an investigation of dual stator winding induction machines

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The no-load starting transient simulation results are shown in Figure 3.10 when the machine is fed with voltages satisfying the constant voltage/Hertz open-loop control algorithm in which the ratios of the frequency of the 6-pole stator winding set to those of the 2-pole stator winding set is 3. The frequencies of the ABC (2-pole) and XYZ (6-pole) stator winding sets are 30 Hz and 90 Hz respectively. The line-to-line voltages of the ABC (2-pole) and XYZ (6-pole) stator winding set are 67 V and 202 V respectively. The rotor speed starts from zero and ramps up to steady state smoothly. The transient current is big, but all the currents are reduced to almost zero at the no load steady state condition. During the steady-state operation, a 3Nm load torque is added to the machine to check the dynamic response of the system. The simulation results of the dynamic response are shown in Figure 3.11. It is observed that the ABC stator winding set contributes a smaller percentage of the generated electromagnetic torque to meet the load demand. This torque distribution is determined by the machine design. Three of the rotor bar currents are chosen for illustration. The rotor bar currents during the starting process are shown in the Figure 3.12 and the rotor bar currents during the steady state at loaded condition are shown in the Figure 3.13. In the second case, the frequency of the input voltages of the ABC winding set is set to 27 Hz while that of the XYZ winding set is set at 90 Hz, both operating with the same Voltz/Hz ratio. It is observed that the 2-pole (ABC) winding set is generating with negative electromagnetic torque, the XYZ (6-pole) winding set needs to provide load torque and counteract the negative torque produced by the ABC winding set. The simulation results for both the starting process and dynamic response are shown in Figure 3.14 and Figure 3.15 respectively. Three of the rotor bar currents are shown in Figure 122
3.16 and Figure 3.17. It is found from the simulation that the rotor bar currents are almost zero under no-load condition. However, under the load condition, the rotor bar current is closed to sinusoidal waveform. 3.10 Air Gap Field Calculation Finite Element Analysis (FEA) is the favored method of plotting the magnetic fields in various parts of electric machines, most especially, the flux density of the air gap. The calculation time for FEA is long and involved if it is required to generate sufficient performance data. Using the stator winding and rotor bar currents obtained from the computer simulation results set forth in Section 8 and the winding functions of the stator windings and rotor loops, the air gap magnetic field contributions from all the stator windings and rotor bars can be calculated using (3.31). This approach, augmented with the B-H curve of the core magnetic material to approximately account for the saturation of the air-gap flux linkage, enables the estimation of the air gap flux density. When the machine is running under rated load at steady state condition, at any instant time, the stator currents and rotor loop currents can be found in the full model simulation. From the rotor model, the bar current is actually the subtraction of the two adjacent rotor loops that share that rotor bar. i b i x At an instant time, the phase currents of the ABC winding set are = −1. 03 A , = 0. 52 A and = 0. 51 A while the phase currents of the XYZ winding set are given as i c = 1. 65 A , = 0. 21 A and = −1. 86 A . Then the total air gap flux density and its i y components are shown in Figures 3.18-3.24. i z 123 i a
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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
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 and 126: A recently developed dual stator wi
Page 127 and 128: stator winding induction machine ba
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: −1 −1 −1 where, λ qdr = Tr L
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 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 207 and 208: the assumption that the rotor skew
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Figure 4.19 Mutual inductance under
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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
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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
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The qd0 voltage equations of a dual
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317 ( ) ( ) ( ) ( ) ( ) ⎥ ⎥ ⎥
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If the rotor speed and the rotor fl
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Infeasible region (a) Vdc1 and Vdc2
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The influences of the saturation of
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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
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In section 10.2, the fundamentals o
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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
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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
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[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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