Literature Number: BPRA073 Texas Instruments Europe February 1998

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Field Orientated Control 3-Phase AC-Motors
Literature Number: BPRA073 Texas Instruments Europe February 1998
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Copyright 1998, Texas Instruments Incorporated
Contents
Contents
Introduction. Classic drives. Field Orientated Control. Space Vector definition projection 3.1.1 (a,b,c)->(,) projection (Clarke transformation) 3.1.2 (,)->(d,q) projection (Park transformation) 3.1.3 (d,q)->(,) projection (inverse Park transformation) basic scheme input 3.3.1 Current sampling 3.3.2 Rotor flux position. Conclusion regulator Space Vector 3-phase Inverter Space Vector Pulse Width Modulation (SVPWM). Comparison SV-sinusoidal PWM. Conclusion. References
Field Orientated Control 3-Phase AC-Motors
Contents
List Figures
Figure Stator current space vector component (a,b,c). Figure Stator current space vector components (a,b). Figure Stator current space vector component (a,b) rotating reference frame. Figure Basic scheme AC-motor. Figure Current, voltage rotor flux space vectors rotating reference frame their relationship with a,b,c stationary reference frame Figure Classical Numerical Regulator Structure Figure Numerical Regulator with Correction Integral Term. Figure Basic scheme 3-phase inverter AC-motor. Figure SVPWM, vectors sectors Figure Reference vector combination adjacent vectors. Figure Pattern SVPWM sector Figure Hexagon SVPWM, pattern Figure Locus comparison SV-sinusoidal
Field Orientated Control 3-Phase AC-Motors
Field Orientated Control 3-Phase AC-Motors
ABSTRACT
principle vector control electrical drives based control both magnitude phase each phase current voltage. long this type control considers three phase system three independent systems control will remain analog thus present several drawbacks. Since high computational power silicon devices, such TMS320F240 from came market been possible realize more precise digital vector control algorithms. most common these accurate vector controls presented this document: Field Orientated Control, digital implementation which demonstrates capability performing direct torque control, handling system limitations achieving higher power conversion efficiency.
Introduction
During last years field controlled electrical drives undergone rapid expansion mainly advantages semiconductors both power signal electronics culminating micro-electronic microprocessors DSPs. These technological improvements have enabled development really effective drive control with ever lower power dissipation hardware ever more accurate control structures. electrical drive controls become more accurate sense that only current voltage controlled also three phase currents voltages managed so-called vector controls. This document describes most efficient form vector control scheme: Field Orientated Control. based three major points: machine current voltage space vectors, transformation three phase speed time dependent system into co-ordinate time invariant system effective Pulse Width Modulation pattern generation. Thanks these factors, control machine acquires every advantage machine control frees itself from mechanical commutation drawbacks. Furthermore, this control structure, achieving very accurate steady state transient control, leads high dynamic performance terms response times power conversion. These different aspects discussed following chapters.
Classic drives
motor control structures generally apply three spatially displaced sinusoidal voltages three stator phases. most classic drives generation three sine waves based motor electromechanical characteristics equivalent model motor steady state. Furthermore, control looks like three separate single phase system controls rather than control three phase system. Some major common drawbacks presented this chapter [1]:
Field Orientated Control 3-Phase AC-Motors
machine models characteristics used valid only steady state. This causes control allow high peak voltage current transients. These damage only drive dynamic performance also power conversion efficiency. Additionally, power components must oversized withstand transient electrical spikes. Great difficulty controlling variables with sinusoidal references: regulators perform sinusoidal regulation without damaging sinusoidal hysteresis controllers introduce high bandwidth noise into system that hard filter out. three phase system imbalance management. consideration phase interactions. Finally, control structure must dedicated according motor type (asynchronous synchronous). following chapters present Field Orientated Control drives. This control solution overcomes each these drawbacks thus improves overall effectiveness drive. Detailed explanations references other helpful documents gives reader good understanding control structure immediate benefits such solution.
Field Orientated Control
Field Orientated Control (FOC) [1][3] consists controlling stator currents represented vector. This control based projections which transform threephase time speed dependent system into co-ordinate co-ordinates) time invariant system. These projections lead structure similar that machine control. Field orientated controlled machines need constants input references: torque component (aligned with co-ordinate) flux component (aligned with co-ordinate). Field Orientated Control simply based projections control structure handles instantaneous electrical quantities. This makes control accurate every working operation (steady state transient) independent limited bandwidth mathematical model. thus solves classic scheme problems, following ways: ease reaching constant reference (torque component flux component stator current) ease applying direct torque control because (d,q) reference frame expression torque
RiSq
maintaining amplitude rotor flux fixed value have linear relationship between torque torque component (iSq). then control torque controlling torque component stator current vector.
Field Orientated Control 3-Phase AC-Motors
Space Vector definition projection three-phase voltages, currents fluxes AC-motors analyzed terms complex space vectors [1][6]. With regard currents, space vector defined follows. Assuming that instantaneous currents stator
phases, then complex stator current vector defined where represent spatial operators. following diagram shows stator current complex space vector:
Figure Stator current space vector component (a,b,c)
where (a,b,c) three phase system axes. This current space vector depicts three phase sinusoidal system. still needs transformed into time invariant co-ordinate system. This transformation split into steps: (a,b,c)(,) (the Clarke transformation) which outputs co-ordinate time variant system (,)(d,q) (the Park transformation) which outputs co-ordinate time invariant system This explained following chapter.
3.1.1 (a,b,c)->(,) projection (Clarke transformation)
space vector reported another reference frame with only orthogonal axis called (,). Assuming that axis axis same direction have following vector diagram:
Field Orientated Control 3-Phase AC-Motors
Figure Stator current space vector components (a,b)
projection that modifies three phase system into dimension orthogonal system presented below. TMS320F240 software implementation refer report (BPRA048). obtain co-ordinate system that still depends time speed.
3.1.2 (,)->(d,q) projection (Park transformation)
This most important transformation FOC. fact, this projection modifies phase orthogonal system rotating reference frame. consider axis aligned with rotor flux, next diagram shows, current vector, relationship from reference frame:
Figure Stator current space vector component (a,b) rotating reference frame
Field Orientated Control 3-Phase AC-Motors
where rotor flux position. flux torque components current vector determined following equations: These components depend current vector components rotor flux position; know right rotor flux position then, this projection, component becomes constant. TMS320F240 software implementation refer report (BPRA048). obtain co-ordinate system with following characteristics: co-ordinate time invariant system with (flux component) (torque component) direct torque control possible easy.
3.1.3 (d,q)->(,) projection (inverse Park transformation)
Here, introduce from this voltage transformation only equation that modifies voltages rotating reference frame phase orthogonal system: Sref Sdref Sqref Sref Sdref Sqref
outputs this block components reference vector that call
voltage space vector applied motor phases. TMS320F240 software implementation refer report (BPRA048). basic scheme following diagram summarizes basic scheme torque control with [1][2][3]:
Field Orientated Control 3-Phase AC-Motors
iSqref iSdref
vSqref vSdref
Park
vSref vSref
3-phase Inverter
Park
a,b,c
Clarke
motor
Figure Basic scheme AC-motor
motor phase currents measured. These measurements feed Clarke transformation module. outputs this projection designated These components current inputs Park transformation that gives current rotating reference frame. components compared references iSdref (the flux reference) iSqref (the torque reference). this point, this control structure shows interesting advantage: used control either synchronous induction machines simply changing flux reference obtaining rotor flux position. synchronous permanent magnet motors, rotor flux fixed (determined magnets) there need create one. Hence, when controlling PMSM, iSdref should zero. induction motors need rotor flux creation order operate, flux reference must zero. This conveniently solves major drawbacks "classic" control structures: portability from asynchronous synchronous drives. torque command iSqref could output speed regulator when speed FOC. outputs current regulators vSdref vSqref; they applied inverse Park transformation. outputs this projection vSref vSref which components stator vector voltage stationary orthogonal reference frame. These inputs Space Vector PWM. outputs this block signals that drive inverter. Note that both Park inverse Park transformations need rotor flux position. Obtaining this rotor flux position depends machine type (synchronous asynchronous machine). Rotor flux position considerations made following paragraph.
Field Orientated Control 3-Phase AC-Motors
input Fundamental requirements knowledge phase currents motor star-connected, third phase current also known, since rotor flux position.
3.3.1 Current sampling
measured phase currents sampled converted converter. correct working depends true measurement these currents.
3.3.2 Rotor flux position
Knowledge rotor flux position core FOC. fact there error this variable rotor flux aligned with d-axis incorrect flux torque components stator current. following diagram shows (a,b,c), (d,q) reference frames, correct position rotor flux, stator current stator voltage space vector that rotates with reference synchronous speed.
Figure Current, voltage rotor flux space vectors rotating reference frame their relationship with a,b,c stationary reference frame
measure rotor flux position different consider synchronous induction motor. synchronous machine rotor speed equal rotor flux speed. Then (rotor flux position) directly measured position sensor integration rotor speed [1]. induction machine rotor speed equal rotor flux speed (there slip speed), then needs particular method calculate basic method current model [1][2][3] which needs equations motor model reference frame.
Field Orientated Control 3-Phase AC-Motors
Conclusion Thanks becomes possible control, directly separately, torque flux machines. Field Orientated Controlled machines thus obtain every machine advantage: instantaneous control separate quantities allowing accurate transient steady state management. addition this advantage, Field Orientated Controlled machines solve mechanical commutation problems inherent with machines. TMS320F240, providing high power highly versatile motor control dedicated peripherals, makes machines obsolete terms power conversion efficiency system reliability, when compared with machines.
regulator
electrical drive based Field Orientated Control needs constants control parameters: torque component reference ISqref flux component reference ISdrefef. classic numerical (Proportional Integral) regulator well suited regulating torque flux feedback desired values able reach constant references, correctly setting both term (Kpi) term (Ki) which respectively responsible error sensibility steady state error. numerical expression regulator follows:
which represented following figure:
yrefk yfbk
Figure Classical Numerical Regulator Structure
According [4], limiting point that during normal operation, during tests, large reference value variations large disturbances occur, resulting saturation overflow regulator variables output. they controlled, this kind non-linearity damages dynamic performance system. solve this problem, solution previous structure correction integral component depicted following diagram:
Field Orientated Control 3-Phase AC-Motors
yrefk yfbk
Kcor
Figure Numerical Regulator with Correction Integral Term
integral term correction algorithm high level language given below: INPUT refk refk >umax THEN umin THEN -ulk
OUTPUT
With umax, umin mean limitations output variable.
Space Vector
3-phase Inverter structure typical 3-phase power inverter shown Figure where voltages applied star-connected motor windings, where continuous inverter input voltage.
Figure Basic scheme 3-phase inverter AC-motor
Field Orientated Control 3-Phase AC-Motors
switches power BJT, GTO, IGBT etc. ON-OFF sequence these devices must respect following conditions: three switches must always three always OFF. upper lower switches same driven with complementary pulsed signals. this vertical conduction possible, providing care taken ensure that there overlap power switch transitions. next paragraph presents technique generating such pulsed signals. Space Vector Pulse Width Modulation (SVPWM) Space Vector supplies machine with desired phase voltages. SVPWM method generating pulsed signals fits above requirements minimizes harmonic contents. Note that harmonic contents determine copper losses machine which account major portion machine losses. Taking into consideration constraints quoted above there eight possible combinations switch commands. These eight switch combinations determine eight phase voltage configurations. diagram below depicts these combinations.
(010
(110
(011) (111) (000)
(011)
(001)
(101)
Figure SVPWM, vectors sectors
vectors divide plan into sectors. Depending sector that voltage reference adjacent vectors chosen. binary representations adjacent basic vectors differ only bit, that only upper transistors switches when switching pattern moves from vector adjacent one. vectors time weighted sample period produce desired output voltage.
Assuming that reference vector Vref sector, have following situation:
Field Orientated Control 3-Phase AC-Motors
(110)
Vref
(100)
Figure Reference vector combination adjacent vectors
Where times during which vectors applied time during which zero vectors applied. When reference voltage (output inverse Park transformation) sample periods known, following system makes possible determine uncertainties Under these constraints locus reference vector inside hexagon whose vertices formed tips eight vectors. generated space vector waveforms symmetrical with respect middle each period [3]. diagram shows waveforms example presented above.
T0/4 T6/2 T6/2 T0/4 T0/4 T6/4 T4/4 T0/4
Figure Pattern SVPWM sector
following diagram shows pattern SVPWM each sector:
Field Orientated Control 3-Phase AC-Motors
(010)
(110)
(011)
(100)
(001)
(101)
Figure Hexagon SVPWM, pattern
conclusion, inputs SVPWM reference vector components (vSr, vSr) outputs times apply each relevant sector limiting vectors. Comparison SV-sinusoidal SVPWM generates minimum harmonic distortion currents winding 3-phase motor. Modulation also provides more efficient supply voltage comparison with sinusoidal modulation methods. fact, with conventional sinusoidal modulation [7][8][9] which sinusoidal signals compared with triangular carrier, know that locus reference vector inside circle with radius modulation shown that length each vectors steady state reference vector magnitude might constant. This fact makes modulation reference vector locus smaller than hexagon described above. This locus narrows itself circle inscribed within hexagon, thus having radius Figure below different reference vector loci presented.
Field Orientated Control 3-Phase AC-Motors
Space Vector OL=2/3VDC OM=1/sqrt(3)VDC ON=1/2VDC
conventional sinusoidal
Figure Locus comparison SV-sinusoidal
Therefore, maximum output voltage based Space Vector theory times large that conventional sinusoidal modulation. This explains why, with SVPWM, have more efficient supply voltage than with sinusoidal method.
Conclusion
This paper dealt with Field Orientated Control three-phase machines. Following description common major drawbacks classic control structures been shown Field Orientated Control overcomes these deficiencies what kind benefits Field Orientated Controlled drives bring. explaining detail each modules necessary this paper presents clear introduction efficient vector control drives. providing high power vector control dedicated peripherals single TMS320F240 chip, giving references necessary software modules, Texas Instruments addresses every start-up requirement allows users Controller rapidly commence development system based vector control with TMS320F240.
Field Orientated Control 3-Phase AC-Motors
References
References
Parasiliti, "Appunti delle lezioni Azionamenti Elettrici: Controllo Vettoriale Orientamento Campo", degli Studi L'Aquila Gabriele, Parasiliti, Tursini, "Digital Field Oriented Control induction motors: implementation experimental results", Universities Power Engineering Conference (UPEC'97) Riccardo Gabriele, "Controllo vettoriale motore asincrono mediante Filtro Kalman Esteso", Tesi Laurea, degli Studi L'Aquila, Anno Accademico 1997-98 J.-P. Favre, "Correction compsante digitaux limitation", EPF- Lausanne Ometto, "Modulation Techniques", degli Studi L'Aquila L.Zhang, Wathanasarn, Hardan, efficient Microprocessor-Based Pulse Width Modulator using Space Vector Modulation Strategy", IEEE 1994 Satoshi Ogasawara, Hirofumi Akagi, Akira Nabae, novel scheme Voltage Source Inverters based Space Vector Theory", Aachen 1989 Joachim Holtz, "Pulsewidth Modulation-A Survey", IEEE 1992 Alberto Pollmann, "Software Pulsewidth Modulation Control ACDrives", IEEE 1986 Transactions industry applications, Vol. IA22,NO.4,July/August 1986
[10] Werner Leonard, "Control Electrical Drives", Completely Revised Enlarged Edition, Springer
Field Orientated Control 3-Phase AC-Motors
Notes
Field Orientated Control 3-Phase AC-Motors
Notes
Field Orientated Control 3-Phase AC-Motors
Notes
Field Orientated Control 3-Phase AC-Motors
Notes
Field Orientated Control 3-Phase AC-Motors
Notes
Field Orientated Control 3-Phase AC-Motors
Notes
Field Orientated Control 3-Phase AC-Motors

Literature Number: BPRA073 Texas Instruments Europe February 1998

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