an investigation of dual stator winding induction machines

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Figure 4.12 Mutual inductance under 20% static and 10% dynamic rotor eccentricity 4.3 Rotor Inductance Calculation The rotor inductances calculation can be divided into three categories based on the relationship between the rotor loop winding function distributions. The first case is the self inductance of rotor loops. In this condition, the turn function and the winding function of the rotor loop will overlap each other in all the integration regions. The second case is the mutual inductance of rotor loops between th i loop and 166 th i + 1 loop, in which the turn functions of the two rotor loops will overlap each other partially. The third case is the mutual inductance of rotor loops between th i loop and The turn function of the th i rotor loop will not overlap the turn function of k ). th i + k loop ( ≠ 1 th i + k loop at all, if k is not equal to 1. It should be noticed that all the above statements are based on
the assumption that the rotor skew factor is considered in the analysis. In the case that the rotor is no skewed, only two types of inductances can be found in the rotor self- inductance and mutual inductance. Since the rotor inductances calculation in this section has no relationship with the stator coil distribution, the results are valid for both the 2- pole and the 6-pole stator winding sets. 4.3.1 Self Inductance of Rotor Loops The expression to calculate the self-inductance of th i rotor loop is: 2π 1 Lii = µ 0rl ∫ ⋅ ni i g where, ( θ ) i 0 ( θ, θ ) rm ( θ ) ⋅ N ( θ ) ⋅ dθ n is the turn function of th rotor loop; g( θ ) rm i rotor loop; ( θ ) 167 i (4.9) N is the winding function of th i θ, is the air gap function; i is the rotor loop number. The rotor loop self inductance maybe a function of the rotor angle depending on the different eccentricity conditions. The waveforms of rotor loop self inductance under the static rotor eccentricity condition, the dynamic rotor eccentricity condition and the mixed rotor eccentricity condition are shown in the Figure 4.13, Figure 4.14 and Figure 4.15 respectively.
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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
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 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 205: Figure 4.10 Mutual inductance under
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
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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
Page 493 and 494:
[8.17]. O. Ojo, “Performance of s
Page 495 and 496:
[10.5]. J. C. Moreira, K. T. Hung,
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[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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an investigation of dual stator winding induction machines

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