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ECE 6319
Electrical Engineering
Mar 7, 2023
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ECE 6319 - Dynamics of Electric Machines Lecture 01 Date: August 25, 2022 by Levent U. Gökdere, PhD Electrical and Computer Engineering Department University of Houston, Houston, TX Fall 2022 P.S. The pictures, notations, formulas, and statements in these lecture 01 notes have been adopted and adapted mainly from the course textbook "Analysis of Electric Machinery and Drive Systems" by P. Krause, O. Wasynczuk, S. Sudhoff, S. Pekarek, Third Edition, 2013.
The relative permeability of a ferromagnetic material: ? 𝑟 = 2000 to 6000 The relative permeability of free space: ? 𝑟 = 1 The relative permeability of medium (no units): ? 𝑟 The permeability of free space: ? 0 = 4𝜋 × 10 −7 [ H/m] THEORY OF ELECTROMECHANICAL ENERGY CONVERSION The basics of the electromechanical energy conversion are reviewed. These include i) the magnetically coupled circuits and magnetomotive force, ii) the electrical, magnetic and mechanical energy relationships, iii) the force and torque generation, and iv) the equivalent circuit models for predicting the dynamic behavior of the electrical (currents and voltages), magnetic (flux) and mechanical (speed and position) variables in an electromechanical system. In addition, elementary ac machines (such as the induction machine, synchronous machine and permanent magnet machine) are studied to get preliminary insight into the relationships between the winding flux linkages and currents of these machines. Magnetically Coupled Circuits The figure on the left shows the two coils wound on a common core that is generally a ferromagnetic material (iron alloys such as silicon steel) with a much larger magnetic permeability than that of air. The number of turns in the two coils are 𝑁 1 and 𝑁 2 , respectively. The permeability of a medium or material in [H/m]: ? = ? 𝑟 ? 0 Permeability is a degree of magnetization that a material obtains in response to an applied magnetic field. ( Electric Machines and Power Electronics, by P.C. Sen, 3rd Edition, 2013. ) A magnetically coupled circuit. coil 1 coil 2
The magnetic flux produced by current ? 1 in coil 1 is ( ?1 + ?1 ) where ?1 and ?1 are the magnetizing and leakage fluxes in webers ([Wb]), respectively. Similarly, the magnetic flux produces by current ? 2 in coil 2 is ( ?2 + ?2 ) where ?2 and ?2 are the magnetizing and leakage fluxes in [Wb], respectively. The positive direction of the flux is determined by applying the right-hand rule to the direction of the current in the coil. Right-Hand Rule for a Coil with Turns If you grip the coil in your right hand with the fingers pointing in the direction of the current i , the thumb points in the direction of the magnetic field H (or, magnetic flux ). i A coil with several turns Magnetic core H The flux linking coil 1: 1 = ?1 + ?1 + ?2 The flux linking coil 2: 2 = ?2 + ?2 + ?1 A magnetically coupled circuit. coil 1 coil 2
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