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Power Systems Nguyen Phung Quang and Jörg-Andreas Dittrich Vector Control of Three-Phase AC Machines
Nội dung tài liệu
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Nguyen Phung Quang · Jörg-Andreas Dittrich Vector Control of Three-Phase AC Machines System Development in the Practice With 230 Figures
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Prof. Dr. Nguyen Phung Quang Dr. Jörg-Andreas Dittrich Hanoi University of Technology Neeserweg 31 Department of Automatic Control 8048 Zürich 01 Dai Co Viet Road Switzerland Hanoi andreas_d@swissonline.ch Vietnam quangnp-ac@mail.hut.edu.vn ISBN: 978-3-540-79028-0 e-ISBN: 978-3-540-79029-7 Power Systems ISSN: 1612-1287 Library of Congress Control Number: 2008925606 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: deblik, Berlin Printed on acid-free paper 9 8 7 6 5 4 3 2 1 springer.com
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Dedicated to my parents, my wife and my son Nguyen Phung Quang To my mother in grateful memory Jörg-Andreas Dittrich
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Formula symbols and abbreviations A System matrix B Input matrix C Output matrix dq Field synchronous or rotor flux orientated coordinate system E Sensitivity function EI, ER Imaginary, real part of the sensitivity function eN Vector of grid voltage f General analytical vector function fp, fr, fs Pulse, rotor, stator frequency G Transfer function Gfe Iron loss conductance H, h Input matrix, input vector of discrete system h General analytical vector function iȝ Vector of magnetizing current running through Lm im Vector of magnetizing current imd, imq dq components of the magnetizing current iN, iT, iF Vectors of grid, transformer and filter current is, ir Vector of stator, rotor current isd, isq, ird, irq dq components of the stator, rotor current isĮ, isȕ Įȕ components of the stator current isu, isv, isw Stator current of phases u, v, w J Torque of inertia K Feedback matrix, state feedback matrix Lfg Lie derivation of the scalar function g(x) along the trajectory f(x) Lm, Lr, Ls Mutual, rotor, stator inductance Lsd, Lsq d axis, q axis inductance Lır, Lıs Rotor-side, stator-side leakage inductance mM, mG Motor torque, generator torque N Nonlinear coupling matrix pCu Copper loss pv Total loss pv,fe, pFe Iron loss
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VIII Formula symbols and abbreviations RI, RIN Two-dimensional current controller RF, RD Filter resistance, inductor resistance Rfe Iron loss resistance Rr, Rs Rotor, stator resistance R Flux controller Z r Vector of relative difference orders r Relative difference order s Complex power S Loss function s Slip T Sampling period Tp Pulse period Tr, Ts Rotor, stator time constant Tsd, Tsq d axis, q axis time constant tD Protection time ton, toff Turn-on, turn-off time tr Transfer ratio tu, tv, tw Switching time of inverter leg IGBT’s u Input vector u0, u1, … , u7 Standard voltage vectors of inverter UDC DC link voltage uN Vector of grid voltage us, ur Vector of stator, rotor voltage usd, usq, urd, urq dq components of the stator, rotor voltage usĮ, usȕ Įȕ components of the stator voltage V Pre-filter matrix w Input vector x State vector xw Control error or control difference z State vector zp Number of pole pair Zs Complex resistance or impedance Įȕ Stator-fixed coordinate system Ɏ Transition or system matrix of discrete system Zȝ Main flux linkage Zp, Zr, Zs Vector of pole, rotor, stator flux Z/ , Z/ Vector of rotor, stator flux in terms of L r s m Zsd, Zsq, Zrd, Zrq dq components of the stator, rotor flux
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Formula symbols and abbreviations IX Z/ , Z/ , Z/ , Z/ Components of Z/ rd rq rB rC r Z/ , Z/ Components of Z/ sd sq s Ȝi Eigen value X, Xr, Xs Mechanical rotor velocity, rotor and stator circuit velocity +, +s Rotor angle, angle of flux orientated coordinate system ı Total leakage factor ϕ Angle between vectors of stator or grid voltage and stator current ADC Analog to Digital Converter CAPCOM Capture/Compare register DFIM Doubly-Fed Induction Machine DSP Digital Signal Processor DTC Direct Torque Control EKF Extended Kalman Filter FAT Finite Adjustment Time GC Grid-side Converter or Front-end Converter IE Incremental Encoder IGBT Insulated Gate Bipolar Transistor IM Induction Machine KF Kalman Filter MIMO Multi Input – Multi Output MISO Multi Input – Single Output MRAS Model Reference Adaptive System NFO Natural Field Orientation PLL Phase Locked Loop PMSM Permanent Magnet Excited Synchronous Machine PWM Pulse Width Modulation SISO Single Input – Single Output VFC Voltage to Frequency Converter VSI Voltage Source Inverter ȝC, ȝP Microcontroller, microprocessor
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Table of Contents A Basic Problems 1 Principles of vector orientation and vector 1 orientated control structures for systems using three-phase AC machines 1.1 Formation of the space vectors and its vector orientated 1 philosophy 1.2 Basic structures with field-orientated control for three-phase 6 AC drives 1.3 Basic structures of grid voltage orientated control for 11 DFIM generators 1.4 References 15 2 Inverter control with space vector modulation 17 2.1 Principle of vector modulation 18 2.2 Calculation and output of the switching times 23 2.3 Restrictions of the procedure 26 2.3.1 Actually utilizable vector space 26 2.3.2 Synchronization between modulation and signal 28 processing 2.3.3 Consequences of the protection time and its compensation 29 2.4 Realization examples 31 2.4.1 Modulation with microcontroller SAB 80C166 33 2.4.2 Modulation with digital signal processor 37 TMS 320C20/C25 2.4.3 Modulation with double processor configuration 45 2.5 Special modulation procedures 49 2.5.1 Modulation with two legs 49 2.5.2 Synchronous modulation 51 2.5.3 Stochastic modulation 53 2.6 References 58
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XII Table of Contents 3 Machine models as prerequisite to design the 61 controllers and observers 3.1 General issues of state space representation 61 3.1.1 Continuous state space representation 61 3.1.2 Discontinuous state space representation 63 3.2 Induction machine with squirrel-cage rotor (IM) 69 3.2.1 Continuous state space models of the IM in stator-fixed 70 and field-synchronous coordinate systems 3.2.2 Discrete state space models of the IM 78 3.3 Permanent magnet excited synchronous machine (PMSM) 85 3.3.1 Continuous state space model of the PMSM in the field 85 synchronous coordinate system 3.3.2 Discrete state model of the PMSM 88 3.4 Doubly-fed induction machine (DFIM) 90 3.4.1 Continuous state space model of the DFIM in the grid 90 synchronous coordinate system 3.4.2 Discrete state model of the DFIM 93 3.5 Generalized current process model for the two machine 95 types IM and PMSM 3.6 Nonlinear properties of the machine models and the way 97 to nonlinear controllers 3.6.1 Idea of the exact linearization 98 3.6.2 Nonlinearities of the IM model 100 3.6.3 Nonlinearities of the DFIM model 102 3.6.4 Nonlinearities of the PMSM model 103 3.7 References 105 4 Problems of actual-value measurement and 107 vector orientation 4.1 Acquisition of the current 108 4.2 Acquisition of the speed 110 4.3 Possibilities for sensor-less acquisition of the speed 116 4.3.1 Example for the speed sensor-less control of an IM drive 118 4.3.2 Example for the speed sensor-less control of a PMSM 125 drive 4.4 Field orientation and its problems 127 4.4.1 Principle and rotor flux estimation for IM drives 128 4.4.2 Calculation of current set points 134 4.4.3 Problems of the sampling operation of the control system 135 4.5 References 139
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Table of Contents XIII B Three-Phase AC Drives with IM and PMSM 5 Dynamic current feedback control for fast torque 143 impression in drive systems 5.1 Survey about existing current control methods 144 5.2 Environmental conditions, closed loop transfer function 155 and control approach 5.3 Design of a current vector controller with dead-beat 159 behaviour 5.3.1 Design of a current vector controller with dead-beat 159 behaviour with instantaneous value measurement of the current actual-values 5.3.2 Design of a current vector controller with dead-beat 163 behaviour for integrating measurement of the current actual-values 5.3.3 Design of a current vector controller with finite 165 adjustment time 5.4 Design of a current state space controller with dead-beat 167 behaviour 5.4.1 Feedback matrix K 168 5.4.2 Pre-filter matrix V 169 5.5 Treatment of the limitation of control variables 172 5.5.1 Splitting strategy at voltage limitation 174 5.5.2 Correction strategy at voltage limitation 180 5.6 References 182 6 Equivalent circuits and methods to determine 185 the system parameters 6.1 Equivalent circuits with constant parameters 186 6.1.1 Equivalent circuits of the IM 186 6.1.1.1 T equivalent circuit 186 6.1.1.2 Inverse Γ equivalent circuit 188 6.1.1.3 Γ equivalent circuit 189 6.1.2 Equivalent circuits of the PMSM 190 6.2 Modelling of the nonlinearities of the IM 191 6.2.1 Iron losses 191 6.2.2 Current and field displacement 194 6.2.3 Magnetic saturation 198 6.2.4 Transient parameters 204 6.3 Parameter estimation from name plate data 204 6.3.1 Calculation for IM with power factor cosϕ 205
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XIV Table of Contents 6.3.2 Calculation for IM without power factor cosϕ 208 6.3.3 Parameter estimation from name plate of PMSM 210 6.4 Automatic parameter estimation for IM in standstill 211 6.4.1 Pre-considerations 211 6.4.2 Current-voltage characteristics of the inverter, stator 213 resistance and transient leakage inductance 6.4.3 Identification of inductances and rotor resistance with 215 frequency response methods 6.4.3.1 Basics and application for the identification of rotor 215 resistance and leakage inductance 6.4.3.2 Optimization of the excitation frequencies by sensitivity 217 functions 6.4.3.3 Peculiarities at estimation of main inductance and 219 magnetization characteristic 6.4.4 Identification of the stator inductance with direct current 221 excitation 6.5 References 223 7 On-line adaptation of the rotor time constant 225 for IM drives 7.1 Motivation 225 7.2 Classification of adaptation methods 231 7.3 Adaptation of the rotor resistance with model methods 235 7.3.1 Observer approach and system dynamics 236 7.3.2 Fault models 239 7.3.2.1 Stator voltage models 239 7.3.2.2 Power balance models 242 7.3.3 Parameter sensitivity 244 7.3.4 Influence of the iron losses 249 7.3.5 Adaptation in the stationary and dynamic operation 251 7.4 References 254 8 Optimal control of state variables and set points 257 for IM drives 8.1 Objective 257 8.2 Efficiency optimized control 258 8.3 Stationary torque optimal set point generation 261 8.3.1 Basic speed range 261 8.3.2 Upper field weakening area 265 8.3.3 Lower field weakening area 269 8.3.4 Common quasi-stationary control strategy 272
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Table of Contents XV 8.3.5 Torque dynamics at voltage limitation 275 8.4 Comparison of the optimization strategies 279 8.5 Rotor flux feedback control 282 8.6 References 285 9 Nonlinear control structures with direct 287 decoupling for three-phase AC drive systems 9.1 Existing problems at linear controlled drive systems 287 9.2 Nonlinear control structure for drive systems with IM 288 9.2.1 Nonlinear controller design based on “exact linearization” 289 9.2.2 Feedback control structure with direct decoupling for IM 293 9.3 Nonlinear control structure for drive systems with PMSM 295 9.3.1 Nonlinear controller design based on “exact linearization” 295 9.3.2 Feedback control structure with direct decoupling for 298 PMSM 9.4 References 300 C Wind Power Plants with DFIM 10 Linear control structure for wind power plants 301 with DFIM 10.1 Construction of wind power plants with DFIM 301 10.2 Grid voltage orientated controlled systems 303 10.2.1 Control variables for active and reactive power 304 10.2.2 Dynamic rotor current control for decoupling of active 305 and reactive power 10.2.3 Problems of the implementation 308 10.3 Front-end converter current control 309 10.3.1 Process model 310 10.3.2 Controller design 312 10.4 References 314 11 Nonlinear control structure with direct 315 decoupling for wind power plants with DFIM 11.1 Existing problems at linear controlled wind power plants 315 11.2 Nonlinear control structure for wind power plants with 316 DFIM 11.2.1 Nonlinear controller design based on “exact linearization” 316 11.2.2 Feedback control structure with direct decoupling for 319 DFIM 11.3 References 323
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XVI Table of Contents 12 Appendices 325 12.1 Normalizing - the important step towards preparation for 325 programming 12.2 Example for the model discretization in the section 3.1.2 328 12.3 Application of the method of the least squares regression 330 12.4 Definition and calculation of Lie derivation 334 12.5 References 335 Index 337
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1 Principles of vector orientation and vector orientated control structures for systems using three-phase AC machines From the principles of electrical engineering it is known that the 3-phase quantities of the 3-phase AC machines can be summarized to complex vectors. These vectors can be represented in Cartesian coordinate systems, which are particularly chosen to suitable render the physical relations of the machines. These are the field-orientated coordinate system for the 3- phase AC drive technology or the grid voltage orientated coordinate system for generator systems. The orientation on a certain vector for modelling and design of the feedback control loops is generally called vector orientation. 1.1 Formation of the space vectors and its vector orientated philosophy The three sinusoidal phase currents isu, isv and isw of a neutral point isolated 3-phase AC machine fulfill the following relation: isu ( )t +isv ( )t +isw ( )t = 0 (1.1) Fig. 1.1 Formation of the stator current vector from the phase currents
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2 Principles of vector orientation and vector orientated control structures These currents can be combined to a vector is(t) circulating with the stator frequency fs (see fig. 1.1). 2 ( ) ( ) jH ( ) j 2H ¯ is = ¡¢isu t +isv t e +isw t e °± with H = 2Q 3 (1.2) 3 The three phase currents now represent the projections of the vector is on the accompanying winding axes. Using this idea to combine other 3- phase quantities, complex vectors of stator and rotor voltages us, ur and stator and rotor flux linkages Zs, Zr are obtained. All vectors circulate with the angular speed ωs. In the next step, a Cartesian coordinate system with dq axes, which circulates synchronously with all vectors, will be introduced. In this system, the currents, voltage and flux vectors can be described in two components d and q. us =usd + jusq;ur =urd + jurq is =isd + jisq; ir =ird + jirq (1.3) Zr = Zrd + jZrq; Zs = Zsd + jZsq Fig. 1.2 Vector of the stator currents of IM in stator-fixed and field coordinates Now, typical electrical drive systems shall be looked at more closely. If the real axis d of the coordinate system (see fig. 1.2) is identical with the direction of the rotor flux Zr (case IM) or of the pole flux Zp (case
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Formation of the space vectors and its vector orientated philosophy 3 PMSM), the quadrature component (q component) of the flux disappears and a physically easily comprehensible representation of the relations between torque, flux and current components is obtained. This representation can be immediately expressed in the following formulae. • The induction motor with squirrel-cage rotor: ( ) Lm 3 Lm Zrd s = isd ; mM = zp Zrd isq (1.4) 1+ sTr 2 Lr • The permanentmagnet-excited synchronous motor: 3 mM = zp Zp isq (1.5) 2 In the equations (1.4) and (1.5), the following symbols are used: mM Motor torque zp Number of pole pairs Zrd ,Zp = Zp Rotor and pole flux (IM, PMSM) isd ,isq Direct and quadrature components of stator current Lm,Lr Mutual and rotor inductance with Lr = Lm + LTr (LTr : rotor leakage inductance) Tr Rotor time constant with Tr = Lr Rr (Rr : rotor resistance) s Laplace operator The equations (1.4), (1.5) show that the component isd of the stator current can be used as a control quantity for the rotor flux Zrd. If the rotor flux can be kept constant with the help of isd, then the cross component isq plays the role of a control variable for the torque mM. The linear relation between torque mM and quadrature component isq is easily recognizable for the two machine types. If the rotor flux Zrd is constant (this is actually the case for the PMSM), isq represents the motor torque mM so that the output quantity of the speed controller can be directly used as a set point for the quadrature component i* . For the case of the sq IM, the rotor flux Zrd may be regarded as nearly constant because of its slow variability in respect to the inner control loop of the stator current. Or, it can really be kept constant when the control scheme contains an outer flux control loop. This philosophy is justified in the formula (1.4) by the fact that the rotor flux Zrd can only be influenced by the direct component isd with a delay in the range of the rotor time constant Tr, which is many times greater than the sampling period of the current control loop. Thus, the set point i* of this field-forming component can be provided by sd the output quantity of the flux controller. For PMSM the pole flux Zp is
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4 Principles of vector orientation and vector orientated control structures maintained permanently unlike for the IM. Therefore the PMSM must be controlled such that the direct component isd has the value zero. Fig. 1.2 illustrates the relations described so far. If the real axis d of the Cartesian dq coordinate system is chosen identical with one of the three winding axes, e.g. with the axis of winding u (fig. 1.2), it is renamed into αβ coordinate system. A stator-fixed coordinate system is now obtained. The three-winding system of a 3-phase AC machine is a fixed system by nature. Therefore, a transformation is imaginable from the three-winding system into a two-winding system with α and β windings for the currents isα and isβ. £¦i =i ¦¦¦ sB su ¤ 1 ( ) (1.6) ¦¦i = i +2i ¦ sC 3 su sv ¦¥ In the formula (1.6) the third phase current isw is not needed because of the (by definition) open neutral-point of the motor. Figure 1.2 shows two Cartesian coordinate systems with a common origin, of which the system with BC coordinates is fixed and the system with dq coordinates circulates with the angular speed Xs = d+s dt . The current is can be represented in the two coordinate systems as follows. • In αβ coordinates: is =i + j i s sB sC • In dq coordinates: i f =i + j i s sd sq (Indices: s - stator-fixed, f - field synchronous coordinates) Fig. 1.3 Acquisition of the field synchronous current components
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Formation of the space vectors and its vector orientated philosophy 5 With £¦¦i = i cos+ +i sin+ sd sB s sC s (1.7) ¤¦ ¦¥isq =isB sin+s +isC cos+s the stator current vector is obtained as: i f = ¡ i cos+ +i sin+ °¯ + j i¡ cos+ i sin+ °¯ s ¢ sB s sC s ± ¢ sC s sB s ± i f = ¡ i + j i °¯[cos+ jsin+ ]= is e j+s s ¢ sB sC ± s s s In generalization of that the following general formula results to transform complex vectors between the coordinate systems: vs = v f ej+s or v f = vs e j+s (1.8) v: an arbitrary complex vector The acquisition of the field synchronous current components, using equations (1.6) and (1.7), is illustrated in figure 1.3. Fig. 1.4 Vectors of the stator and rotor currents of DFIM in grid voltage (uN) orientated coordinates In generator systems like wind power plants with the stator connected directly to the grid, the real axis of the grid voltage vector uN can be chosen as the d axis (see fig. 1.4). Such systems often use doubly-fed induction machines (DFIM) as generators because of several economic advantages. In Cartesian coordinates orientated to the grid voltage vector, the following relations for the DFIM are obtained. • The doubly-fed induction machine: Zs Lm irq 3 L sinK = ; m = z m Z i (1.9) i G 2 p L sq rd s s
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6 Principles of vector orientation and vector orientated control structures In equation (1.9), the following symbols are used: mG Generator torque Zsq,Zs Stator flux is Vector of stator current ird ,irq Direct and quadrature components of rotor current Lm,Ls Mutual and stator inductance with Ls = Lm + LTs (LTs : stator leakage inductance) K Angle between vectors of grid voltage and stator current Because the stator flux Zs is determined by the grid voltage and can be viewed as constant, the rotor current component ird plays the role of a control variable for the generator torque mG and therefore for the active power P respectively. This fact is illustrated by the second equation in (1.9). The first of both equations (1.9) means that the power factor cosK or the reactive power Q can be controlled by the control variable irq. 1.2 Basic structures with field-orientated control for three-phase AC drives DC machines by their nature allow for a completely decoupled and independent control of the flux-forming field current and the torque- forming armature current. Because of this complete separation, very simple and computing time saving control algorithms were developed, which gave the dc machine preferred use especially in high-performance drive systems within the early years of the computerized feedback control. In contrast to this, the 3-phase AC machine represents a mathematically complicated construct with its multi-phase winding and voltage system, which made it difficult to maintain this important decoupling quality. Thus, the aim of the field orientation can be defined to re-establish the decoupling of the flux and torque forming components of the stator current vector. The field-orientated control scheme is then based on impression the decoupled current components using closed-loop control. Based on the theoretical statements, briefly outlined in chapter 1.1, the classical structure (see fig. 1.5) of a 3-phase AC drive system with field- orientated control shall now be looked at in some more detail. If block 8 remains outside our scope at first, the structure, similar as for the case of a system with DC motor, contains in the outer loop two controllers: one for the flux (block 1) and one for the speed (block 9). The inner loop is formed of two separate current controllers (blocks 2) with PI behaviour for the field-forming component isd (comparable with the field current of the DC
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