Steady-State Analysis of Static Power Converters

Steady-state analysis of static power converters using thyristors and linear circuit elements is formulated using state space method. The circuit goes into n modes and has different describing matrices for each mode. Steady-state condition is obtained in terms of these matrices and the firing and extinction angles. A Newton-Raphson algorithm is given as an interactive method for obtaining the steady-state solution. Closed form expressions are given for the derivative matrix D used in the algorithm. These expressions take into account the variation of the extinction angles during transient as is the case with naturally commutated thyristors. Three alternatives are discussed for the computation of the matrix D. The first method uses the exact expressions whereas the second method uses an approximate expression that neglects the variation of the extinction angles during transient. The third method uses numerical differentiation. Results are then given for an ac-ac and an ac-dc converters. A comparison is made with contraction mapping where it is shown that a remarkable reduction in computation time is achieved especially for lightly damped loads.