Entirely harmonic domain calculation of multiphase nonsinusoidal steady state

This paper proposes an algorithm for obtaining the periodic steady-state solution of a multiphase network including nonlinear, switching, and frequency dependent elements. Unlike existing methods which deal with nonlinear and switching elements in the time domain, the approach presented is entirely in the harmonic domain. The method will be used for the harmonic analysis of power systems and for steady-state initialization in electromagnetic transient analysis. The algorithm takes rigorously into account the inter-harmonic couplings in the Jacobian matrix of the proposed Newton-Raphson iteration process so that a quadratic convergence rate is achieved. Linear, nonlinear, switching, and frequency dependent elements are modeled in a modular approach, and any network topology can be handled by extending the Modified Nodal Equations approach to the harmonic domain case. First the algorithm is described and then applied to a test case to demonstrate its computational performance.