an investigation of dual stator winding induction machines

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$TMTA Math Contest at Tenn Tech University. Tuesday, April 19 ...$

$TMTA Math Contest at Tenn Tech University. Wednesday, April 17 ...$




DEDICATION To GOD, Lirong, Daniel and my parents My soul finds rest in God alone; my salvation comes from him. He alone is my rock and my salvation; he is my fortress, I will never be shaken. Psalm 62:1-2 iii
ACKNOWLEDGEMENTS I would like to express my sincere appreciation to my advisor and the chairperson of my committee, Dr. Joseph O. Ojo, for his professional guidance and support through the period of my PhD Program. I would like to thank the other members of my committee, Dr. Sastry Munukutla, Dr. Arun Sekar, Dr. Brian M. O'Connor and Dr. Mohamed A. Abdelrahman for their wonderful courses and their efforts in evaluating my research works. I would also like to thank Gan Dong, Conard Murray, L.V. Randolph, David Walker and Robert (Bob) Peterson for their invaluable help during the course of this project. I would also like to thank the Office of Naval Research (ONR) and Center for Energy Systems Research for the financial support provided during my study. I am also grateful to Dr. Jiahong Zhu, Dr. Ying Zhang and some Chinese friends in Cookeville for their help and support during my study. I would like to thank my parents for a lifetime support, selfless love, endless patience and encouragement. Finally, I would like to give my most sincere thanks to my wife Lirong and my son Daniel for their moral support, invaluable help and encouragement during the course of my PhD Program. iv
Page 1 and 2: AN ABSTRACT OF A DISSERTAION AN INV
Page 3 and 4: coupling and interaction terms are
Page 5: CERTIFICATE OF APPROVAL OF DISSERTA
Page 9 and 10: vi Page 2.2 Machine Design I.......
Page 11 and 12: viii Page 4.2.3 Self Inductances of
Page 13 and 14: x Page 7.3.4 f = 30 Hz and f = 95 H
Page 15 and 16: xii Page 10.8 D-decomposition Metho
Page 17 and 18: LIST OF FIGURES xiv Page Figure 1.1
Page 19 and 20: Figure 3.10 The simulation of the s
Page 21 and 22: Figure 3.34 Measured flux densities
Page 23 and 24: xx Page Figure 4.8 Self-inductance
Page 25 and 26: Figure 5.2. Simulation results for
Page 27 and 28: Figure 6.8. The dynamic response of
Page 29 and 30: Figure 7.22. Copper losses of the m
Page 31 and 32: Figure 8.7. The dynamic response of
Page 33 and 34: Figure 9.4 Steady state analysis, (
Page 35 and 36: Figure 9.12. The steady state wavef
Page 37 and 38: xxxiv Page Figure 10.16 Pole-zero m
Page 39 and 40: Figure 11.2 Per phase equivalent ci
Page 41 and 42: CHAPTER 1 INTRODUCTION AND LITERATU
Page 43 and 44: The last is the recently developed
Page 45 and 46: It should be noted that at any time
Page 47 and 48: A. R. Munoz and T.A. Lipo are pione
Page 49 and 50: has to be modified to adapt to thes
Page 51 and 52: circuit model of an induction machi
Page 53 and 54: ωr stator rotor 13 ωr rotor (a) (
Page 55 and 56: 1.2.4 Field Analysis Method In [5.1
Page 57 and 58:
separated dc source, etc. From the
Page 59 and 60:
in [8.14]. In [8.15-8.17], the stud
Page 61 and 62:
[8.22] and the total losses of the
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proposed. The switching frequency i
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The actual rotor mechanical speed i
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1.2.9 Induction Machine Drive---Vec
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stator windings were used as flux s
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The rotor flux can be obtained by:
Page 73 and 74:
The basic idea of a closed loop flu
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estimation. It has been claimed in
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{ k [ ˆ* ( i iˆ ) ] ( k) [ ˆ* Im
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integral and a new stretch-turn ope
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The most recent overview paper is g
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CHAPTER 2 DUAL STATOR WINDING INDUC
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Table 2.1 Parameters of machine des
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A C B 2.2.2 Air Gap Flux Density X
Page 89 and 90:
where, ω s1 and s2 respectively.
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There are two unknown variables in
Page 93 and 94:
Since small machines typically have
Page 95 and 96:
N s E = (2.18) 4. 44 fK φ 1 m Flux
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conduct away the heat produced in t
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k cs τ s = 2 2b ⎪ ⎧ ⎡ ⎤⎪
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are: Fts = H ts( ave) d s ( ave) =
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1 2 1 = H o ( ) + H o ( ) + H cr 90
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The skew of the stator winding is n
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0 bs Figure 2.5. Detailed stator sl
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y: The pole pitch at the mid point
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L lsk = L m ( α 2) ⎪⎧ ⎡sin
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2.3.4 Rotor Bar Resistance r b The
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2.3.7 Rotor Resistance Referred to
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Substituting δ = π into (2.97) an
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atio also increases. The air gap fl
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From (2.105-2.108), the ratio of th
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2.5 Conclusions In this chapter, a
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A recently developed dual stator wi
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stator winding induction machine ba
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∫ H ⋅ dl = ∫ J ⋅ ds = N ⋅
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theory itself is correct. The inacc
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( θ ) ⋅ g( θ, θ ) − H ( 0)
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where ( θ ) n A is the average of
Page 137 and 138:
Since the definition of the mutual
Page 139 and 140:
3Cs1 Cs1 − Cs1 − 3Cs1 6Cs1 4Cs1
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3.4.2 Mutual Inductances of the ABC
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where, ( θ ) n is the average of t
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1 0 α 1 − r 2π α − r 2π Fig
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When the skewing factor of the roto
Page 149 and 150:
3.6 Calculation of Stator-Rotor Mut
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dλ v = R ⋅ i + (3.58) dt where,
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3.7.1.3 Stator flux linkage in ABC
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where, r R is the resistance matrix
Page 157 and 158:
Only terms in equation (3.77) which
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119 ( ) ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥
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−1 −1 −1 where, λ qdr = Tr L
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3.16 and Figure 3.17. It is found f
Page 165 and 166:
Figure 3.11 The simulation of the d
Page 167 and 168:
Figure 3.14 The simulation of the s
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Figure 3.16 Rotor bar currents duri
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Phase Y Figure 3.20 Air gap flux de
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Figure 3.24 Total air gap flux dens
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Figure 3.27 The air gap flux densit
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Figure 3.29 Air gap flux density co
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Figure 3.33 Air gap flux density in
Page 181 and 182:
All the waveforms shown above are t
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Figure 3.39 Air gap flux density pr
Page 185 and 186:
Figure 3.42 Normalized spectrum of
Page 187 and 188:
Page 189 and 190:
Page 191 and 192:
Page 193 and 194:
CHAPTER 4 FULL MODEL SIMULATION OF
Page 195 and 196:
Substituting (3.28) and (3.29) into
Page 197 and 198:
Figure 4.3 Self-inductance under 20
Page 199 and 200:
Figure 4.4 Mutual inductance under
Page 201 and 202:
that L AB = L BA , L BC = L CB and
Page 203 and 204:
Page 205 and 206:
Page 207 and 208:
the assumption that the rotor skew
Page 209 and 210:
Page 211 and 212:
Page 213 and 214:
Page 215 and 216:
4.4 Mutual Inductances Calculation
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Figure 4.24 Stator rotor mutual ind
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Figure 4.25 Stator rotor mutual ind
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varying inductances excited by four
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Equations similar to (4.15-4.16) we
Page 225 and 226:
the number of poles for the winding
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Figure 4.29 Dynamic response of dua
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(a) (b) (c) (d) Figure 4.32. Normal
Page 231 and 232:
CHAPTER 5 FIELD ANALYSIS OF DUAL ST
Page 233 and 234:
In the analysis that follows the fu
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where, C s1 is the number of series
Page 237 and 238:
θ , ∂B1 µ 0r = ⋅ J1 θ ∂θ
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C C = k π ⋅ d s2 s2 s2 199 (5.19
Page 241 and 242:
the XYZ winding set is obtained by
Page 243 and 244:
u rpi 2π ' k − jk θ −( i−1)
Page 245 and 246:
The corresponding flux densities in
Page 247 and 248:
The first term in equation (5.55) i
Page 249 and 250:
The second term in (5.64) is zero u
Page 251 and 252:
5.2.2 Torque Equation The calculati
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Re j( ω ) ⎧ 1t− P1θ µ 0r j(
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* ( ) ( ) ( ) ⎛ P1 ⋅ ⋅ ⎞ j
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* Since both ( ) C 2π ∫ 0 2 * Cs
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(A) Induced voltage in the ABC wind
Page 261 and 262:
5.3.3 Equation of Torque Contribute
Page 263 and 264:
winding set works as a generator, w
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possible for the brushless doubly-f
Page 267 and 268:
Since the number of rotor bar is n,
Page 269 and 270:
5.6 Computer Simulation and Experim
Page 271 and 272:
Figure 5.2. Simulation results for
Page 273 and 274:
5.7. Conclusions In this chapter, u
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good steady-state predictions and c
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which are superimposed some space h
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(a) (b) (c) Figure 6.1: Main flux s
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(a) (b) (c) (d) (e) Figure 6.3: Fin
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(a) (b) Figure 6.5: Induced air-gap
Page 285 and 286:
Substituting (6.7) into (6.4-6.6),
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L L L L L L L λ + lr1 m1 ls1 m1 lr
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6.4 Simulation and Experimental Res
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Figure 6.7 . Simulation results for
Page 293 and 294:
Figure 6.9 Experimental results for
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diminish the contribution of the 6-
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CHAPTER 7 STEADY STATE ANALYSIS OF
Page 299 and 300:
where, L L = (7.11) si mi iqdri λq
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Overall efficiency of the dual stat
Page 303 and 304:
Figure 7.2 Stator current speed cha
Page 305 and 306:
Figure 7.6 Power factor speed chara
Page 307 and 308:
Figure 7.9 Power factor speed chara
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7.3.5 f = 35Hz and f = 90 Hz abc xy
Page 311 and 312:
Figure 7.16 Torque speed characteri
Page 313 and 314:
this conclusion is based on the ass
Page 315 and 316:
Figure 7.21. ω s1 vs s2 ω when to
Page 317 and 318:
Figure 7.25 ω s1 vs s2 ω when the
Page 319 and 320:
Figure 7.28. Copper losses of the m
Page 321 and 322:
7.4 Conclusions Based on the steady
Page 323 and 324:
applications and possible use as st
Page 325 and 326:
L pλ + λ = I − = σ (8.3) ( ω
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espectively. The stator q and d axi
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* 3 * ( V I ) V Re( M I ) 3 P p = R
Page 331 and 332:
the modulation index of the rectifi
Page 333 and 334:
Lie derivative and relative order d
Page 335 and 336:
The above algorithm requires that t
Page 337 and 338:
σ = 3 1+ K ( Vqs1iqs1 + Vds1 ds1)
Page 339 and 340:
Butterworth polynomial with the den
Page 341 and 342:
Table 8.1 Parameters of controllers
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generally the case to get a good pe
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Table 8.2 Machine parameters for si
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(a) (b) (c) (d) (e) (f) (g) Figure
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(a) (b) (c) (d) (e) (f) (g) (h) (i)
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(a) (b) (c) (d) (e) (f) (g) (h) (i)
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CHAPTER 9 HIGH PERFORMANCE CONTROL
Page 355 and 356:
The qd0 voltage equations of a dual
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317 ( ) ( ) ( ) ( ) ( ) ⎥ ⎥ ⎥
Page 359 and 360:
If the rotor speed and the rotor fl
Page 361 and 362:
Infeasible region (a) Vdc1 and Vdc2
Page 363 and 364:
The influences of the saturation of
Page 365 and 366:
Figure 9.5(a), by varying the q-axi
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Figure 9.5 Steady state analysis, (
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L1 L3 2 ( 1− K ) Vdc1 3 = ( Vqs1i
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If the PI controllers are used and
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egulation capabilities of the contr
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(a) (b) (c) (d) (e) (f) (g) (h) (k)
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(a) (b) Figure 9.11. The starting p
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9.6 Conclusions The high performanc
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induction machine are applicable to
Page 383 and 384:
In section 10.2, the fundamentals o
Page 385 and 386:
The vector control of an induction
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possibilities for fault conditions,
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where, where, − r r L = (10.18) (
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qsi qsi * ( I I ) σ = K ⋅ − (1
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In the proposed control scheme, rot
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* ωr * ωr + + − ωr k p + ki s
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The value of ω 0 determines the dy
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10.4.4 Stator D-axis Current Contro
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(a) (b) (c) (d) (e) (f) Figure 10.4
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The proposed control scheme has als
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(a) (b) (c) (d) (e) (f) (g) Figure
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10.6 Full-order Flux Observer The c
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while the second three-phase windin
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L r L p ˆ λ ˆ ˆ (10.66) ri si r
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373 [ ] ( ) ( ) ( ) ( ) ( ) ( ) ( )
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t 2bi ⎛ rsiLri K iL ⎞ ⎛ ri K
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ri D i si ri ri si mi ri 2 ( K )
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esults show that the selected obser
Page 421 and 422:
Figure 10.12 The poles of the 6-pol
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383 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
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⎧t s ⎨ ⎩ts 1 2 = t = t 1 2 Th
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Figure 10.15 The poles of the machi
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X i i = X Y = Y i i ( σ , ω) ( σ
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this error is used as the feedback.
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ˆ ω rm The output error is expres
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The expressions of t1 i and t2 i ar
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397 ( ) ( ) ( ) bi ei i bi ei i ai
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The transfer function of rotor spee
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(a) (b) (c) (d) Figure 10.16 Pole-z
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Figure 10.19 Pole-zero maps with di
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Figure 10.22 Pole-zero maps with di
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should ensure the stability under a
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The boundary of the speed controlle
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10.11 Simulation Results for Sensor
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Figure 10.28 Speed estimation for 2
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(a) (b) Figure 10.31 Speed estimati
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(a) (b) (c) (d) (e) (f) Figure 10.3
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Figure 10.34 Actual and estimated v
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CHAPTER 11 HARDWARE IMPLEMENTATION
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esistance for two phase windings. T
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11.2.3 Short Circuit Test The short
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When the input voltages of 2-pole A
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winding set is generating and the o
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11.4 Per Unit Model For the fixed p
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1 = 12 2 0. 0024414 The transformat
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ase values of voltage/current. The
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Start System configuration Initiali
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CHAPTER 12 CONCLUSIONS AND FUTURE W
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Using the rotating-field theory and
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each winding have been clearly show
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voltages of different frequencies,
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REFERENCES 447
Page 489 and 490:
[2.2]. P. C. Roberts, "A Study of B
Page 491 and 492:
[5.3]. R. A. McMahon, P. C. Roberts
Page 493 and 494:
[8.17]. O. Ojo, “Performance of s
Page 495 and 496:
[10.5]. J. C. Moreira, K. T. Hung,
Page 497 and 498:
[10.27]. M. Hinkkanen, “Analysis
Page 499 and 500:
[10.48]. K. Lee and F. Blaabjerg,
Page 501 and 502:
VITA Zhiqiao Wu was born in Shashi,
Page 503:
3. Zhiqiao Wu and O. Ojo, "High Per
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