SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

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Figure 3.6 – One electrical cycle of unit-amplitude, balanced sinusoidal general quantities. Now let Figure 3.6 represent the phase currents of a wye-connected stator with an isolated neutral. As a first example, use the ordinate as a reference line ( 0 ) and determine the three phase currents: IA is equal to 1.0 while IB and IC are both equal to –0.5. Since IA is positive and unity, its MMF component is exactly that shown in Figure 3.4. Since IB and IC are both negative and half-unity, their MMF components are of opposite polarity and are half the amplitude of those shown in Figure 3.4. At this position (zero electrical degrees), the component of MMF in the airgap due to each phase is shown in Figure 3.7. Also shown is the overall (“total” 12 ) MMF in the airgap; the peak of the total MMF is coincident with the electrical position of the three-phase currents (zero electrical degrees). 12 “Resultant” would be a more appropriate term but it is nearly always reserved to describe the combination of stator and rotor magnetic fields and these will be discussed later. 68
Figure 3.7 – Developed view at zero electrical degrees. As the reference line in Figure 3.6 moves forward in electrical angular position, the current in each phase will increase or decrease and the component MMF of that phase will increase or decrease proportionally. The component MMF of each phase maintains a cosinusoidal shape in space—that is, with respect to the stationary stator conductors. As the current in a phase varies cosinusoidally this space distribution does not change in shape. Rather, the magnitude increases and decreases cosinusoidally with time; that is, the amplitude of the cosinusoidal space distribution is modulated cosinusoidally in time. For any given electrical angle, the total MMF will also be cosinusoidally distributed in space (it is a general property that when two or more cosine waves of the same period are added, the result is another cosine wave of the same period). Further, as the component MMFs (with their fixed spatial axes) increase and decrease, the peak of this total cosinusoid will move in space. Figure 3.8 is the same as Figure 3.7 except the electrical reference line in Figure 3.6 has been moved to 30 . Here, I 3/2, I 0 , and I 3/2. Again compare (the instantaneous MMF of each phase with the maximum A possible) in conjunction with the values of current at this instant. A B 69
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SENSORLESS FIELD ORIENTED CONTROL O
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Table of Contents List of Figures..
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CHAPTER 5 - Field Oriented Control
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List of Figures Figure 2.1 - Radial
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Figure 3.29 - Arbitrary space vecto
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Figure 4.44 - ZS components of some
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Figure C.13 - Single-turn full-pitc
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List of Symbols Symbol Meaning Unit
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Abbreviations ACIM AC induction mot
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Superscripts * commanded value ref
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CHAPTER 1 - Introduction Historical
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vector theory to model a machine, w
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publications and magazines, and Int
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elationship between SVM and other P
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CHAPTER 2 - Fundamentals of Electri
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Preliminaries In reading the litera
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Taxonomy of Motors There is any num
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characteristics (the DC load curren
Page 37 and 38: torque component, sturdily construc
Page 39 and 40: Figure 2.7 - Cross sections of some
Page 41 and 42: draw the line between the solenoida
Page 43 and 44: These texts generally attribute the
Page 45 and 46: N B A B Y x(t) (2.6) The induc
Page 47 and 48: extended to the rotational case lat
Page 49 and 50: present analysis). When this is tru
Page 51 and 52: Figure 2.16 - Components of total f
Page 53 and 54: As aforementioned a spatial analysi
Page 55 and 56: clear the meaning, but the reader i
Page 57 and 58: Figure 2.20 - Elementary brushless
Page 59 and 60: called the per-phase torque functio
Page 61 and 62: Expressing bEMF in terms of the bEM
Page 63 and 64: Equation (2.44) is the component of
Page 65 and 66: d R( r) ke( r) kt( r) sin( r) (2.
Page 67 and 68: General Electromechanical Models Th
Page 69 and 70: Figure 2.28 - Phase-variable simula
Page 71 and 72: Trapezoidal and Sinusoidal BPMS Mot
Page 73 and 74: Figure 2.29 - Back-EMF and drive cu
Page 75 and 76: Figure 2.31 - Back-EMF and drive cu
Page 77 and 78: 3 KT Ke 2 (sinusoidal) K 2 K (tra
Page 79 and 80: control scheme must keep sinusoidal
Page 81 and 82: with misconceptions. The primary is
Page 83 and 84: Part I - Sinusoidal BPMS Motors wit
Page 85 and 86: grounded-neutral wye or delta conne
Page 87: N e f A ( ) i 2 N e f B ( ) i 2
Page 91 and 92: Figure 3.9 - Developed view showing
Page 93 and 94: Although Equations (3.6) or (3.7) a
Page 95 and 96: direction. The contributions always
Page 97 and 98: sinusoidal electrical variable will
Page 99 and 100: Figure 3.14 - Cross section of two
Page 101 and 102: 3 N e (3.6): f ( , t) I p cos(
Page 103 and 104: In the previous chapter the per-pha
Page 105 and 106: peak value is represented as an upp
Page 107 and 108: Figure 3.21 - Time relationship bet
Page 109 and 110: another and thus could be placed in
Page 111 and 112: more widely understood theory (such
Page 113 and 114: other methods, although it has clos
Page 115 and 116: The SV as a Vector The first facet
Page 117 and 118: j0 j0 j0 aˆ 1 0 1 bˆ j e e e
Page 119 and 120: j j ee 1 cos( ) (3.45) 2 3 j t x
Page 121 and 122: Notice that the amplitude of the MM
Page 123 and 124: Figure 3.27 - Equivalent MMF produc
Page 125 and 126: Ne 1 jj f , t i e i * e 2 2
Page 127 and 128: distribution that is cosinusoidal i
Page 129 and 130: 3 Ne j t f Ie p 2 2 . This
Page 131 and 132: j set θ to anything. Taking the re
Page 133 and 134: epresent any physically-distributed
Page 135 and 136: lumped-parameter model in this repo
Page 137 and 138: x kCx (3.75) abc The set of varia
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phase variable axes; three axes in
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The component MMFs act away from th
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common choice is to force the power
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As an example, find the SV that cor
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the same magnitude, the projection
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Figure 3.32 - Arbitrary SV referenc
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universal and the choice of convent
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stator’s perspective and at R fr
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The potential discrepancy (p.108) w
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x cos( r) sin( r) xd x sin(
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It must be emphasized that we have
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in relative time like an oscillogra
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Part III - SV Theory Applied to Sin
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In Equation (3.135) Z has elements
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to use SV theory. It may be helpful
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Figure 3.42 - Coupling between d- a
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R R d R R v Ri Li j Li dt s
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current does not influence the valu
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d v Ri L i e dt d v Ri L i e
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Figure 3.47 - Simulation diagram fo
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e je ), and (2) it was demonstrate
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Overview of Voltage Source Inverter
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In addition to measuring voltages w
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then there would be periods during
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Figure 4.9 - Gating and POLE voltag
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Figure 4.11 - Ideal voltage wavefor
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inverter is called sine-triangle co
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and it offers the fastest dynamic r
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Figure 4.18 - Fundamental gain and
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In the literature this is called th
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voltage will be below (above) the b
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Figure 4.24 - Instantaneous phase-A
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Figure 4.26 - Base SVs showing the
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Figure 4.27 - Transformed voltage w
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also correspond to six-step squarew
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was fed to the SVM inverter as a SV
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Figure 4.31 - Temporal limit of inv
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Figure 4.34 - SVM overmodulation re
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Checking sextant s 23 again for thi
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SVM Implementation The block diagra
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has been made of using THI in the S
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different triplen signal would be i
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Similarly, when the modulation inde
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Summary and Conclusion The two-leve
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CHAPTER 5 - Field Oriented Control
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torque production; this is called d
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Figure 5.3 - Torque control of sinu
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obviously a change in perspective.
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Figure 5.9 - Comparison of referenc
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variables to the stationary referen
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Figure 5.13 - Torque control of sin
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To analyze a salient machine one mu
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Figure 5.16 - Torque functions: (a)
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Figure 5.19 - Buried permanent magn
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Figure 5.21 - Flux weakening in the
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appears that this is very much rela
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Stationary and Synchronous Regulato
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stationary regulator had. For compl
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This coupling can be mitigated by m
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educes to two independent circuits,
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D, some of the 120° methods are ap
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d d v Ri Ls i R dt dt The r
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section a state-space model for the
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Figure 6.6 - Full state feedback (o
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State-Space Model of BPMS Motor A s
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Figure 6.9 - FOC block diagram. The
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loop). A second way to implement th
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knowing the rotor position from ini
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[11] E. Clarke, Circuit analysis of
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Control Systems, Linear Analysis [4
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[77] J.M.D. Murphy, F.G. Turnbull,
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Machine Modeling, Analysis [103] J.
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THI, SVM, SPWM [127] J.A. Houldswor
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Wisconsin-Madison. [Online]. Availa
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Angle Tracking [175] D. Morgan, “
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Appendix A - Elementary Electromagn
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L i (A.8) S SS S SR S SS SR (A.9
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First the self-flux-linkage of an i
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vAN R iA LM iA eA d v R i
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Figure B.3 - One-half of the flux p
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Equations (B.27) and (B.28) are for
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Fundamental Relationships Figure C.
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Figure C.3 - Sinusoidal winding den
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manufactured compared to the steppe
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phase winding of Figure C.4 will ha
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Distributed N Fp i 2 (C.5) Figu
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alanced machine only odd harmonics
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sinusoidal windings with a sinusoid
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0, and since the direction of inte
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That the rotor-stator flux linkage
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Figure C.17 - Summary of rotor-stat
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Figure C.19 - Amplitudes of harmoni
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triangle with an amplitude whose nu
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Returning to Figure C.18 it is clea
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torque will describe the torque pro
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However, Equation (D.2) is incorrec
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the same order as the PS set (arran
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Implications of the ZS Component Th
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Figure D.6 - Neutral voltage of loa
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3v 3e 3v v v v v v v 3v AM BM CM A
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components of source voltage sum to
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Equation (D.25) and instantaneous q
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If a ZS component could possibly be
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xA X1cos( t) X3cos(3 t) X5cos(5 t)
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Figure D.11 - 3-D base vectors of 1
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the Clarke transform is used. Howev
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Appendix E - Park Transforms This a
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Appendix F - Useful Mathematical Re
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335
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