Abstract: A method of detecting faults on a power transmission line system includes simultaneously measuring phase current samples at each phase of each transmission terminal; calculating real and imaginary phaselets comprising partial sums of the phase current samples; for each phaselet, calculating a respective partial sum of squares of each phase current sample; calculating the sums of the real and imaginary phaselets over a variable size sliding sample window; calculating real and imaginary phasor components from the phaselets and a sum of the partial sums of the squares over the sample window; using the sums of the real and imaginary phaselets, the real and imaginary phasor components, and the sum of the partial sums of the squares to calculate a sum of squares of errors between the phase current samples and a fitted sine wave representative of the real and imaginary phasor components; using the sum of squares of errors to calculate a variance matrix defining an elliptical uncertainty region; determining whether a

Abstract: A digital decaying current offset correction method and apparatus, in one aspect, separates the requirements of detecting fault existence from the requirements of detecting fault location. Once the decaying offset removal routine is initiated, current and voltage are sampled and, for each current and voltage sample, current and voltage phasors are generated. The current phasor values, which are not offset corrected, may be used to determine whether to trip a breaker. Once the breaker is tripped, the decaying offsets are removed from the current phasors. The offset corrected current phasors are then used to locate the fault.

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.

Abstract: A method for estimating rotor shaft velocity includes adding two counter rotating signal components to a fundamental motor control signal to provide a combined control signal; sensing at least one motor phase signal; determining an extracted portion of the motor phase signal representative of the two counter rotating signal components; and using the extracted portion to estimate rotor shaft velocity. The step of adding two counter rotating signal components may include either adding a single phase signal in a reference frame synchronous to the fundamental motor control signal or adding two separate signals.