser = HeatExchanger('condenser')
evaporator = HeatExchanger('evaporator')
valve = Valve('expansion valve')
compressor = Compressor('compressor')
pump = Pump('pump')

ambIn1 = Source('ambIn1')
ambIn2 = Source('ambIn2')
ambOut1 = Sink('ambOut1')
ambOut2 = Sink('ambOut2')

from tespy.connections import Connection

# connections of heat pump
c0 = Connection(evaporator, 'out2', compressor, 'in1', label= 'Starting point')
c1 = Connection(compressor, 'out1', condenser, 'in1', label= 'Post compression')
c2 = Connection(condenser, "out1", closer, "in1", label= "Post cooling")
c3 = Connection(closer, "out1", pump, "in1", label= "Cycle Closer")
c4 = Connection(pump, "out1", valve, "in1", label= "Post pumping")
c5 = Connection(valve, "out1", evaporator, "in2", label= "Post expantion")

c10 = Connection(ambIn1, "out1", condenser, "in2", label= "Cold air 1 cold")
c11 = Connection(condenser, "out2", ambOut1, "in1", label= "Cold air 1 hot")

c20 = Connection(ambIn2, "out1", evaporator, "in1", label= "Cold air 2 cold")
c21 = Connection(evaporator, "out1", ambOut2, "in1", label= "Cold air 2 hot")

heatPump.add_conns(c0, c1, c2, c3, c4, c5, c10, c11, c20, c21)

wf = "R1234yf"
massRateWF = 0.04
T_wf_in = -23
pressureIn = 1e5
pressureOut = 8e5
h0 = PSI("H", "P", pressureIn, "T", 273.15 + T_wf_in, wf) / 1000
fluidCheck = PSI("T", "P", pressureIn, "Q", 1, wf) - 273.15

T_exterior = -20
coolingHeated = 20
coolingVolumeRate = 500 / 3600 #m3/s
coolingFluid = "Air"
coolingDensity = PSI("D", "T", 273.15 + T_exterior, "P", 1.01325e5, coolingFluid)
massRateCooling = coolingVolumeRate * coolingDensity


if T_wf_in <= fluidCheck:
    print("Existência de líquido / mistura bifásica no compressor. Aumente a temperatura de entrada.")
else:
    condenserPressureLossRatioHot = 0.95 
    evaporatorPressureLossRatioHot = 0.95 

    efficiencyCompressor = 0.85

    efficiencyPump = 0.65

    condenser.set_attr(pr1 = condenserPressureLossRatioHot, pr2 = 1, design=["pr1"], offdesign=["zeta1", "kA_char"])
    compressor.set_attr(eta_s = efficiencyCompressor, pr = pressureOut / pressureIn, design=["eta_s"], offdesign=["eta_s_char"])
    evaporator.set_attr(pr1 = evaporatorPressureLossRatioHot, design=["pr1"], offdesign=["zeta1", "kA_char"])
    pump.set_attr(eta_s = efficiencyPump)
    valve.set_attr(pr = pressureIn / pressureOut)

    c0.set_attr(fluid={wf: 1}, m = massRateWF, h = h0, p = pressureIn)
    c4.set_attr(p = pressureOut)

    c10.set_attr(fluid={coolingFluid: 1}, m = massRateCooling, p = 1e5, T = T_exterior)
    c11.set_attr(T = coolingHeated)

    c20.set_attr(fluid={coolingFluid: 1}, m = massRateCooling * 10, p = 1e5, T = T_exterior)

    heatPump.solve(mode='design')
    heatPump.save('hp_design')
    heatPump.print_results()

    print(f'COP = {abs(condenser.Q.val) / compressor.P.val}')

    
    for m in np.linspace(0.005, 0.04, 21):
        c0.set_attr(m=m)
        heatPump.solve(mode='offdesign', design_path='hp_design', max_iter=200)
        print(f'COP = {abs(condenser.Q.val) / compressor.P.val}')

4 replies

fwitte Apr 19, 2024
Maintainer

Hi again, and good to hear that you were able to solve the issue :).

With the off design it is really just a switch from specifications you applied in the design calculation to some that will be specified instead using the value that was calculated in design as a result. That said, you have to put two more parameters to the design parameters which become degrees of freedom for off design. What those are depends on how you want to simulate the control of the plant.

In your case I guess you'd have to control either mass flow or outlet temperature at the condenser cold side, and maybe evaporator outlet state? What do you want to investigate in your design?

Best

Have a nice weekend

rafaelmarqferreira Apr 19, 2024
Author

Hi @fwitte

The goal would be to evaluate by how much the working fluid flow rate would change (increase/decrease) depending on the variance of outside air temperatures in the condenser inlet side (either higher or lower temperatures) assuming that same air would still leave the condenser at 20 ºC and the working fluid would have the same enthalpy value as in the design case.

I would assume that if I wanted to apply a similar case with the evaporator, the thought process wouldn't change much.

So far, this is what I've been able to put up together, but it seems that I'm messing 1 parameter, which I haven't been able to figure out.

from tespy.networks import Network
from CoolProp.CoolProp import PropsSI as PSI
import matplotlib.pyplot as plt
import numpy as np

heatPump = Network()
heatPump.set_attr(T_unit='C', p_unit='Pa', h_unit='kJ / kg', iterinfo=False)

from tespy.components import (
    CycleCloser, Compressor, Valve, Pump, HeatExchanger, Source, Sink
)

closer = CycleCloser('cycle closer')
condenser = HeatExchanger('condenser')
evaporator = HeatExchanger('evaporator')
valve = Valve('expansion valve')
compressor = Compressor('compressor')
pump = Pump('pump')

ambIn1 = Source('ambIn1')
ambIn2 = Source('ambIn2')
ambOut1 = Sink('ambOut1')
ambOut2 = Sink('ambOut2')

from tespy.connections import Connection

c0 = Connection(evaporator, 'out2', compressor, 'in1', label= 'Starting point')
c1 = Connection(compressor, 'out1', condenser, 'in1', label= 'Post compression')
c2 = Connection(condenser, "out1", closer, "in1", label= "Post cooling")
c3 = Connection(closer, "out1", pump, "in1", label= "Cycle Closer")
c4 = Connection(pump, "out1", valve, "in1", label= "Post pumping")
c5 = Connection(valve, "out1", evaporator, "in2", label= "Post expantion")

c10 = Connection(ambIn1, "out1", condenser, "in2", label= "Cold air 1 cold")
c11 = Connection(condenser, "out2", ambOut1, "in1", label= "Cold air 1 hot")

c20 = Connection(ambIn2, "out1", evaporator, "in1", label= "Cold air 2 cold")
c21 = Connection(evaporator, "out1", ambOut2, "in1", label= "Cold air 2 hot")

heatPump.add_conns(c0, c1, c2, c3, c4, c5, c10, c11, c20, c21)

wf = "R1234yf"
massRateWF = 0.04
T_wf_in = -23
pressureIn = 1e5
pressureOut = 8e5
h0 = PSI("H", "P", pressureIn, "T", 273.15 + T_wf_in, wf) / 1000
fluidCheck = PSI("T", "P", pressureIn, "Q", 1, wf) - 273.15

T_exterior = -20
coolingHeated = 20
coolingVolumeRate = 500 / 3600 #m3/s
coolingFluid = "Air"
coolingDensity = PSI("D", "T", 273.15 + T_exterior, "P", 1.01325e5, coolingFluid)
massRateCooling = coolingVolumeRate * coolingDensity


if T_wf_in <= fluidCheck:
    print("Existência de líquido / mistura bifásica no compressor. Aumente a temperatura de entrada.")
else:
    condenserPressureLossRatioHot = 0.95 
    evaporatorPressureLossRatioHot = 0.95 

    efficiencyCompressor = 0.85

    efficiencyPump = 0.65

    condenser.set_attr(pr1 = condenserPressureLossRatioHot, pr2 = 1)
    compressor.set_attr(eta_s = efficiencyCompressor, pr = pressureOut / pressureIn)
    evaporator.set_attr(pr1 = evaporatorPressureLossRatioHot)
    pump.set_attr(eta_s = efficiencyPump)
    valve.set_attr(pr = pressureIn / pressureOut)

    c0.set_attr(fluid={wf: 1}, m = massRateWF, h = h0, p = pressureIn)
    c4.set_attr(p = pressureOut)

    c10.set_attr(fluid={coolingFluid: 1}, m = massRateCooling, p = 1e5, T = T_exterior)
    c11.set_attr(T = coolingHeated)

    c20.set_attr(fluid={coolingFluid: 1}, m = massRateCooling * 10, p = 1e5, T = T_exterior)

    heatPump.solve(mode='design')
    # heatPump.save('hp_design')
    heatPump.print_results()
    
    cop = {abs(condenser.Q.val) / compressor.P.val}

    print(f'COP = {abs(condenser.Q.val) / compressor.P.val}')


    # Estudo paramétrico - ar exterior a 20 ºC

    plt.rc('font', **{'size': 18})

    dataX = {
        'tamb1in': np.linspace(-30, 10, 41),
        'tWFpump': np.linspace(-20, 20, 41),
        'COP': np.linspace(2, 5, 41),
    }

    # print(np.linspace(-30, 10, 41))

    tamb1out = {
        'tamb1in': [],
        'tWFpump': [],
        'COP': []
    }

    description = {
    'tamb1in': 'Caudal mássico do fluído de trabalho (kg/s)',
    'tWFpump': 'Temperatura de saída do ar no condensador (ºC)',
    'COP': 'COP do circuito'
    }

    for T in dataX['tamb1in']:
        c10.set_attr(T=T)
        c0.set_attr(m=None)
        heatPump.solve('design')
        tamb1out['tamb1in'] += [c11.T.val]

Best wishes

fwitte Apr 24, 2024
Maintainer

It is quite a lot to process and think about. You'll have to be patient for a little bit.

I'd advise you to play around with your model, and try to find the parameter by changing one after the other and have a look at the results. From that you might be able to deduct what you are searching for.

fwitte Apr 24, 2024
Maintainer

There is also the tespy online user meeting, next appointment is May 27 at 17:00 CEST.

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Heat pump issue - Possiblie linear dependencies #503

rafaelmarqferreira Apr 16, 2024

Replies: 2 comments · 7 replies

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