This paper presents a unified method of analysis for a three-phase inductio
n generator self-excited with a single capacitance and supplying a single-p
hase load. Symmetrical components analysis is used to establish the input i
mpedance of the generator, while the pattern search method of Hooke and Jee
ves enables the per-unit frequency and magnetizing reactance of the machine
to be determined, a crucial step in computing the generator performance. B
est machine performance is obtained using the Steinmetz connection, with th
e excitation capacitance connected across the lagging phase. Experiments ca
rried out using a 2.2 kW induction machine confirm the accuracy of the theo
retical analysis and the solution method.