ABSTRACT
This chapter will explain how steady-state terminal voltage builds up during the selfexcitation process and during the recovery of voltage during perturbations across the terminal voltage and stator current due to load changes. A set of state equations are derived to obtain the instantaneous output voltage and current in the self-excitation process. In the example in this chapter, the equations describe an induction machine with the following rated data: 220/380 V, 26/15 A, 7.5 kW, and 1765 rpm. We also show that the equations in this chapter can be easily used to calculate output voltage, including the variation of mutual inductance with the magnetizing current discussed further in Chapter 4. Furthermore, we will present a general matrix equation for simulation of the parallel aggregation of induction generators (IG). In any case, for every machine at a given speed, we show that there is a minimum capacitance value causing self-excitation in agreement with the steady state case shown in Chapter 2. We will discuss rotor parameter variation and demonstrate that it has little effect on the accuracy of these calculations and that comparable results can be achieved using the standard open circuit and locked rotor parameters. Saturation effects are also considered in this chapter by taking into account the nonlinear relationship between magnetizing reactance and the magnetizing current of a machine; using this approach, the mutual inductance, M, will be shown to vary continually.
