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Iron saturation causes the lumped circuit parameters to vary with the point of operation. Experimental evidence shows that the field excitation voltage and the direct axis reactance are not affected significantly by the armature reaction. This can be attributed to the presence in the direct axis of the magnets whose thickness represents a large effective air gap. In the quadrature axis, instead, the contribution of the air gap to the reluctance is small. Therefore, the quadrature axis reactance depends strongly on both the quadrature and direct axis components of armature magnetomotive force. This suggests a simple, albeit approximate, approach for predicting the parameter variation with operating point. As a result, both the design and analysis of synchronous motors excited by permanent magnets (PM's) are facilitated.
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Chen et al. (1985) studied this question.
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