Steady-state and transient analysis of self-excited induction generators C. Grantham, BSc, PhD, CEng, MIEE D. Sutanto, BE, PhD B. Mismail Indexing terms: Generators, Induction motors, Transmission and distribution plant Abstract: This paper describes a method for accu- rately predicting the minimum value of capac- itance necessary to initiate self-excitation with a stand-alone induction generator. Final steady- state self-excitation voltages and frequencies are also calculated for loaded and unloaded oper- ations, taking into account the rotor parameter variations with the frequency. It is shown that the calculated and measured results are in strong agreement, and for the loaded generator they agree considerably more so than when constant rotor parameters are used. The theory is also extended to include the transient build up of voltage during the initiation stage of self- excitation, and the perturbations of the terminal voltage and the stator current which result from load changes. List of symbols = base frequency at which machine parameters are measured, Hz = self-excitation frequency, Hz =fjf, rat i° of self-excitation to base frequency = rotor speed, electric rad/sec = p.u. speed / f s co o L s ,L r = stator and rotor inductance, H M = mutual inductance, H R s , R r = stator and rotor resistance, Q C = self-excitation capacitance, F X c = self-excitation capacitive reactance, Q X s , X r = stator and rotor leakage reactance, Q X m = magnetisation reactance, Q V m = voltage across magnetisation reactance, V R = load resistance, fi i m , I m = instantaneous and RMS magnetisation current, A *D 5 U = instantaneous stator and rotor direct axis current, A i Q , i q = instantaneous stator and rotor quadrature axis current, A 1 Introduction The phenomenon of self-excitation in induction machines has been known for over 50 years, [1]. In most practical Paper 6488B (PI), first received 14th December 1987 and in revised form 16th September 1988 The authors are with the Department of Electric Power Engineering, School of Electrical Engineering and Computer Science, The University of New South Wales, PO BOX 1, Kensington, New South Wales, Aus- tralia, 2033 circumstances, however, such self-excitation is undesir- able as it can cause severe overvoltages [2, 3] thereby stressing the insulation of the machine, or it can cause torque and machine speed fluctuations [4,5] which detract from the performance of the machine and may cause significant overheating. In recent years the self-excited induction generator has been identified as a possible source of power in micro- hydro and wind power applications and this has led to renewed research in the subject [6-12]. Elder et al. [7] reported that a major problem in starting stand-alone induction generators is that of guaranteeing self- excitation. They showed that the reliability of starting can be increased by passing a DC current through the machine, switching in charged capacitors, increasing the speed above its rated value, or by increasing the rated terminal capacitance. Hitherto, the method used to analyse self-excited induction generators has been to use the standard per phase equivalent circuit of the induction motor, modified for the self-excited case [8] as shown in Fig. 1. This equivalent circuit is a steady-state equivalent circuit and cannot readily be used for calculating transient phenome- non. Elder et al. [11] use D-Q axes to analyse the induc- tion generator, but their model is also based on a steady-state representation and is effectively a variation of the steady-state equivalent circuit approach. In this investigation, the authors show that the self- excited induction generator can be analysed using the generalised-machine-theory transient representation of the machine. Such an analysis produces instantaneous currents which can be used to investigate the process of current and voltage build up during self-excitation and similarly perturbations due to load changes. If required, a relatively straight forward extension of this would be to use the instantaneous currents thus calculated to predict transient torque during the process of self-excitation. While taking into account the variation of magne- tisation reactance due to magnetic saturation, previous authors have assumed that the remainder of the machine's parameters are constant. However, Brown and RJF F 2 ~T -i« (F-V) Fig. 1 Per phase equivalent circuit of the unloaded self-excited three- phase induction generator IEE PROCEEDINGS, Vol. 136, Pt. B, No. 2, MARCH 1989 61