SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

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CHAPTER 4 - Inverters and Space Vector Modulation In the subject of motor control there are three areas that can be very tightly integrated and hard to discuss separately: commutation or phasing (the synchronizing of the current waveforms with the shaft position), current control (controlling the shape and amplitude of current to produce the correct value of torque), and the motor control system structure (how references are generated, how commands are passed to the power converter, and how feedback is used). This chapter discusses inverters and space vector modulation. As a consequence it cannot avoid discussing current control, but the main discussion of current control must be delayed until the next chapter when FOC is presented. This chapter begins by discussing the general structure common to all inverters. The common inverters will be divided into to classes (120° and 180°) and the control methods for each will be investigated. As the 120° class is discussed it will be natural to also discuss the 120° six-step commutation (“trapezoidal commutation”) mentioned in Chapter 2; from that point on only 180° inverters will be treated. The second section deals exclusively with SVM. It is first shown how SVM uses the 180° inverter. As a continuation of the space vector material from Chapter 3, the meaning of the magnitude and trajectories of space vectors is discussed. SVM overmodulation will be compared to PWM overmodulation and will reveal the concept of “maximum” inverter output. Finally, details regarding SVM implementation and relationships to PWM are discussed. 160
Overview of Voltage Source Inverters There are many different inverter types reported in the literature, such as matrix, multi-level, soft- switched, and various resonant topologies. Only hard-switched, two-level, three-phase inverters are discussed here because they are the only common topologies in brushless permanent magnet motor control. The current source inverter (CSI) is only used in very large power ratings [75] thus the voltage source (or stiff) inverter (VSI) is the dominant topology, even though it is ultimately motor current that we desire to control. In a three-phase VSI there are three output terminals, each connected to a leg (also known as a half-bridge) that is connected across the DC link or bus. The bus could be supplied by a DC power supply or it could be created using a rectifier and a large bulk capacitor as shown in Figure 4.1. At no time can both transistors in one leg be ON otherwise they will short-circuit the bus (a shoot-through fault). Since each terminal can be connected to only two potentials (with respect to the bus midpoint) this is called a two- level inverter. Figure 4.1 – VSI topology with controlled-rectifier front end. In the VSI topology the output voltage waveform and frequency are controlled only by the transistor switching scheme (which will be called commutation regardless of whether a motor is considered). However, the magnitude of the voltage can be controlled using the transistors or by using the controlled rectifier at the input. (This is true even if the inverter is fed from a DC supply—the controlled rectifier is simply replaced with a chopper.) In order to get the largest possible amplitude, the output waveforms are synthesized about the midpoint of the DC bus, which is labeled M as shown in Figure 4.2. Many sources in the literature specify output voltages in terms of V BUS because that it is the actual bus voltage. But the output waveforms are AC, thus it makes more sense to the author to specify them in terms of V DC as shown (the output is at maximum when it reaches V DC , as opposed to V BUS /2). A 161
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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
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torque component, sturdily construc
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Figure 2.7 - Cross sections of some
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draw the line between the solenoida
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These texts generally attribute the
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N B A B Y x(t) (2.6) The induc
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extended to the rotational case lat
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present analysis). When this is tru
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Figure 2.16 - Components of total f
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As aforementioned a spatial analysi
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clear the meaning, but the reader i
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Figure 2.20 - Elementary brushless
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called the per-phase torque functio
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Expressing bEMF in terms of the bEM
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Equation (2.44) is the component of
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d R( r) ke( r) kt( r) sin( r) (2.
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General Electromechanical Models Th
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Figure 2.28 - Phase-variable simula
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Trapezoidal and Sinusoidal BPMS Mot
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Figure 2.29 - Back-EMF and drive cu
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Figure 2.31 - Back-EMF and drive cu
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3 KT Ke 2 (sinusoidal) K 2 K (tra
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control scheme must keep sinusoidal
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with misconceptions. The primary is
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Part I - Sinusoidal BPMS Motors wit
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grounded-neutral wye or delta conne
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N e f A ( ) i 2 N e f B ( ) i 2
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Figure 3.7 - Developed view at zero
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Figure 3.9 - Developed view showing
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Although Equations (3.6) or (3.7) a
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direction. The contributions always
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sinusoidal electrical variable will
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Figure 3.14 - Cross section of two
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3 N e (3.6): f ( , t) I p cos(
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In the previous chapter the per-pha
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peak value is represented as an upp
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Figure 3.21 - Time relationship bet
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another and thus could be placed in
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more widely understood theory (such
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other methods, although it has clos
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The SV as a Vector The first facet
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j0 j0 j0 aˆ 1 0 1 bˆ j e e e
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j j ee 1 cos( ) (3.45) 2 3 j t x
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Notice that the amplitude of the MM
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Figure 3.27 - Equivalent MMF produc
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Ne 1 jj f , t i e i * e 2 2
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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
Page 139 and 140: phase variable axes; three axes in
Page 141 and 142: The component MMFs act away from th
Page 143 and 144: common choice is to force the power
Page 145 and 146: As an example, find the SV that cor
Page 147 and 148: the same magnitude, the projection
Page 149 and 150: Figure 3.32 - Arbitrary SV referenc
Page 151 and 152: universal and the choice of convent
Page 153 and 154: stator’s perspective and at R fr
Page 155 and 156: The potential discrepancy (p.108) w
Page 157 and 158: x cos( r) sin( r) xd x sin(
Page 159 and 160: It must be emphasized that we have
Page 161 and 162: in relative time like an oscillogra
Page 163 and 164: Part III - SV Theory Applied to Sin
Page 165 and 166: In Equation (3.135) Z has elements
Page 167 and 168: to use SV theory. It may be helpful
Page 169 and 170: Figure 3.42 - Coupling between d- a
Page 171 and 172: R R d R R v Ri Li j Li dt s
Page 173 and 174: current does not influence the valu
Page 175 and 176: d v Ri L i e dt d v Ri L i e
Page 177 and 178: Figure 3.47 - Simulation diagram fo
Page 179: e je ), and (2) it was demonstrate
Page 183 and 184: In addition to measuring voltages w
Page 185 and 186: then there would be periods during
Page 187 and 188: Figure 4.9 - Gating and POLE voltag
Page 189 and 190: Figure 4.11 - Ideal voltage wavefor
Page 191 and 192: inverter is called sine-triangle co
Page 193 and 194: and it offers the fastest dynamic r
Page 195 and 196: Figure 4.18 - Fundamental gain and
Page 197 and 198: In the literature this is called th
Page 199 and 200: voltage will be below (above) the b
Page 201 and 202: Figure 4.24 - Instantaneous phase-A
Page 203 and 204: Figure 4.26 - Base SVs showing the
Page 205 and 206: Figure 4.27 - Transformed voltage w
Page 207 and 208: also correspond to six-step squarew
Page 209 and 210: was fed to the SVM inverter as a SV
Page 211 and 212: Figure 4.31 - Temporal limit of inv
Page 213 and 214: Figure 4.34 - SVM overmodulation re
Page 215 and 216: Checking sextant s 23 again for thi
Page 217 and 218: SVM Implementation The block diagra
Page 219 and 220: has been made of using THI in the S
Page 221 and 222: different triplen signal would be i
Page 223 and 224: Similarly, when the modulation inde
Page 225 and 226: Summary and Conclusion The two-leve
Page 227 and 228: CHAPTER 5 - Field Oriented Control
Page 229 and 230: 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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