The modal series method and multi-dimensional laplace transforms for the analysis of nonlinear effects in power systems dynamics

In this paper, a procedure based on an extended modal series method and multidimensional Laplace transforms is proposed to examine nonlinear effects on power system dynamic behavior. The procedure is designed to handle nonlinearities of the power series type and to identify nonlinear modal interactions which are presented in the dynamics of nonlinear systems. A perturbation model based on the properties of Laplace transform kernels is presented. Using the method of association of variables in multidimensional Laplace transforms and Volterra series theory a reliable, easier and more systematic alternative to obtain approximate closed-form solutions of a perturbation model of the power system is then suggested. The approach is extended to consider the more general case of high-dimensional nonlinear systems described by forced nonlinear differential equations. The application of the method is illustrated with a 3-machine, 9-bus test power system. Comparisons with direct numerical solutions using both linear and nonlinear formulations are provided to validate the accuracy and computational effort of the proposed method.