an investigation of dual stator winding induction machines

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Table 10.1 Parameters of controllers in simulation 2-pole ABC winding 6-pole XYZ winding Q-axis current controller k = 3. 8 , k = 1018. 9 k = 3. 8, k = 1018. 9 pq D-axis current controller k = 0. 20 , k = 254. 7 k = 0. 20 , k = 254. 7 pd Rotor flux linkage controller k = 5.0 , k = 25 k = 5.0 , k = 25 pr Speed controller kω p = 70. 71, kω i = 2500 The values of ω 0 for controllers are given as: Speed controller : ω 0 = 50 Flux controller : ω 0 = 5 q-axis current controller : ω 0 = 200 d-axis current controller : ω 0 = 100 The simulation results for the starting process of the dual stator winding induction motor are shown in Figure 10.4, where the simulation results for the ABC winding set (2- pole) are represented by blue solid line while the simulation results for the XYZ winding set (6-pole) are represented by red dashed line. The DC bus voltage is kept to be constant 300 V and 2 Nm load torque is added to the system at 4.5 seconds. The torque distribution factor K is 0.5 during the starting process. The reference rotor speed ramps up from 0 to 126 rad/s and is kept at 126 rad/s after that. It is found from the simulation results that the actual speed tracks the command speed very well and the system runs at the steady state. The torque distribution factor K works very well so that the electromagnetic torques from both winding sets are equal when K = 0.5. The dynamic responses of the system are given in Figure 10.5. The rotor speed ramps down and up and down between 126 rad/s and -126 rad/s while the torque distribution factor K changes from 0.5 to 0.25 at 18 seconds. During all these dynamic changes, the rotor speed accurately tracks the speed command. The torque distribution factor works effectively as shown in the simulation results. iq 360 id ir pq pd pr iq id ir
(a) (b) (c) (d) (e) (f) Figure 10.4 Starting process of dual stator winding induction motor, (a) q-axis voltage V qsi , (b) daxis voltage V dsi , (c) reference and actual rotor mechanical speed ω rm , (d) slip frequency ω sli , (e) electromagnetic torque T ei, (f) total torque T e. 361
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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
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Figure 7.2 Stator current speed cha
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Figure 7.6 Power factor speed chara
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Figure 7.9 Power factor speed chara
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7.3.5 f = 35Hz and f = 90 Hz abc xy
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Figure 7.16 Torque speed characteri
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this conclusion is based on the ass
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Figure 7.21. ω s1 vs s2 ω when to
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Figure 7.25 ω s1 vs s2 ω when the
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Figure 7.28. Copper losses of the m
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7.4 Conclusions Based on the steady
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applications and possible use as st
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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
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the modulation index of the rectifi
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Lie derivative and relative order d
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The above algorithm requires that t
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σ = 3 1+ K ( Vqs1iqs1 + Vds1 ds1)
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Butterworth polynomial with the den
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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
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: 10.4.4 Stator D-axis Current Contro
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
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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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