Quadratic integration method for transient simulation and harmonic analysis

This paper elaborates on a newly introduced approach for time-domain transient simulation of electric power systems with highly nonlinear and/or switching subsystems. The new methodology is based on a numerical integration scheme that assumes that the system model states vary quadratically within a time step (quadratic integration). The proposed method is an implicit integration scheme which demonstrates improved numerical 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 highly nonlinear and switching systems. Details about the numerical properties of the method are briefly discussed in the paper. The proposed methodology and its performance are demonstrated on two test systems including (a) linear R-L-C electric circuit representing a simple converter model, and (b) highly nonlinear saturable inductor model. The methodology is very useful for analysis of systems with power electronics and nonlinear devices such as saturable transformers/reactors and surge arresters.