Advanced knowledge of the minimum capacitor value required for self-excitation of an induction generator is of practical interest. To find this capacitor value two nonlinear equations have to be solved. Different numerical methods for solving these equations are known from previous literature. However, these solutions involve some guessing in a trial-and-error procedure. In the paper a new simple and direct method is developed to find the capacitance requirement under R L load. Exact values are derived for the minimum capacitance required for self-excitation and the output frequencies under no-load, inductive and resistive loads. These calculated values can be used to predict theoretically the minimum value of the terminal capacitance required for selfexcitation. For stable operation C must be chosen to be slightly greater than Crnin. Furthermore, it is found that there is a speed threshold, below which no excitation is possible no matter what the capacitor value. This threshold is called the cutoff speed. Expressions for this speed under no-load and inductive load are also given.
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RS, R , , R= p.u. per phase stator, rotor (referred to stator) and load resistance, respectively X h , Xb, X, X , = p.u. per phase stator leakage, rotor leakage (referred to stator), load and magnetising reactances (at base frequency), respectively = p.u. maximum saturated magnetising reactance = per phase terminal-excitation capacitance = p.u. per phase capacitive reactance (at base frequency) of the terminalexcitation capacitor = p.u. frequency and speed, respectively = base speed in rev/min = per phase base impedance = per phase airgap and output voltages,
Dependency of the output voltage and frequency of the isolated self-excited induction generator on the speed, load, and terminal capacitance causes certain limitations on its performance. This paper presents the performance of the induction generator under a wide range of varying conditions. It is found that the machine operates only in certain element ranges and that all generated currents and voltages are bounded. Furthermore, an optimal combination, for maximum power generation, of these elements exists. Such theoretical results are important as a guide in operating such machines.
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