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Complex harmonic analysis (CHA) provides a computationally efficient alternative to finite element analysis (FEA) for modelling multi-phase wound field synchronous machines. This paper presents three methods that could improve the accuracy of the CHA: by improving the equivalent air gap, by including a saturation factor, and by using image methods for computing end-winding inductance. The comparison against a finite element method and experiment shows the improved complex harmonic method could predict waveforms reliably, where a dynamic finite element method would be time-consuming. This paper shows the method is valid for a five-phase generator.