Determining the joint moments of a motor driveʹs 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 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.