Frequency-Domain Computation of Steady and Dynamic States Including Nonlinear Elements

This paper presents a Newton-type methodology to calculate the transient or periodic steady state of an electrical network including nonlinear elements. The basic idea is to decompose the complete network into linear and nonlinear subnetworks. On one hand, a nodal representation of the linear network is considered. On the other hand, a Jacobian corresponding to a nonlinear element is calculated numerically via input perturbations, with the terminal voltage being the input and the device current as being the output. The latter is calculated in the time domain, via a polynomial representation, and converted back into the frequency domain by numerical Laplace transform operations. Finally, the solutions corresponding to the linear and nonlinear subnetworks are included in a Newton-type iterative scheme having a current mismatch (at the point of coupling) as its basis. Two examples involving nonlinear loads in a network are presented for illustration of the aforementioned procedures.