Periodic steady-state solution of a synchronous generator based on a voltage-behind-reactance formulation and the Poincaré map method

Abstract

A powerful blend based on a voltage-behind-reactance (VBR) model and the Poincaré map method, suitable to carry-out harmonic oriented analyses, is presented in this paper to compute the periodic steady-state solution of a synchronous generator. The VBR model, as originally conceived, is modified and instead a per-unit version, tailored to the acceleration procedure, is used. The acceleration of the convergence to the periodic steady-state is accomplished with a Newton method and the Poincaré map. A Numerical Differentiation approach allows the computation of the transition matrix involved in the acceleration procedure using a sequential perturbation of the state variables. The periodic steady-state solution of synchronous generators is reported for a set of operating conditions such as change of load, a three-phase fault and a single-phase fault. Furthermore, the harmonic analysis of a system comprising a RLC circuit with a varying degree of unbalance, fed from a synchronous generator is carried-out with the acceleration procedure. Important speedup factors up to 145 are reported for large turbine generators. The application of a Newton based acceleration procedure to a VBR synchronous machine model yields important benefits for the efficient computation of periodic steady-state solutions and it is particularly useful for test cases involving large rotary machines with an inherently large inertia.