Sensorless Field Oriented Control (FOC) Induction Motor (ACIM) Using F
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AN1206
Sensorless Field Oriented Control (FOC) Induction Motor (ACIM) Using Field Weakening
Mihai Cheles Microchip Technology Inc. Co-author: Dr.-Ing. Hafedh Sammoud APPCON Technologies SUARL Author:
CONTROL STRATEGY
Sensorless Field Oriented Control
Field oriented control principles applied ACIM based decoupling between current components used magnetizing flux generation torque generation. decoupling allows induction motor controlled simple motor. field oriented control implies translation coordinates from fixed reference stator frame rotating reference rotor frame. This translation makes possible decoupling stator current's components, which responsible magnetizing flux torque generation. decoupling strategy based induction motor's equations related rotating coordinate axis rotor. translate stator fixed frame motor equations rotor rotating frame, position rotor flux needs determined. position rotor determined through measurement estimated using other available parameters such phase currents voltages. term "sensorless" control indicates lack speed measurement sensors. control block diagram field oriented control presented Figure with descriptions each component block. particular, field weakening block motor's mechanical speed input, with output generating reference d-axis current corresponding magnetizing current generation. additional information field oriented control induction motor, refer AN1162 (see "References").
INTRODUCTION
utilization induction motor (ACIM) ranges from consumer automotive applications, with variety power sizes. From multitude possible applications, some require achievement high speed while having high torque value only speeds. applications needing this requirement washing machines consumer applications traction powertrain applications. These requirements impose certain type approach induction motor control, which known "field weakening." This application note describes sensorless field oriented control (FOC) with field weakening induction motor using dsPIC® Digital Signal Controller (DSC), while implementing high performance control with extended speed range. This application note extension AN1162: Sensorless Field Oriented Control (FOC) Induction Motor (ACIM), which contains design details field weakening block. concepts this application note presented with assumption that have previously read familiar with content provided AN1162.
2008 Microchip Technology Inc.
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FIGURE
SENSORLESS ACIM BLOCK DIAGRAM
DS01206A-page 2008 Microchip Technology Inc.
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Iqref
3-Phase Bridge
Idref Field Weakening mech estim
ACIM
Angle Estimation Estimator Speed Estimation
Software Hardware blocks induction motor. 3-Phase Bridge rectifier, inverter, acquisition protection circuitry software blocks (run dsPIC® device). Clarke forward transform block. Park forward inverse transform block. Angle speed estimator block. Proportional integral controller block. Field weakening block. Space vector modulation block.
Hardware
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Field Weakening
Field weakening denotes strategy which motor's speed increased above value maximum achieved constant torque functioning region. constant torque region field oriented control induction motor delimited from field weakening constant power region maximum voltage that provided motor. constant power region, maximum voltage characteristic inverter's output most cases. breakdown torque constant entire range speeds below field weakening region limit, once speed increases above this limit, breakdown torque value will decrease, shown Figure
FIGURE
CHARACTERISTIC INDUCTION MOTOR (THEORETICAL)
Torque, Voltage, Current
Constant Torque
Constant Power Field Weakening
Voltage
Breakdown Torque
Phase Current
Speed (Frequency)
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torque induction motor expressed Equation rated torque motor obtained selecting magnetizing current achieve maximum torque ratio. theory, magnetic saturation taken into consideration, maximum peak torque achieved when magnetizing current (imR) equal torqueproducing component stator current (iSq) steady state condition permitted ranges stator currents. magnetizing current responsible magnetizing flux generation. dependency d-component current expressed Equation
EQUATION
where: torque number poles magnetizing flux torque producing current component rotor inductance mutual inductance
EQUATION
where: rotor time constant magnetizing current magnetizing flux-producing current component
FIGURE
Torque
MAXIMUM TORQUE (THEORETICAL)
saturating iron (ideal) Saturating iron (real)
0,707
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real-world case saturating machine, maximum torque longer obtained same ratio magnetizing current torque command current same range stator currents. magnetizing flux increase nonlinear dependency magnetizing current, which small flux increase requiring greater current needs. Therefore, achieve maximum torque ratio, recommended most current increase torque-producing current component. power limit inverter necessity speed increase achieved delivering lower torque. Field weakening well suited case traction home appliances where high torque value necessary only speeds. When lowering torque field weakening, same concerns keeping high ratio torque considered. same time, considering Equation back electromagnetic force (BEMF) proportional rotor speed. This limits maximum reachable speed once right term equation equal inverter maximum voltage (i.e., left term). BEMF amplitude decrease, achieved lowering magnetizing current, would leave more space speed increase, same time, would lead torque decrease according Equation Figure depicts graphical representation Equation where Umax maximum voltage. Considering components stator voltage, d-q, their relation with respect stator voltage vector expressed Equation modulus).
EQUATION
where: stator voltage magnetizing flux-producing voltage component torque-producing voltage component maximum stator voltage limitation fact limitation component terms, resulting from Equation Referring back control scheme, this limitation confirmed fact that current controllers saturated. Decreasing magnetizing current would unsaturate controllers system limitation presented Figure
EQUATION
BEMF where: stator voltage vector stator current vector stator resistance angular speed stator inductance rotor inductance mutual inductance
2008 Microchip Technology Inc.
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AN1206
FIGURE REPRESENTATION STATOR EQUATION
Inverter output limit Umax
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presented solution uses rotor speed input field weakening block. magnetizing current adjusted speed function that control system limitation described previously avoided. BEMF steady state amplitude value, which depends magnetizing current, must result that right term Equation less than maximum inverter voltage amplitude operating range. This depicted Figure criteria must considered when determining designated steady state feed voltage amplitude supplied from inverter field weakening operation: Having time possibility react load change acceleration demand increasing output voltage this being translated maximum voltage reserve and; Having maximum inverter output voltage minimize motor current resulting high efficiency this being translated minimum voltage reserve According experience, voltage reserve should between fulfill both criteria. current application choice voltage reserve based consideration that application does require high dynamic load change. Since variation speed done slowly (i.e., dynamic), there need additional flux controller. Instead, output field weakening block connected directly current controller. determination magnetizing current function rotor speed achieved with series open loop load experiments. each series experiments, V/Hz ratio modified. experiments consist varying frequency, maximum inverter voltage, d-component current measured (representing magnetizing current steady state). assumption that when motor running under load, there torque produced (except friction bearings, which very small), that steady state, d-current component equal magnetizing current. shown Figure values obtained several side experiments summarized graph representing magnetizing current function frequency.
FIGURE
VOLTAGE RESERVE STATOR EQUATION
Inverter output limit Umax
Voltage reserve
2008 Microchip Technology Inc.
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FIGURE MAGNETIZING CURRENT FUNCTION SPEED (EXPERIMENTAL)
Load Test f(Speed)
6000
5500
Magnitizing Current Normalized
5000
4500
4000
3500
3000
2500
2000 0.00
50.00
100.00
150.00 Frequency Hertz
200.00
250.00
300.00
indicated previously, variation rotor flux with magnetizing current linear, since saturation iron implied. Equation expresses relation between rotor flux, magnetizing current, mutual inductance.
EQUATION
where: stator voltage stator current stator inductance stator resistance angular stator speed
EQUATION
where: magnetizing flux (mutual inductance) magnetizing current determine inductance, assumed that Under load condition, calculated, shown Equation
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2008 Microchip Technology Inc.
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Considering that variations supposed identical, determination variations would sufficient extrapolate results other inductances. Figure shows experimental results, observed that maximal variation approximately measured between inductivity base maximum speed. experimental results obtaining both magnetizing curve stator inductance (LS) variation, presented example Excel file, MagnetizingCurve_FW.xls, which provided software archive (see Appendix "Source Code").
FIGURE
VARIATION INDUCTANCE WITH SPEED (EXPERIMENTAL)
Load Test f(Imr)
0.180
0.170
0.160 Henry
0.150
0.140
0.130
0.120 0.00 50.00 100.00 150.00 Frequency Hertz 200.00 250.00 300.00
2008 Microchip Technology Inc.
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SOFTWARE IMPLEMENTATION
This application note represents enhancement AN1162, Sensorless Field Oriented Control (FOC) Induction Motor (ACIM) (see "References"). enhancement effort consists designing field weakening block adaptation existing variables, which affected field weakening. division term measure granularity samples obtained experimentally from magnetizing curve previously described. reference value magnetizing current between FdWeakParm.qFwCurve[ FdWeakParm.qIndex FdWeakParm.qFwCurve[ FdWeakParm.qIndex MotorEstimParm.qL0FW represents division stator inductance (LS), which results from magnetizing curve determination experiments with double base speed value stator inductance (LS0). order have more accurate results, computed interpolation between consecutive experimental results determination stator inductance variation. interpolation part calculated, shown Example function implementing field weakening functionality, FieldWeakening, defined file, FieldWeakening.c, following performances: Execution time: cycles Clock speed: 7.2-8.5 29.491 Code size: words RAM: words
Programming Functions Variables
field weakening block input, reference mechanical speed output, reference magnetizing current. function called every milliseconds, call frequency being dFwUpdateTime constant defined include file, UserParms.h. magnetizing curve defined lookup table UserParms.h. Field weakening applied when reference speed (output ramp generator) above defined lower limit determined constant torque functioning region. integer array defined initialized with lookup table. calculate reference value magnetizing current imR, interpolation used ensure smooth field variation. every speed reference index access lookup table calculated, shown Example Example qMotorSpeed represents speed reference qFwOnSpeed speed from which field weakening strategy begun. Their difference divided index lookup table.
indicated previous section, mutual inductance must adapted when running field weakening region. adaptation mutual inductance, considering premise that inductance variation identical, follows Equation Figure depicts mutual inductance (L0) variation according motor's speed variation.
EXAMPLE
Index FW-Table FdWeakParm.qIndex (qMotorSpeed FdWeakParm.qFwOnSpeed
EXAMPLE
Interpolation between results from Table FdWeakParm.qIdRef=
EQUATION
MotorEstimParm.qL0Fw
Where measures having index base speed corresponding values.
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2008 Microchip Technology Inc.
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FIGURE ADAPTATION MUTUAL INDUCTANCE FIELD WEAKENING
Speed Time Seconds
qL0FW Normalized Value
15000
10000
5000
Time Seconds others variables used field oriented control that incorporate motor's constants also adapted minimize errors case field weakening. variables are: MotorEstimParm.qInvTr MotorEstimParm.qLsDt MotorEstimParm.qInvPsi MotorEstimParm.qRrInvTr
software functionality initially designed constant power region, which takes into consideration motor parameter's constant; therefore, adaptation function designed consider variation parameter's value with speed increase field weakening region. function implementing adaptation functionality, AdaptEstimParm, defined FieldWeakening.c following performances: Execution time: 1800 cycles Clock speed: 7.2-8.5 29.491 Code size: words RAM: words
experimental results Figure show high stability proper trajectory speed control with field weakening.
2008 Microchip Technology Inc.
DS01206A-page
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FIGURE EXPERIMENTAL RESULTS SENSORLESS ACIM WITH FIELD WEAKENING
Speed Speed Reference Estimated Rotor Speed
Time Seconds
10000 Normalized Value 5000 ld,lq
-5000 Time Seconds Table presents experimental results terms torque-speed efficiency (calculated both inverter motor).
TABLE
EXPERIMENTAL RESULTS TORQUE-SPEED
Torque (N*m) 0.147 0.172 1.15 Mechanical Power Electrical Input Power Efficiency 61.6 65.4 76.6 54.0
Speed (RPM) 9400 8500 6800 1100
CONCLUSION
This application note presents solution implementing field weakening sensorless field oriented control ACIM using Microchip's dsPIC30F dsPIC33F digital signal controllers. developed addendum previously published application note AN1162, which offers solution high-performance, high-speed control induction motor drive.
REFERENCES
AN1162 Sensorless Field Oriented Control (FOC) Induction Motor (ACIM) (DS01162), Microchip Technology Inc., 2008
DS01206A-page
2008 Microchip Technology Inc.
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APPENDIX SOURCE CODE
Software License Agreement
software supplied herewith Microchip Technology Incorporated (the "Company") intended supplied you, Company's customer, solely exclusively with products manufactured Company. software owned Company and/or supplier, protected under applicable copyright laws. rights reserved. violation foregoing restrictions subject user criminal sanctions under applicable laws, well civil liability breach terms conditions this license. THIS SOFTWARE PROVIDED CONDITION. WARRANTIES, WHETHER EXPRESS, IMPLIED STATUTORY, INCLUDING, LIMITED IMPLIED WARRANTIES MERCHANTABILITY FITNESS PARTICULAR PURPOSE APPLY THIS SOFTWARE. COMPANY SHALL NOT, CIRCUMSTANCES, LIABLE SPECIAL, INCIDENTAL CONSEQUENTIAL DAMAGES, REASON WHATSOEVER.
software covered this application note available single WinZip archive file. This archive downloaded from Microchip corporate site www.microchip.com
2008 Microchip Technology Inc.
DS01206A-page
AN1206
NOTES:
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