The d-q harmonic balance technique is utilized to extract the closed-form expressions for currents induced in the rotor cage of a line-start single-phase synchronous reluctance motor under steady-state conditions as a function of load angle and auxiliary winding run-capacitor value.
The equations show a non-negligible amount of current flow in the rotor of the machine, even at synchronous speed operation; there is, therefore, an added I2R loss. The calculated I2R loss in the rotor d-axis circuit is higher and diminishes rapidly with increase in load angle, while the q-axis
circuit loss increases slightly with load angle. A rapid increase in loss is also observed in both the d- and q-axes with increase in run-capacitor values.