Application of Semi Analytical Methods for Large Power System Simulations

Abstract

Power system dynamics can be accurately modelled in time domain by using nonlinear differential and algebraic equations (DAEs). The challenge lies in solving the large number of nonlinear DAEs faster than real-time in order to provide the operator with sufficient information on the unfolding critical contingencies to take preventive control measures. Research is being carried out in this regard on the application of new computing architectures and development of faster solvers including efficient parallelization techniques. Semi analytical methods are frequently used for numerical simulations of real world systems in the applied sciences and engineering including nonlinear ODE, PDE and DAE problems. Applicability of two widely used semi-analytical methods called Adomian Decomposition Method (ADM) and Homotopy Analysis Method (HAM) have been explored for the time domain simulations of large power systems in this thesis. Since these methods have a very narrow region of convergence, they are applied over successive time intervals. These are called multi-stage methods. The multi-stage ADM and HAM (MADM and MHAM respectively) have been tested on 7 widely used test systems ranging from 10 generators, 39 buses to 4092 generators, 13659 buses. Studies on the number of terms, impact of time step on stability and accuracy and maximum step size have been conducted. 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 and Modified Euler methods respectively. This thesis also proposes a Z-transform based method to quantify the error generated by MADM application in time domain simulation. The error of MADM has been compared to the errors generated by various numerical integration methods. It is found that the number of algebraic equations to be solved are much less than the differential equations in large systems but they take much longer time for execution. A model of multi-machine system including the network and stator transients has been developed to convert the DAE model into an ODE model and validated with EMTP. Various numerical methods have been tested on this ODE model to improve the execution time.