Synchronous machine stability analysis using an efficient time domain methodology: unbalanced operation analysis

This paper describes a methodology for the efficient stability analysis of the synchronous machine. The state space phase coordinates model of the synchronous machine incorporates the effects of time-varying and inter-spatial harmonic inductances. The dynamics of the synchronous machine are represented by a set of ordinary differential equations (ODEs). The machine behaviour is analyzed under severe unbalanced operation conditions. The level of detail and accuracy obtained with the machine model in phase coordinates can not be achieved with conventional models based on the dq0 framework for unbalanced fault analysis. A Newton technique based on a numerical differentiation process is used for the acceleration of the convergence of the state variables to the limit cycle to obtain the machine initial conditions and the steady state previous to the fault application and after the fault is removed. The combined response obtained with methodology for swift time domain transient and periodic steady state analysis and the phase domain synchronous machine model is compared in terms of accuracy and computational efficiency against a widely used and accepted machine model of an Electro-Magnetic Transient Program (EMTP-ATP).