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Jun-03-18 08:11:46
I am receiving errors for a closed loop power cycle model and I need help in identifying the...

I am modelling a concentrated solar thermal power plant using OpenModelica. I have created a model for a pump and a condenser, and they successfully calculate the outlet conditions when tested individually. However for testing purposes, when I connect the pump and condenser models in a closed loop the model will not simulate and I receive the following errors:

Code:

[1] 22:16:26 Translation Error

Internal error Circular Equalities Detected for Variables:
condenser2.o.mdot
condenser2.i.mdot
----------------------------------
pump2.i.mdot
condenser2.o.mdot
----------------------------------
pump2.o.mdot
pump2.i.mdot
----------------------------------
[2] 22:16:26 Symbolic Error
[PTC: 995:5-995:122]: Model is structurally singular, error found sorting equations

This most likely has something to do with the connectors and the mass flow rate in particular, however, I do not know what I need to change to solve this issue.

The system model is shown below:

Code:

model Pump_condenser

  PTC.Pump2 pump2 annotation();
  PTC.Condenser2 condenser2 annotation();
equation
  connect(condenser2.o, pump2.i) annotation();
  connect(pump2.o, condenser2.i) annotation();
end Pump_condenser;

The model for the pump is shown below:

Code:

model Pump2

extends PTC.PartialModels.PartialCSTComponentSISO;
  // Imports
  import Modelica.SIunits.*;
  import ThermoCycle.Media.*;
  import Modelica.Constants;
  // Outlet isentropic state
  Medium.ThermodynamicState state_isentropic;
  // Parameters
  parameter Length D = 2 "Diameter of pump";
  parameter Length w = 1 "Width of pump";
  parameter Real eta(unit = "1") = 0.7 "Isentropic efficiency of pump";
  constant Real pi = 2 * Modelica.Math.asin(1.0) "3.14159265358979";
  // Variables
  Power Wdot "Power input to pump";
  SpecificEntropy s_i "Specific entropy at inlet";
  SpecificEnthalpy hs "Specific enthalpy after isentropic compression";
initial equation
  medium_i.T = 363;
  medium_i.p = 80000;
  medium_o.T = 450;
  medium_o.p = 800000;
  i.h = Medium.specificEnthalpy(medium_i.state);
equation
  // Energy balance
  m * der(u) = (-Wdot) + i.mdot * actualStream(i.h) + o.mdot * actualStream(o.h);
  // Isentropic efficiency
  s_i = Medium.specificEntropy(medium_i.state) "Get inlet entropy";
  state_isentropic = Medium.setState_ps(medium_o.p, s_i) "Isentropic state";
  hs = Medium.specificEnthalpy(state_isentropic);
  eta = (hs - medium_i.h) / (medium_o.h - medium_i.h) "Isentropic efficiency";
  // Inlet pressure
  medium_i.p = 80000;
  // Mass
  m = pi * D ^ 2 * w * d / 4 "Mass of fluid in control volume";
  // Simulation parameters
  annotation();
  annotation();
end Pump2;

The model for the condenser is shown below:

Code:

model Condenser2

extends PTC.PartialModels.PartialCSTComponentSISO;
  // Imports
  import Modelica.SIunits.*;
  // Parameters
  parameter Length L = 5 "Length of one tube";
  parameter Area A = 0.02 "Cross sectional area of tubes";
  parameter Integer N(unit = "1") = 10 "Number of tubes";
  parameter Temperature Tinf = 298 "Ambient temperature";
  parameter CoefficientOfHeatTransfer k = 3000 "Convection coefficient";
  // Variables
  HeatFlowRate Qdot "Heat flow rate from power block to condenser fluid";
  Temperature T "Average temp in CV";
initial equation
  medium_i.T = 450;
  medium_i.p = 8000000;
  medium_o.T = 363;
  medium_o.p = 80000;
  i.h = Medium.specificEnthalpy(medium_i.state);
equation
  // Energy balance
  m * der(u) = Qdot + i.mdot * actualStream(i.h) + o.mdot * actualStream(o.h);
  // Inlet pressure
  medium_i.p = 8000000;
  // Average temperature
  T = (medium_i.T + medium_o.T) / 2;
  // Heat flow rate
  Qdot = -k * (T - Tinf) "Newtons law of cooling";
  // Mass
  m = N * L * A * d "Mass of fluid in CV";
  // Simulation parameters
  annotation();
  annotation();
end Condenser2;

Both models extend the following partial model:

Code:

partial model PartialCSTComponentSISO

  // Imports
  import Modelica.SIunits.*;
  // Fluid imports
  replaceable package Medium = Modelica.Media.Water.StandardWater annotation(
    choicesAllMatching = true);
  // Set up inlet and outlet media
  Medium.BaseProperties medium_i;
  Medium.BaseProperties medium_o;
  // Connectors
  PTC.inlet i(redeclare package Medium = Medium) annotation();
  PTC.outlet o(redeclare package Medium = Medium) annotation();
  // Variables
  SpecificInternalEnergy u "Average specific internal energy in CV (control volume)";
  Mass m "Mass contained in CV";
  Density d "Average density of fluid in CV";
  // Parameters
  parameter MassFlowRate mdotCV = 3.0 "Mass flow rate through CV";
equation
  // Fluid equations
  medium_i.h = i.h;
  medium_i.p = i.p;
  medium_o.p = o.p;
  medium_o.h = o.h;
  // Mass flow rate
  i.mdot = mdotCV;
  o.mdot + i.mdot = 0 "Mass balance";
  // Internal energy
  u = (medium_i.u + medium_o.u) / 2 "Internal energy in CV is average of inlet and outlet u";
  // Miscellaneous
  d = (medium_i.d + medium_o.d) / 2 "d in CV is average of inlet and outlet densities";
end PartialCSTComponentSISO;

The inlet and outlet connectors have the following structure:

Code:

connector inlet

  // Imports //
  import Modelica.SIunits.*;
  // Fluid imports //
  replaceable package Medium = Modelica.Media.Interfaces.PartialMedium "Medium model" annotation(
    choicesAllMatching = true);
  // Energy variables //
  Medium.AbsolutePressure p;
  stream Medium.SpecificEnthalpy h;
  // Flow variables //
  flow Medium.MassFlowRate mdot;
  annotation();
end inlet;

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