Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Electrical and Computer Engineering


In recent years, power system harmonic levels have increased significantly due to the ever-increasing use of nonlinear loads which primarily consist of power electronic devices. The effect of these harmonics on power system components represents a serious problem to utility companies and consumers. A survey of power system harmonics as generated mainly by static ac/dc power converters is presented. Aspects concerning harmonic injection, their effects on system components and harmonic reduction techniques are included. Harmonic analysis methodologies are discussed and compared in terms of efficiency and accuracy. The need of a stochastic treatment of harmonic voltages and currents is clearly explained. A novel probabilistic model of analyzing power system harmonics is developed. Depending on their operating modes and switching states, nonlinear loads connected to each distribution bus are decomposed into four distinct categories of harmonic current injection. The probability distribution of the total random current injected at each bus is determined after making some reasonable assumptions. Probability characteristics of the resulting harmonic voltages are calculated. Two computational methods, i.e., the direct integration method and the Monte Carlo simulation method, are presented for determining the statistical characteristics of the harmonic signals. The procedure is demonstrated by an example which illustrates the probability aspects of power system harmonics. Potential applications of the probabilistic model are also considered. In harmonic modeling of a transmission line, the use of the (pi)-equivalent does not provide the location of maximum heating and insulation stress on the line. In this study, the differential equations describing voltage and current wave propagation along transmission lines are solved by modal decomposition. The resulting solution is transformed back into phase quantities. Two efficient numerical algorithms are developed to compute and locate maximum heating and insulation stress on untransposed transmission lines with distorted voltage and current waveforms. The numerical algorithms developed will guarantee convergence to the global solution. Other applications of these algorithms, such as determining maximum values of individual harmonics for communication interference studies and maximum distortion factors on the transmission lines, are included. The numerical methods are demonstrated by an example.