New method for measuring Xd and Xq based on the P-Q diagram of the lossy salient-pole machine

The P-Q diagram of the lossy salient-pole synchronous machine is derived from the familiar machine voltage phasor diagram. The diagram contains a reluctance circle with a centre and diameter which are dependent on machine loss resistance. Steady-state stability limits are determined for the lossy salient-pole machine, and it is shown that it is not possible to operate on the extreme motoring point of the reluctance circle. A method of measuring Xd, Xq and R for the lossy salient-pole synchronous machine or lossy reluctance machine presented which involves measuring three convenient characteristic points on the reluctance circle of the P-Q diagram. This method is found to have better accuracy than the slip test for smaller machines. The theory presented in the paper is applied to a 5 k VA test machine and is found to give accurate results.