Fast periodic steady state solution of a synchronous machine model in phase coordinates incorporating the effects of magnetic saturation and hysteresis

The synchronous machine has a relevent importance, among the power system components. It is, by nature, an element complex by itself Therefore, a detailed model of this component is needed to analyze its behaviour under different operation conditions and its influence of the rest of the system. In this state space model developed in the time domain, novel algorithms are used for the representation of nonlinear phenomena of magnetic saturation and hysteresis. In addition, the model can incorporate any number of damper windings and higher harmonic terms in the time-varying inductance matrix. The dynamics of the synchronous machine are represented by a set of Ordinary Differential Equations (ODE's) and solved numerically with the fourth order Runge-Kutta integration method. The synchronous machine is analyzed under balanced and unbalanced operation conditions. Fast periodic steady state solutions are obtained with the application of a Newton Raphson method, for the acceleration of the machine's state variables to the Limit Cycle. The potential of the Newton methods for achieving efficient time domain solutions of the synchronous machine model is demostrated.