ArgumentError: Cannot find the parent of

General Usage
1

I’m trying to get started using modeling toolkit, but I’m hitting an ArgumentError that I can’t interpret. This is my code:

using Plots; pyplot()
using ControlSystemsBase, RobustAndOptimalControl, LinearAlgebra
using ModelingToolkit
@parameters Li::Real Ri::Real Lg::Real Rg::Real ωn::Real Vn::Real kp::Real kq::Real ωf::Real
j=1im

Ap = -(Ri+Rg)/(Li+Lg)-j*ωn
A1 = (Rg*Li-Ri*Lg)/(Lg+Li)
A2 = [Lg/(Lg+Li) Li/(Lg+Li)]
A3 = 1/(Li+Lg)
kp = 0.2*2π/1000
kq = 20/1000
@variables t P(t)::Real=0 Q(t)::Real=0 Pf(t)::Real=0 Qf(t)::Real=0 vo(t)::Complex=0 ig(t)::Complex=0 vi(t)::Complex=0 vamp(t)::Real=0 theta(t)::Real=0 ω(t)::Real=0 vg(t)::Complex=0
D = Differential(t)
eqs = [P ~ 3/2*real(vo*conj(ig))    # P calc
       D(Pf) ~ ωf*(P-Pf)            # low pass filter
       Q ~ 3/2*imag(vo*conj(ig))    # Q calc
       D(Qf) ~ ωf*(Q-Qf)             # low pass filter
       vi ~ vamp*exp(j*theta)       # output voltage generation
       D(theta) ~ ω                 # angle integration
       vo ~ A1*ig+(A2*[vi; vg])[1] # output admittance
       D(ig) ~ Ap*ig+A3*vi-A3*vg # output admittance
       vamp ~ Vn-kq*Qf              # Q-droop
       ω ~ -kp*Pf]                  # P-droop
@named sys = ODESystem(eqs, t, [Pf Qf ig theta], [Li Ri Lg Rg ωn Vn kp kq ωf], tspan = [0,1])

Complex variables should be supported, right?

2

in the past I had a similar problem.
Below my approach (not perfect, but sufficient for me):

  • substitute real(cVAR) and imag(cVAR) by cVAR_re and cVAR_im
using Plots; pyplot()
using ControlSystemsBase, RobustAndOptimalControl, LinearAlgebra
using ModelingToolkit
@parameters Li::Real Ri::Real Lg::Real Rg::Real ωn::Real Vn::Real kp::Real kq::Real ωf::Real
j=1im

function NewVars(eqName::String, CCX::Vector{Complex{Num}})::Tuple{Expr, Expr}
    vari::String = "newVariables = @variables "
    substi::String = ""
    for cx in CCX
        stcx = string(cx)[1:end-3]  # without '(t)'
        vari = string(vari,stcx*"₋re(t) ",stcx*"₋im(t) ")
        substi = string(substi,"$eqName = substitute($eqName,(real($stcx)=>$(stcx)₋re)); ")
        substi = string(substi,"$eqName = substitute($eqName,(imag($stcx)=>$(stcx)₋im)); ")
    end
    return (Meta.parse(vari), Meta.parse(substi))
end

Ap = -(Ri+Rg)/(Li+Lg)-j*ωn
A1 = (Rg*Li-Ri*Lg)/(Lg+Li)
A2 = [Lg/(Lg+Li) Li/(Lg+Li)]
A3 = 1/(Li+Lg)
kp = 0.2*2π/1000
kq = 20/1000

@variables begin
        t
        P(t)::Real=0
        Q(t)::Real=0
        Pf(t)::Real=0
        Qf(t)::Real=0
        vamp(t)::Real=0
        theta(t)::Real=0
        ω(t)::Real=0
    end


CX = @variables begin   # Complex VARS
        vo(t)::Complex
        ig(t)::Complex
        vi(t)::Complex
        vg(t)::Complex
    end

D = Differential(t)
eqs = [P ~ 3/2*real(vo*conj(ig))    # P calc
       D(Pf) ~ ωf*(P-Pf)            # low pass filter
       Q ~ 3/2*imag(vo*conj(ig))    # Q calc
       D(Qf) ~ ωf*(Q-Qf)             # low pass filter
       vi ~ vamp*exp(j*theta)       # output voltage generation
       D(theta) ~ ω                 # angle integration
       vo ~ A1*ig+(A2*[vi; vg])[1] # output admittance
       D(ig) ~ Ap*ig+A3*vi-A3*vg # output admittance
       vamp ~ Vn-kq*Qf              # Q-droop
       ω ~ -kp*Pf]                  # P-droop


eqs1=deepcopy(eqs)

(Bvaria, Bsubst) = NewVars("eqs1",CX)
eval(Bvaria) # create new variables
eval(Bsubst) # substitute


# @named sys = ODESystem(eqs, t, [Pf Qf ig theta], [Li Ri Lg Rg ωn Vn kp kq ωf], tspan = [0,1])
@named model = ODESystem(eqs1, t)
# sys = structural_simplify(model)

Check your system again: Model model with 13 equations, States (15):