Determining the joint moments of a motor drive´s harmonic current phasors

It has been previously demonstrated that if a sufficiently large number of harmonic current sources are operating, a complete probabilistic characterization of the resulting power system-wide harmonic voltages can be found with knowledge of only the first and second order joint moments of each harmonic current´s rectangular components. However, little consideration has been given to the problem of determining these joint moments for specific types of harmonic sources. This paper presents a method for analytically determining the joint moments of the resolved harmonic current components produced by two motor drives which utilize a phase-controlled rectifier. It is shown that when given the load torque as a function of the randomly varying motor speed, the means, variances and covariance of each harmonic current phasor´s rectangular components can be expressed in terms of the probability density function of the motor speed