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Electrical Machinery Analysis

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Introduction• Principles for electrical machine analysis :

Electromechanical energy conversion is fundamental

Electromechanical torque paremater : Current and displacement of mechanical system

Derivations of equivalent circuit Concept of MMF Sinusoidally distribution of windings Derivations of windings inductance

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Magnetically Couple

• Fundamental for transformer dan electrical machine operation.• Components :

– Core (µr generally 2000-80000 ; µ steel = 2000-4000 ; µo = 4π x 10-7 H/m)

– winding/coils

Flux linking for each coil

Flux linkage

Voltage equation :

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Linear Magnetic System• If saturation is neglected

Where reluctance :Ni = MMF

i1 in

iHdl

Ampere law :

H (A/m)

m

mmk

kk iNlH

µ= µo µr

Flux intensity

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Flux Flux Linkage

When system is linear, flux linkage is experessed by inductance and current.

Leakage Inductance Coil 2

Magnetizing Inductance Coil 2

Finally, Flux Linkage :

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Equivalent Circuit with coil 1 as reference Voltage equation

where

where

Equivalent T circuitUsing the substitute variable i2’, when flowing throuh coil 1 produce the same MMF as actual i2 flowing to coil 2.

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Example• Open circuit and short circuit test of transformer

– Open circuit coil 2 : power input to coil 1 = 12 W when applied voltage 100 V 60 Hz and current 1 A.

– Short circuit test : power during test 22 W, applied voltage 30 V 60 Hz, current 1 A

• Determine parameters in T equivalent circuit, reference coil 1 ?

r1 = 12 Ω and Xl1 + Xm1 = 109,3 Ω

From Open Circuit Test

From Short Circuit Test

Z =

r2’ = 10 Ω , assume xl1=xl2’

xm = 109,3 – 10,2 = 99.1 Ω

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T equivalent circuit

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Non Linear Magnetic System• Magnetic system has non linearity when saturation is occured

and cause heating due to hysterisis.

ΔBΔH

µ=B

H

Non linear for dynamic transient analysis

Numerical computation

B = µHFlux density

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Electromechanical Energy Conversion

• Energy relationship

Energy distribution :

+

E transfered E loss E stored

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Total energy transfer to the coupling field :

E coupilng E dissipated

Energy conservation in electromechanical system:

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Energy Balanced

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Electric system :

Mechanical system dynamic:

Electric energy:

EE tranfs. to the coupling

EE tranfs. to the coupling

Electromechanical System

M = massK = springD = friction

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• Energy balance

Differential form :

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Steady State and Dynamic Condition

• Electrical system

• Steady state behaviour

• Mechanical system

Constant voltage Constant mechanical force

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• What is the diferent between magnet permanent and non permanent magnet material ?

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Electrical Motor Development

• Basic Priciples of Electrical Machine Analysis• DC Machine• Reference Frame Theory• Induction Machine• Synchronous Machine• BLDC Machine