an investigation of dual stator winding induction machines

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For the current model flux observer, the measured stator currents and rotor speed are used. The influence of parameter estimation errors on the estimated flux linkage are studied using FRF analysis. It is found that under high slip condition, the magnitude of rotor flux linkage is sensitive to rotor resistance while the phase angle of the estimated rotor flux linkage is very insensitive. Both the magnitude and phase angle of estimated rotor flux linkage are sensitive to the rotor resistance and magnetizing inductance under rated slip condition. It should be noted that the accuracy can be affected by the rotor leakage inductance under any operating condition. The measured stator voltages and rotor speed are utilized in the full order open loop flux observer, in which the stator currents are estimated as intermediary quantities. It has been found that the sensitivity to stator resistance decreases with increasing rotor speed and the influence of leakage inductance is relatively small and nearly constant. However, the need for accurately measured stator voltages are low and zero speed range is a main limitation of this observer. In addition to these, a cancellation method open loop flux estimator has been presented, in which stator voltages and currents as well as rotor speed are used. The inherent drawback of this observer lies in huge flux estimation error when the rotor speed is near zero due to the division by rotor speed. In this range, the quantization noise due to the numerical differentiation will be significant. Based on the above analysis, an improved closed loop Gopinath model for flux estimation has been proposed in [10.14], in which the voltage model and current model were combined to be a closed loop observer. A similar flux observer with a generalized analysis method can be found in [10.15]. 32
The basic idea of a closed loop flux observer is that the current error can be driven to zero through the use of proper feedback acting on the estimated rotor flux linkage since the rotor flux linkage acts as a state feedback of stator current. In the design of the observer, the limitations on gains and eigenvalues selection are given in [10.14] as the disturbances in the form of measured signal quantization noise and harmonic noise. It should be noted that an interesting conclusion about the accuracy of the observer has been given in [10.14] also. For the closed loop flux observer, the accuracy of the estimated quantities is determined by the accuracy of the open loop observer model, observer topology and observer controller gains. The conclusion is that the accuracy of a closed loop estimator is primarily determined by the accuracy of the measured variables (sensor and signal conditioning accuracy) and secondarily by the controller design in the way the controller rejects disturbances. The extended Kalman filter based speed estimation algorithm is another equivalent circuit based method, in which a complete mathematical model of the induction machine is used [10.16]. The Kalman filters have the ability to obtain accurate estimation under noisy conditions. However, the intensive computation makes this approach less attractive and difficult for real implementation. The most popular speed estimation methodology in the first category is based on Model Reference Adaptive System (MRAS). The MRAS for sensorless control was firstly proposed by Schauder in [10.17], where the adaptive mechanism of MRAS has been explained clearly and an error function based on q- and d-axis rotor fluxes has been proposed. Popov’s criterion has been used to prove the stability of the adaptive algorithm. A similar method was presented in [10.18] with discussion of flux observer design. The 33
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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
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: The rotor flux can be obtained by:
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
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2.5 Conclusions In this chapter, a
Page 125 and 126:
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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Page 213 and 214:
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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,
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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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