an investigation of dual stator winding induction machines

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analysis results based on a very simple converter model have also been shown under the unity power factor condition. In this chapter, a steady state analysis of the dual winding induction machine with series connected ac-dc boost rectifiers is presented for the first time with the high regulatory output dc voltage control scheme. Experimental and computer simulation results are provided to validate analysis and control methodologies. Application areas for this generating scheme may include hybrid electric vehicle starter-generator, battery charging facility for stand-alone systems and aerospace power dc power systems. 9.2 System Model The proposed generation system is schematically shown in Figure 9.1. At most three output dc voltages can be obtained, however only two of them can be controlled independently. ωr Dual-winding induction generator S11a S21a S31a I a1 I b1 I c1 C1 S12a S22a S32a Ia 2 I b2 I c2 S11b S21b S31b S12b S22b S32b 314 I p1 I p2 C2 I L RL1 RL2 Figure 9.1. The Series connection of generation system diagram RL3
The qd0 voltage equations of a dual winding induction generator feeding two ac-dc boost PWM rectifiers expressed in the synchronous reference frames of the winding rotor flux linkages are given in (9.1-9.10). The subscripts 1 and 2 correspond to the parameters or state variables for the 2-pole (ABC) three-phase winding set and the 6-pole (XYZ) three-phase winding set, respectively: r L L L + σ (9.1) r1 m1 m1 σ 1 pI qs1 r1I qs1 = Vqs1 −ω e1Lσ 1I ds1 + λ 2 qr1 −ω r1 λdr1 = qs1 Lr1 Lr1 r L L L + σ (9.2) r1 m1 m1 σ 1 pI ds1 r1I ds1 = Vds1 + ωe1Lσ 1I qs1 + λ 2 dr1 + ωr1 λqr1 = ds1 Lr1 Lr1 r r L pλ + λ = I − = σ (9.3) ( ωe1 − ωr1) λdr1 1 r1 r1 m1 qr1 Lr1 qr1 Lr1 qs1 qr r r L pλ + λ = I + = σ (9.4) ( ωe1 −ωr 1) λqr1 1 r1 r1 m1 dr1 Lr1 dr1 Lr1 ds1 dr r L L L + σ (9.5) r2 m2 m2 σ 2 pIqs2 r2I qs2 = Vqs2 −ωe2 Lσ 2I ds2 + λ 2 qr2 −ωr 2 λdr2 = qs2 Lr2 Lr2 r L L L pI + r I = V + L I + + = σ (9.6) r 2 m2 m2 σ 2 ds2 2 ds2 ds2 ωe2 σ 2 qs2 λ 2 dr2 ωr 2 λqr2 ds2 Lr 2 Lr 2 r r L pλ + λ = I − = σ (9.7) ( ω 2 −ω 2 ) λ 2 2 r 2 r 2 m2 qr2 Lr 2 qr2 Lr 2 qs2 e r dr qr r r L pλ + λ = I + = σ (9.8) C C 1 2 ( ω 2 − ω 2 ) λ 2 2 r1 r 2 m2 dr2 Lr1 dr2 Lr 2 ds2 e r qr dr pV pV 3 ( M I + M I ) V V dc1 dc1 dc 2 dc1 = − qs1 qs1 ds1 ds1 − − (9.9) 2 RL1 RL3 3 ( M I + M I ) V 315 + V + V dc 2 dc1 dc 2 dc 2 = − qs 2 qs 2 ds 2 ds 2 − − (9.10) 2 RL 2 RL3 V
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AN ABSTRACT OF A DISSERTAION AN INV
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coupling and interaction terms are
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CERTIFICATE OF APPROVAL OF DISSERTA
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ACKNOWLEDGEMENTS I would like to ex
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vi Page 2.2 Machine Design I.......
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viii Page 4.2.3 Self Inductances of
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x Page 7.3.4 f = 30 Hz and f = 95 H
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xii Page 10.8 D-decomposition Metho
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LIST OF FIGURES xiv Page Figure 1.1
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Figure 3.10 The simulation of the s
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Figure 3.34 Measured flux densities
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xx Page Figure 4.8 Self-inductance
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Figure 5.2. Simulation results for
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Figure 6.8. The dynamic response of
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Figure 7.22. Copper losses of the m
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Figure 8.7. The dynamic response of
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Figure 9.4 Steady state analysis, (
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Figure 9.12. The steady state wavef
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xxxiv Page Figure 10.16 Pole-zero m
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Figure 11.2 Per phase equivalent ci
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CHAPTER 1 INTRODUCTION AND LITERATU
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The last is the recently developed
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It should be noted that at any time
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A. R. Munoz and T.A. Lipo are pione
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has to be modified to adapt to thes
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circuit model of an induction machi
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ωr stator rotor 13 ωr rotor (a) (
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1.2.4 Field Analysis Method In [5.1
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separated dc source, etc. From the
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in [8.14]. In [8.15-8.17], the stud
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[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:
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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
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where, ω s1 and s2 respectively.
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There are two unknown variables in
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Since small machines typically have
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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
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Since the definition of the mutual
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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
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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
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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
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Figure 3.11 The simulation of the d
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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
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All the waveforms shown above are t
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Figure 3.39 Air gap flux density pr
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Figure 3.42 Normalized spectrum of
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CHAPTER 4 FULL MODEL SIMULATION OF
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Substituting (3.28) and (3.29) into
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Figure 4.3 Self-inductance under 20
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Figure 4.4 Mutual inductance under
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that L AB = L BA , L BC = L CB and
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the assumption that the rotor skew
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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
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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
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CHAPTER 5 FIELD ANALYSIS OF DUAL ST
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In the analysis that follows the fu
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where, C s1 is the number of series
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θ , ∂B1 µ 0r = ⋅ J1 θ ∂θ
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C C = k π ⋅ d s2 s2 s2 199 (5.19
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the XYZ winding set is obtained by
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u rpi 2π ' k − jk θ −( i−1)
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The corresponding flux densities in
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The first term in equation (5.55) i
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The second term in (5.64) is zero u
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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
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5.3.3 Equation of Torque Contribute
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winding set works as a generator, w
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possible for the brushless doubly-f
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Since the number of rotor bar is n,
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5.6 Computer Simulation and Experim
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Figure 5.2. Simulation results for
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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
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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
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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
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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
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: CHAPTER 9 HIGH PERFORMANCE CONTROL
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
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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
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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
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[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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