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A Simple Graphical Method to Assess Induction Machine Performance Using per Phase Current as the Controlling Variable in Lieu of PerUnit Slip

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2012 ASEE Annual Conference & Exposition


San Antonio, Texas

Publication Date

June 10, 2012

Start Date

June 10, 2012

End Date

June 13, 2012



Conference Session

Energy Education Courses, Labs, and Projects

Tagged Division

Energy Conversion and Conservation

Page Count


Page Numbers

25.102.1 - 25.102.17

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Paper Authors


Donald L. Skaar San Diego State University

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Donald L. Skaar received the five-year bachelor's of electrical engineering degree from the University of Minnesota in 1949 and the master's of science degree with a major in electrical engineering from Oregon State University in 1966. He worked in the aerospace industry for a number of years for Honeywell, Convair Astronautics, and Kinetics Teledyne. He was a faculty member in the Department of Electrical and Computer Engineering at San Diego State University for more than 40 years and is a Professor Emeritus of that institution. His email address is

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A Simple Graphical Method To Assess Induction Machine Performance Using Per-Phase Current As The Controlling Variable In Lieu Of Per Unit SlipAbstract: Fixed-frequency induction machines are the most widely-used electromechanical energyconversion devices encountered in engineering practice; therefore a very simple and insightfulassessment of machine performance should be of interest to faculty members and students across theengineering spectrum. The per-phase electrical model illustrated in IEEE Standard 112 has been usedby most authors of engineering textbooks in a traditional analysis of induction machines - almostexclusively motors - using 'per unit slip' as the controlling variable. The concept of per unit slip isadmittedly brilliant; however, the traditional method of analysis based upon that term is tedious,requires a repetition of the most cumbersome steps for each specific machine speed of interest, andlacks insight. In contrast the proposed analysis offers a graphical assessment using the magnitude ofthe current as the controlling variable. Analysts need only draw an impedance line and resistance lineat a specific current magnitude upon a circular plot designated as the Normalized Impedance Locusbefore completing a reasonably-complete machine assessment. Given the Locus for a specificmachine, analysts may complete that assessment at any valid magnitude of current knowing only themachine name-plate data and the machine constant [D]. Machine manufacturers could provide copiesof the Locus for each of their various machines as easily as they provide the model element valueslisted in traditional texts; until they do so, the interested analyst may transform a generic Unit Circleinto the Locus for a specific machine, given those model element values along with no load data. Thecomputations required in the graphical method are so basic that an assessment of the performance maybe completed speedily – even without a calculator if judicious model element values are provided;therefore the procedure is particularly useful for classroom work. While obviously lacking theaccuracy of a computer analysis, the percentage error of results should not exceed a few percent so longas the Unit Circle used has a diameter of at least 20 centimeters.While valuable to electrical engineering power majors because of its simplicity and insightfulness, it isparticularly-suited for engineers/students outside that specialty; those in the latter group usually have abackground in basic circuit theory and would appreciate knowing how to assess induction machineperformance (input and output power, efficiency, and power factor) simply - without having to dealwith per unit slip, synchronous speed, and the manipulation of complex numbers associated withtraditional induction machine analysis. With the widespread contemporary interest in “green” energygeneration, an assessment of induction generators should also be of general interest; coverage ofinduction generators in traditional texts is difficult to find. Using the proposed graphical method, theassessment of such generators is as easy to understand as that of induction motors. Numericalexamples of single phase and three phase motors, and a three phase asynchronous generator clarify thedetails.

Skaar, D. L. (2012, June), A Simple Graphical Method to Assess Induction Machine Performance Using per Phase Current as the Controlling Variable in Lieu of PerUnit Slip Paper presented at 2012 ASEE Annual Conference & Exposition, San Antonio, Texas.

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