Abstract: A method for obtaining a power system phasor includes sampling a power system signal at instants determined by a nominal power system frequency to provide a plurality of data samples; using the data samples to estimate a phasor having an elliptical trajectory; generating a deviation formula representing a frequency deviation between actual and nominal power system frequencies; and using the deviation formula to perform a coordinate transform of the estimated phasor to provide a scaled phasor having a substantially circular trajectory. If the data samples are unevenly spaced, a method in another embodiment includes minimizing squares of errors between the unevenly spaced data samples and an approximating sinusoidal function of the data samples.

Abstract: A method for detecting turn faults in an induction motor includes obtaining motor current and voltage waveforms and converting the motor current and voltage waveforms to digitized current and voltage waveforms. Fundamental phasors of the digitized current and voltage waveforms are extracted and, a symmetrical component transform is applied to the fundamental phasors to obtain symmetrical component current and voltage phasors including a negative sequence voltage phasor (V.sub.-) and negative sequence current phasor (I.sub.-). A fault injected negative sequence current (Ii.sub.-) is estimated according to the following equation:Ii.sub.- =I.sub.- -V.sub.- /Z.sub.- -Ir,wherein Z.sub.- is a characteristic negative sequence impedance and Ir is a residual injected negative sequence current. The existence of a turn fault is determined by comparing the estimated fault injected negative sequence current with a threshold fault injected negative sequence current.