distributed winding - lecture 7

distributed winding - lecture 7 - Distributed Windings and...

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Distributed Windings and Rotating MMF S.D. Sudhoff Spring 2008
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Spring 2008 ECE321 2 Distributed Windings and Rotating MMF • Objective ¾ In this chapter, we will set the stage to study ac machinery including permanent magnet synchronous machines as well as induction machines • Reading ¾ Electromechanical Motion Devices, Chapter 4 ¾ Techniques for Analysis of Electromechanical Systems . Section 4 up to and including 4.6.1. Skip 4.2.5
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Spring 2008 ECE321 3 4.1 Notation sm φ rm φ rm θ Stator Reference Axis Arbitrary Position Rotor Reference Axis
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Spring 2008 ECE321 4 4.2 Distributed Windings • Thus far, we have mostly considered lumped windings. We must now consider distributed winding. This is a more difficult concept. • Two Representations ¾ Discrete Winding Representation ¾ Continuous Winding Representation
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Spring 2008 ECE321 5 4.2.1 Discrete Winding Representation • Let N xy,i denote number of conductors of a x-phase winding in the i’th slot ¾ i ’ designates the slot number ¾ ‘x’ denotes winding or phase and is typically ‘a’, ‘b’, or ‘c’ ¾ ‘y’ is ‘s’ for stator or ‘r’ for rotor ¾ A positive value indicates the conductor directed out of the page
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Spring 2008 ECE321 6 4.2.1 Discrete Winding Representation • Location of i’th stator slot (4.2-1) • Location of i’th stator tooth (4.2-2) • Comments ¾ N yslt is number of slots ) 1 2 ( , = i N yslt i ys π φ ) 2 2 ( , = i N yslt i yt
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Spring 2008 ECE321 7 4.2.1 Discrete Winding Representation a b c d 1 , as N 2 , as N 3 , as N 4 , as N 5 , as N 7 , as N 8 , as N 6 , as N sm φ
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Spring 2008 ECE321 8 4.2.1 Discrete Winding Representation • Restriction on number of conductors (4.2-3) • Total number of conductors associated with winding (4.2-4) • Comments ¾ Here ‘x’ represents the phase may be ‘a’, ‘b’, ‘c’ (recall ‘y’ was ‘s’ or ‘r’) 0 1 , = = yslt N i i xy N = = yslt N i i xy i xy xy N u N N 1 , , ) (
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Spring 2008 ECE321 9 4.2.1 Discrete Winding Representation • Developed diagram a b c d 1 , as N 2 , as N 3 , as N 4 , as N 5 , as N 7 , as N 8 , as N 6 , as N sm φ
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Spring 2008 ECE321 10 4.2.2 Continuous Winding Description • Conductor density (turns/rad) of a winding denoted n xy ( φ ym ) where ¾ ‘x’ denotes winding/phase ‘a’, ‘b’, or ‘c’ ¾ ‘y’ is location (‘s’ for stator, ‘r’ for rotor) ¾ a positive value indicates conductors out of the page • For example, the a-phase conductor density may be given by ¾ (4.2-5) ) 2 / 3 cos( ) 2 / cos( ) ( 3 1 sm s sm s sm as P n P n n =
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Spring 2008 ECE321 11 4.2.2 Continuous Winding Description • The total number of conductors of such a winding may be expressed (4.2-6) = π φ 2 0 )) ( ( ) ( d n u n N xy xy xy
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Spring 2008 ECE321 12 4.3 The Winding Function • The winding function is a measure of how many times a winding links flux at a given place • The winding function will be used to ¾ Find self-inductance of a distributed winding
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This note was uploaded on 09/22/2011 for the course ECE 321 taught by Professor Staff during the Spring '08 term at Purdue University-West Lafayette.

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distributed winding - lecture 7 - Distributed Windings and...

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