Large Multi-Machine Power System Simulations Using Multi-Stage Adomian Decomposition

Abstract

Multi-stage Adomian decomposition method (MADM) is a proven semi-analytical approximation solution technique for ordinary differential equations (ODEs), which provides a rapidly convergent series by integrating over multiple time intervals. Applicability of MADM for large nonlinear differential algebraic systems (DAEs) is established for the first time in this paper using the partitioned solution approach. Detailed models of power system components are approximated using MADM models. MADM applicability is verified on 7 widely used test systems ranging from 10 generators, 39 buses to 4092 generators, 13659 buses. Impact of the step size and the number of terms is investigated on the stability and accuracy of the method. An average speed up of 42% and 26% is observed in the solution time of ODEs alone using the MADM when compared to the midpoint-trapezoidal (TrapZ) method and the modified-Euler (ME) method, respectively. MADM accuracy is found to be similar to the ME and comparable to the TrapZ method. MADM stability properties are found to be better than the ME and weaker than the TrapZ method. An average speed up of 13% and 5.85% is observed in the overall solution time using MADM w.r.t. TrapZ and ME methods, respectively.