Nonlinear transfer function based on forced response modal series analysis

This paper describes the so called nonlinear transfer functions oriented to a disturbed power system model based on the decomposition of the nonlinear power system model in uncoupled modal series. The technique of modal series is extended to the inclusion of input excitation functions, thus allowing the determination of transfer function for a set of selected variables operating within of the power system. A superposed definition of transfer functions, where each term due to the Taylor Series expansion is analyzed following similar rules defined for the Volterra series expansion, that is, a set kernels decomposition defined each for first, second, etc. order terms. The method can determine both time domain (through the inverse Laplace domain transform) and frequency domain responses of the transfer function. The accuracy of the methodology is exemplified by applying two test power systems, i.e. the synchronous machine infinite busbar simple power system and finally the 3 SM, 3 loads, 9 buses power system.