an investigation of dual stator winding induction machines

More documents

Recommendations

Info

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

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




Finite Element Analysis (FEA) is the favored method of plotting the steady state magnetic fields of various parts of electric machines. Using FEA, repeated and time- consuming simulations are needed to obtain comprehensive performance profiles of electric machines. Although FEA yields very accurate results, its use to study the dynamics of electric machines and machines with multiple windings and excitations of different frequencies is still a difficult task. With the benefit of the winding function approach in which the winding distributions are accounted for, and the proposed coupled circuit model of the dual stator winding machines which yields currents in stator coils and rotor bars, the air gap flux density can be approximately determined under all operating conditions. The influence of the air gap magnetic saturation is approximated using the B- H curve of the magnetic core material of the machine. Both the FEA and the experimental results on a 3 hp 2/6 dual winding, squirrel-cage induction machine confirm the accuracy and utility of the air gap flux linkage calculation scheme. The arrangement of the chapter is as follows: Some preliminaries are listed in section 3.2. The winding function approach used for the calculations of the machine inductances with a general non-constant air gap length is presented in Section 3.3. Sections 3.4, 3.5, 3.6, respectively outline the calculations of the stator inductance, rotor inductance and stator-rotor mutual inductance matrices. The dual stator winding induction machine model is presented in section 3.7. A general complex variable transformation for n-phase systems is outlined in Section 3.8 and is utilized to transform the phase variable voltage and electromagnetic torque equations (set forth in Section 3.7) of the machine to the rotor reference frame. This transformation retains the space harmonics in the rotor currents and enables the determination of the bar currents. Computer simulation results of the dual 86
stator winding induction machine based on the proposed model are given in Section 3.9. The steady state simulation results are used in Section 3.10 to calculate the air gap flux density of the machine. FEA and experimental results validate the approximate field calculation technique. Conclusions are drawn in Section 3.11. Although the proposed analysis tools are applied to 2/6 dual stator winding, squirrel-cage induction machines, they have wider applicability to other multi-phase machines with multi-frequency excitations. 3.2 Preliminaries The following definitions are fundamental to the magnetic circuit analysis. Definition 3.1: Gauss 's Law If E is the electric field in the space and ρ ( r) is a distribution of charge density, then the Gauss’s Law is expressed as: get: Φ = ∫ S 1 E ⋅ ds = ρ ∫ V ( ∇ ⋅ E) ⋅ dv = () r ∫ ε 0 V ⋅ dv 87 (3.1) Since the total charge density within the space is zero, then from Gauss theorem we ∫ S B ⋅ ds = 0 (3.2) where, B is the magnetic field in the space and S enclosed a volume V ,
Page 1 and 2:
AN ABSTRACT OF A DISSERTAION AN INV
Page 3 and 4:
coupling and interaction terms are
Page 5 and 6:
CERTIFICATE OF APPROVAL OF DISSERTA
Page 7 and 8:
ACKNOWLEDGEMENTS I would like to ex
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
Page 63 and 64:
proposed. The switching frequency i
Page 65 and 66:
The actual rotor mechanical speed i
Page 67 and 68:
1.2.9 Induction Machine Drive---Vec
Page 69 and 70:
stator windings were used as flux s
Page 71 and 72:
The rotor flux can be obtained by:
Page 73 and 74:
The basic idea of a closed loop flu
Page 75 and 76: estimation. It has been claimed in
Page 77 and 78: { k [ ˆ* ( i iˆ ) ] ( k) [ ˆ* Im
Page 79 and 80: integral and a new stretch-turn ope
Page 81 and 82: The most recent overview paper is g
Page 83 and 84: CHAPTER 2 DUAL STATOR WINDING INDUC
Page 85 and 86: Table 2.1 Parameters of machine des
Page 87 and 88: A C B 2.2.2 Air Gap Flux Density X
Page 89 and 90: where, ω s1 and s2 respectively.
Page 91 and 92: 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
Page 97 and 98: conduct away the heat produced in t
Page 99 and 100: k cs τ s = 2 2b ⎪ ⎧ ⎡ ⎤⎪
Page 101 and 102: are: Fts = H ts( ave) d s ( ave) =
Page 103 and 104: 1 2 1 = H o ( ) + H o ( ) + H cr 90
Page 105 and 106: The skew of the stator winding is n
Page 107 and 108: 0 bs Figure 2.5. Detailed stator sl
Page 109 and 110: y: The pole pitch at the mid point
Page 111 and 112: L lsk = L m ( α 2) ⎪⎧ ⎡sin
Page 113 and 114: 2.3.4 Rotor Bar Resistance r b The
Page 115 and 116: 2.3.7 Rotor Resistance Referred to
Page 117 and 118: Substituting δ = π into (2.97) an
Page 119 and 120: atio also increases. The air gap fl
Page 121 and 122: From (2.105-2.108), the ratio of th
Page 123 and 124: 2.5 Conclusions In this chapter, a
Page 125: A recently developed dual stator wi
Page 129 and 130: ∫ H ⋅ dl = ∫ J ⋅ ds = N ⋅
Page 131 and 132: theory itself is correct. The inacc
Page 133 and 134: ( θ ) ⋅ g( θ, θ ) − H ( 0)
Page 135 and 136: 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
Page 141 and 142: 3.4.2 Mutual Inductances of the ABC
Page 143 and 144: where, ( θ ) n is the average of t
Page 145 and 146: 1 0 α 1 − r 2π α − r 2π Fig
Page 147 and 148: When the skewing factor of the roto
Page 149 and 150: 3.6 Calculation of Stator-Rotor Mut
Page 151 and 152: dλ v = R ⋅ i + (3.58) dt where,
Page 153 and 154: 3.7.1.3 Stator flux linkage in ABC
Page 155 and 156: where, r R is the resistance matrix
Page 157 and 158: Only terms in equation (3.77) which
Page 159 and 160: 119 ( ) ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥
Page 161 and 162: −1 −1 −1 where, λ qdr = Tr L
Page 163 and 164: 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
Page 169 and 170: Figure 3.16 Rotor bar currents duri
Page 171 and 172: Phase Y Figure 3.20 Air gap flux de
Page 173 and 174: Figure 3.24 Total air gap flux dens
Page 175 and 176: Figure 3.27 The air gap flux densit
Page 177 and 178:
Figure 3.29 Air gap flux density co
Page 179 and 180:
Figure 3.33 Air gap flux density in
Page 181 and 182:
All the waveforms shown above are t
Page 183 and 184:
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
Page 217 and 218:
Figure 4.24 Stator rotor mutual ind
Page 219 and 220:
Figure 4.25 Stator rotor mutual ind
Page 221 and 222:
varying inductances excited by four
Page 223 and 224:
Equations similar to (4.15-4.16) we
Page 225 and 226:
the number of poles for the winding
Page 227 and 228:
Figure 4.29 Dynamic response of dua
Page 229 and 230:
(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
Page 235 and 236:
where, C s1 is the number of series
Page 237 and 238:
θ , ∂B1 µ 0r = ⋅ J1 θ ∂θ
Page 239 and 240:
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
Page 253 and 254:
Re j( ω ) ⎧ 1t− P1θ µ 0r j(
Page 255 and 256:
* ( ) ( ) ( ) ⎛ P1 ⋅ ⋅ ⎞ j
Page 257 and 258:
* Since both ( ) C 2π ∫ 0 2 * Cs
Page 259 and 260:
(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
Page 265 and 266:
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
Page 275 and 276:
good steady-state predictions and c
Page 277 and 278:
which are superimposed some space h
Page 279 and 280:
(a) (b) (c) Figure 6.1: Main flux s
Page 281 and 282:
(a) (b) (c) (d) (e) Figure 6.3: Fin
Page 283 and 284:
(a) (b) Figure 6.5: Induced air-gap
Page 285 and 286:
Substituting (6.7) into (6.4-6.6),
Page 287 and 288:
L L L L L L L λ + lr1 m1 ls1 m1 lr
Page 289 and 290:
6.4 Simulation and Experimental Res
Page 291 and 292:
Figure 6.7 . Simulation results for
Page 293 and 294:
Figure 6.9 Experimental results for
Page 295 and 296:
diminish the contribution of the 6-
Page 297 and 298:
CHAPTER 7 STEADY STATE ANALYSIS OF
Page 299 and 300:
where, L L = (7.11) si mi iqdri λq
Page 301 and 302:
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
Page 309 and 310:
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
Page 327 and 328:
espectively. The stator q and d axi
Page 329 and 330:
* 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
Page 343 and 344:
generally the case to get a good pe
Page 345 and 346:
Table 8.2 Machine parameters for si
Page 347 and 348:
(a) (b) (c) (d) (e) (f) (g) Figure
Page 349 and 350:
(a) (b) (c) (d) (e) (f) (g) (h) (i)
Page 351 and 352:
(a) (b) (c) (d) (e) (f) (g) (h) (i)
Page 353 and 354:
CHAPTER 9 HIGH PERFORMANCE CONTROL
Page 355 and 356:
The qd0 voltage equations of a dual
Page 357 and 358:
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
Page 367 and 368:
Figure 9.5 Steady state analysis, (
Page 369 and 370:
L1 L3 2 ( 1− K ) Vdc1 3 = ( Vqs1i
Page 371 and 372:
If the PI controllers are used and
Page 373 and 374:
egulation capabilities of the contr
Page 375 and 376:
(a) (b) (c) (d) (e) (f) (g) (h) (k)
Page 377 and 378:
(a) (b) Figure 9.11. The starting p
Page 379 and 380:
9.6 Conclusions The high performanc
Page 381 and 382:
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
Page 387 and 388:
possibilities for fault conditions,
Page 389 and 390:
where, where, − r r L = (10.18) (
Page 391 and 392:
qsi qsi * ( I I ) σ = K ⋅ − (1
Page 393 and 394:
In the proposed control scheme, rot
Page 395 and 396:
* ωr * ωr + + − ωr k p + ki s
Page 397 and 398:
The value of ω 0 determines the dy
Page 399 and 400:
10.4.4 Stator D-axis Current Contro
Page 401 and 402:
(a) (b) (c) (d) (e) (f) Figure 10.4
Page 403 and 404:
The proposed control scheme has als
Page 405 and 406:
(a) (b) (c) (d) (e) (f) (g) Figure
Page 407 and 408:
10.6 Full-order Flux Observer The c
Page 409 and 410:
while the second three-phase windin
Page 411 and 412:
L r L p ˆ λ ˆ ˆ (10.66) ri si r
Page 413 and 414:
373 [ ] ( ) ( ) ( ) ( ) ( ) ( ) ( )
Page 415 and 416:
t 2bi ⎛ rsiLri K iL ⎞ ⎛ ri K
Page 417 and 418:
ri D i si ri ri si mi ri 2 ( K )
Page 419 and 420:
esults show that the selected obser
Page 421 and 422:
Figure 10.12 The poles of the 6-pol
Page 423 and 424:
383 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
Page 425 and 426:
⎧t s ⎨ ⎩ts 1 2 = t = t 1 2 Th
Page 427 and 428:
Figure 10.15 The poles of the machi
Page 429 and 430:
X i i = X Y = Y i i ( σ , ω) ( σ
Page 431 and 432:
this error is used as the feedback.
Page 433 and 434:
ˆ ω rm The output error is expres
Page 435 and 436:
The expressions of t1 i and t2 i ar
Page 437 and 438:
397 ( ) ( ) ( ) bi ei i bi ei i ai
Page 439 and 440:
The transfer function of rotor spee
Page 441 and 442:
(a) (b) (c) (d) Figure 10.16 Pole-z
Page 443 and 444:
Figure 10.19 Pole-zero maps with di
Page 445 and 446:
Figure 10.22 Pole-zero maps with di
Page 447 and 448:
should ensure the stability under a
Page 449 and 450:
The boundary of the speed controlle
Page 451 and 452:
10.11 Simulation Results for Sensor
Page 453 and 454:
Figure 10.28 Speed estimation for 2
Page 455 and 456:
(a) (b) Figure 10.31 Speed estimati
Page 457 and 458:
(a) (b) (c) (d) (e) (f) Figure 10.3
Page 459 and 460:
Figure 10.34 Actual and estimated v
Page 461 and 462:
CHAPTER 11 HARDWARE IMPLEMENTATION
Page 463 and 464:
esistance for two phase windings. T
Page 465 and 466:
11.2.3 Short Circuit Test The short
Page 467 and 468:
When the input voltages of 2-pole A
Page 469 and 470:
winding set is generating and the o
Page 471 and 472:
11.4 Per Unit Model For the fixed p
Page 473 and 474:
1 = 12 2 0. 0024414 The transformat
Page 475 and 476:
ase values of voltage/current. The
Page 477 and 478:
Start System configuration Initiali
Page 479 and 480:
CHAPTER 12 CONCLUSIONS AND FUTURE W
Page 481 and 482:
Using the rotating-field theory and
Page 483 and 484:
each winding have been clearly show
Page 485 and 486:
voltages of different frequencies,
Page 487 and 488:
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
show all

an investigation of dual stator winding induction machines

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?