Request help solving a Mathematical Programming with Equilibrium Constraints problem in JuMP?

Specific Domains Optimization (Mathematical)
6

When trying to write out each component as a separate constraint, I need to add an index i to the original constraint_T function like this

function constraint_T(i, Θ...)
    vΘ = collect(Θ)
    θ₁ = vΘ[1]
    θ₃ = vΘ[2:4]
    RC = vΘ[5]
    EV = reshape(vΘ[6:end], 2, S)

    θ = BusParameters(θ₁=θ₁, θ₃=θ₃, RC=RC)
    EVᵢ = T(EV, θ, i)
    return EVᵢ - EV[i]
end

Then register the function with one additional parameter

JuMP.register(model, :constraint_T, 1+5+2*S, constraint_T, autodiff=true )

And add the separate constraints

for i in 1:2*S
    @NLconstraint(model, constraint_T(i, Θ...) == 0)
end

But this introduces the additional parameter i that Autodiff is trying to differentiate, which of course will cause problems. How should let Autodiff skops to differentiate with i? Any suggestions @odow?