This paper proposes new analytical expressions of indicators for inter-turn and phase-to-phase short-circuit fault diagnosis in permanent-magnet synchronous machines. The proposed indicators are deduced from symmetrical components of phase currents in the alpha beta reference frame. They are able to reflect the fault severity and location, are independent from the electrical pulsation and the rotor initial angle, and are robust regarding the loss of some measurements. Hence, they can be used for fault isolation and identification. Experimental tests have been carried out and show promising results. Furthermore, the presented algorithm does not use fast Fourier transforms and, therefore, avoids delays in fault isolation inherent to this technique.