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APPLICATION OF VECTOR ANALYSIS IN ELECTRIC ENERGY CONVERSION USING MATLAB TM

Bruno Osorno

Department of Electrical And Computer Engineering California State University Northridge 18111 Nordhoff St Northridge CA 91330-8436 Email:Bruno@ecs.csun.edu

Abstract

In electrical engineering, specifically in Electric Power Systems, complex numbers are used widely throughout. More specifically in Electric Energy Conversion there is a concept called the “revolving magnetic field”, which simply describes how the stator of an electrical machine generates a rotating magnetic field. This concept is modeled with a set of differential equations and with some manipulations we arrive to a set of vectors. These vectors in turn indicate the rotating field in space. The ma nipulation of such theory is simple yet hard to present to the students. It is for this reason that the use of MATLABT M and/or MatCadT M is recommended. This paper presents a mathematical manipulation applied to electrical engineering of a “revolving magnetic field”. Furthermore it takes the mathematical approach to a MATLABT M simulation.

Three-phase analysis of an stator

Three phase induction machines are the work- horse of industry, and these machines have a “rotating magnetic field”. We will give a brief physical description of the stator of these machines. Consider a sequence a-b-c and a symmetric distribution of the phases by 1200 electrical degrees each in space and around the air gap. The basic three-phase machine will have three coils that we consider to have the following terminals:

a a’ b b’ c c’

These coils are excited by a time dependent sinusoidal alternating current producing a sinusoidal magneto- motive force (mmf) wave at the center of the magnetic axis of particular phase. Therefore the three-space sinusoidal mmf waves are displaced 1200 electrical degrees in space. Figure 1 shows how we determine the magnetic axis of a coil. Figure two indicates the three magnetic-axis of three coils placed in space around the stator. A three-phase sys tem requires three coils to create three magnetic Proceedings of the 2002 American Society for Engineering Education Annual Conference & Exposition Copyright © 2002, American Society for Engineering Education

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Osorno, B. (2002, June), Application Of Vector Analysis In Electric Energy Conversion Using Matlabtm Paper presented at 2002 Annual Conference, Montreal, Canada. 10.18260/1-2--11102