Extract linear algebraic equations

Specific Domains Modelling & Simulations
1

I’m trying to use ModelingToolkit.jl to generate a system of linear algebraic equations. It’s quite simple: my system is a resistor network with a constant voltage source. I use ModelingToolkit to create a topology, and I would like to extract the equations and variables from rnet_model.

using ModelingToolkit, Plots, DifferentialEquations
using ModelingToolkit: t_nounits as t, D_nounits as D
using Symbolics

@connector Pin begin
    v(t)
    i(t), [connect = Flow]
end

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

@mtkmodel OnePort begin
    @components begin
        p = Pin()
        n = Pin()
    end
    @variables begin
        v(t)
        i(t)
    end
    @equations begin
        v ~ p.v - n.v
        0 ~ p.i + n.i
        i ~ p.i
    end
end

@mtkmodel Resistor begin
    @extend OnePort()
    @parameters begin
        R = 1.0 # Sets the default resistance
    end
    @equations begin
        v ~ i * R
    end
end


@mtkmodel ConstantVoltage begin
    @extend OnePort()
    @parameters begin
        V = 1.0
    end
    @equations begin
        V ~ v
    end
end

@mtkmodel RNetModel begin
    @components begin
        R1 = Resistor(R = 1.0)
        R2 = Resistor(R = 1.0)
        R3 = Resistor(R = 1.0)
        source = ConstantVoltage(V = 1.0)
        ground = Ground()
    end
    @equations begin
        connect(source.p, R1.p)
        connect(R1.p,R2.p)
        connect(R2.n,R3.p)
        connect(R3.n, ground.g)
        connect(R1.n, ground.g)
    end
end

@mtkbuild rnet_model = RNetModel()

println("equations", equations(expand_connections(rnet_model) ))
println("unknowns: ", unknowns(rnet_model) )
println("observed: ", observed(rnet_model) )

solution =Symbolics.solve_for(equations(expand_connections(rnet_model)), unknowns(rnet_model))
println(solution)

I see that the equations are there, rnet_model.observed, rnet_model.eqs, and the variables as well in rnet_model. My goal is to get the equation

AX=B

, which is not overdetermined, and then solve the system either symbolically or numerically. How can I get a system of linearly independent equations from rnet_model?