Frequency Estimation under Stationary and Non-stationary ...
AC Motor Control and EV Applicationsphome.postech.ac.kr/user/cmdlab/ACMC(CH2).pdf · • abc dq...
Transcript of AC Motor Control and EV Applicationsphome.postech.ac.kr/user/cmdlab/ACMC(CH2).pdf · • abc dq...
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AC Motor Control and EV Applications
Rotating Field Theory
Chapter 2
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Wound Stator of an Induction Machine
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Cross Sectional View of AC Machine
b`
a`
a
c
c`
b
a-axis
b-axis
c-axis
(a)
a
b
c
(b)
Phase windings are separated by 120o.
Apply right hand rule to determine current axis.
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a1a2a3a4
a1a2a3a4 a1 ’a2 ’a3 ’a4 ’
a1a2a3a4 a1 ’a2 ’a3 ’a4 ’ a1a2a3a4
Cut and Stretch
a1 ̀
a1
a2 ̀
a2
a3 ̀
a4 ̀
a3a4
Superposition of MMFs of Distributed Winding
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Fourier Series Expansion of MMF
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MMFa
• x• x
+a -ax
x
-a -a +a -a
Stator core
(a)
(b)
Fourier Series Expansion of MMF
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MMF Made by Sinusoidally Distributed Winding
a
a’
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High Order Space Harmonics
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High Order Space Harmonics
Negative sequence
Positive sequence
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Rotation of Current Vector to Three Phase Current
(1, - ½, - ½ ) (-½,1, -½) (-½, -½,1) (½,-1, ½)(½, ½, -1) (-1, ½, ½ )
1
-1/2
(1, - ½, - ½)
Current
Current vectorcomponents
Vector sum
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Space Vector Representation
Mapping into the complex plane
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Example
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Transformation into Rotating Frame
Mapping into the rotating frame
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DQ Transformation
Complex Variable
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Break-down into Two Steps (Matrix Formulation)
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Two Steps
In Stationary d-q axes
In Synchronous d-q axes
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• abc dq (Stationary)
Coordinate Transformation into Stationary DQStep 1
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Coordinate Transformation into Rotating DQ
• dq stationary dq synchronous
(Exciting Frame)
Step 2
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An Example
In the synchronous reference frame, the vector looks as a constant vector.
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Inverse Transformation
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Coordinate Change Formulae
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Stator Inductance Matrix
Thus,
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Stator Inductance Matrix
Thus,
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Power Relations