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ABSTRACT
BALLAL, SIDDHARTH. Flux and Torque Estimation in Direct Torque Controlled (DTC) Induction Motor Drive. (Under the direction of Dr. Srdjan Lukic.) Estimation of flux and torque without any errors is the key to good control of induction motors. The main reasons of inaccuracy, especially at low speeds, are increased sensitivity against mismatch between model and drive parameters, nonlinear behavior of power converter and nonideality in current and voltage sensing. These can cause serious deterioration of estimated values of stator flux and electromagnetic torque, and can lead to drive instability. Techniques used to compensate for the inaccuracy caused due to problems mentioned above are discussed in detail. Solutions suggested in literature for deadtime and inverter nonlinearity compensation has been implemented both in simulation and in hardware, and results are presented. This thesis presents an algorithm for accurate estimation of stator flux and electromagnetic torque in a threephase induction motor drive when current and voltage measurement offset are present. The main feature of this algorithm is its ability to recognize the erroneous sensor and to quantify the offset error in that sensor. This is accomplished by analyzing the first harmonic of the estimated torque and the dc value in stator flux. The proposed algorithm has been implemented in simulation and on hardware. A series of experiments have been performed to study the performance and stability of the algorithm. The results of these experiments have been presented.
© Copyright 2010 by Siddharth Ballal All Rights Reserved
Flux and Torque Estimation in Direct Torque Controlled (DTC) Induction Motor Drive
by Siddharth Ballal
A thesis submitted to the Graduate Faculty of North Carolina State University in partial fulfillment of the requirements for the Degree of Master of Science Electrical Engineering
Raleigh, North Carolina 2010
APPROVED BY:
____________________ Dr. MoYuen Chow
____________________ Dr. Subhashish Bhattacharya
____________________ Dr. Srdjan Lukic Chair of Advisory Committee
BIOGRAPHY
Siddharth Ballal was born on June 01, 1985 in Manipal, Karnataka, India to Geetha and Bharath Ballal. He spent his childhood and did his schooling in Mumbai, Maharashtra. He received his Bachelor of Engineering degree in Electrical and Electronics Engineering in 2006 from Sri Jayachamarajendra College of Engineering, Mysore, Karnataka. He is currently a graduate student at North Carolina State University under the guidance of Dr. Srdjan Lukic.
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ACKNOWLEDGMENTS
My deepest gratitude goes toward all the people who have made this work possible. I have benefited greatly by being a student at the Advanced Transportation Energy Center (ATEC) at North Carolina State University. I would like to thank Dr. Srdjan Lukic, whose advice and extensive knowledge have contributed immensely to the work presented here. Thank you for you guidance and wisdom in the field of electric drive systems. I would like to thank Ewan Pritchard, who constantly gave support and encouragement throughout the course of my studies. I would like to thank Zeljko Pantic, Arvind Govindaraj, Shashank Bodhankar, Edward Van Brunt, Shane Hutchinson, Arun Kadavelugu, Misha Kumar, Vijay Shanmugasundaram and Sumit Dutta. This degree would have been achieved in vain if it were done without your friendships. I would like to thank my family for the love and support you have given me my entire life, and for providing me with the opportunity to study and succeed. I am greatly indebted to all of you. Thank you for your support.
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TABLE OF CONTENTS
LIST OF TABLES ................................................................................................................................ vii LIST OF FIGURES ..............................................................................................................................viii Introduction ...................................................................................................................................... 1 1.1 Background ............................................................................................................................. 1 1.2 Thesis Objective ....................................................................................................................... 1 1.3 Outline .................................................................................................................................... 2 Speed Control of Induction Motors ................................................................................................... 4 2.1 Introduction ............................................................................................................................. 4 2.2 Openloop scalar control .......................................................................................................... 5 2.3 Field oriented control ............................................................................................................... 6 2.3.1 Axis transformation .......................................................................................................... 6 2.3.2 DC motor analogy ............................................................................................................. 7 2.3.3 Principles of stator flux oriented vector control ................................................................ 8 2.4 Direct Torque Control............................................................................................................. 10 2.4.1 Control Strategy of DTC................................................................................................... 13 2.4.2 Simulation of DTC Controller ........................................................................................... 16 Flux and Torque Estimation ............................................................................................................. 20 3.1 Introduction ........................................................................................................................... 20 3.2 Open loop flux estimators ...................................................................................................... 20 3.3 Flux estimation problems ....................................................................................................... 21 3.3.1 Dead time ....................................................................................................................... 22 3.3.2 Stator resistance variation .............................................................................................. 30 3.3.3 Voltage drop in power electronic devices ........................................................................ 32
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3.3.4 Measurement errors in sensors ...................................................................................... 34 Proposed Algorithm for Sensor Offset Identification and Correction ................................................ 37 4.1 Introduction ........................................................................................................................... 37 4.2 Influence of voltage and current sensor dc offset on flux and torque estimation ..................... 37 4.3 Proposed algorithm ............................................................................................................... 42 4.4 Software Simulation .............................................................................................................. 46 4.4.1 Cascaded lowpass filter based flux estimation implementation...................................... 46 4.4.2 Proposed algorithm with VoltsHertz control .................................................................. 48 Experimental Setup ......................................................................................................................... 52 5.1 Introduction ........................................................................................................................... 52 5.2 Load Motor............................................................................................................................ 53 5.3 Azure Controller and Inverter ................................................................................................. 53 5.3.1 CAN Controller ................................................................................................................ 54 5.3.2 ccShell Program .............................................................................................................. 55 5.4 dSPACE DS1104 Controller ..................................................................................................... 55 5.5 Test Motor Inverter................................................................................................................ 58 5.6 Feedback sensing ................................................................................................................... 62 5.7 Torque Transducer ................................................................................................................. 62 5.8 Test Motor and Motor Parameter Estimation......................................................................... 63 Experimental Results ....................................................................................................................... 67 6.1 Implementation of deadtime and inverter nonlinearity compensation .................................. 67 6.2 Implementation of proposed algorithm with openloop VoltsHertz control............................ 71 6.2.1 Experiment 1 .................................................................................................................. 75 6.2.2 Experiment 2 .................................................................................................................. 76
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6.2.3 Experiment 3 .................................................................................................................. 79 Conclusion ...................................................................................................................................... 84 References ...................................................................................................................................... 85
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LIST OF TABLES
Table 21 Optimum voltage switching vector lookup table ............................................................. 16 Table 51 AC55 motor nameplate data ............................................................................................ 53 Table 52 DMOC operating mode based on higher level control inputs ............................................ 54 Table 53 Baldor M3313T (test motor) Nameplate data ................................................................... 64 Table 54 Performance Data at 208V, 60Hz ..................................................................................... 64 Table 55 Estimated Motor Parameters ........................................................................................... 66
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LIST OF FIGURES
Figure 21 Open loop Volts/Hertz speed control with voltagefed inverter ........................................ 5 Figure 22 Axis transformation .......................................................................................................... 6 Figure 23 Vector controlled induction motor .................................................................................... 8 Figure 24 Block diagram of Stator Flux Oriented Control .................................................................. 9 Figure 25 Stator fluxlinkage and stator current space vectors........................................................ 11 Figure 26 Switching voltage space vectors ...................................................................................... 11 Figure 27 Control of Stator Flux ...................................................................................................... 12 Figure 28 Block diagram of a DTC controller ................................................................................... 14 Figure 29 Speed control loop and flux reference generator ............................................................ 14 Figure 210 Simulink block diagram of DTC algorithm ...................................................................... 17 Figure 211 Rotor speed in rpm and electromagnetic torque in Nm ................................................. 17 Figure 212 Stator flux linkage vector. 1) qaxis component of stator flux. 2) daxis component of stator flux. 3) magnitude of stator flux linkage vector. ..................................................................... 18 Figure 213 Stator current at .......................................................................................... 19
Figure 214 Trajectory of stator flux ................................................................................................ 19 Figure 31 Flux Estimator block........................................................................................................ 20 Figure 32 Ideal flux and torque estimation. Open loop V/f control, stator frequency  5Hz ............. 22 Figure 33 Single phase configuration of PWM inverter ................................................................... 22 Figure 34 Time delay between turn OFF and turn ON of two switches on the same inverter leg ..... 23 Figure 35 T1 transition from ON to OFF, (a) ia is positive. (b) ia is negative ...................................... 24 Figure 36 T1 transition from OFF to ON, (a) ia is positive. (b) ia is negative ...................................... 25 Figure 37 Simulation  Simulink model of deadtime compensation implementation ...................... 26 Figure 38 Simulation  block diagram of "V/f to duty" block............................................................ 27 Figure 39 "Deadtime compensator" block ..................................................................................... 27 Figure 310 Stator current with 1 s deadtime; without deadtime compensation .......................... 28 Figure 311 Estimated stator flux and electromagnetic torque with 1 s deadtime; without deadtime compensation ......................................................................................................................... 28 Figure 312 Stator current with 1 s deadtime; with deadtime compensation ............................... 29
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Figure 313 Estimated stator flux and electromagnetic torque with 1 s deadtime; with deadtime compensation ......................................................................................................................... 29 Figure 314 Estimated stator flux and electromagnetic torque; stator resistance variation from 50% to 150% of original value ......................................................................................................... 31 Figure 315 Inverter output characteristics. Dotted line: modeled approximation. (Reproduced from Product datasheet  BSM50GP120, Infineon) .......................................................................... 32 Figure 316 Estimated stator flux and electromagnetic torque when inverter nonlinearities are present ........................................................................................................................................... 33 Figure 317 Stator current when inverter nonlinearities are present................................................ 34 Figure 41 Estimated stator flux when nonzero sensor dc offset is present ..................................... 39 Figure 42 Estimated torque when nonzero sensor dc offset is present. .......................................... 41 Figure 43 Measuring offset identification and advanced flux and torque estimation algorithm ...... 43 Figure 44 Internal structure of ESTIMATOR block ........................................................................... 43 Figure 45 Cascaded lowpass filter for flux estimation .................................................................... 47 Figure 46 Stator flux trajectory and estimated torque using cascaded filters for flux estimation ..... 48 Figure 47 Simulink block diagram of proposed offset correction algorithm ..................................... 49 Figure 48 Simulation results  q and d axis current offset correction terms ..................................... 50 Figure 49 Simulation Results  q and d axis voltage offset correction terms .................................... 50 Figure 410 Simulation Results  Estimated stator flux trajectory and estimated electromagnetic torque ............................................................................................................................................. 51 Figure 411 Simulation results  qaxis and daxis components of stator flux .................................... 51 Figure 51 Dynamometer testbed block diagram ............................................................................ 52 Figure 52 Dynamometer testbed................................................................................................... 53 Figure 53 DMOC with typical connections (Source: DMOC445 and DMOC645 User Manual for Azure Dynamics DMOC Motor Controller) ........................................................................................ 54 Figure 54 Screenshot of the ccShell software ................................................................................. 55 Figure 55 dSPACE DS1104 Controller Card ...................................................................................... 56 Figure 56 Internal blocks of dSPACE DS1104 Controller Card (Source: dSPACE DS1104 Catalog 2010) .............................................................................................................................................. 57 Figure 57 ControlDesk software screenshot with virtual instrumentation ....................................... 58
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Figure 58 Dual IGBT gate driver pin configuration .......................................................................... 59 Figure 59 Test motor inverter with capacitor bank ......................................................................... 59 Figure 510 IGBT Module circuit diagram ......................................................................................... 60 Figure 511 Power Converter block diagram .................................................................................... 60 Figure 512 Circuit diagram of the inverter board ............................................................................ 61 Figure 513 Perphase equivalent circuit of induction motor with respect to the stator ................... 63 Figure 61 Deadtime and inverter nonlinearity compensation ........................................................ 67 Figure 62 Inverter nonlinearity compensation ................................................................................ 67 Figure 63 Stator current with 1 s deadtime (Conditions: no deadtime compensation; no inverter nonlinearity compensation). .............................................................................................. 69 Figure 64 Stator current with 1s deadtime (Conditions: no deadtime compensation; inverter nonlinearity compensation enabled). .............................................................................................. 69 Figure 65 Stator current with 1s deadtime (Conditions: deadtime compensation enabled; no inverter nonlinearity compensation). .............................................................................................. 70 Figure 66 Stator current with 1s deadtime (Conditions: deadtime compensation enabled; inverter nonlinearity compensation enabled). ................................................................................. 70 Figure 67 Simulink diagram  VoltsHertz control; Stator flux and torque estimation using proposed algorithm......................................................................................................................... 71 Figure 68 Simulink diagram  "V/f control" block ............................................................................ 72 Figure 69 Simulink diagram  "offset algorithm" block .................................................................... 73 Figure 610 Simulink diagram  "voltage sensor offset correction" block .......................................... 74 Figure 611 Simulink diagram  "current sensor offset correction" block .......................................... 74 Figure 612 Stator flux trajectory (Conditions: Correction disabled; No software created offset) ..... 75 Figure 613 Estimated torque (Conditions: Correction disabled; No software created offset) .......... 76 Figure 614 Stator flux trajectory (Conditions: Correction enabled; No software created offset) ...... 77 Figure 615 Estimated torque (Conditions: Correction enabled; No software created offset) ........... 77 Figure 616 Current correction terms (Conditions: Correction enabled; No software created offset) ............................................................................................................................................. 78 Figure 617 Voltage correction terms (Conditions: Correction enabled; No software created offset) ............................................................................................................................................. 78
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Figure 618 Stator flux components (Conditions: Correction enabled; No software created offset).. 79 Figure 619 Stator flux trajectory (Conditions: Correction enabled; Software created offset) ........... 80 Figure 620 Estimated torque (Conditions: Correction enabled; Software created offset) ................ 80 Figure 621 Current correction terms (Conditions: Correction enabled; Software created offset) .... 81 Figure 622 Voltage correction terms (Conditions: Correction enabled; Software created offset) .... 81 Figure 623 Stator flux components (Conditions: Correction enabled; Software created offset) ....... 82 Figure 624 Estimated torque and measured torque ....................................................................... 83
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Chapter 1
Introduction
1.1 Background
In the past, dc motors were used in areas where variable speed operation was required, since their flux and torque could be easily controlled by the field and the armature current. Separately excited dc motors have been used extensively due to their fast response and good four quadrant operation with high performance at near zero speeds. However, their complex construction means that dc motors are expensive to maintain. Squirrel cage induction motors are ideal for traction applications. They have a simple and rugged structure, high reliability and robustness and low maintenance. High performance control of induction machines requires fast transient response and good energy efficiency. Torque control in ac machines is achieved in ac motors by controlling the motor currents, just like in dc motors. However, in ac machines, both phase angle and magnitude of the current need to be controlled. Unlike in dc machines, the dynamic system in ac machines is nonlinear and the flux and torque producing currents are not orthogonal. Thus, these quantities need to be decoupled before independent control of torque and flux can be employed. Vector control and direct torque control techniques are employed to accomplish this task. Accurate estimation of stator flux and electromagnetic torque is the key to good control of induction motors. Main reasons of inaccuracy, especially at low speeds, are increased sensitivity against mismatch between model and drive parameters, nonlinear behavior of the power converter and nonideality in current and voltage sensing. These can cause serious deterioration of stator flux linkage and electromagnetic torque estimation, and can lead to instability in drive operation.
1.2 Thesis Objective
The aim of this thesis is to present an algorithm for accurate stator flux and electromagnetic torque estimation in a threephase induction machine when current and voltage measurement offset are present. The main feature of this algorithm is its ability to identify the erroneous sensor and to
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compensate for the error. This is accomplished by analyzing the first harmonic of the estimated torque and the dc value in stator flux. The proposed algorithm is implemented in simulation and on hardware on an openloop VoltsHertz controlled threephase induction motor drive.
1.3 Outline
Chapter 2 introduces concepts of speed control of induction motors. Openloop scalar control, field oriented control and direct torque control (DTC) techniques are discussed. The axis transformation convention throughout this document is also defined in this chapter. An implementation of a DTC algorithm in simulation is presented. In chapter 3, open loop estimation of stator flux and electromagnetic torque and problems associated with estimation are discussed. Factors influencing the accuracy of flux estimation, and hence of the estimated torque, are mentioned. Effect of deadtime and inverter nonlinearity on the estimated flux and torque is shown and compensation techniques are discussed. A deadtime compensation technique is implemented in simulation. Estimation errors in flux and torque due to drift in stator resistance is discussed. Finally, effect of sensor measurement errors on the estimation of flux and torque is introduced. Chapter 4 consists of further discussion of the impact of errors in sensor measurement. An algorithm for identification and correction of erroneous sensor measurement is proposed. The proposed algorithm is implemented in simulation on an openloop scalar controller for a threephase induction motor. A cascaded filter based flux estimation algorithm, suggested in literature, is also implemented in simulation. The laboratory setup is described in chapter 5. All hardware experiments have been performed on this setup. The different components of the dynamometer testbed the test motor and its inverter, the load motor and its controller, the torque transducer and the dSPACE controller are introduced and the setup is described in detail. Motor parameters of the test motor are identified based on nameplate details.
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Experimental results are presented in chapter 6. Results of hardware implementation of compensation algorithms for deadtime and inverter nonlinearity are shown. Three experiments are performed to validate the performance of the proposed measurement offset correction algorithm. In the first experiment, the effect of measurement offset when the correction algorithm is not enabled is observed. In the second experiment, the correction algorithm is enabled and the correction terms for current and voltage measurements are calculated. To confirm that the correction terms computed in the second experiment are correct, additional offset in current and voltage measurement is artificially created and the experiment is repeated with the correction algorithm enabled. The results of all the three experiments are presented.
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Chapter 2
Speed Control of Induction Motors
2.1 Introduction
Induction motors, especially those of squirrel cage type, are the most common source of mechanical power in the industry. The control of ac drives is generally more complex than control of dc drives. This complexity increases substantially if high performances are demanded. The main reason for the complexity is the need for variable frequency power supplies, the complex dynamics of the ac machines and machine parameter variations. A majority of the induction motor drives are powered by high frequency switching PWM inverters. Processing of feedback signals in the presence of harmonics is difficult. Induction motors are controlled in many ways. Scalar control of induction motors is the most popular method used for speed control in low performance drives. Typically, motor speed is openloop controlled, with no speed sensor required. The magnitude and frequency of the fundamental voltage and current supplied to the motor is adjusted to change motor speed. In dc motors, the torque and the flux are decoupled and can be controlled separately. In induction motors, in order to obtain decoupled control of torque and flux producing components of the stator current, both the magnitude and phase of the stator quantities need to be controlled [1]. Also, in squirrel cage induction motors, there is no access to rotor quantities such as rotor currents and fluxes. To overcome these difficulties, high performance vector and direct torque control algorithms have been developed that decouple the stator phase currents using measured stator currents, stator voltages and rotor speed. These algorithms are primarily designed to maintain continuity of the developed torque during transient conditions. In this chapter, three common methods of control of induction motors are discussed. Openloop scalar speed control (constant Volts/Hertz control) is explained in section 2.2. Section 2.3 describes field oriented control (vector control) of induction motors. In section 2.4, the direct torque control (DTC) method is introduced.
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2.2 Openloop scalar control
Scalar control disregards the coupling effect in the machine and adjusts only the magnitude variations of the control variable. In adjustable speed drives, the frequency of the power supply needs to be controlled. Neglecting the voltage drop across the stator resistance, the input voltage has to be proportional to frequency so that the stator flux ( ) remains constant.
Vs
Vo
we
Vo
G
V s*
e*
+ VDC va* vb* vc*
* v a 2V s sin e * v b 2V s sin( e 2 / 3)
Inverter
* we
v 2V s sin( e 2 / 3)
* c
IM
Figure 21 Open loop Volts/Hertz speed control with voltagefed inverter
Figure 21 shows the block diagram of the Volts/Hertz speed control method. Ideally, no speed feedback is needed. The frequency rotor speed is the primary control variable and is almost equal to the . The voltage reference value, , is
, neglecting the small slip frequency
computed by multiplying the frequency command by a gain factor G so that the flux remains constant. For frequencies higher than rated frequency, flux weakening is applies and the reference voltage is saturated at the rated voltage. If the stator resistance and the leakage inductance of the machine are neglected, the flux will also correspond to the airgap flux ( ) of the rotor flux ( ). (2.1) At low speeds, the voltage drop due to stator resistance becomes significant compared to the commanded voltage. This drop can no longer be neglected and needs to be compensated. The boost voltage ( ) is added so that the rated flux and the corresponding full torque be available down to zero speed. The effect of the boost voltage becomes negligible at higher frequencies. The speed reference signal ( ) is integrated to produce the angle signal and the corresponding phase
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voltages are generated using the equations shown in Figure 21. The PWM generator, not shown in the figure, has been merged with the inverter.
2.3 Field oriented control
The invention of vector control in the beginning of 1970s, and the demonstration that the induction motor can be controlled like a separately excited dc motor brought a revolution in the high performance control of ac drives. In this section, the convention used for axis transformation from 3phase to 2phase and viseversa is explained. A DC motor analogy is used to describe the concept of vector control and the concept of stator flux oriented vector control is explained. 2.3.1 Axis transformation Consider a symmetrical threephase induction machine stationary asbscs axes at / angle apart,
as shown in Figure 22. The goal is to transform the threephase stationary reference frame variables into twophase stationary reference frame variables (dsqs) and then transform these to synchronously rotating reference frame (deqe).
qs as
vqss
vas
vdss vbs bs vcs cs
Figure 22 Axis transformation
ds
Assuming the dsqs axes to be oriented at an angle
as shown in Figure 22, the twophase
quantities can be resolved from the asbscs components. In matrix form, this can be represented as
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[ where
]
[
( (
) )
( (
) )] [
]
(2.2)
is added as the zero sequence component, which may or may not be present. is set to zero, the qsaxis aligns with the asaxis. Assuming the three phases are
If the angle
balanced and that the zero sequence component is not present, equation (2.2) (3.1) can be simplified as
equivalent twophase quantities. (
)
(2.3)
Equation (2.3) can also be used to transform the stator currents from threephase to corresponding
The synchronously rotating reference frame is at an angle
with respect to the stationary
reference frame. The transformation from the stationary reference frame to the synchronous reference frame is defined in equation. [ 2.3.2 DC motor analogy In a dc machine, neglecting the armature reaction and the effect of field saturation, the torque developed by the motor can be defined in equation (2.5)(3.1). (2.5) where is the armature current and is the field current. The construction of the dc motor is such ) ] [ ][ ] (2.4)
that the field flux ( ) produced by the field current is perpendicular to the armature flux (
produced by the armature current. These space vectors, which are stationary in space, are decoupled in nature. This means that when the torque is controlled by changing the armature
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current, the field flux ( ) is not affected and a fast torque response is possible. Similarly, changing the field current does not affect the armature flux ( ).
If the induction machine control is considered in a synchronously rotating reference frame, where the sinusoidal voltage and current variables appear as dc quantities in steady state, the dc motor analogy can be extended to the induction motor as well. The daxis current current and the qaxis current is analogous to the armature current is analogous to field of a dc motor.
Therefore, the torque can be expressed as or (2.7) This dc machine like behavior is possible only if is aligned in the direction of the flux and is (2.6)
established perpendicular to it. Figure 23 shows a block diagram of a vector controlled induction motor drive. From the space vector diagram on the right of Figure 23, it can be seen that when is controlled, it affects the qaxis current only, and does not affect the flux . Similarly, when
is controlled, it affects the flux only and does not affect the
component of current. This vector or
field orientation of currents is essential under all operating conditions in a vector controlled drive.
e i qs
e i qs*
e i ds*
Vector Control
Inverter
IM
^ r
i
Figure 23 Vector controlled induction motor
e ds
2.3.3 Principles of stator flux oriented vector control There are essentially two methods of vector control direct field oriented control and indirect field oriented control. The methods are different essentially by the way the field angle is acquired. If the field angle is calculated using terminal voltages and currents or Hall sensors or fluxsensing windings,
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then it is called direct vector control. The field angle can also be obtained using rotor position measurement and partial estimation with only machine parameters. This leads to a class of control schemes called indirect vector control. Figure 24 shows the block diagram of a stator flux oriented control method. Dependence on many machine parameters is greatly reduced when stator flux linkages are used and the electromagnetic torque is calculated using only stator flux linkages and the stator currents. Accurate estimation of stator flux is much easier than that of the rotor flux vector since only stator resistance is needed to calculate the value of the stator flux. However, in stator flux oriented control, the flux and torque producing currents are not naturally decoupled. The flux currents. This means that if the torque is changed by is a function of both and
, it will also change the flux. The coupling
effect needs to be dynamically eliminated by feedforward control. Equation (2.8) defines the term to be added to the output of the flux controller to nullify the coupling effect. It can be seen that the decoupling term is a function of , and .
(2.8)
Flux controller VDC + + + PI Speed controller + + PI
*s
w*m
+ 
PI
v
e ds
e v qs
deqe to abc
Voltage Source Interter
PI
i dq
Decoupling term
i eqs i eds
abc to deqe
s
sds
Stator flux Estimator
i as i bs
VDC
wm
IM
Figure 24 Block diagram of Stator Flux Oriented Control
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Figure 24 shows a block diagram of a stator flux oriented control scheme. The flux and speed PI controllers produce the reference signals for the flux and the torque producing currents respectively in the synchronously rotating reference frame. Figure 24 shows the decoupling term the output of the stator flux controller to produce the reference current controller. The accuracy of the decoupling term is added to
for the daxis current
can be affected by parameter variation.
However, since this term is in a feedback loop, this effect can be neglected [1]. The reference current signals are compared with the measured values of the d and qaxis currents. Two PI regulators produce the required reference voltage signals that are fed in to the inverter.
2.4Direct Torque Control
Direct torque control (DTC) is an alternative approach to control of induction motors in high performance adjustable speed drives (ASDs). It makes use of specific properties of the induction motor for direct selection of consecutive states in the inverter. The selection of optimum inverter switching modes is made to restrict the torque and flux errors within respective torque and flux hysteresis bands, to obtain fast torque response, low inverter switching frequency and lower harmonic losses. The electromagnetic torque in a symmetrical threephase induction machine is proportional to the crossvector product of the stator flux linkage and the stator current in the stationary reference frame [2]. Equation (3.1) shows the expression for electromagnetic torque. ( ) (2.9)
where is the stator flux linkage space vector and is the stator current space vector in the stationary reference frame. The term "P" is the number of pole pairs. From Figure 25, equation (3.9) can be rewritten as    where vector. ( ( )    (2.10)
) is the angle between the stator flux linkage and the stator current space
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qs
is
s
s
s
ds
Figure 25 Stator fluxlinkage and stator current space vectors
For a given rotor speed, if the modulus of the stator flux linkage is kept constant, and the angle
is
changed rapidly, then the electromagnetic torque can be quickly changed. If the actual developed electromagnetic torque is smaller than the reference value, the torque should be increased as fast as possible by using the fastest possible. However, when is equal to the reference, the
rotation is stopped. If the stator fluxlinkage vector is accelerated, positive torque is produced, and when it is decelerated, negative torque is produced. To summarize, the electromagnetic torque can be quickly changed by controlling the stator flux
linkage space vector, which can be changed by using appropriate stator voltages. Thus, direct stator flux and torque control can be achieved. In contrast, in a vector controlled induction motor drive, the stator currents are used as control quantities.
qs
v3 (010)
v2 (110)
v4 (011)
v1 (100)
ds
Sector 1
v5 (001)
v6 (101)
Figure 26 Switching voltage space vectors
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Figure 26 shows the six nonzero active voltage switching space vectors ( , , ... ). These can be written as where ( ( ) )
(2.11)
is the dclink voltage. The two zero space vectors ( , ) where the stator windings are . It follows from the definition of the switching vectors given above that since , is aligned with the real axis (ds axis) of the stationary reference frame.
qs
short circuited,
Sector 3
Sector 2
P2
P1
sref s
Sector 4
P0
Sector 1
ds
sref
2 s
Sector 5
Sector 6
Figure 27 Control of Stator Flux
The goal is to keep the modulus of the stator fluxlinkage vector ( ) within the hysteresis band (denoted by the two circles), whose width is as shown in Figure 27. The locus of the flux
linkage space vector is divided into several sectors, and due to the sixstep inverter, the minimum number of sectors required is six. The six sectors are also shown in Figure 27. It is assumed that initially the stator fluxlinkage space vector is at position , thus is in sector 1. Assuming that the the
stator fluxlinkage space vector is rotating anticlockwise, it follows that since at position
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stator fluxlinkage space vector is at the upper limit (

), it must be reduced. This can be
achieved by applying a suitable switching vector, which is the switching vector , as shown in Figure 27. Thus the stator fluxlinkage space vector will move rapidly from point be seen that point is in sector 2. It can be seen that at point to , and it can
the stator fluxlinkage space
vector is again at the upper limit. On the other hand, it should be noted that if the stator fluxlinkage space vector moves in the clockwise direction from point , then the switching vector would
have been selected, since this would ensure the required rotation and also the required flux decrease. Since at point , the stator fluxlinkage space vector again reaches the upper limit, it has to be reduced when it is rotated in the anticlockwise direction. For this purpose, switching vector has to be selected, and then moves from point to as shown in Figure 27, which is also in a quick anticlockwise rotation is
sector 2. It should be noted that if, for example, at point . On the other hand, if at point
required, then it can be seen that the quickest rotation is achieved by applying the switching vector the rotation of the stator fluxlinkage space vector has to be stopped, then a zero switching vector has to be applied, so either or can be applied. Stopping the rotation of the stator fluxlinkage space vector corresponds to the case when the electromagnetic torque does not need to be changed (reference value of electromagnetic torque is equal to its actual value). When the electromagnetic torque has to be changed (in the clockwise or anticlockwise direction), the stator fluxlinkage space vector has to be rotated in the appropriate direction. 2.4.1 Control Strategy of DTC The block diagram for direct torque control is shown in Figure 28. The speed control loop and the flux reference generator as a function of speed are shown in Figure 29. The speed controller utilizes a linear speed regulator producing the reference value . Linear speed regulators are typically of
proportionalintegral (PI) type. The flux reference is computed as a function of speed. Rated stator flux ( ) is demanded for speeds less than the rated speed ( ). At speeds higher than
the rated speed, flux weakening is applied.
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* s
s
+ Flux Hysteresis +
VDC
H
Vector Selection Table Voltage Source Interter
Te

T *e
Torque Hysteresis
H Te
Sector Detection
s qs
T
e
s ds
i as i bs
V DC
s
Torque and Flux Estimator
IM
Figure 28 Block diagram of a DTC controller
The command stator flux linkage ( ) and electromagnetic torque (
) are compared to their
respective estimated values, and the errors are processed through hysteresisband controllers, as shown. The flux loop controller has two levels of digital output according to the following relations: {            
(2.12)
w m
Speed control scheme
T *e
wm
Flux control scheme
* s
Figure 29 Speed control loop and flux reference generator
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The torque loop has three levels of digital output, which have the following relations:
{
(2.13)
The feedback stator flux and electromagnetic torque are calculated from the machine terminal voltages and currents. The dc link voltage is measured and the machine terminal voltages are recreated from the switching pulses generated by the vector selector block. The sector number ( ) is calculated to identify the sector in which the stator flux linkage space vector lies. The voltage vector table block receives the input signals , and ( ) from the flux controller, the torque
controller and the sector detector blocks respectively. Appropriate control voltage vector (switching states) for the inverter are computed by a lookup table as shown in Table 21. Neglecting the effect of stator resistance of the machine, an incremental change in the stator flux linkage space vector can be written as: (2.14)
It can be seen that the stator flux linkage space vector will move fast if nonzero switching vectors are applied. For a zero switching vector, it will almost stop (it will move very slowly due to the small ohmic voltage drop). For a sixpulse VSI, the stator flux linkage moves along a hexagonal path with constant linear speed, due to the six switching vectors. In the DTC drive, switching vectors are selected on the basis of keeping the stator flux linking errors within the required tolerance band, and keeping the torque error in the hysteresis band. It is assumed that the widths of the two hysteresis bands are and respectively. If the flux vector lies in the , and , , and sector, then its magnitude can be increased by using the space vectors , stator flux linkage can be decreased by selecting
. The magnitude of the
. The selected voltage vectors
will affect the electromagnetic torque as well. In general, if an increase in torque is required, then the torque is controlled by applying voltage vectors that advance the stator flux linkage space vector in the direction of rotation. If a decrease in torque is required, voltage vectors are applied which oppose the direction of torque. The speed of the stator flux linkage space vector is zero if a zero switching vector is selected, and it is possible to change this speed by changing the output ratio
15
between the zero and nonzero vectors. It is important to note that the duration of the zero states has a direct impact on the electromagnetic torque oscillations [2].
Table 21 Optimum voltage switching vector lookup table
( ) 1 1 0 1 1 0 0 1
( )
( )
( )
( )
( )
In a DTC induction motor drive, the stator flux linkage components need to be estimated due to two reasons. First, these components are required in the optimum switching vector selection table described in this section. Secondly, they are also required for the estimation of electromagnetic torque. Stator flux estimation is discussed in more detail in Chapter 3. 2.4.2 Simulation of DTC Controller A direct torque control algorithm was implemented in simulation based on the ideas discussed above. The software package Matlab/ Simulink® was used to implement the proposed algorithm for a 3phase induction motor model. The "SimPowerSystems" toolbox available in Simulink was used to model the power electronics components. Figure 210 shows the Simulink® implementation of the DTC algorithm. A fixed time step size of 100 s is used for simulation. A reference speed command of 150 rpm is used. The load torque demanded is 0 Nm (no load condition). The "induction motor" block has the induction motor model. The motor parameters used for this simulation are the same as that for the motor used to perform the hardware experiment. The "induction motor" block also contains the block for stator flux and electromagnetic torque estimation. The d and qaxis of the estimator stator flux is fed into the "sector determinator" block. This block calculates the sector in which the stator flux is located.
16
Continuous powergui sector determinator
Psi_qs m Psi_ds
Discrete PI Controller Speed ref psisn PI
sector K
Torque error Sign=1 > 1  sign Sign=1 > 0 Torque error Torque error Flux error Flux error Sign=1 > 1  sign Sign=1 > 0
dTe new vector sel. vect
ua ub uc
a b c
psi_qs psi_ds speed Torque psi Is_a
K
60 speed
Flux reference
dpsi
SVPWM Inverter
Induction M otor
Vector selector
Figure 210 Simulink block diagram of DTC algorithm
200 150
wm (rpm)
100 50 0
0
0.5
1
1.5
2
2.5 time (s)
3
3.5
4
4.5
5
6 4
T (Nm)
2 0 2
e
0
0.5
1
1.5
2
2.5 time (s)
3
3.5
4
4.5
5
Figure 211 Rotor speed in rpm and electromagnetic torque in Nm
The speed reference is compared with the speed feedback signal to produce a speed error. This quantity is processed through a PI regulator to produce the reference signal for the electromagnetic torque. This reference signal is compared with the estimated torque and processed though a torque hysteresis controller. Flux error is computed by comparing the stator flux reference signal with the
17
estimated value of the stator flux. This error signal is processed by the flux hysteresis controller. The outputs of the two hysteresis controllers along with the sector information are fed in to the "vector selector" block. This block has the lookup table described in Table 21. The output of the "vector selector" block is synthesized by the SVPWM inverter block to produce the voltage signals to be fed in to the motor.
1
s qs (Wb)
0.5 0 0.5 1 0 0.5 1 1.5 2 2.5 time (s) 3 3.5 4 4.5 5
1
s ds (Wb)
0.5 0 0.5 1 0 0.5 1 1.5 2 2.5 time (s) 3 3.5 4 4.5 5
0.8 0.6
s (Wb)
0.4 0.2 0 0 0.5 1 1.5 2 2.5 time (s) 3 3.5 4 4.5 5
Figure 212 Stator flux linkage vector. 1) qaxis component of stator flux. 2) daxis component of stator flux. 3) magnitude of stator flux linkage vector.
Figure 211 shows a plot of the rotor speed and the developed electromagnetic torque. Figure 212 shows the plot of the stator flux linkage vector as a function of time. The first subplot shows the qaxis component of the stator flux in the stationary reference frame. The second subplot shows the daxis component of the stator flux. The magnitude of the stator flux is plotted in the third subplot. It can be seen that the magnitude of the stator flux remains constant
18
80
60
40
20
Is (A)
0
20
40
60
80
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
time (s)
Figure 213 Stator current at
1 0.8 0.6
qaxis component of stator flux
0.4 0.2 0 0.2 0.4 0.6 0.8 1 1
0.8
0.6
0.4
0.2
0
0.2
0.4
0.6
0.8
1
daxis component of stator flux
Figure 214 Trajectory of stator flux
Figure 213 shows a plot of the stator current and Figure 214 shows the trajectory of the stator flux in the stationary reference frame. The daxis component of the stator flux in the stationary reference frame is plotted on the xaxis, and the qaxis component is plotted on the yaxis.
19
Chapter 3
Flux and Torque Estimation
3.1 Introduction
In this chapter, the stator flux and torque equations will be derived and formulated in the reference frame fixed to the statorflux linkage space vector. The open loop flux estimator is explained in section 3.2. Problems associated with using the open loop estimator are discussed in section 3.3. Each of the issues causing errors in flux estimation has been explained in detail.
3.2 Open loop flux estimators
The stator flux space vector is obtained by the integration of the difference of the terminal voltage and the stator ohmic voltage drop. ( (3.1) ) is the stator resistance. Figure 31 shows a
Here, denotes the statorflux space vector and
block diagram description of the flux estimator. The flux error is calculated from the difference of the reference value of the statorflux and the estimated value. The flux error acts as the input to the hysteresis controller.
Flux Estimator
Rs
is vs
*s
(vs is Rs )
X
s *s
s
Figure 31 Flux Estimator block
The direct and quadrature axis components of the stator flux vector in the stator reference frame can be written as
20
( ( where , and .
) ) (3.2)
The values of the direct and quadrature axis of the stator voltages and currents in (3.2) can be obtained from the corresponding 3phase quantities as follows:
(
)
(
)
(3.3)
(
)
(
)
(3.4)
The voltage and the currents are assumed to be balanced. Hence the zero sequence components do not exist. The angle of the stator fluxlinkage vector can be obtained from the dq axis as follows ( The electromagnetic torque is given by, ( where P is the number of poles. ) (3.6) ). (3.5)
3.3 Flux estimation problems
It should be noted that the accuracy of the estimated flux vector depends on the accuracy of the measured voltages and currents. The most important reasons that can cause incorrect flux estimation can be enumerated as follows: 1. Time delay (deadtime) between switching OFF of one device and switching ON of the other device on the same inverter leg. 2. Nonlinear characteristics of the PWM inverter which cause differences between the reference voltage and the output of the inverter. 3. Discrepancy between motor and model parameters caused by parameter thermal drift. 4. Inaccuracy (offset and gain) in measurement of voltage and current.
21
2
0.5
Estimated Electromagnetic Torque (Nm)
1.5 1 0.5 0 0.5 1 1.5 2
qaxis component of stator flux (Wb)
1.5 1 0.5 0 0.5 1 1.5 2 2
0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0
4
4.2
4.4
4.6
4.8
daxis component of stator flux (Wb)
time (s)
Figure 32 Ideal flux and torque estimation. Open loop V/f control, stator frequency  5Hz
Figure 32 shows a plot of the estimated stator flux and electromagnetic torque at no load. The effect of each of these issues mentioned above has been discussed in detail in this section. 3.3.1 Dead time Due to definite turnoff and turnon times of the switching devices in PWM inverters, it is necessary to insert a time delay between the switching OFF of a device and the switching ON of the other device on the same inverter leg. Figure 33 shows one phase of a PWM inverter
gate
T1
D1 VDC T2
ia
D2
gate
PWM Generator
Figure 33 Single phase configuration of PWM inverter
22
Figure 34 shows the time delay (tdead) between the switches T1 and T2. . TON is the time for which the switch T1 is ON. TSW is the switching period. At time t1, T2 transitions from ON to OFF. The turning ON of T1 is delayed by time t dead. This prevents the short circuit across both the switches of the inverter leg and the input dc voltage source. The introduction of the time delay between switching leads to reduced and distorted voltage at the output of the inverter. To examine the effect of deadtime on the output voltage, switching waveforms on one leg of the inverter are examined. The current is positive in the direction of the load. The IGBTs T1 and T2
conduct when they are ON. During the deadtime period, when both T1 and T2 are OFF, either the reverse recovery diode D1 or D2 will conduct depending on the direction of .
Ideal switching
T1 T2
Switching with deadtime
T1 T2
t2 tdead TON Tsw
t1
Figure 34 Time delay between turn OFF and turn ON of two switches on the same inverter leg
Depending on the direction of the switching transition and the sign of the current are possible. Each of the possibilities is discussed below. The current
, four conditions
is positive, T1 transitions from ON to OFF, T2 transitions from OFF to ON:
During the deadtime period, D2 conducts and D1 blocks the flow of current. Thus, this
23
condition results in the correct voltage being applied to the motor terminals. Figure 35(a) shows the output voltage waveform during the transition. The current is negative, T1 transitions from ON to OFF, T2 transitions from OFF to ON:
During the deadtime period, D1 continues to conduct and D2 blocks the flow of current. Thus, this condition results in a gain in the voltage being applied to the motor terminals. Figure 35(b) shows the output voltage waveform during the transition. The current is positive, T1 transitions from OFF to ON, T2 transitions from ON to OFF:
During the deadtime period, D2 continues to conduct and D1 blocks the flow of current. Thus, this condition results in a loss of voltage being applied to the motor terminals. Figure 36(a) shows the output voltage waveform during the transition. The current is negative, T1 transitions from OFF to ON, T2 transitions from ON to OFF:
During the deadtime period, D1 continues to conduct and D2 blocks the flow of current. Thus, this condition results in the correct voltage being applied to the motor terminals. Figure 36(b) shows the output voltage waveform during the transition.
T1 T2
T1 T2
Van
T1 conducts
Van
T1 conducts
D2 conducts tdead Tsw/2
D1 conducts tdead Tsw/2
(a) ia > 0
(b) ia < 0
Figure 35 T1 transition from ON to OFF, (a) ia is positive. (b) ia is negative
24
In each switching cycle, T1 transitions from OFF to ON (T2 from ON to OFF) once and from ON to OFF (T2 from OFF to ON) once. Due to the distortions discussed above, the output voltage of the inverter is not equal to the desired reference voltage. In order to overcome the effect of deadtime, various approaches have been suggested. The compensation techniques can be broadly classified into two categories. In the first category, the voltage error is averaged over an entire cycle and in the second category, the voltage error is evaluated within the PWM pattern. The methods based on averaging theory look to modify the reference voltage by adding the average value of the voltage lost/gained due to the deadtime effect [35].
T1 T2
T1 T2
Van
T2 conducts
Van
T2 conducts
D2 conducts tdead Tsw/2
D1 conducts tdead Tsw/2
(a) ia > 0
(b) ia < 0
Figure 36 T1 transition from OFF to ON, (a) ia is positive. (b) ia is negative
A pulse based deadtime compensation technique that adjusts the symmetric PWM pulses to correct for the voltage distortion has been proposed in [6]. This compensator compensates for the pulse errors on a pulse by pulse basis, without significantly affecting the magnitude and phase of the terminal voltages. A new low cost online deadtime compensation technique based on back calculation of current phase angle is presented in [4]. This compensator has been implemented for an openloop V/f motor drive and it does not need any hardware modification to the PWM inverter. A linear polarity based compensation method presented in [7] proposes to minimize the voltage
25
distortion at the zero crossing regions. This solution, however, requires accurate detection of current. In [8], the analysis of the zero current clamping phenomena is discussed and the compensation method to eliminate zero current clamping is proposed. The PWM strategy in [9] presents a solution to the zero current clamping problems, but it requires extra hardware and a special PWM pattern in the neighborhood of zero crossing current. This PWM strategy restricts the number of switchings in the phase switches which convey the quasizero current to a small value. This increases the current ripple when the current is nearly zero. The compensation technique presented in [6] was implemented both in simulation and in hardware. Experimental results will be discussed in section 6.1. The simulation results of the implementation are presented here. Figure 37 shows the Simulink model of the implemented algorithm on an openloop VoltsHertz controlled induction motor drive. A fixed step size of 100 s was used for simulation. The parameters for the induction motor used are the same as the actual motor on which hardware implementation is done. The motor was excited by a voltage with a stator frequency of
5Hz and amplitude corresponding to the rated V/f ratio. The amplitude of the input voltage was compensated for the drop in voltage due to the stator resistance. This effect is more prominent at low speeds when the magnitudes of the two voltages are comparable. The machine is operated at noload conditions. The effects of the nonlinear behavior of the inverter have not been considered.
Continuous powe rgui
14.5 Io 5 fs
KRs KGain
f Vm Vabc
Krpm
<Rotor speed (wm)>
rad/s to rpm Tm
100 Vdc1
Vdc duty_a_b_c Iabc
Subsystem4
In1 Out1 Vdc+ Vdcabc Vdc+ VdcA B C
Tm A B C m In1
is_a
is_a
is_abc
V/f to duty
Vdc Memory
Subsystem1
Asynchronous Machine SI Units
Subsystem
Figure 37 Simulation  Simulink model of deadtime compensation implementation
26
Figure 38 shows the "V/f to duty" block from Figure 37. The reference the dc link voltage
value is normalized by
and three sinusoidal signals phase shifted by 120o at the stator frequency is
generated. These act as duty ratios for the gate signals of the PWM inverter. The maximum and minimum values of the three duty signals (a, b and c) are limited to 95% and 5%. These signals are fed to the deadtime compensator block, shown in Figure 39, along with the measured stator currents and the value of the deadtime introduced in the input to the PWM inverter.
3 Vdc 1 Vm 2 f Divide
f wt
u(1)*cos(u(2))+0.5 a u(1)*cos(u(2)2*pi/3)+0.5 b u(1)*cos(u(2)+2*pi/3)+0.5 c c limit 4 Iabc b limit a limit
a a_corr b
Subsystem
c
b_corr
1 duty_a_b_c
Iabc c_corr
0.01 deadtime
deadtime
deadtime compensator
Figure 38 Simulation  block diagram of "V/f to duty" block
Figure 39 "Deadtime compensator" block
27
The ideal pulse ONtime is modified based on the sign of the current though that phase. If the phase current , then the compensation algorithm adds the deadtime to the ideal ONtime. The
corrected pulse is processed through the dead time generator. The resulting pulse position not symmetric and is shifted by onehalf the deadtime. If the phase current compensation algorithm subtracts the deadtime to the ideal ONtime. , then the
15
10
5
Current (A)
0
5
10
15
4
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
5
time (s)
Figure 310 Stator current with 1 s deadtime; without deadtime compensation
1 5
qaxis component of stator flux (Wb)
0.8 0.6 0.4 0.2 0 0.2 0.4 0.6 0.8 1 1
Estimated Electromagnetic Torque (Nm)
1
deadtime ideal
4 3 2 1 0 1 2 3 4 5
0.5
0
0.5
4
4.2
4.4
4.6
4.8
5
daxis component of stator flux (Wb)
time (s)
Figure 311 Estimated stator flux and electromagnetic torque with 1 s deadtime; without deadtime compensation
Figure 310 shows the effect of deadtime on the stator current. The stator current waveform is distorted. Figure 311 shows a plot of the estimated stator flux and electromagnetic torque with an
28
uncompensated deadtime of 1
. In the estimated stator flux trajectory plot, the dotted circle
represents the estimated trajectory of the flux under ideal conditions. The solid circle represents the estimated flux trajectory when a time delay between switching is present, and has not been compensated for.
15
10
5
Current (A)
0
5
10
15
20
4
4.1
4.2
4.3
4.4
4.5 4.6 time (s)
4.7
4.8
4.9
5
Figure 312 Stator current with 1 s deadtime; with deadtime compensation
1 5
qaxis component of stator flux (Wb)
0.8 0.6 0.4 0.2 0 0.2 0.4 0.6 0.8 1 1
Estimated Electromagnetic Torque (Nm)
1
deadtime ideal
4 3 2 1 0 1 2 3 4 5
0.5
0
0.5
4
4.2
4.4
4.6
4.8
5
daxis component of stator flux (Wb)
time (s)
Figure 313 Estimated stator flux and electromagnetic torque with 1 s deadtime; with deadtime compensation
Figure 312 shows the waveform of the stator current with the deadtime compensation algorithm operational. We see that the current waveform is sinusoidal, without any distortions. Also, deadtime compensation makes sure that the correct voltage, equal to the reference voltage, is applied to
29
the motor. Thus, the magnitude of the stator current is higher when correct gate signals are applied. Figure 313 shows the plot of the estimated stator flux trajectory and the estimated electromagnetic torque when the deadtime compensation algorithm is operational. It can be seen that the estimated flux trajectory and the ideal estimated flux trajectory are very close to each other. Also, the pulsation in the estimated electromagnetic torque is substantially lower. 3.3.2 Stator resistance variation The primary reason for the misalignment of the estimated stator resistance with its real value is thermal drift of motor parameters. Load dependent variations of the winding temperature may result in the stator resistance changing from 0.5 to 1.5 times the modeled value. The effect of using an incorrect value of stator resistance for flux estimation has been discussed by several scholars [10]. This effect is more prominent at low speeds [11, 12]. Several methods to estimate the variation in stator resistance with temperature have been presented based on state observers, PI and fuzzy controllers [13, 14]. For accurate flux estimation, the estimated value of stator resistance should be continuously adapted for temperature changes. A decrease in the stator resistance of the motor leads to larger currents in the stator windings for the same input voltages. This results in increased flux and electromagnetic torque generation in the motor. Let the value of the stator resistance decrease by to ( ). If the flux and
electromagnetic torque references do not change, this will result in an increase in the stator current by . Thus (3.1) can now be rewritten as ( (( ((( ( ) ) ( ( )) ( )( ) )) )) (3.7)
If the flux estimator uses the constant value of the stator resistance, the equation for estimated flux can be written as ( (( ( ) ( )) ))
(3.8)
where represents the estimated flux. The difference between the actual stator flux in the motor and the estimated stator flux gives the error in estimation as shown in (3.9).
30
(
)
(3.9) . A decrease in the stator
The estimated value of the flux is smaller than the actual value by
resistance results in a positive stator flux error. Since the electromagnetic torque is calculated using (3.6), the estimated value of the electromagnetic torque will also be lower than the actual value. Open loop flux VoltsHertz control algorithm was implemented and stator flux and torque were estimated. Six different values of stator resistance were used , , , and .
The value of the stator resistance used for estimating the stator flux and the electromagnetic torque was for all the cases. Figure 314 shows a plot of estimated stator flux and electromagnetic
torque for each case. It can be seen that there is offset in the estimated stator flux, and there is significant oscillations in the estimated torque. The oscillations are higher when the value of decreases from its nominal value.
2 1.5 1 0.5 0 0.5 1 1.5 2 2
30
Estimated Electromagnetic Torque (Nm)
0.50 Rs 0.75 Rs 20 1.00 Rs 1.25 Rs 10 1.50 Rs
qaxis component of stator flux (Wb)
0
10
20
1
0
1
2
30
5
5.2
5.4
5.6
5.8
6
daxis component of stator flux (Wb)
time (s)
Figure 314 Estimated stator flux and electromagnetic torque; stator resistance variation from 50% to 150% of original value
When a closed loop flux controller is used, in a vector control or direct torque control (DTC) algorithm, the offset in stator flux estimation will produce an error signal even when the real value of the stator flux is equal to the reference value. This error signal will cause the controller to increase (or decrease) the input voltage to the motor to minimize the error. This would lead to an increase (decrease) in the motor currents, which would lead to an even smaller (larger) estimation
31
of the flux and the electromagnetic torque. This positive feedback can lead to an unstable system leading to a runoff condition. 3.3.3 Voltage drop in power electronic devices At low speeds, the voltage distortions caused by the nonlinear behavior of the PWM inverter become significant [15]. This is due to the forward voltage drop of the power devices when they conduct. This can be modeled by an average threshold voltage resistance as marked by the dotted line in Figure 315.
100 90 80 70 60 50 40 30 20 10 0 1 vth 2 VCE [V] 3 4 5
and an average differential
25oC
IC [A]
rd
125oC
Figure 315 Inverter output characteristics. Dotted line: modeled approximation. (Reproduced from Product datasheet BSM50GP120, Infineon)
The differential resistance can be viewed as a series quantity that adds to the stator resistance. The effect of uncompensated differential resistance on the estimated flux and electromagnetic torque is the same as that when an increase in the stator resistance is not compensated.
The effect of the threshold voltage, however, is nonlinear and requires a study of the inverter model. Depending on the switching state of the inverter, the stator phase currents will flow through an active device or through a reverse recovery diode. The direction of the phase currents does not change in a larger interval of onesixth of a fundamental cycle. The effect of the threshold voltages does not change as the switching states change. The inverter always introduces a voltage component of identical magnitude ( ) to all the three phases. The sign of the voltage component
is determined by the direction of the phase currents. The voltage threshold vector can be defined as ( ) ( ) ( ) (3.10)
32
where
(
). Equation (3.10) can be rewritten as () (3.11)
where () ( ( ) ( ) ( )) (3.12)
is the sector indicator. The sector indicator defines the 60 o sector where is located. The value of the stator voltage estimated from the dc bus voltage and the PWM switching signals can now be modified as ( ) (3.13)
The term represents the actual voltage at the terminals of the motor. Figure 316 shows a plot of the estimated stator flux trajectory and the estimated electromagnetic torque when inverter nonlinearities are present. It can be seen that the estimated flux trajectory is lower than the ideal trajectory. Figure 317 shows the stator current when inverter nonlinearities are present and have not been compensated. Compensation of inverter nonlinearity based on the description above is discussed in section 6.1.
1
2
qaxis component of stator flux (Wb)
0.8 0.6 0.4 0.2 0 0.2 0.4 0.6 0.8 1 1
Estimated Electromagnetic Torque (Nm)
1
ideal nonlinear
1.5 1 0.5 0 0.5 1 1.5 2
0.5
0
0.5
4
4.2
4.4
4.6
4.8
5
daxis component of stator flux (Wb)
time (s)
Figure 316 Estimated stator flux and electromagnetic torque when inverter nonlinearities are present
33
20 15 10 5 0 5 10 15 20
current (A)
4
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
5
time (s)
Figure 317 Stator current when inverter nonlinearities are present
3.3.4 Measurement errors in sensors Switching frequencies of PWM inverters today are much greater than the electric time constant of the motor. Thus, it is possible to measure the dc link voltage and reconstruct the phase voltages from the voltage reference signal available inside the digital controller. This voids the need to measure each of the phase voltages separately. The result of measuring the dc link voltage instead of the phase voltages means that the nonlinear behavior of the inverter has to be modeled and accounted for. This effect is more prominent at low speeds, where the inverter output voltage is low. The following problems can be associated with measurement of the stator currents and voltages: 1. Uncompensated measuring offset 2. Unequal sensor gains 3. Quantization noise introduced by nonideal A/D converter 4. High frequency harmonics in the measured signal these are the consequence of discrete inverter output voltage 5. Phase lagging introduced by measuring low pass filter
34
The first two points predominantly describe the sensor characteristics in an electric drive control structure [16]. Various solutions have been suggested in literature to eliminate this influence. The most common approaches include feedforward offset correction and calibration [2]. The sensors are calibrated every time the drive is started. For this purpose, during the calibration stage (prior to starting up the drive), average offset values of voltages and currents can be obtained by taking hundreds of readings. During normal operation of the drive, these average values are then subtracted from the measured values. However, sensor or ambient warmup during drive operation causes a thermal drift in sensor output, which causes sensor output values to be slightly different from the values stored in memory during the calibration stage. Use of a low pass filter application with adaptive time constant is suggested instead of an ideal integrator for stator flux estimation [17]. Using this approach, the authors were able to achieve 30 second long torque control for 0.005 p.u. relative stator frequency. Shin et al. in [18] propose using a programmable low pass filter with phase compensation. The phase compensation angle is adjusted to give right angle between the estimated stator flux and the electromotive forces. Bose and Patel in [19] suggest the replacement of the integrator with a software programmable cascade of low pass filters. They reported two problems increased computational requirements and low frequency instability (below 0.5 Hz). In [20], Hu and Wu present three algorithms for flux estimation in high performance drives. The idea is based on adaptively introducing correction signals. The differences between algorithms are the methods used to calculate the correction signals. In the first algorithm, a modified integrator with a saturable feedback is used. This requires additional processing of the estimator output. The second algorithm computes the correction signal in the synchronously rotating reference frame. In the third method, the correction signal is applied with the intention to correct the angle between the estimated flux and the stator electromotive forces to 90o for appropriately estimated stator flux vector. One widely accepted solution for the flux estimation problem is given in [21] where the ideal integrator is replaced a low pass filter. At the same time, flux reference is included in the calculation. That way, the estimator output is made to converge to the flux reference as the stator frequency
35
decreases. Multimotor speed regulation in 1:100 speed range with an accuracy in speed regulation better than 0.1% have been reported. A comprehensive method directed towards solving the problems of flux estimation considering all the main sources of error the effect of offset error, scaling error, parameter mismatch and inverter nonlinearity is discussed in [22] and [23]. The offset compensation term is calculated by measuring the flux trajectory dislocation from the origin during the period of stator flux signal. The switches are modeled and the output voltage loss due to the conducting switches is compensated. Realtime identification of stator resistance is employed and error due to deadtime is compensated. As a consequence, an ideal integrator could be used for flux estimation leading to a significantly wider regulation bandwidth. Drive operation at 0.0003 p.u. relative stator frequency, drive starting after a long standstill period, and speed reverse operation have been reported. In [24], the impact of current measurement error is analyzed on the characteristics of current regulated indirect vector controlled drive. Oscillation in motor torque caused due to offset and scaling error is discussed and feed forward compensation method based on spectral analysis of measured speed is suggested. The explained method is able to reduce the amplitude of the first and second harmonic speed oscillations to approximately onethird of the uncompensated value. A detailed description of the influence of measurement offset in voltage and current sensors on the estimation of stator flux and electromagnetic torque is presented in Chapter 4.
36
Chapter 4
Proposed Algorithm for Sensor Offset Identification and Correction
4.1 Introduction
In this chapter, a new flux and torque estimation algorithm is presented. In section 4.2, the influence of voltage and current sensor dc offset on stator flux and electromagnetic torque estimation is explained. In section 4.2, an algorithm intended for high precision flux and torque estimation in drives where the current and/or voltage sensors have unknown offset error is introduced. The main characteristic of this algorithm is its ability to recognize the sensor(s) that introduces the error and to estimate the error. The algorithm is able to compensate the offset error at its source. Thus, all estimation/compensation blocks which need the stator currents and voltages as inputs will have access to errorfree quantities.
4.2 Influence of voltage and current sensor dc offset on flux and torque estimation
Equations (3.1) and (3.2) can be used to estimate the value of stator flux as follows: The terms , and ( ( ( ) ) ) (4.1) (4.2)
denote the estimated values of the stator flux. The "^" sign above the and
and the terms are used to denote measured values of voltages and currents. Further,
represent the estimated value of the stator flux vector before time t=0, when the estimation started. From (4.1) and (4.2), it appears that the open loop flux estimator, also called the "ideal integrator", imposes very low calculation requirements. Pure integration also permits highest estimation bandwidth (from standstill to maximum rotor speed) which could be very useful for servo
37
applications. However, implementation of an integrator for motor flux estimation is quite complicated. A pure integrator will accumulate dc drift and has initial value problems. Any discrepancy between model parameter Rs and the motor stator resistance directly influences the value of the estimated flux. The lower limit of the basic openloop flux estimation is reached when the stator frequency is around 35Hz. When currents and/or voltages sensors introduce offsets ( , , , ), the relation between , , )
the measured quantities ( , , , ) and the real (actual) measured quantities ( , can be described as: ( ( ) ) ( ( ) ) } ( ) } ( )
(4.3)
(4.4)
Since the three phases of the input voltage and current are assumed to be symmetric, the "c" component of the phase current is not measured. It is calculated from the "a" and "b" phase currents. If the "a" and "b" phase sensors have measurement offsets, then the offset in the third phase is a linear combination of the first two phases, as is shown in (4.3). It should be noted that the effect of measuring voltage offset in measured current: * + (4.5) ( ) on estimated flux is the same as the following offset
Thus, when the goal is to estimate the stator flux, the effect of voltage sensor measuring offset can be neglected since the same effect can be obtained with a different value of current measuring offset. However, the same approach cannot be applied for torque estimation. This will be explained later in this chapter.
38
Equations (4.1) and (4.2) show that the cumulative effect of the integration process results in deterioration of the estimated trajectory of stator flux even for very small value of measuring offset. The deterioration can be identified when the center of the estimated flux vector starts to deviate from the origin. If an appropriate selfcommissioning procedure is applied, the main cause of measurement offset is thermal drift in sensor electronic components. The thermal drift time constant is much larger than the electric time constant of the induction motor. Thus, the offset in current measurement can be treated as a constant vector which translates the circular trajectory of estimated flux away from the origin. The shape of the final flux trajectory is the combined effect of accumulated offset and a limiter which is a standard part of the flux estimator. Figure 41 presents the effect that current offset has on estimated trajectory of stator flux. The saturation effect protects the trajectory of estimated flux from drifting further away from the origin.
2.5 2
component of stator flux (Wb) qaxis component of statorflux (Wb)
1.5 1 0.5 0 0.5 1 1.5 2 2.5 2 1 0 1 2
daxis component stator flux (Wb) component ofof stator flux (Wb)
Figure 41 Estimated stator flux when nonzero sensor dc offset is present
Assuming that the bandwidth of the current loop is wide enough, the current error at the input to the current regulator can be expected to be zero.
(4.6)
This means that the result of the current measurements will exactly follow the reference values. Since the sensors introduce an offset, the d and q components of the stator current in the motor
39
windings will be different than the commanded values. The terms
and
in (4.7) denote the
current measurement offset transformed into the synchronously rotating rotor flux oriented reference frame.
(4.7) From (4.8), a conclusion can be drawn that in steady state a constant dc current sensor offset produces sinusoidal d and q components with a stator frequency, ( ( . ) (4.8) )
The amplitude is directly proportional to the length of current offset vector and the phase is shifted from the phase of the rotor flux by the current offset error phase angle. Electromagnetic torque ( ) can be estimated in the rotor flux oriented reference frame using (4.9), where P is the number of pole pairs, and is the magnetization inductance, ). (4.9) Equation (4.10) describes the relation between the daxis stator current and the rotor flux. A periodic variation in will cause a corresponding variation in . The rate of these variations is is the rotor inductance
is the rotor flux entirely positioned along the daxis (
described by the rotor time constant
. If the stator frequency is typically above 5Hz, the rotor flux , and to be approximately equal to the
can be safely assumed to be "inert" towards variations in reference value .
(4.10) The sinusoidal part of frequency. current component produces oscillations in motor torque at the stator
40
( where (
)
(4.11)
)
(4.12)
The same phenomenon can be seen in estimated torque if current regulators are not applied (e.g. if scalar speed control is applied), and this effect would be misinterpreted as variations in load torque. The effect of on the current regulator is equivalent to the influence of variable machine load. If
the induction motor is part of a speed loop with a speed or position sensor, the final rotor speed variations caused by depends on the stator frequency. For low stator frequency, a speed
regulator with wide enough bandwidth will recognize and compensate for the speed variations. For high stator frequencies, the low pass behavior of the mechanical system is able to suppress the speed variations. It is the middle range of frequencies that is problematic. In [24], the authors have suggested use of appropriate values of integral and proportional gain in the speed regulator as a function of mechanical parameters of the motor to alleviate this problem. However, if the speed feedback information is not available, as in the case of a sensorless drive, this method cannot be applied.
Figure 42 Estimated torque when nonzero sensor dc offset is present.
41
Figure 42 shows a plot of the estimated motor torque for a scalar controlled drive when a sensor dc offset is present. A current offset of is applied at a stator frequency of =5Hz. The first
harmonic in the estimated torque due to measuring offset can be seen. When the stator frequency ( ) is comparable to or less than the reciprocal of the rotor time constant ( ), the variations in will cause sinusoidal flux oscillations around the reference value
and the influence of voltage sensor offset error on the estimated torque can no longer be neglected. The overall effect can be summarized in the following expression. ( ) (4.13)
Linearization of (4.13) around steady state operating point results in 23. ( ) (4.14)
4.3 Proposed algorithm
A block diagram of the suggested algorithm is shown in Figure 43. The "ESTIMATOR" block in Figure 43 is explained in figure2. The main goal is to be able to use the pure integrator in (4.15) for flux estimation. The terms , , and ( ( ) (4.15) )
are corrected values of the q and daxis components of stator
voltages and currents in the stator flux oriented reference frame. The relation between the corrected values and the measured values is described in (3.10). (4.16)
42
^s vqs,k
E S T I M A T O R
^s ids ,k
^s vds,k
^ s qs
^ s , 0 ds
Fourier Analysis
0Hz
s ( fdq )* s ( fdq )*
PI PI
s (wdq )*
LP filter LP filter
^s v qs
^ s ds ^ Te
^ s , 0 qs
s (wdq )*
^s vds
s i^qs
^  r  D
^ Te, filt
s ^dq
^ T1
s i^ds
Fourier Analysis
X
2Lr 3PL m
^ I s0
I 0
P àR
^s I ds , 0 I^ s
PI
LP filter
qs , 0
PI
^s iqs ,k
LP filter
Figure 43 Measuring offset identification and advanced flux and torque estimation algorithm
vqs _ k
^s v qs
^
Estimators: Stator flux (eq. 41) Rotor flux (eq. 422)
^s v ds
^ ds
^ D
s ^dq
vds_ k
^ s qs
s i^qs
^ s ds
Estimator: Electromagnetic Torque (eq. 419)
^ Te
iqs _ k
s i^qs
LP filter
^ iqs , filt
i^ds
i ds , k
s i^ds
Estimator:
^ Te, filt
LP filter
i^qs , filt
Electromagnetic Torque (eq. 420)
Figure 44 Internal structure of ESTIMATOR block
43
The terms
and
are obtained by lowpass filtering the current measurements. The and is based on the on the zero frequency and ). These values are
calculation of voltage correction signals
components of estimated stator flux vector components (
processed through a PI regulator. The time constant of changes in sensor offset is usually very high. Thus, any abrupt changes in the correction signals should be avoided. This is achieved using adaptive filters at the output of the PI regulators. This process is described in (4.17) and (4.18). It is enough to have an IIR filter with a corner frequency that is ten times lower than the stator frequency.
( ) ( ( ) (
) )
( (
) (4.17) )
( ) ( ( ) (
) (4.18) )
It can be seen that in Figure 44, the electromagnetic torque is estimated two times. Measured values of the stator currents and voltages are used to compute the value of the electromagnetic torque in (3.6). ( ) (4.19)
In equation, lowpass filtered values of stator currents are used instead of instantaneous values to calculate the electromagnetic torque. ( ) (4.20)
The value of the electromagnetic torque estimated in (4.19) has been estimated from errorfree voltages and currents and should be free of any offset error. This value is not required by the algorithm, but it can be used outside this algorithm in a speed / torque controller. The filtered value of the electromagnetic torque is used to extract the sinusoidal component generated due to the offset. Fourier analysis of the estimated filtered electromagnetic torque signal at the stator
44
frequency yields the magnitude obtain the correction signals to be calculated.
and phase and
of the sinusoidal error component. In order to
, the amplitude and phase of the current offset vector has
where (
) (4.21)
is the estimated angular position of the synchronously rotating rotor flux oriented
reference frame. The value of the rotor flux needs to be calculated to obtain the estimated value of . Rotor flux is calculated from the estimated stator flux vector and the estimated value of the stator current as shown in (3.9). ( ) (4.22)
The current offset vector calculated in (4.21) is transformed from the rotor reference frame to stationary reference frame to get the error values and . These errors are inputs to a PI
regulator followed by an adaptive lowpass filter as shown in equation. ( ) ( ( ) ( ) ( ) ( ) (4.24) )
(4.23)
It should be noted that the inputs to the PI controllers are the average values of the estimated flux components ( ( and and ) and the components of the actual estimated stator current offset errors
). If the gains of the PI controllers are properly tuned, the values of all the four signals
should be zero. Thus, any of them can be treated as an error signal inside the algorithm. The role of the integrating part of the PI regulators is to find the correction signals ( so that the error signals are eliminated in steady state. , , and )
45
4.4 Software Simulation
The software package Matlab/ Simulink® was used to implement the proposed algorithm for a 3phase induction motor model. The "SimPowerSystems" toolbox available in Simulink was used to model the power electronics components. An openloop VoltsHertz controlled voltage supplied PWM induction motor drive was built. A fixed step size of 100 s was used for simulation. The induction motor used for hardware implementation was modeled and its parameters were used for simulation. 4.4.1 Cascaded lowpass filter based flux estimation implementation The algorithm suggested in [19] was implemented for an openloop VoltsHertz controlled induction motor drive. The motor was excited by a voltage with a stator frequency of 5Hz and amplitude
corresponding to the rated V/f ratio. The amplitude of the input voltage was compensated for the drop in voltage due to stator resistance. The machine is operated at noload condition. The main idea behind this implementation is explained as follows. A single integrator is resolved into a number of cascaded low pass filters with a short time constant. Thus, the problem of dc offset decay time can be sharply attenuated. Consider a low pass filter with the following transfer function. ( ) where is the time constant and (4.25)
is the angular frequency. The phase lag and gain of the filter
can be written as (  ( ) ) ( ) . The total gain (4.26) (4.27) . If the and
If "n" identical filters are cascaded, the total phase shift
combined effect of the nidentical filters is to behave like an integrator, then / , where is the gain compensation term needed for integration. ( ) ( )
(4.28)
46
(
)
(
)
(4.29)
Equations (4.28) and (4.29) can be used to form a set of cascaded filters which can replace the integrator for flux estimation. Ideally, a large number of "n" is desirable. A set of cascaded filters with n=3 was implemented.
spd*2*pi 1 V_abc
abc qds_s
we offsetV 1 den(s) 1 den(s) Rs K1 den(s) 1 den(s) 1 den(s) 1 den(s) f(u) gain_comp_qs f(u) gain_comp_ds 1 flux_qs_s 2 flux_ds_s
Vabc to Vqds_s
2 I_abc
abc
qds_s
Iabc to Iqds_s
offsetI1
offsetI2
Figure 45 Cascaded lowpass filter for flux estimation
Figure 45 shows the Simulink model of the implemented 3level cascaded low pass filter. The value of is calculated using equation (4.28) and the gain needed for compensation is calculated using
equation (4.29). Torque estimation is done using equation (3.6) and is not shown in the block diagram above. Constant offset terms ( , , and )
were introduced to the measured stator currents and voltages. Figure 46 shows the plot of estimated stator flux trajectory and estimated electromagnetic torque. It can be seen that the estimated flux trajectory has some mismatch form the actual trajectory (shown in dotted line). This results in oscillations at the fundamental frequency in the estimation of electromagnetic torque.
47
1
3 cascaded filter actual
0.8 0.6 0.4 0.2 0 0.2 0.4 0.6 0.8 1 1 0.5 0
Estimated Electromagnetic Torque (Nm)
1
qaxis component of stator flux (Wb)
2
1
0
1
2
0.5
3 18
18.5
19
19.5
20
daxis component of stator flux (Wb)
time (s)
Figure 46 Stator flux trajectory and estimated torque using cascaded filters for flux estimation
4.4.2 Proposed algorithm with VoltsHertz control The motor was excited by a voltage with a stator frequency of 5Hz and amplitude corresponding
to the rated V/f ratio. The amplitude of the input voltage was compensated for the drop in voltage due to the stator resistance. This effect is more prominent at low speeds when the magnitudes of the two voltages are comparable. The machine is operated at noload conditions. Figure 47 shows a block diagram of the proposed algorithm implemented in simulation. The following offset errors were introduced to simulate offset errors in current and voltage measurement: , , and . Current and voltage
signal sampling time was chosen to be 1ms. The same sampling time was also used for experimental testing. The estimation algorithm is started at the time of the start of the drive. Figure 48 shows the correction terms necessary to compensate for the offset errors in the q and daxis components of the stator current. It can be seen that the q and daxis components settle at 100mA and 100mA respectively, which are equal to the offset introduced.
48
psi_s
1 Vabc
abc
qds_s
V_qds_s theta I_qs_s_meas_corr
Vabc to Vqds_s
Torque estimation
I_qs_s_meas_corr T_em_amp I_ds_s_meas_corr T_em_est I_qs_s_meas_corr_filt I_ds_s_meas_corr_filt T_em_amp_filt psi_qs_s_est psi_ds_s_est T_em_angle_filt T_em_angle
2 Iabc
abc
qds_s
I_qds_s I_ds_s_meas_corr I_qs_s_meas_corr_filt I_qds_s_corr1 I_ds_s_meas_corr_filt psi_qs_s V_qds_s_corr1 psi_ds_s
Iabc to Iqds_s
T_em_amp i_qs_s_corr
flux estimation
I_qs_s_est I_ds_s_est psi_qs_s_est psi_r_est_angle psi_ds_s_est psi_r_est_angle psi_r_est_amp psi_r_est_amp i_ds_s_corr
i_qds_s_corr
psi_qs_s 1 2 psi_ds_s 5 basic harmonic
rotor flux calculation
psi_qs_s_est psi_ds_s_est f_s_ref V_ds_s_corr V_qs_s_corr
current sensor offset calculation
V_qds_s_corr
voltage sensor offset calculation
Figure 47 Simulink block diagram of proposed offset correction algorithm
Figure 4 9 shows correction values for the q and daxis components of the stator voltage. The correction terms settle at 1V and 0V respectively, which are equal to the offsets introduced. Figure 4 11 shows the estimated trajectory of the stator flux and the estimated electromagnetic torque. The xaxis represents the daxis component of the stator flux, and the yaxis represents the qaxis component of the stator flux. It should be noted that the effect of the current offset shown in Figure 4 1 has been corrected by the algorithm in Figure 4 11 and the center of the trajectory is back at the origin. The proposed algorithm is able to successfully estimate current and voltage sensor offset error, achieving this with a relative error of less than 0.5% for voltage and 0.4% for current sensors. Thus, very accurate estimation of stator flux is possible and the constant term is reduced to less than 0.05pu. The strength of the algorithm is to recognize the problematic sensor and its offset error. This means that the inputs to the flux and torque estimators are error free.
49
2
Iqs correction (A)
1
0
1
0
20
40
60
80
100
120
140
160
time (s)
0.8
Ids correction (A)
0.6 0.4 0.2 0
0
20
40
60
80
100
120
140
160
time (s)
Figure 48 Simulation results  q and d axis current offset correction terms
Vqs correction (V)
1.5
1
0.5
0
0
20
40
60
80
100
120
140
160
time (s)
Vds correction (V)
0.15 0.1 0.05 0 0.05
0
20
40
60
80
100
120
140
160
time (s)
Figure 49 Simulation Results  q and d axis voltage offset correction terms
50
1
0.14
qaxis component of stator flux (Wb)
0.8 0.6 0.4 0.2 0 0.2 0.4 0.6 0.8 1 1
Estimated Electromagnetic Torque (Nm)
0.5 0 0.5 1
0.138 0.136 0.134 0.132 0.13 0.128 0.126 0.124 0.122 0.12 158
158.5
159
159.5
160
daxis component of stator flux (Wb)
time (s)
Figure 410 Simulation Results  Estimated stator flux trajectory and estimated electromagnetic torque
qaxis stator flux (Wb)
0.5
0
0.5 158
158.2 158.4 158.6 158.8
159
159.2 159.4 159.6 159.8
160
time (s)
daxis stator flux (Wb)
0.5
0
0.5 158
158.2 158.4 158.6 158.8
159
159.2 159.4 159.6 159.8
160
time (s)
Figure 411 Simulation results  qaxis and daxis components of stator flux
51
Chapter 5
Experimental Setup
5.1 Introduction
A motorgenerator dynamometer testbed was built to perform the experiments described in chapters 3 and 4. This chapter describes the testbed in detail. Figure 51 shows a block diagram representation of the electric drive system and its major components. The load and the test motors are squirrel cage 3phase AC induction motors. The two motors are coupled with an inline torque transducer. Figure 52 shows a photograph of the testbed. The test motor can be seen on the left and the load motor is on the right. The torque transducer can be seen connected inline between the two motors. The capacitor bank, the controller for the load motor and the test motor inverter can also be seen.
Control Center
Controller (dSPACE)
Azure Controller
Inverter
Test Motor
Torque Transducer
Load Motor
Inverter
Capacitor Bank
AC Supply
DC Power Supply
Figure 51 Dynamometer testbed block diagram
52
Figure 52 Dynamometer testbed
5.2 Load Motor
The load motor is the Azure Dynamics (http://www.azuredynamics.com) AC55 3phase AC induction motor with DMOC445 Drive System controller. The name plate details of the AC55 motor is listed in Table 51.
Table 51 AC55 motor nameplate data
Rated Power [kW (HP)] Rated rotor speed [rpm] Voltage [V] NEMA Nominal Efficiency [%] Power Factor Rated Frequency [Hz]
11.2 (15) 1730 95 89.5 0.86 60
5.3 Azure Controller and Inverter
The DMOC445 controller is a DSPcontrolled, rugged, waterproof inverter for controlling 3phase induction motors. The typical connection of the DMOC motor controller is illustrated in Figure 53. The controller employs a field oriented control algorithm and generates Space Vector PWM signals to provide gate signals to the inverter. A CAN controlled application layer configures the DMOC for a system where an external controller (Control Center) commands the DMOC over CAN. Diagnostics and configuration of the DMOC is achieved by means of a PC based diagnostic tool called "ccShell". The CAN signal from the DMOC is converted into RS232 serial data using an EasySYNCTM S1A7001 CANtoRS232 adapter. This adapter operates at up to 1Mbps on both RS232 and CANbus interfaces.
53
This RS232 terminal of this adapter is connected to the serial port (COM1) of the PC and reference signals are sent to the DMOC via HyperTerminal.
Figure 53 DMOC with typical connections (Source: DMOC445 and DMOC645 User Manual for Azure Dynamics DMOC Motor Controller)
5.3.1 CAN Controller In the CAN controller, higher level control signals like upper/lower level torque commands and speed setpoint commands are communicated to the DMOC over the CAN network. Speed and position information is fed back to the DMOC using a quadrature encoder with a 60tooth sensor disc.
Table 52 DMOC operating mode based on higher level control inputs
Condition LowerTorqueLimit < UpperTorqueLimit LowerTorqueLimit = UpperTorqueLimit LowerTorqueLimit > UpperTorqueLimit
Controller Mode Speed control mode Torque control mode Motor torque set to zero
The CAN application layer consists of a PI controller with output saturation and antiwindup. The drive is operated in speedcontrolled mode or torquecontrolled mode depending on the three scenarios described in Table 52. The DMOC requires a 12V auxiliary dc power supply to power the
54
internal circuits. This acts as an "enable" signal for the internal power supply of the DMOC. The auxiliary supply needs to be able to source 10A current, and must be protected by a 15A fuse. 5.3.2 ccShell Program The ccShell program allows the user to access and modify the DMOC calibration parameters, and to visualize and capture variables in realtime. Figure 54 shows a screenshot from the ccShell program. The "viewer" is used to view and log variables.
Figure 54 Screenshot of the ccShell software
5.4 dSPACE DS1104 Controller
The test motor controller is implemented on a dSPACE DS1104 R&D Controller Board. It is a single PCI board with realtime hardware and comprehensive I/O features. Figure 55 shows the dSPACE DS1104 PCI controller card. The dSPACE DS1104 Controller card has MasterSlave processor architecture. The connector panel CP1104 gives access to all the I/O hardware available on dSPACE DS1104. The MPC8240 master processor consists of A/D and D/A converters, digital I/O channels, a digital incremental encoder interface and a serial interface. The Texas Instruments TMS320F240 slave DSP has PWM channels (3phase and 1phase), capture inputs and a serial peripheral interface. Figure 56 illustrates the internal blocks of the dSPACE DS1104 Controller card.
55
Figure 55 dSPACE DS1104 Controller Card
The dSPACE DS1104 is a powerful system for rapid control prototyping and along with Real Time Interface (RTI), it provides Matlab/Simulink® blocks for graphical I/O configuration. The RTI is the link between dSPACE's realtime hardware and the Matlab/Simulink® development software. It extends the C code generator Real Time Workshop® so that the Simulink models can be very easily implemented on dSPACE realtime hardware. Once the I/O has been configured and the controller has been programmed in a Simulink® block diagram, model code can be generated using RealTime Workshop®. The realtime model is compiled and downloaded to the dSPACE hardware. The compilation of the "<filename>.mdl" file in Simulink® using RTI also generates a file with extension "<filename>.sdf". This file can be accessed in ControlDesk software that helps in managing and instrumenting realtime and Simulink® experiments.
56
Figure 56 Internal blocks of dSPACE DS1104 Controller Card (Source: dSPACE DS1104 Catalog 2010)
ControlDesk test and experiment software allows the user to manage, control and automate experiments. The model parameters can be changed via mouse and keyboard, without interrupting the realtime experiment. This means reference speed and torque quantities can be set while the experiment is running. Figure 57 shows a screenshot of the ControlDesk software with the virtual instrumentation. ControlDesk can record both individual time intervals and continuous data. Recording length, downsampling and trigger properties can be specified and the recorded signals can be saved for later analysis in Matlab. The control algorithm is programmed in Matlab/Simulink environment and appropriate gate signals are generated at the digital I/O channels. The slave processor of the dSPACE DS1104 has dedicated hardware modules to generate 3phase PWM and Space Vector PWM signals. The outputs of these
57
channels are connected to the input of the gate drivers of the power converter. Figure 511 shows a block diagram of the power converter that supplies power to the test motor.
Figure 57 ControlDesk software screenshot with virtual instrumentation
5.5 Test Motor Inverter
To power the test motor, a PWM voltage source inverter (VSI) built using an IGBT module from Infineon (BSM50GP120) is used. Figure 510 shows the internal circuit diagram of the IGBT module. The six IGBTs in the module are powered using dual IGBT gate drivers. A pin configuration diagram of the gate driver is shown in Figure 58. Figure 511 shows a block diagram of the test motor power converter.
58
8 7 6 5 4 3 2 1
+12V GND FLT IN1 +5V GND FLT IN0 Dual IGBT Driver
GND
12 11
GND
10 9
Figure 58 Dual IGBT gate driver pin configuration
Figure 59 Test motor inverter with capacitor bank
The IGBT module is powered from a dc power supply. Three capacitors rated at 450V, 8200 F each are connected in parallel between the power supply and the input to the IGBT module. The inverter also houses a sensing module to measure two stator currents and the dclink voltage. Figure 59 shows a picture of the test motor inverter with the capacitor bank connected in parallel. Figure 512 shows the circuit diagram of the inverter board.
59
21
22 20 19 18 17 16 15
1
2
3
7
4 5 6
14 23 24
13
12
11 10
Figure 510 IGBT Module circuit diagram
7 5 3 1
GND GND 1 IN 1 GND 0 GND IN 0
12 11
10 13 1
Dual IGBT Driver 10 9
19 20
2
3ph power supply input
3
12 11 Dual IGBT Driver GND 1 IN 0 10 9
7
GND GND 1 IN 1 GND 0
10 12 IGBT Module (BSM50GP120) 17 18
Gate Signals (from dSPACE)
5 3
ia
4
Feedback Signals (ia, ib, Vdc; to dSPACE)
current sensors ib
5
8 7 6 5 4 3 2 1
To motor
+12V GND 1 FLT 1 IN 1 +5V GND 0 FLT 0 IN 0 Dual IGBT Driver
GND
12 11
15 16
GND
10 9
ic
10 11 21 23 24 22 6
DC Bus Cap
Vdc
Figure 511 Power Converter block diagram
60
Figure 512 Circuit diagram of the inverter board
61
5.6 Feedback sensing
The implemented current sensing module consists of two current sensors. Since the stator windings of the motor are a threephase wye connection, and assuming balanced threephase currents, the third stator current can be calculated from the other two as shown in equation (5.1) . ( ) (5.1)
The current transducers used are LEM LA 150P. The sensor output is rated at 0 to 75mA when the input current varies from 0 to 150A. The output needs to be conditioned before it can be sampled at the ADC channel of dSPACE. Figure 512 shows the signal conditioning circuit for the current transducer. Typically, the ADC channels available on microcontrollers can read only positive voltages. However, the current sensed by the transducers are sinusoids. Thus, a DC offset is introduced to ensure that the voltage input at the ADC does not go below zero. The input to output relation of the signal conditioning circuit is as follows ( where is the actual current and ) (5.2)
is the voltage measured at the output of the signal
conditioner. The 2V offset introduced by the signal conditioner is removed in software by subtracting the offset value from the measured value. The voltage on the dc bus is measured using a voltage transducer (LEM LV 20P). Figure 512 shows the signal conditioning circuit for the voltage sensor. When the voltage input to the signal conditioner varies from 0 to 240.8V, the output varies from 0 to 5V. These measured current and voltage quantities are fed back to the dSPACE controller via the A/D channels. The encoder speed signal from the load motor is also fed to the incremental encoder available in dSPACE.
5.7 Torque Transducer
The inline torque transducer is a standard rotting shaft slip ring torque sensor (Honeywell Sensotec/Lebow, Model 1104500) designed for general test and measurement applications, such as motor testing. The torque sensor is rated for 55 Nm (500 lbin) and a maximum speed of 9000 rpm.
62
The differential torque applied on the torque sensor is translated into a voltage signal by the change in resistance of the strain gages that are connected to the torque sensor. The change in resistance indicates the degree of deformation, and thus the amount of torque applied. The output voltage of the torque transducer is usually in the range of millivolts and is too small to be read by the A/D converters with reasonable accuracy. A wide bandwidth strain gage input module signal conditioner (Dataforth SCM5B3802 with SCM5B03 backplane) is used to convert the output of the torque sensor in to a voltage signal with an output voltage range of 5V to 5V so that it can be connected to the A/D channel on dSPACE.
5.8 Test Motor and Motor Parameter Estimation
The test motor is a Baldor 7.45 kW (10 HP) M3313T motor. A per phase equivalent model is used for analysis of an induction motor. Figure 513 shows a per phase equivalent circuit of the induction motor with respect to the stator.
Rs Is Vs Lm L ls L lr
Ir
Rr __ s
Airgap Power P
g
Figure 513 Perphase equivalent circuit of induction motor with respect to the stator
The stator resistance and the stator leakage inductance are denoted by R s and Lls respectively. The term Lm refers to the magnetizing inductance. The terms Rr/s and Llr are used to denote the rotor resistance and the inductance referred to the stator side. Here, the term for the equivalent resistance for core loss, Rm, has been neglected since its effect is small compared to that of the magnetic inductance.
63
Based on the nameplate data and the datasheet of an induction motor, the electrical parameters of the motors can be estimated. Table 53 lists the data from the nameplate of the motor. Typical performance characteristics of the motor at 208V and 60Hz are listed in Table 54.
Table 53 Baldor M3313T (test motor) Nameplate data
Rated Power [HP] Rated Voltage [V] Rated Current [A] Rated rotor speed [rpm] NEMA Nominal Efficiency [%] Power Factor Rated Frequency [Hz] Number of poles
10 208 26 1755 89.5 0.82 60 4
Table 54 Performance Data at 208V, 60Hz
General Characteristics 40.4337 PullUp Torque [Nm] 11.1 LockedRotor Torque [Nm] 0.288 Ohms A Ph / Lineline Resistance Starting Current [A] 0.000 Ohms B Ph BreakDown Torque [Nm] 1.10144 Load Characteristics % of Rated Load 25 50 75 Speed [rpm] 1789 1780 1770 Line Amperes [A] 12.6 16.5 21.6 Efficiency [%] 85.4 90.4 90.4 Power Factor 0.46 0.69 0.79 Full Load Torque [Nm] NoLoad Current [A]
60.1983 67.2485 166.00
100 1758 27.7 89.7 0.83
When rated voltage is applied to the motor at no load, the slip, s, is very close to zero and the rotor current Ir is very small. Thus, it is safe to assume that at no load, all of the stator current is used to excite the field. The motor draws a noload current of 11.1A at a rated voltage of 120V (per phase).
(5.3)
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From (1), we have Lm = 28.6765mH. The expression for stator current, Is, and the airgap power, Pg, can be written shown in (5.5) and (5.6). The value of the per phase stator resistance Rs can be calculated from the data given in
Table 54. (5.4) (5.5)
(
)
(
)
(5.6)
In equation (5.6), the term ns denotes the stator frequency in radians/second. From Table 54, substituting values for slip, stator current, phase voltage and the full load torque, the value of rotor resistance can be calculated. ( ) (5.7)
The values of the combined inductances can be calculated from (5.5) by substituting the values of the stator and rotor resistances and the values of the stator current and voltage at full load.
( (
) )
( ( (
) ( ) ( ) (
) ) ) (5.8)
The stator and rotor leakage inductances are divided into two equal halves. The estimated motor parameters have been summarized in Table 55.
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Table 55 Estimated Motor Parameters
Stator Resistance [Ohm] Rotor Resistance [Ohm] Stator Leakage Inductance [H] Rotor Leakage Inductance [H] Magnetizing Inductance [H]
0.144 0.077257 0.003446 0.003446 0.0286765
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Chapter 6
Experimental Results
6.1 Implementation of deadtime and inverter nonlinearity compensation
The compensation techniques discussed in sections 3.3.1 and 3.3.3 was implemented on the dSPACE controller. Figure 61 shows the implementation of deadtime and inverter nonlinearity compensation algorithms.
Figure 61 Deadtime and inverter nonlinearity compensation
Figure 62 Inverter nonlinearity compensation
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The block "nonlinear comp", shown in Figure 62, is based on equations (3.10) to (3.13). The values of the threshold voltage ( ) and the difference resistance ( ) are calculated from the datasheet. and can be calculated as . (6.1) (6.2) Equation (3.13) can be rewritten as ( ) (6.3)
From Figure 315, the value of
The reference voltage vector to the PWM inverter is modified by adding the compensation term ( ) to the ideal reference voltage vector ( ).
The block "deadtime comp" is used to compensating the effect due to the necessary deadtime that needs to be introduced. The algorithm for compensation, as shown in Figure 39, is written as a Matlab embeddedfunction. The same algorithm was used for simulations in section 3.3.1. Figure 63 shows the effect of deadtime and inverter nonlinearity on stator current. The drive was operated using openloop VoltsHertz control at a supply frequency of . Distortion in stator current can be seen at the 6th harmonic of the fundamental frequency. Figure 64 shows a plot of the stator current when only inverter nonlinearity compensation was enabled. Deadtime compensation was not enabled.
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Figure 63 Stator current with 1 s deadtime (Conditions: no deadtime compensation; no inverter nonlinearity compensation).
Figure 64 Stator current with 1s deadtime (Conditions: no deadtime compensation; inverter nonlinearity compensation enabled).
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Figure 65 Stator current with 1s deadtime (Conditions: deadtime compensation enabled; no inverter nonlinearity compensation).
Figure 66 Stator current with 1s deadtime (Conditions: deadtime compensation enabled; inverter nonlinearity compensation enabled).
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Figure 65 shows a plot of the stator current when only deadtime compensation was enabled. Inverter nonlinearity compensation was not enabled. It can be seen that the RMS value of the stator current increased from 8.782A (in Figure 63) to 10.68A (in Figure 65). This is in agreement with the results obtained during simulation in section 3.3.1. Finally, in Figure 66, a plot of stator current when both deadtime compensation and inverter nonlinearity compensation algorithms were enabled is presented. The resulting waveform is relatively clean from distortions due to the effects of deadtime and inverter nonlinearity.
6.2 Implementation of proposed algorithm with openloop VoltsHertz control
The proposed algorithm was implemented for an open loop VoltsHertz controlled threephase induction motor drive. Figure 67 shows the Simulink block diagram of the VoltsHertz control. The proposed algorithm is implemented at 1 kHz. The "V/f control" block is triggered using a builtin hardware timer and is implemented at 10 kHz. Figure 68 shows the internal structure of this block.
Figure 67 Simulink diagram  VoltsHertz control; Stator flux and torque estimation using proposed algorithm
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Figure 68 Simulink diagram  "V/f control" block
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Figure 69 Simulink diagram  "offset algorithm" block
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Figure 610 Simulink diagram  "voltage sensor offset correction" block
Figure 611 Simulink diagram  "current sensor offset correction" block
The "ADC Sampling" block contains the code to read the dcbus voltage and the stator currents through ADC channels. This block is triggered by an interrupt generated by the PWM generator block. The switching frequency of the PWM inverter is 10 kHz. This means that the ADC channels are also sampled at 10 kHz. ADC channels are sampled at the center of each PWM switching cycle. This is done to make sure sampling is not done when the inverter is switching states. Thus, high frequency noise in measured quantities is avoided. Figure 69 shows the implementation of the proposed offset correction algorithm. Figure 610 and Figure 611 show the "voltage sensor offset correction" and "current sensor offset correction" blocks respectively.
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Three experiments were performed at stator frequency are discussed below. 6.2.1 Experiment 1
Hz. The results of the three experiments
The goal of the first experiment is to show that estimated flux and torque have unacceptably high levels of distortion when the correction algorithm was not activated. The drive was started and the flux and torque estimation blocks were started. The correction algorithm was not enabled. Figure 612 shows the trajectory of stator flux in the stator reference frame. The daxis component of the stator flux in plotted on the xaxis and the qaxis component is on the yaxis. It can be seen that with no correction, the stator flux trajectory is not centered at the origin. In Figure 613, large oscillations can be seen in the estimated torque when the correction algorithm is not enabled.
Figure 612 Stator flux trajectory (Conditions: Correction disabled; No software created offset)
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Figure 613 Estimated torque (Conditions: Correction disabled; No software created offset)
6.2.2 Experiment 2 In the second experiment, the correction algorithm is enabled. Figure 614 and Figure 615 show the estimated flux trajectory and the estimated electromagnetic torque respectively. It can be seen that the stator flux is now centered at the origin. Also, the correction algorithm is able to eliminate the sinusoidal term as stator frequency in the estimated torque. Figure 616 and Figure 617 show the current and voltage correction terms. Figure 618 presents the daxis and qaxis stator flux components in the stator reference frame.
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Figure 614 Stator flux trajectory (Conditions: Correction enabled; No software created offset)
Figure 615 Estimated torque (Conditions: Correction enabled; No software created offset)
77
Figure 616 Current correction terms (Conditions: Correction enabled; No software created offset)
Figure 617 Voltage correction terms (Conditions: Correction enabled; No software created offset)
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Figure 618 Stator flux components (Conditions: Correction enabled; No software created offset)
The result of the second experiment can be summarized as follows: Operation interval is 160s. Current correction terms at the end of the experiment: Voltage correction terms at the end of the experiment: , , . .
6.2.3 Experiment 3 In order to check the accuracy of the correction and estimation algorithms, the third experiment was performed. Known values of constant values were added to the measured values of currents and voltages. The constant terms have the following values: and , ,
. Because the original signals have unchanged offset (detected in
the second experiment), we expect to find the total current and voltage offset error values to be the sum of the original offset and the offset introduced in software. The drive, the estimation and the correction algorithms are started and the resulting estimated stator flux trajectory and estimated torque are given in Figure 619 and Figure 620. Figure 621 and
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Figure 622 show the correction terms in stator current and stator voltage. As can be seen, the algorithm showed satisfactory accuracy in estimating the errors.
Figure 619 Stator flux trajectory (Conditions: Correction enabled; Software created offset)
Figure 620 Estimated torque (Conditions: Correction enabled; Software created offset)
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Figure 621 Current correction terms (Conditions: Correction enabled; Software created offset)
Figure 622 Voltage correction terms (Conditions: Correction enabled; Software created offset)
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Figure 623 Stator flux components (Conditions: Correction enabled; Software created offset)
Figure 623 shows the daxis and qaxis stator flux components in the stator reference frame. As can be seen from the plots in Figure 619 to Figure 623, the algorithm showed satisfactory performance. The identified errors from this experiment as: Current correction terms at the end of the experiment: . Voltage correction terms at the end of the experiment: , . ,
The correction terms are approximately equal to the sum of the correction terms in the second experiment and the software introduced offset terms. At no load, the electromagnetic torque produced the motor should be a constant value corresponding to the torque needed to overcome the friction and inertia of the motor. The estimated torque in Figure 620 is not constant and has fluctuations. To confirm that this is not due to error in torque estimation and that the fluctuations are real, the output of the torque sensor was compared to the estimated torque. Figure 624 shows the estimated and measured values of the
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electromagnetic torque. It can be seen that the fluctuations in torque are real and not due to errors in estimation.
Figure 624 Estimated torque and measured torque
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Chapter 7
Conclusion
An algorithm for accurate estimation of stator flux linkage and electromagnetic torque in an induction motor drive has been proposed, when measurement offsets in current and voltage sensors are present. The necessity of accurate flux and torque estimation is especially important at low speeds. In this thesis, impact of motor parameter variation, deadtime and inverter nonlinearity and offsets in sensor measurement on flux and torque estimation has been described. Compensation techniques proposed in literature to solve the deadtime and inverter nonlinearity problems have been discussed and implemented, both in simulation and in hardware. Influences of uncompensated sensor offset are analytically described and numerically quantified. The goal of the proposed algorithm is to detect and compensate the offset of voltage and current sensors and thus eliminate errors in the estimated quantities. Unlike other algorithms available in literature, this algorithm is designed to identify the sensor that introduces an uncompensated offset and to quantify the offset level. This approach allows us to eliminate the offset at its source, correcting all estimated quantities estimated using these corrected signals. The characteristics of the algorithm are investigated through simulation and through implementation on a hardware controller. The obtained results show good accuracy and stability. Additional testing on hardware is part of future work. The algorithm needs to be tested in dynamic operating conditions and in feedback as part of a closed loop drive.
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