Real-time thermal management of electrical machines relies on sufficiently accurate indicators of internal temperature. One indicator of temperature in a permanent-magnet synchronous motor (PMSM) is the stator winding resistance. Detection of PMSM winding resistance in the literature has been made on machines with relatively high resistances, where the resistive voltage vector is significant under load. This paper describes two techniques, which can be applied to detect the winding resistance, through "angle" and "magnitude" current injection. Two further methods are described, which discriminate injected current and voltages from motoring currents and voltages: "unipolar" and "bipolar" separation. These enable the resistance to be determined, and hence the winding temperature in permanent-magnet machines. These methods can be applied under load, and in a manner that does not disturb motor torque or speed. The method distinguishes between changes in the electromotive force constant and the resistive voltage. This paper introduces the techniques, while a companion paper covers the application of one of the methods to a PMSM drive system.