Question about the components HeatCapacitor in the Modelica Standard Library

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When I check Modelica.Thermal.HeatTransfer.Components.HeatCapacitor using OpenModelica, it tells me that HeatCapacitor has 4 equations and 4 variables. But I can only find 3 equations in the model listed below for 4 variables(i.e, T, port.T, der_T, port.Q_flow):

T = port.T;
der_T = der(T);
C*der(T) = port.Q_flow;

I created a new model named MyHeatCapacitor by deleting der_T and the second equation listed above. The tool indicates that MyHeatCapacitor has 3 equations for 3 variables.

The two heat-capacitor models can give me the correct answers. I was just wondering where I can find the equation which does not appear in the equation section.

Thanks!!!

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1 Answers

The missing equation will be generated when you create an instance of the HeatCapacitor and connect the thermal port with the port of another instance of a thermal class. From the connect statement the tool will generate topology equations, which add to the number of equations when you check a model.

Topology equations are generated as follows:

  • all flow variables of connected connectors are summed up to zero

    for the HeatPort this is Q_flow, giving e.g. the following equation for 2 instances:

    instance1.Q_flow + instance2.Q_flow = 0

  • non-flow variables in connectors are treated as potential variables. the potentials of connected instances are set equal.

    for the HeatPort this is T, giving e.g. the following equations for 2 connected instances:

    instance1.T = instance2.T

As the heat capacitor uses an a-causal connector (the thermal port), on check the tool knows that it will be later connected to another instance, resulting in the equations stated above. So two HeatCapacitor instances have 2*4=8 variables and 2*3=6 equations. With the 2 topology equations we get 8 equations in total.

If nothing is connected, a default connection is assumed, where the flow is set on zero.

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