# Algebraic and Graphical Method to Find Performance Extreme Values of a Three-Phase Induction Machine

Powerful Essays
Y.J. Wang S.Y. Huang

J. Electrical Systems x-x (2010): x-xx

JES
Journal of Electrical Systems

Regular paper Determination of the Performance Extreme Values of a Three-phase Induction Machine Using Algebraic and Graphical Methods

This paper proposes an algebraic and a graphical method for finding all the performance extreme values of a three-phase induction machine when it operates as a motor or a generator. The performance extreme include maximum efficiency, maximum power factor, maximum electric power, maximum torque and maximum mechanical power in both motoring and generating modes. In addition to the algebraic method, this paper shows how an old graphical method can be used to accurately find the performance extreme values of a three-phase induction machine. With the use of modern graph drawing software that draws geometric graphs with their parameters as accurate as four places past the decimal, the circle diagram method, which is not well known to most young electrical engineers, merits a new revaluation of its usefulness. Comparison between algebraic and graphical calculations shows that in most cases the relative errors of the proposed graphical method are less than one percent. Keywords: induction machine, circle diagram method, performance extreme values.

1. Introduction Analysis of the steady-state performance of a three-phase induction machine can be achieved by analyzing its equivalent circuit. In most cases, as long as the parameters of the equivalent circuit are known, the operating characteristics of the machine such as power factor, efficiency, input power, output power, and torque, at a given slip, can be calculated. Among these performance characteristics, the maximum torque is the most often discussed extremum in textbooks of electric machines (e.g., [1]-[2]). On the other hand, other performance extrema are rarely documented. Although the maximum torque is the most important performance extremum to be considered, other

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