Determination of the performance extreme values of a three-phase induction machine using algebraic and graphical methods

الملخص EN

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.