# HARMONIC RESONANCE IN POWER SYSTEMS (VOLTAGE, CONVERGENCE, PREDICTION)

#### Abstract

Although the study of harmonics in power systems dates back to the early 1900's, renewed interest in this area has recently developed. This increased interest is directly attributable to the proliferation of nonlinear devices appearing as loads, sources, and components in the system. The nonlinear loads, sources and components have the potential of causing problems in system protection, communications interference, load disruption, component failure, losses, and other areas. The focus of this research is on the particular problem of harmonic resonance. Various system configurations can produce high and/or low impedance paths for the harmonic currents produced by the nonlinear devices. These conditions will cause abnormally high voltage and/or current levels, respectively. Through this research, a method is developed which identifies the system configurations which produce these conditions. In addition, a method is developed to predict the magnitudes of harmonic voltages for any system configuration and operating strategy. Although the harmonic power flow algorithms were developed to accurately calculate the harmonic voltage magnitudes and their phase relationships, the object of this research is to determine the harmonic voltage magnitudes with reasonable accuracy expending much less computer time than the harmonic power flow algorithm would require.^ An additional research area addressed in this thesis involves the harmonic power flow algorithm: this area deals with the convergence of Newton's method. The problem observed is that the iterative process does not reliably converge to a solution for system configurations which produce the abnormally high harmonic voltage conditions. This thesis contains a theoretical and empirical analysis of both the cause of this problem and an efficient solution.^ In summary, the significant contributions of this thesis are: (i) Convergence properties of the harmonic power flow algorithm. (1) A second order modified method, suitable for the harmonic power algorithm was developed. (2) The improvement of convergence characteristics were demonstrated theoretically and in practical applications. (3) The reduction of number of calculations required for a solution was shown. (ii) Harmonic resonance. (1) A prediction method for points harmonic resonance was developed. (2) Two methods for predicting bus voltage magnitude at resonance were formulated. (3) Practical applications were presented to illustrate the use of the proposed algorithms. (4) The IEEE Standards were used in the formulation of these algorithms. (5) Methods were given to evaluate P, Q, D, and S flows near resonance. ^

#### Degree

Ph.D.

#### Subject Area

Electrical engineering

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