Initialization question for the RC system with HeatingResistor

[wang890]

Question❓

The MTK code for initialization may change starting from September 2024. Before that, for example, in version 9.19.0, the following MRE code of RC system with HeatingResistor worked.

Although I went through the tutorial Parameter initialization by example and have done some tests (github page of the Jupyter file), I still don't know how to debug it according to the physical laws of RC. Could you help me, please? Thanks a lot!

Error: Initialization system is overdetermined. 1 equations for 0 unknowns.
isys3_prob.f.initializeprob.f.sys out:
0 =−resistor.v(t)+resistor.i(t)resistor.R(t), if deleted this equation in the model of HeatingResistor, Error:
ExtraVariablesSystemException: The system is unbalanced.
There are 25 highest order derivative variables and 24 equations.

If using the common Resistor model without heat_port, there is no error.

ENV

  julia 1.11.0
  [961ee093] ModelingToolkit v9.72.0
  [1dea7af3] OrdinaryDiffEq v6.93.0
  [91a5bcdd] Plots v1.40.11
  [0c5d862f] Symbolics v6.37.1

Jupyter test file of the MRE is on the github page
Here is the copy-paste MRE:

using ModelingToolkit, OrdinaryDiffEq, Plots
using ModelingToolkit: t_nounits as t, D_nounits as d

@connector Pin begin
    v(t) # Potential at the pin
    i(t), [connect = Flow] # Current flowing into the pin
end

@mtkmodel OnePort begin
    @components begin
        p = Pin()
        n = Pin()
    end
    @variables begin
        v(t) # Voltage drop of the two pins (= p.v - n.v)
        i(t) # Current flowing into the pin
    end
    @equations begin
        v ~ p.v - n.v
        0 ~ p.i + n.i
        i ~ p.i
    end
end

@connector HeatPort begin
    T(t)
    Q_flow(t), [connect = Flow]
end

@connector HeatPort_a begin
    @extend T, Q_flow = heatPort_a = HeatPort()
end

@connector HeatPort_b begin
    @extend T, Q_flow = heatPort_b = HeatPort()
end

@mtkmodel FixedTemperature begin
    @components begin
        port = HeatPort_b()
    end
    @parameters begin
        T, [description = "Fixed temperature boundary condition"]
    end
    @equations begin
        port.T ~ T
    end
end

# copy from ModelingToolkitStandardLibrary
@mtkmodel HeatingResistor begin
    @extend v, i = oneport = OnePort()
    @components begin
        heat_port = HeatPort()
    end
    @parameters begin
        R_ref = 1.0, [description = "Reference resistance"]
        T_ref = 300.15, [description = "Reference temperature"]
        alpha = 0, [description = "Temperature coefficient of resistance"]
    end
    @variables begin
        R(t)#, [guess = R_ref]
    end
    @equations begin
        R ~ R_ref * (1 + alpha * (heat_port.T - T_ref))
        heat_port.Q_flow ~ -v * i # -LossPower
        v ~ i * R # if delete this equation, ExtraVariablesSystemException: The system is unbalanced. 
        # There are 25 highest order derivative variables and 24 equations.
    end
end

@mtkmodel Ground begin
    @components begin
        p = Pin()
    end
    @equations begin
        p.v ~ 0
    end
end

@mtkmodel Capacitor begin
    @extend i,v = oneport = OnePort()
    @parameters begin
        C # Capacitance
    end
    @equations begin
        i ~ C * d(v)
    end
end

@mtkmodel ConstantVoltage begin
    @extend v, = oneport = OnePort()    
    @parameters begin
        V # Value of constant voltage
    end
    @equations begin
        v ~ V
    end
end

@mtkmodel RcHeating begin    
    @components begin
        resistor = HeatingResistor()           
        capacitor = Capacitor()
        source = ConstantVoltage()
        ground = Ground()
        fixedTemperature = FixedTemperature()
        
    end      
    @equations begin        
        connect(source.p, resistor.p)
        connect(resistor.n, capacitor.p)
        connect(capacitor.n, source.n, ground.p) 
        connect(resistor.heat_port, fixedTemperature.port)       
    end
end

@mtkbuild sys = RcHeating()
"""
Unknowns (2)
    capacitor₊v(t) ▪ Unassigned ▪ Voltage drop of the two pins (= p.v - n.v)
    resistor₊i(t) ▪ Unassigned ▪ Current flowing from pin p to pin n
Parameters (6)
    resistor₊alpha ▪ 0 ▪ Temperature coefficient of resistance
    fixedTemperature₊T ▪ Unassigned ▪ Fixed temperature at port
    source₊V ▪ Unassigned ▪ Value of constant voltage
    resistor₊R_ref ▪ 1.0 ▪ Reference resistance
    resistor₊T_ref ▪ 300.15 ▪ Reference temperature
    capacitor₊C ▪ Unassigned ▪ Capacitance
Equations (2)
    Differential(t)(capacitor₊v(t)) ~ capacitor₊i(t) / capacitor₊C
    0 ~ -resistor₊v(t) + resistor₊i(t)*resistor₊R(t)
"""

isys3 = generate_initializesystem(sys; 
            u0map = [sys.capacitor.v => 0.0, sys.resistor.i => 0.0],
            pmap = [sys.capacitor.C => 1.0, sys.source.V=>1.0,sys.fixedTemperature.T=>400.15],
            guesses = [sys.resistor.R=>sys.resistor.R_ref])

isys3_prob = ODEProblem(sys, [sys.capacitor.v => 0.0, sys.resistor.i => 0.0], (0.0, 10.0),
                [sys.capacitor.C => 1.0, sys.source.V=>1.0,sys.fixedTemperature.T=>400.15],
                guesses = [sys.resistor.R=>sys.resistor.R_ref])
                                
isys3_prob_initsys = isys3_prob.f.initializeprob.f.sys
# out: 0 =−resistor.v(t)+resistor.i(t)resistor.R(t)

if without guesses, the error is the same.