# Algebraic and a Graphical Method for Finding All the Performance Extreme Values of a Three-Phase Induction Machine

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• Topic: Electric motor, Power factor, Energy
• Pages : 8 (1791 words )
• Published : March 7, 2012

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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 performance extrema may also be of importance in some applications. For example, when energy saving is the objective to be achieved, the slip at which the maximum efficiency occurs is of interest. The performance extreme values of an induction machine also provide a valuable guide both to machine designers and to power engineers. Machine designers can see the effects of modifying one or several machine design parameters on the performance limits of the machine. Similarly, power engineers can quickly know whether a machine can safely be operated under a specific condition. The information on maximum efficiency and maximum power factor is helpful for the induction motor designer to make a compromise between high power factor and high efficiency. Typically, the rated slip of an induction motor falls somewhere between maximum efficiency and maximum power factor. Maximum torque and maximum output power are two important mechanical characteristics of a motor. If a motor’s load torque is Corresponding author : S.Y. Huang Unité de recherche en CSSS, Graduate School of Engineering Science and Technology (Doctoral Program), National Yunlin University of Science & Technology, 123 University Road, Section 3, Douliou, Yunlin 64002, Taiwan, R.O.C. E-mail:g8910814@yuntech.edu.tw Copyright © JES 2009 on-line : journal.esrgroups.org/jes

increased beyond the maximum torque, the motor will stall and come to a rapid stop. Hence, high maximum (pullout) torque is necessary for applications that may undergo frequent overloading. Maximum output power is a performance indicator when the motor is used as a mechanical power source in an electric (or hybrid) vehicle. Maximum output power of the motor is often compared with that of a conventional engine. When an induction machine operates as a generator, its maximum torque (also known as pushover torque) and maximum input power are two critical mechanical limits beyond which the torque and power applied by the prime mover can cause overspeed to the...