DETERMINING THE JOINT MOMENTS OF A MOTOR-DRIVES HARMONIC CURRENT PHASORS

It has been previously demonstrated that if a sufficiently large numbe r 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 co nsideration has been given to the problem of determining these joint m oments for specific types of harmonic sources. This paper presents a m ethod for analytically determining the joint moments of the resolved h armonic current components produced by two motor drives which utilize a phase-controlled rectifier. It is shown that when given the load tor que as a function of the randomly varying motor speed, the means, vari ances and covariance of each harmonic current phasor's rectangular com ponents can be expressed in terms of the probability density function of the motor speed.