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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 non-ideality 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 dead-time 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 three-phase 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. Mo-Yuen 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 Open-loop 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 low-pass filter based flux estimation implementation...................................... 46 4.4.2 Proposed algorithm with Volts-Hertz 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 dead-time and inverter nonlinearity compensation .................................. 67 6.2 Implementation of proposed algorithm with open-loop Volts-Hertz 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 2-1 Optimum voltage switching vector look-up table ............................................................. 16 Table 5-1 AC55 motor nameplate data ............................................................................................ 53 Table 5-2 DMOC operating mode based on higher level control inputs ............................................ 54 Table 5-3 Baldor M3313T (test motor) Nameplate data ................................................................... 64 Table 5-4 Performance Data at 208V, 60Hz ..................................................................................... 64 Table 5-5 Estimated Motor Parameters ........................................................................................... 66

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LIST OF FIGURES

Figure 2-1 Open loop Volts/Hertz speed control with voltage-fed inverter ........................................ 5 Figure 2-2 Axis transformation .......................................................................................................... 6 Figure 2-3 Vector controlled induction motor .................................................................................... 8 Figure 2-4 Block diagram of Stator Flux Oriented Control .................................................................. 9 Figure 2-5 Stator flux-linkage and stator current space vectors........................................................ 11 Figure 2-6 Switching voltage space vectors ...................................................................................... 11 Figure 2-7 Control of Stator Flux ...................................................................................................... 12 Figure 2-8 Block diagram of a DTC controller ................................................................................... 14 Figure 2-9 Speed control loop and flux reference generator ............................................................ 14 Figure 2-10 Simulink block diagram of DTC algorithm ...................................................................... 17 Figure 2-11 Rotor speed in rpm and electromagnetic torque in Nm ................................................. 17 Figure 2-12 Stator flux linkage vector. 1) q-axis component of stator flux. 2) d-axis component of stator flux. 3) magnitude of stator flux linkage vector. ..................................................................... 18 Figure 2-13 Stator current at .......................................................................................... 19

Figure 2-14 Trajectory of stator flux ................................................................................................ 19 Figure 3-1 Flux Estimator block........................................................................................................ 20 Figure 3-2 Ideal flux and torque estimation. Open loop V/f control, stator frequency - 5Hz ............. 22 Figure 3-3 Single phase configuration of PWM inverter ................................................................... 22 Figure 3-4 Time delay between turn OFF and turn ON of two switches on the same inverter leg ..... 23 Figure 3-5 T1 transition from ON to OFF, (a) ia is positive. (b) ia is negative ...................................... 24 Figure 3-6 T1 transition from OFF to ON, (a) ia is positive. (b) ia is negative ...................................... 25 Figure 3-7 Simulation - Simulink model of dead-time compensation implementation ...................... 26 Figure 3-8 Simulation - block diagram of "V/f to duty" block............................................................ 27 Figure 3-9 "Dead-time compensator" block ..................................................................................... 27 Figure 3-10 Stator current with 1 s dead-time; without dead-time compensation .......................... 28 Figure 3-11 Estimated stator flux and electromagnetic torque with 1 s dead-time; without deadtime compensation ......................................................................................................................... 28 Figure 3-12 Stator current with 1 s dead-time; with dead-time compensation ............................... 29

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Figure 3-13 Estimated stator flux and electromagnetic torque with 1 s dead-time; with deadtime compensation ......................................................................................................................... 29 Figure 3-14 Estimated stator flux and electromagnetic torque; stator resistance variation from 50% to 150% of original value ......................................................................................................... 31 Figure 3-15 Inverter output characteristics. Dotted line: modeled approximation. (Reproduced from Product datasheet - BSM50GP120, Infineon) .......................................................................... 32 Figure 3-16 Estimated stator flux and electromagnetic torque when inverter nonlinearities are present ........................................................................................................................................... 33 Figure 3-17 Stator current when inverter nonlinearities are present................................................ 34 Figure 4-1 Estimated stator flux when non-zero sensor dc offset is present ..................................... 39 Figure 4-2 Estimated torque when nonzero sensor dc offset is present. .......................................... 41 Figure 4-3 Measuring offset identification and advanced flux and torque estimation algorithm ...... 43 Figure 4-4 Internal structure of ESTIMATOR block ........................................................................... 43 Figure 4-5 Cascaded low-pass filter for flux estimation .................................................................... 47 Figure 4-6 Stator flux trajectory and estimated torque using cascaded filters for flux estimation ..... 48 Figure 4-7 Simulink block diagram of proposed offset correction algorithm ..................................... 49 Figure 4-8 Simulation results - q and d axis current offset correction terms ..................................... 50 Figure 4-9 Simulation Results - q and d axis voltage offset correction terms .................................... 50 Figure 4-10 Simulation Results - Estimated stator flux trajectory and estimated electromagnetic torque ............................................................................................................................................. 51 Figure 4-11 Simulation results - q-axis and d-axis components of stator flux .................................... 51 Figure 5-1 Dynamometer test-bed block diagram ............................................................................ 52 Figure 5-2 Dynamometer test-bed................................................................................................... 53 Figure 5-3 DMOC with typical connections (Source: DMOC445 and DMOC645 User Manual for Azure Dynamics DMOC Motor Controller) ........................................................................................ 54 Figure 5-4 Screenshot of the ccShell software ................................................................................. 55 Figure 5-5 dSPACE DS1104 Controller Card ...................................................................................... 56 Figure 5-6 Internal blocks of dSPACE DS1104 Controller Card (Source: dSPACE DS1104 Catalog 2010) .............................................................................................................................................. 57 Figure 5-7 ControlDesk software screenshot with virtual instrumentation ....................................... 58

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Figure 5-8 Dual IGBT gate driver pin configuration .......................................................................... 59 Figure 5-9 Test motor inverter with capacitor bank ......................................................................... 59 Figure 5-10 IGBT Module circuit diagram ......................................................................................... 60 Figure 5-11 Power Converter block diagram .................................................................................... 60 Figure 5-12 Circuit diagram of the inverter board ............................................................................ 61 Figure 5-13 Per-phase equivalent circuit of induction motor with respect to the stator ................... 63 Figure 6-1 Dead-time and inverter nonlinearity compensation ........................................................ 67 Figure 6-2 Inverter nonlinearity compensation ................................................................................ 67 Figure 6-3 Stator current with 1 s dead-time (Conditions: no dead-time compensation; no inverter nonlinearity compensation). .............................................................................................. 69 Figure 6-4 Stator current with 1s dead-time (Conditions: no dead-time compensation; inverter nonlinearity compensation enabled). .............................................................................................. 69 Figure 6-5 Stator current with 1s dead-time (Conditions: dead-time compensation enabled; no inverter nonlinearity compensation). .............................................................................................. 70 Figure 6-6 Stator current with 1s dead-time (Conditions: dead-time compensation enabled; inverter nonlinearity compensation enabled). ................................................................................. 70 Figure 6-7 Simulink diagram - Volts-Hertz control; Stator flux and torque estimation using proposed algorithm......................................................................................................................... 71 Figure 6-8 Simulink diagram - "V/f control" block ............................................................................ 72 Figure 6-9 Simulink diagram - "offset algorithm" block .................................................................... 73 Figure 6-10 Simulink diagram - "voltage sensor offset correction" block .......................................... 74 Figure 6-11 Simulink diagram - "current sensor offset correction" block .......................................... 74 Figure 6-12 Stator flux trajectory (Conditions: Correction disabled; No software created offset) ..... 75 Figure 6-13 Estimated torque (Conditions: Correction disabled; No software created offset) .......... 76 Figure 6-14 Stator flux trajectory (Conditions: Correction enabled; No software created offset) ...... 77 Figure 6-15 Estimated torque (Conditions: Correction enabled; No software created offset) ........... 77 Figure 6-16 Current correction terms (Conditions: Correction enabled; No software created offset) ............................................................................................................................................. 78 Figure 6-17 Voltage correction terms (Conditions: Correction enabled; No software created offset) ............................................................................................................................................. 78

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Figure 6-18 Stator flux components (Conditions: Correction enabled; No software created offset).. 79 Figure 6-19 Stator flux trajectory (Conditions: Correction enabled; Software created offset) ........... 80 Figure 6-20 Estimated torque (Conditions: Correction enabled; Software created offset) ................ 80 Figure 6-21 Current correction terms (Conditions: Correction enabled; Software created offset) .... 81 Figure 6-22 Voltage correction terms (Conditions: Correction enabled; Software created offset) .... 81 Figure 6-23 Stator flux components (Conditions: Correction enabled; Software created offset) ....... 82 Figure 6-24 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 non-ideality 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 three-phase 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 open-loop Volts-Hertz controlled three-phase induction motor drive.

1.3 Outline

Chapter 2 introduces concepts of speed control of induction motors. Open-loop 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 dead-time and inverter nonlinearity on the estimated flux and torque is shown and compensation techniques are discussed. A dead-time 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 open-loop 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 test-bed ­ 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 dead-time 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. Open-loop 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 Open-loop 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 2-1 Open loop Volts/Hertz speed control with voltage-fed inverter

Figure 2-1 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 air-gap 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 2-1. 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 3-phase to 2-phase and vise-versa 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 three-phase induction machine stationary as-bs-cs axes at / angle apart,

as shown in Figure 2-2. The goal is to transform the three-phase stationary reference frame variables into two-phase stationary reference frame variables (ds-qs) and then transform these to synchronously rotating reference frame (de-qe).

qs as

vqss

vas

vdss vbs bs vcs cs

Figure 2-2 Axis transformation

ds

Assuming the ds-qs axes to be oriented at an angle

as shown in Figure 2-2, the two-phase

quantities can be resolved from the as-bs-cs 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 qs-axis aligns with the as-axis. 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 two-phase quantities. (

)

(2.3)

Equation (2.3) can also be used to transform the stator currents from three-phase 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 d-axis current current and the q-axis 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 2-3 shows a block diagram of a vector controlled induction motor drive. From the space vector diagram on the right of Figure 2-3, it can be seen that when is controlled, it affects the q-axis 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 2-3 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 flux-sensing 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 2-4 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 feed-forward 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

de-qe to abc

Voltage Source Interter

PI

i dq

Decoupling term

i eqs i eds

abc to de-qe

s

sds

Stator flux Estimator

i as i bs

VDC

wm

IM

Figure 2-4 Block diagram of Stator Flux Oriented Control

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Figure 2-4 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 2-4 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 d-axis 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 q-axis 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 three-phase induction machine is proportional to the cross-vector 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 2-5, 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 2-5 Stator flux-linkage 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 flux-linkage 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 2-6 Switching voltage space vectors

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Figure 2-6 shows the six non-zero active voltage switching space vectors ( , , ... ). These can be written as where ( ( ) )

(2.11)

is the dc-link 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 2-7 Control of Stator Flux

The goal is to keep the modulus of the stator flux-linkage vector (| |) within the hysteresis band (denoted by the two circles), whose width is as shown in Figure 2-7. The locus of the flux-

linkage space vector is divided into several sectors, and due to the six-step inverter, the minimum number of sectors required is six. The six sectors are also shown in Figure 2-7. It is assumed that initially the stator flux-linkage space vector is at position , thus is in sector 1. Assuming that the the

stator flux-linkage space vector is rotating anticlockwise, it follows that since at position

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stator flux-linkage 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 2-7. Thus the stator flux-linkage 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 flux-linkage space

vector is again at the upper limit. On the other hand, it should be noted that if the stator flux-linkage 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 flux-linkage 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 2-7, 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 flux-linkage 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 flux-linkage 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 flux-linkage 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 2-8. The speed control loop and the flux reference generator as a function of speed are shown in Figure 2-9. The speed controller utilizes a linear speed regulator producing the reference value . Linear speed regulators are typically of

proportional-integral (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 2-8 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 hysteresis-band 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 2-9 Speed control loop and flux reference generator

14

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 look-up table as shown in Table 2-1. 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 non-zero 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 six-pulse 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 non-zero vectors. It is important to note that the duration of the zero states has a direct impact on the electromagnetic torque oscillations [2].

Table 2-1 Optimum voltage switching vector look-up 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 3-phase induction motor model. The "SimPowerSystems" toolbox available in Simulink was used to model the power electronics components. Figure 2-10 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 q-axis 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 2-10 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 2-11 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 look-up table described in Table 2-1. 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 2-12 Stator flux linkage vector. 1) q-axis component of stator flux. 2) d-axis component of stator flux. 3) magnitude of stator flux linkage vector.

Figure 2-11 shows a plot of the rotor speed and the developed electromagnetic torque. Figure 2-12 shows the plot of the stator flux linkage vector as a function of time. The first sub-plot shows the qaxis component of the stator flux in the stationary reference frame. The second sub-plot shows the d-axis component of the stator flux. The magnitude of the stator flux is plotted in the third sub-plot. 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 2-13 Stator current at

1 0.8 0.6

q-axis 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

d-axis component of stator flux

Figure 2-14 Trajectory of stator flux

Figure 2-13 shows a plot of the stator current and Figure 2-14 shows the trajectory of the stator flux in the stationary reference frame. The d-axis component of the stator flux in the stationary reference frame is plotted on the x-axis, and the q-axis component is plotted on the y-axis.

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 stator-flux 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 3-1 shows a

Here, denotes the stator-flux space vector and

block diagram description of the flux estimator. The flux error is calculated from the difference of the reference value of the stator-flux 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 3-1 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 3-phase 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 flux-linkage 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 (dead-time) 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

q-axis 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

d-axis component of stator flux (Wb)

time (s)

Figure 3-2 Ideal flux and torque estimation. Open loop V/f control, stator frequency - 5Hz

Figure 3-2 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 turn-off and turn-on 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 3-3 shows one phase of a PWM inverter

gate

T1

D1 VDC T2

ia

D2

gate

PWM Generator

Figure 3-3 Single phase configuration of PWM inverter

22

Figure 3-4 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 dead-time 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 dead-time 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 dead-time

T1 T2

t2 tdead TON Tsw

t1

Figure 3-4 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 dead-time 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 3-5(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 dead-time 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 3-5(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 dead-time 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 3-6(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 dead-time 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 3-6(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 3-5 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 dead-time, 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 dead-time effect [3-5].

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 3-6 T1 transition from OFF to ON, (a) ia is positive. (b) ia is negative

A pulse based dead-time 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 on-line dead-time compensation technique based on back calculation of current phase angle is presented in [4]. This compensator has been implemented for an open-loop 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 quasi-zero 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 3-7 shows the Simulink model of the implemented algorithm on an open-loop Volts-Hertz 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 no-load 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 3-7 Simulation - Simulink model of dead-time compensation implementation

26

Figure 3-8 shows the "V/f to duty" block from Figure 3-7. 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 dead-time compensator block, shown in Figure 3-9, along with the measured stator currents and the value of the dead-time 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 3-8 Simulation - block diagram of "V/f to duty" block

Figure 3-9 "Dead-time compensator" block

27

The ideal pulse ON-time is modified based on the sign of the current though that phase. If the phase current , then the compensation algorithm adds the dead-time to the ideal ON-time. The

corrected pulse is processed through the dead time generator. The resulting pulse position not symmetric and is shifted by one-half the dead-time. If the phase current compensation algorithm subtracts the dead-time to the ideal ON-time. , 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 3-10 Stator current with 1 s dead-time; without dead-time compensation

1 5

q-axis 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

d-axis component of stator flux (Wb)

time (s)

Figure 3-11 Estimated stator flux and electromagnetic torque with 1 s dead-time; without dead-time compensation

Figure 3-10 shows the effect of dead-time on the stator current. The stator current waveform is distorted. Figure 3-11 shows a plot of the estimated stator flux and electromagnetic torque with an

28

uncompensated dead-time 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 3-12 Stator current with 1 s dead-time; with dead-time compensation

1 5

q-axis 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

d-axis component of stator flux (Wb)

time (s)

Figure 3-13 Estimated stator flux and electromagnetic torque with 1 s dead-time; with dead-time compensation

Figure 3-12 shows the waveform of the stator current with the dead-time 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 3-13 shows the plot of the estimated stator flux trajectory and the estimated electromagnetic torque when the dead-time 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 re-written 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 Volts-Hertz 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 3-14 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

q-axis component of stator flux (Wb)

0

-10

-20

-1

0

1

2

-30

5

5.2

5.4

5.6

5.8

6

d-axis component of stator flux (Wb)

time (s)

Figure 3-14 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 3-15.

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 3-15 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 one-sixth 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 re-written 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 3-16 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 3-17 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

q-axis 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 non-linear

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

d-axis component of stator flux (Wb)

time (s)

Figure 3-16 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 3-17 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 non-ideal 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 feed-forward 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 warm-up 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. Multi-motor 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 non-linearity 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. Real-time identification of stator resistance is employed and error due to dead-time 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 one-third 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 error-free 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 open-loop flux estimation is reached when the stator frequency is around 3-5Hz. 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 self-commissioning 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 4-1 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) q-axis component of statorflux (Wb)

1.5 1 0.5 0 -0.5 -1 -1.5 -2 -2.5 -2 -1 0 1 2

d-axis component stator flux (Wb) component ofof stator flux (Wb)

Figure 4-1 Estimated stator flux when non-zero 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 d-axis 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 d-axis (

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 4-2 Estimated torque when nonzero sensor dc offset is present.

41

Figure 4-2 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 4-3. The "ESTIMATOR" block in Figure 4-3 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 d-axis 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 4-3 Measuring offset identification and advanced flux and torque estimation algorithm

vqs _ k

^s v qs

^

Estimators: Stator flux (eq. 4-1) Rotor flux (eq. 4-22)

^s v ds

^ ds

^ D

s ^dq

vds_ k

^ s qs

s i^qs

^ s ds

Estimator: Electromagnetic Torque (eq. 4-19)

^ 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. 4-20)

Figure 4-4 Internal structure of ESTIMATOR block

43

The terms

and

are obtained by low-pass 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 4-4, 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, low-pass 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 error-free 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 low-pass 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 open-loop Volts-Hertz 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 low-pass filter based flux estimation implementation The algorithm suggested in [19] was implemented for an open-loop Volts-Hertz 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 no-load 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 n-identical 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 4-5 Cascaded low-pass filter for flux estimation

Figure 4-5 shows the Simulink model of the implemented 3-level 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 4-6 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

q-axis component of stator flux (Wb)

2

1

0

-1

-2

0.5

-3 18

18.5

19

19.5

20

d-axis component of stator flux (Wb)

time (s)

Figure 4-6 Stator flux trajectory and estimated torque using cascaded filters for flux estimation

4.4.2 Proposed algorithm with Volts-Hertz 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 no-load conditions. Figure 4-7 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 4-8 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 d-axis 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 4-7 Simulink block diagram of proposed offset correction algorithm

Figure 4 9 shows correction values for the q- and d-axis 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 x-axis represents the d-axis component of the stator flux, and the y-axis represents the q-axis 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 4-8 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 4-9 Simulation Results - q and d axis voltage offset correction terms

50

1

0.14

q-axis 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

d-axis component of stator flux (Wb)

time (s)

Figure 4-10 Simulation Results - Estimated stator flux trajectory and estimated electromagnetic torque

q-axis 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)

d-axis 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 4-11 Simulation results - q-axis and d-axis components of stator flux

51

Chapter 5

Experimental Setup

5.1 Introduction

A motor-generator dynamometer test-bed was built to perform the experiments described in chapters 3 and 4. This chapter describes the test-bed in detail. Figure 5-1 shows a block diagram representation of the electric drive system and its major components. The load and the test motors are squirrel cage 3-phase AC induction motors. The two motors are coupled with an in-line torque transducer. Figure 5-2 shows a photograph of the test-bed. 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 5-1 Dynamometer test-bed block diagram

52

Figure 5-2 Dynamometer test-bed

5.2 Load Motor

The load motor is the Azure Dynamics (http://www.azuredynamics.com) AC55 3-phase AC induction motor with DMOC445 Drive System controller. The name plate details of the AC55 motor is listed in Table 5-1.

Table 5-1 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 DSP-controlled, rugged, waterproof inverter for controlling 3-phase induction motors. The typical connection of the DMOC motor controller is illustrated in Figure 5-3. 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 S1-A-7001 CAN-to-RS232 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 5-3 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 set-point 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 60-tooth sensor disc.

Table 5-2 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 anti-windup. The drive is operated in speed-controlled mode or torque-controlled mode depending on the three scenarios described in Table 5-2. 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 real-time. Figure 5-4 shows a screenshot from the ccShell program. The "viewer" is used to view and log variables.

Figure 5-4 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 real-time hardware and comprehensive I/O features. Figure 5-5 shows the dSPACE DS1104 PCI controller card. The dSPACE DS1104 Controller card has Master-Slave 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 (3-phase and 1-phase), capture inputs and a serial peripheral interface. Figure 5-6 illustrates the internal blocks of the dSPACE DS1104 Controller card.

55

Figure 5-5 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 real-time 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 real-time 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 Real-Time Workshop®. The real-time 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 real-time and Simulink® experiments.

56

Figure 5-6 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 real-time experiment. This means reference speed and torque quantities can be set while the experiment is running. Figure 5-7 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 3-phase 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 5-11 shows a block diagram of the power converter that supplies power to the test motor.

Figure 5-7 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 5-10 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 5-8. Figure 5-11 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 5-8 Dual IGBT gate driver pin configuration

Figure 5-9 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 dc-link voltage. Figure 5-9 shows a picture of the test motor inverter with the capacitor bank connected in parallel. Figure 5-12 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 5-10 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

3-ph 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 5-11 Power Converter block diagram

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Figure 5-12 Circuit diagram of the inverter board

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5.6 Feedback sensing

The implemented current sensing module consists of two current sensors. Since the stator windings of the motor are a three-phase wye connection, and assuming balanced three-phase 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 150-P. 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 5-12 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 20-P). Figure 5-12 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 in-line torque transducer is a standard rotting shaft slip ring torque sensor (Honeywell Sensotec/Lebow, Model 1104-500) designed for general test and measurement applications, such as motor testing. The torque sensor is rated for 55 Nm (500 lb-in) and a maximum speed of 9000 rpm.

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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 milli-volts 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 SCM5B38-02 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 5-13 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 5-13 Per-phase 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.

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Based on the nameplate data and the datasheet of an induction motor, the electrical parameters of the motors can be estimated. Table 5-3 lists the data from the nameplate of the motor. Typical performance characteristics of the motor at 208V and 60Hz are listed in Table 5-4.

Table 5-3 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 5-4 Performance Data at 208V, 60Hz

General Characteristics 40.4337 Pull-Up Torque [Nm] 11.1 Locked-Rotor Torque [Nm] 0.288 Ohms A Ph / Line-line Resistance Starting Current [A] 0.000 Ohms B Ph Break-Down 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] No-Load 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 no-load 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 air-gap 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 5-4. (5.4) (5.5)

(

)

(

)

(5.6)

In equation (5.6), the term ns denotes the stator frequency in radians/second. From Table 5-4, 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 5-5.

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Table 5-5 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 dead-time and inverter nonlinearity compensation

The compensation techniques discussed in sections 3.3.1 and 3.3.3 was implemented on the dSPACE controller. Figure 6-1 shows the implementation of dead-time and inverter nonlinearity compensation algorithms.

Figure 6-1 Dead-time and inverter nonlinearity compensation

Figure 6-2 Inverter nonlinearity compensation

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The block "nonlinear comp", shown in Figure 6-2, 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 3-15, 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 "dead-time comp" is used to compensating the effect due to the necessary dead-time that needs to be introduced. The algorithm for compensation, as shown in Figure 3-9, is written as a Matlab embedded-function. The same algorithm was used for simulations in section 3.3.1. Figure 6-3 shows the effect of dead-time and inverter nonlinearity on stator current. The drive was operated using open-loop Volts-Hertz control at a supply frequency of . Distortion in stator current can be seen at the 6th harmonic of the fundamental frequency. Figure 6-4 shows a plot of the stator current when only inverter nonlinearity compensation was enabled. Dead-time compensation was not enabled.

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Figure 6-3 Stator current with 1 s dead-time (Conditions: no dead-time compensation; no inverter nonlinearity compensation).

Figure 6-4 Stator current with 1s dead-time (Conditions: no dead-time compensation; inverter nonlinearity compensation enabled).

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Figure 6-5 Stator current with 1s dead-time (Conditions: dead-time compensation enabled; no inverter nonlinearity compensation).

Figure 6-6 Stator current with 1s dead-time (Conditions: dead-time compensation enabled; inverter nonlinearity compensation enabled).

70

Figure 6-5 shows a plot of the stator current when only dead-time 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 6-3) to 10.68A (in Figure 6-5). This is in agreement with the results obtained during simulation in section 3.3.1. Finally, in Figure 6-6, a plot of stator current when both dead-time compensation and inverter nonlinearity compensation algorithms were enabled is presented. The resulting waveform is relatively clean from distortions due to the effects of dead-time and inverter nonlinearity.

6.2 Implementation of proposed algorithm with open-loop Volts-Hertz control

The proposed algorithm was implemented for an open loop Volts-Hertz controlled three-phase induction motor drive. Figure 6-7 shows the Simulink block diagram of the Volts-Hertz control. The proposed algorithm is implemented at 1 kHz. The "V/f control" block is triggered using a built-in hardware timer and is implemented at 10 kHz. Figure 6-8 shows the internal structure of this block.

Figure 6-7 Simulink diagram - Volts-Hertz control; Stator flux and torque estimation using proposed algorithm

71

Figure 6-8 Simulink diagram - "V/f control" block

72

Figure 6-9 Simulink diagram - "offset algorithm" block

73

Figure 6-10 Simulink diagram - "voltage sensor offset correction" block

Figure 6-11 Simulink diagram - "current sensor offset correction" block

The "ADC Sampling" block contains the code to read the dc-bus 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 6-9 shows the implementation of the proposed offset correction algorithm. Figure 6-10 and Figure 6-11 show the "voltage sensor offset correction" and "current sensor offset correction" blocks respectively.

74

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 6-12 shows the trajectory of stator flux in the stator reference frame. The d-axis component of the stator flux in plotted on the x-axis and the q-axis component is on the y-axis. It can be seen that with no correction, the stator flux trajectory is not centered at the origin. In Figure 6-13, large oscillations can be seen in the estimated torque when the correction algorithm is not enabled.

Figure 6-12 Stator flux trajectory (Conditions: Correction disabled; No software created offset)

75

Figure 6-13 Estimated torque (Conditions: Correction disabled; No software created offset)

6.2.2 Experiment 2 In the second experiment, the correction algorithm is enabled. Figure 6-14 and Figure 6-15 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 6-16 and Figure 6-17 show the current and voltage correction terms. Figure 6-18 presents the d-axis and q-axis stator flux components in the stator reference frame.

76

Figure 6-14 Stator flux trajectory (Conditions: Correction enabled; No software created offset)

Figure 6-15 Estimated torque (Conditions: Correction enabled; No software created offset)

77

Figure 6-16 Current correction terms (Conditions: Correction enabled; No software created offset)

Figure 6-17 Voltage correction terms (Conditions: Correction enabled; No software created offset)

78

Figure 6-18 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 6-19 and Figure 6-20. Figure 6-21 and

79

Figure 6-22 show the correction terms in stator current and stator voltage. As can be seen, the algorithm showed satisfactory accuracy in estimating the errors.

Figure 6-19 Stator flux trajectory (Conditions: Correction enabled; Software created offset)

Figure 6-20 Estimated torque (Conditions: Correction enabled; Software created offset)

80

Figure 6-21 Current correction terms (Conditions: Correction enabled; Software created offset)

Figure 6-22 Voltage correction terms (Conditions: Correction enabled; Software created offset)

81

Figure 6-23 Stator flux components (Conditions: Correction enabled; Software created offset)

Figure 6-23 shows the d-axis and q-axis stator flux components in the stator reference frame. As can be seen from the plots in Figure 6-19 to Figure 6-23, 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 6-20 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 6-24 shows the estimated and measured values of the

82

electromagnetic torque. It can be seen that the fluctuations in torque are real and not due to errors in estimation.

Figure 6-24 Estimated torque and measured torque

83

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, dead-time and inverter nonlinearity and offsets in sensor measurement on flux and torque estimation has been described. Compensation techniques proposed in literature to solve the dead-time 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.

84

References [1] B. K. Bose, Modern Power Electronics and AC Drives. Upper Saddle River (NJ): Prentice Hall, 2002. [2] P. Vas, "Sensorless Vector and Direct Torque Control". Oxford, Eng. ; New York: Oxford University Press, 1998. [3] Seung-Gi Jeong and Min-Ho Park. (1991, "The analysis and compensation of dead-time effects in PWM inverters". Industrial Electronics, IEEE Transactions on 38(2), pp. 108-114. [4] A. R. Munoz and T. A. Lipo. (1999, "On-line dead-time compensation technique for open-loop PWM-VSI drives". Power Electronics, IEEE Transactions on 14(4), pp. 683-689. [5] G. L. Wang, D. G. Xu and Y. Yu. "A novel strategy of dead-time compensation for PWM voltagesource inverter". Presented at Applied Power Electronics Conference and Exposition, 2008. APEC 2008. Twenty-Third Annual IEEE. [6] D. Leggate and R. J. Kerkman. (1997, "Pulse-based dead-time compensator for PWM voltage inverters". Industrial Electronics, IEEE Transactions on 44(2), pp. 191-197. [7] A. C. Oliveira, C. B. Jacobina, A. M. N. Lima and E. R. C. da Silva. "Dead-time compensation in the zero-crossing current region". Presented at Power Electronics Specialist Conference, 2003. PESC '03. 2003 IEEE 34th Annual. [8] J. W. Choi and Seung-Ki Sul. (1995, "A new compensation strategy reducing voltage/current distortion in PWM VSI systems operating with low output voltages". Industry Applications, IEEE Transactions on 31(5), pp. 1001-1008. [9] Y. Murai, A. Riyanto, H. Nakamura and K. Matsui. "PWM strategy for high frequency carrier inverters eliminating current clamps during switching dead-time". Presented at Industry Applications Society Annual Meeting, 1992., Conference Record of the 1992 IEEE.

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[10] M. E. Haque and M. F. Rahman. "Influence of stator resistance variation on direct torque controlled interior permanent magnet synchronous motor drive performance and its compensation". Presented at Industry Applications Conference, 2001. Thirty-Sixth IAS Annual Meeting. Conference Record of the 2001 IEEE. [11] F. Bonanno, A. Consoli, A. Raciti and A. Testa. (1997, "An innovative direct self-control scheme for induction motor drives". Power Electronics, IEEE Transactions on 12(5), pp. 800-806. [12] R. J. Kerkman, B. J. Seibel, T. M. Rowan and D. Schlegel. "A new flux and stator resistance identifier for AC drive systems". Presented at Industry Applications Conference, 1995. Thirtieth IAS Annual Meeting, IAS '95., Conference Record of the 1995 IEEE. [13] B. S. Lee and R. Krishnan. "Adaptive stator resistance compensator for high performance direct torque controlled induction motor drives". Presented at Industry Applications Conference, 1998. Thirty-Third IAS Annual Meeting. the 1998 IEEE. [14] S. Mir, M. E. Elbuluk and D. S. Zinger. "PI and fuzzy estimators for tuning the stator resistance in direct torque control of induction machines". Presented at Power Electronics Specialists Conference, PESC '94 Record., 25th Annual IEEE. [15] J. Holtz. (2002, "Sensorless control of induction motor drive". Proc IEEE 90(8), pp. 1359. [16] Z. Pantic. (2007, "Estimacija fluksa i brzine obrtanja asinhronog motora bez davaca na vratilu". [17] K. D. Hurst, T. G. Habetler, G. Griva and F. Profumo. (1998, "Zero-speed tacholess IM torque control: Simply a matter of stator voltage integration". IEEE Trans. Ind. Appl. 34(4), pp. 790. [18] Myoung-Ho Shin, Dong-Seok Hyun, Soon-Bong Cho and Song-Yul Choe. (2000, "An improved stator flux estimation for speed sensorless stator flux orientation control of induction motors". IEEE Transactions on Power Electronics 15(2), pp. 312.

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[19] B. K. Bose and N. R. Patel. (1997, "A programmable cascaded low-pass filter-based flux synthesis for a stator flux-oriented vector-controlled induction motor drive". IEEE Trans. Ind. Electron. 44(1), pp. 140. [20] J. Hu and B. Wu. (1998, "New integration algorithms for estimating motor flux over a wide speed range". IEEE Transactions on Power Electronics 13(5), pp. 969. [21] T. Ohtani, N. Takada and K. Tanaka. (1992, "Vector control of induction motor without shaft encoder". IEEE Trans. Ind. Appl. 28(1), pp. 157. [22] J. Holtz and J. Quan. (2002, "Sensorless vector control of induction motors at very low speed using a nonlinear inverter model and parameter identification". IEEE Trans. Ind. Appl. 38(4), pp. 1087. [23] J. Holtz and J. Quan. "Drift and parameter compensated flux estimator for persistent zero stator frequency operation of sensorless controlled induction motors". Presented at Industry Applications Conference, 2002. 37th IAS Annual Meeting. Conference Record of the. [24] Dae-Woong Chung and Seung-Ki Sul. (1998, "Analysis and compensation of current measurement error in vector-controlled AC motor drives". Industry Applications, IEEE Transactions on 34(2), pp. 340-345.

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