Improved Numerical Integration Method for Power/Power Electronic Systems Based on Three-Point Collocation

This paper presents a new approach for time-domain transient simulation of electric power systems with or without power electronic (switching) subsystems. The new methodology has been named quadratic integration method. The method is based on the following two innovations:(a) the nonlinear system model equations (in general differential-algebraic) are reformulated to a fully equivalent system of quadratic equations, by introducing additional state variables, and (b) the system model equations are integrated assuming that the system states vary quadratically within a time step (quadratic integration). The proposed method yields an implicit integration scheme which demonstrates improved convergence characteristics and most importantly improved solution precision. The approach also demonstrates superior behavior compared to traditionally used methods in power system transient analysis (such as the trapezoidal integration rule) in terms of accuracy and numerical stability properties, especially for switching systems. Details about the numerical properties of the method are discussed in the paper. The proposed methodology and its performance is demonstrated on two test systems including (a) nonlinear R-L electric circuit, and (b) power electronic circuit (switching system). The methodology is very useful for systems with power electronics and nonlinear devices such as saturable transformers/reactors and surge arresters.