SENSORLESS SPEED ESTIMATION IN THREE PHASE INDUCTION MOTORS by Matthew Govindsamy NHD: Electrical Engineering A research dissertation submitted in compliance with the requirements for the degree Magister Technologiae: Electrical Engineering in the Faculty of Engineering Port Elizabeth Technikon Promoter: Dr H. A. van der Linde Phd:Elctrical Engineering
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SENSORLESS SPEED ESTIMATION IN THREE
PHASE INDUCTION MOTORS
by
Matthew Govindsamy NHD: Electrical Engineering
A research dissertation submitted in compliance with the
requirements for the degree
Magister Technologiae: Electrical Engineering
in the
Faculty of Engineering
Port Elizabeth Technikon
Promoter: Dr H. A. van der Linde Phd:Elctrical Engineering
i i
DECLARATION
This dissertation has not been submitted previously for
qualification purposes but has been created by the author
during 2001/2002.
The references are utilized to establish the background.
20 January
------------------ -------------------
M. Govindsamy Date
ii ii
ABSTRACT
This thesis proposes a technique to determine and improve the performance of
a sensorless speed estimator for an induction motor based on Motor Current
Signature Analysis (MCSA). The theoretical concepts underlying the parameter
based observer are developed first and then the model of the observer is built
using Simulink. The observer is developed based on Model Reference Adaptive
System (MRAS). The dynamic performance of the observer and its behavior due
to variation of machine parameters is studied. The error in speed estimated
using this observer is shown and the ability of MCSA to retune the rotor speed
from the stator current spectrum. The spectrum estimation technique has been
implemented using a software routine in Matlab. Both the observer and MCSA
techniques were implemented practically on an induction motor. The
performance of the combined sensorless speed estimation system was tested
and verified.
iii iii
ACKNOWLEDGEMENTS
The following persons are acknowledged for their valued participation that
contributed to the successful completion of this research project:
* Dr. A vd Linde for his continued academic guidance, motivation and
dedication during the course of my study.
• My family who provided me the mental support and motivation, to keep up
my spirit and carry out my work successfully.
• Mrs N Sam for her meticulous administrative assistance.
• Port Elizabeth Technikon for their financial commitment.
iv iv
TABLE OF CONTENTS
DECLARATION i
ABSTRACT ii
ACKNOWLEDGEMENTS iii
CONTENTS iv
LIST OF TABLES ix
LIST OF ABBREVIATIONS AND TERMS x
CHAPTER 1: INTRODUCTION 1
1.1 BACKGROUND 1
1.2 PROBLEM STATEMENT 2
1.3 OBJECTIVES 2
1.4 METHODOLOGY 3
1.5 SCOPE OF THE DISSERTATION 3
1.6 SIGNIFICANCE OF THE RESEARCH 3
1.7 HYPOTHESIS 5
1.8 GENERAL 5
v v
1.8.1 Speed Estimation using Induction
Motor Models 5
1.8.1.1 Stator field orientation based
Estimation 6
1.8.1.2 Back emf based Estimation 6
1.8.1.3 Speed Estimation Independent 7
Of Secondary Resistance
1.8.1.4 Speed Estimation using the
Extended Kalman Filter
Approach 8
1.8.1.5 Model Reference Adaptive
System 9
1.8.2 Speed Estimation using Motor Current
Signature Analysis 12
1.8.3 Fine Tuning for Better Speed
Estimation 13
1.9 STRUCTURE OF THE DISSERTATION 14
vi vi
2 MOTOR CURRENT SIGNATURE ANALYSIS
2.1 INTRODUCTION 15
2.2 MATHEMATICAL ANALYSIS OF MCSA 15
2.3 REVIEW OF SENSORLESS SPEED ESTIMATION
USING MCSA 18
2.3.1 LABVIEW IMPLEMENTATION OF
MCSA 18
2.3.2 REAL TIME IMPLEMENTATION
USING DSP 20
2.3.3 DISCUSSION ON RELATED WORK
IN SENSORLESS SPEED
ESTIMATION 22
3 OBSERVER BASED SPEED ESTIMATION
3.1 INTRODUCTION 28
3.2 INDUCTION MACHINE MODEL 29
3.3 OPEN LOOP OBSERVER 34
3.4 CLOSED LOOP OBSERVER 37
3.4.1 Model Reference Adaptive System
(MRAS) 37
vii vii
3.4.2 MRAS In Speed Estimation 38
3.4.3 Design And Synthesis Of Observer 40
3.4.4 Analysis Of Dynamics Of The Observer
System 44
3.4.5 Performance Analysis Of The Observer 49
3.5 REAL TIME IMPLEMENTATION OF THE SPEED
OBSERVER 55
4. IMPLEMENTATION OF SENSORLESS
SPEED ESTIMATION
4.1 INTRODUCTION 59
4.2 EXPERIMENTAL SETUP FOR SPEED
ESTIMATION 59
4.2.1 Current And Voltage Transducers 61
4.2.2 Analog Interface 63
4.2.3 Induction Motor And Load 64
4.3 SPEED ESTIMATION AND FINE TUNING 65
4.3.1 Speed Estimation Using Observer 65
4.3.2 Effect Of Parameter Variation 67
viii viii
4.3.3 Speed Estimation Using MCSA 70
4.3.3 Fine Tuning Of The Observer
Speed Estimate 75
5. SUMMARY AND CONCLUSION
5.1 SUMMARY 78
5.2 SCOPE FOR FUTURE WORK 80
6. REFERENCES 82
7. APPENDIX A A1
8. APPENDIX B B1
9. APPENDIX C C1
ix ix
LIST OF TABLES
3.1 Effect of parameter variation on speed estimate –
Simulation results 52
4.1 Effect of parameter variation on speed estimate –
Experimental results 69
1 1
CHAPTER 1
INTRODUCTION
1.1 BACKGROUND
Electric motors for variable speed drives have been
widely used in many industrial applications. In the
early years dc motors were widely used for adjustable
speed drives because of their ease of control.
However, due to advances in both digital technology and
power semiconductor devices, ac drives have become more
economical and popular. For accurate torque control
and precise operating speeds, more sophisticated
techniques are necessary in the control of ac motors.
These techniques employ high speed Digital Signal
Processors and control techniques based on estimation
or identification of speed and other machine states.
Speed estimation is an issue of particular interest
with respect to induction motor drives as the rotor
speed is generally different from the speed of the
revolving magnetic field.
2 2
The measurement of speed in adjustable speed drives is
done using opto-electronic or electromagnetic speed
transducers. The opto-electronic transducers experience
errors in speed detection as a result of mounting,
vibration and the ingress of contaminant; in addition
they are usually the least reliable drive component.
Therefore sensorless speed detection is highly
desirable.
1.2 PROBLEM STATEMENT
Commercially available speed measurement devices
require direct contact with the shaft of the motor and
are often inaccurate and unreliable after prolonged
use.
1.3 OBJECTIVES
• Investigate speed estimation using techniques
that are dependant and those that are
independant on machine parameters
• Correction of one technique using the other for
greater accuracy.
3 3
1.4 METHODOLOGY
A literary review is undertaken in order to establish
the required background, new trends in industry as well
as the relevancy, and application of the research. The
implementation of sensorless speed estimation is
carried out experimentally. The method and results are
dealt with in chapter 4.
1.5 SCOPE OF THE DISSERTATION
This research dissertation only considers:
• ac induction motors
• three phase supply
• The application of Motor Current Signature
Analysis is limited to speed estimation only.
1.6 SIGNIFICANCE OF THE RESEARCH
Speed measurement is normally accomplished with a
tachometer. Some tachometers require direct contact
with the shaft of the motor, whilst others such as
photo tachometer and stroboscope tachometer require
close proximity to the shaft.
4 4
Many motors are located in inaccessible locations or
are operated in hazardous environments e.g. motor
operated valves in a nuclear plant. In such instances
personal safety may often preclude the monitoring of
these motors, even when it otherwise would be
desirable.
Many motors, even when accessible, do not provide an
exposed shaft due to their mounting configurations.
For example, many compressors used in air conditioning
and refrigeration equipment are coupled to the motors
inside a sealed compartment, thus preventing motor
speed measurement by all commercially available
tachometers.
All these problems can be overcome by means of
sensorless speed estimation. Sensorless speed
estimation permits the speed sensing to be done
remotely, even some distance from the motor. All that
is needed is access to the motor electric cables. This
could even be at the control centre situated remotely.
As the proposed technique of sensorless speed
estimation is non – intrusive, it is a very safe
method.
5 5
1.7 HYPOTHESIS
The combination of the machine parameter dependent and
machine parameter independent techniques will provide
accurate and reliable speed estimation in three phase
induction motors that does not require contact with the
rotating shaft.
1.8 General
A brief introduction to observer based speed detection
and current based methods is now given.
1.8.1 Speed Estimation using Induction Motor Models
Many control and estimation strategies for induction
motor (IM) drives are based on electrical equivalent
circuit models of the motor. In many cases, the model
is a steady-state equivalent circuit model, but for
high performance drives, a transient model of the motor
is required. Many schemes based on simplified motor
models have been devised to sense the speed of the IM
from measured terminal quantities. A few of the
techniques based on machine parameters available in the
literature are discussed here with their relative
merits and demerits.
6 6
1.8.1.1 Stator Field Orientation based Estimation
Some of the earlier work on sensorless speed
estimation was based on the method of field
orientation, relative to the rotor flux linkages or its
time derivative. In [1], the stator flux vector is
estimated from measured machine terminal quantities to
provide the field transformation angle δ. An estimate
of the rotor frequency is obtained from the condition
for field orientation. These two can be used to
estimate the angular mechanical velocity. At low
stator frequencies, stator flux estimation is sensitive
to an inaccurate stator resistance value in the
estimation model. It has also been shown that the
accuracy of the speed estimate is poor under load due
to the amplitude error of the stator flux.
1.8.1.2 Back-emf based Estimation
Another method of speed estimation [2] uses the back-
emf vector. This is based on the fact that the back-
emf vector leads the rotor flux vector by 90º, provided
the rotor flux magnitudes changes slowly. Here the
estimate of rotor speed is based on the stator input
voltage and the synchronous speed. This method has
moderate dynamic performance at lower speeds.
7 7
Some work has been done based on the stator current
and the phase angle of the stator voltage reference
vector [2]. Speed estimation here depends on the
stator frequency signal and the active stator current,
which is proportional to the rotor frequency. The
speed estimation techniques discussed so far, are based
on stator current or the rotor flux vector and are
essentially open-loop types of estimation. More
accurate speed can be obtained when compared to the
above techniques. A few of these techniques are now
presented.
1.8.1.3 Speed Estimation Independant of Secondary Resistance
In the work done in [3], speed estimation is done
without prior knowledge of the rotor resistance. The
machine characteristic equations are derived without
involving the rotor resistance and the estimate is
based on the rotor current and flux vector. Here, the
characteristic equations of the induction motor are
used to express the rotor current and flux linkages in
terms of the stator voltages and currents.
8 8
The speed of the motor is estimated making use of the
outer product and inner product of the flux linkages
and currents. This method has a disadvantage of
division by zero when the machine is supplied from
sinusoidal mains. Means to avoid this has been shown,
but involves estimation of the rotor resistance. This
method is also influenced by parameter variations,
especially the errors due to stator resistance, stator
and rotor leakage inductances.
1.8.1.4 Speed Estimation using the Extended Kalman Filter
Approach
A different approach to speed estimation is based on
the Extended Kalman Filter (EKF) algorithm. The
estimation technique [5] is based on a closed-loop
observer that incorporates mathematical models of the
electrical, mechanical and thermal processes occurring
within the induction motor. However, this work
addresses only the thermal effects by incorporating a
thermal model of the motor in the estimation process.
Here, a two twin axis stator reference frame is used to
model the motor’s electrical behaviour.
9 9
The thermal model is derived by considering the power
dissipation, heat transfer and the rate of temperature
rise in the stator and rotor.
The well known linear relationship between resistance
and temperature are also taken into account in the
model. These yield a non-linear model, which is
linearized for the EKF estimator. The EKF estimator
for speed and temperature is a predictor-corrector
estimator. It has been shown that the speed estimation
correlates with the measured speed in both the
transient and steady state conditions. Though this
method of speed estimation is independent of the
drive’s operating mode, closed loop estimation is
possible only if the stator current is nonzero.
1.8.1.5 Model Reference Adaptive System
The Model Reference Adaptive System (MRAS) is one of
the more recent techniques in speed estimation based on
the machine model [4]. Here the induction motor is
used as the reference and a vector-controlled induction
motor model is used as the adjustable model.
10 10
This model is adjusted to drive the error in speed
between the two models to zero. The method described
here uses the synchronous reference frame in the model.
In order to obtain an accurate dynamic representation
of the motor speed, it is necessary to base the
calculation on the coupled circuit equations of the
motor. This technique is used in [6]. In this technique
of speed estimation, the IM is modelled based on a
state-space model of the machine using two axis
variables. This may be done in the stationary or
synchronous frames, both having been used widely. Since
the motor voltages and currents are measured in the
stationary reference frame, it is convenient if the
motor equations are also in the stationary reference
frame. With complete knowledge of the motor parameters
and variables like the resistance, inductance, poles,
electrical angular velocity, stator voltages and
current, the instantaneous speed of the rotor can be
estimated on a closed-loop basis from the equations of
the machine. This technique will be dealt in chapter
3.
11 11
This method of speed detection has disadvantages
because of its dependence on machine parameter. The
frequency dependence of the rotor electrical circuit
parameters, non-linearity of the magnetic circuit and
temperature dependence of the stator and rotor
electrical circuits all have an impact on the accuracy
of the observer and hence the speed estimation. At high
frequencies and no-load conditions these errors are
usually quite negligible.
However, the speed accuracy is generally sensitive to
model parameter mismatch if the machine is loaded,
especially in the field-weakening region and in the
low-speed range. The parameter contributing to this
variation are [1][6]:
• Rotor resistance variation with temperature
• Stator resistance variation with temperature
• Stator inductance variation due to saturation of the
stator teeth
A parameter independent technique is discussed next.
12 12
1.8.2 Speed Estimation using Motor Current Signature
Analysis
Motor current signature analysis was developed as a
powerful monitoring tool by Oak Ridge National
Laboratories for motors and motor driven equipment. It
can provide “ signatures” or information regarding the
condition of the machine like bearings, windings and
speed of the rotor. These signatures arise as a result
of the variation in permeance of the air-gap field,
which are due to the rotor slotting and eccentricity.
Further, this signature is available in the stator
current dawn by the machine from the power supply.
This avoids the use of a separate cable being used for
speed estimation using conventional transducers.
The stator current can be sensed using a current
transducer and then can be sampled to convert it into a
discrete time signal. This is used to analyse the
spectrum of the current in the frequency domain using
digital techniques by means of a DSP and PC. Frequency
domain analyses give a better representation of the
contents of the stator current and bring out the
harmonics related to speed.
13 13
The transformation from the time domain to the
frequency domain is achieved using the Fast Fourier
Transform technique. The improvement that can be
obtained using other spectral estimation techniques
other than the FFT has also been studied. The FFT
technique of speed estimation has a disadvantage of
poor dynamic performance. A conceptual understanding
of the MCSA and the related mathematics is given in the
next chapter. It also gives a comparison of the
various techniques being followed and their relative
merits and demerits.
1.8.3 Fine-tuning for better Speed Estimation
The current harmonics based method of speed
estimation, MCSA, has a disadvantage at low speeds and
accurate estimation can be made only at the cost of
longer response time. On the other hand, observer
based techniques used are affected by variations in
machine parameters. Hence, it is proposed in this
thesis to use the current harmonic method to fine tune
observer based estimation technique already presented
in the literature.
14 14
1.9 STRUCTURE OF THE DISSERTATION
The remainder of this thesis is organised into 4
chapters. Chapter 2 has a detailed discussion of the
various techniques for sensorless speed estimation
using current harmonics. In the 3rd chapter the
various steps involved in developing an observer based
speed estimator and the effects of parameter variations
are presented. Then, methods of fine-tuning the
observer based estimation with the motor current
signature analysis based techniques is presented in the
4th chapter. The 5th chapter concludes the thesis and
makes recommendations on further work that can be done
in sensorless speed estimation.
15 15
CHAPTER 2
MOTOR CURRENT SIGNATURE
ANALYSIS
2.1 Introduction
In this chapter the theory underlying sensorless speed
estimation using the stator current spectrum, namely
motor current signature analysis (MCSA) is discussed.
Different techniques that have been employed are
explained and an indication of how this thesis follows
the previous works by Schauder.C, Zibai.X [7,8], is
presented.
2.2 Mathematical Analysis of MCSA
In an induction motor, speed associated harmonics
arise in the stator current due to variations in air-
gap permeance interacting with the air-gap MMF, which
[14]Hurst K. D and Habetler T.G.( 1997). A comparison of spectrum
estimation techniques for sensorless speed detection IM, IEEE Trans.
Ind.Apps., Vol.33, No4, July/Aug , pp 898-905.
[15]Landau Y.D. (1979). Adaptive Control – The Model Reference
Approach”, Marcel Dekker Inc., New York.
[16]Chee-Mun Ong (1998). Dynamic simulation of Electric machinery –
using MATLAB/SIMULINK , Prentice Hall, New Jersey.
[17]Nise Norman S. (1995). Control System Engineering”,
Addison-Wesley publishing company, California.
lxxxv
APPENDIX A A1. 1 Details of Induction motor used in Experiment 3Ph, 60Hz, Squirrel cage Induction motor Rated voltage-208 V Rated power- 1/3 HP Rated current –1.7 A Rated Speed- 1725 RPM
A1.1.1 Determination of Motor parameters A 1.1. 2. DC Resistance test
DC V (V) 1 (A) RsΩ 5 0.31 15.9 10 0.63 15.87
A.1.1.3 No load test
V (V) I (A) W1 (Watts) W2 (Watts) Speed (RPM) 200 0.85 110 -52 1789
A. 1.1.4 Blocked rotor test
I (A) V (V) W1 (Watts) W2 (Watts) 1.7 59 88 8
From the above tests and using the standard machine equations, the equivalent circuit parameters of the machine were determined. The inertia of the machine was determined from the manufacturer’s details on the rotor. Using DC resistance test: Stator resistance Rs = 15.9Ω directly from DC resistance test. Using no-load test results: P1nt = Pnt/3 = 19.33 Watts V1nt = 200V =Qnl = = Xnt = V1nt
2 /Qnt = 415.5 Ω = Lm = Xnt/ 2∏ƒ =1.102H
A1
lxxxvi
Using Blocked rotor test results P1br = Pbr/3 = 32 Watts V1br = Vbr = 59V I1br =Ibr 3 = 0.98 A ⇒ Qbr = ⇒Xbr = Q1br / I 1br
2 = 50.14Ω ⇒Xs =Xr =Xbr/2 =25.08 ⇒ Ls = Lr
` =0.0665 H ⇒ Rbr – 1br / I 1br
2 = 33.32Ω ⇒Rr` = Rbr - Rs = 17.42Ω
From above equations the parameters of the machine are given below, Rs- Stator resistance –15.9Ω Rr- Rotor resistance – 17.42Ω
Ls- Stator self inductance –6.94mH Lr –Rotor self inductance-6.94mH
Lm- Mutual inductance –163.73 mH J- Inertia of the rotor-0.1Kg.m2
A2
lxxxvii
APPENDIX B
/*This program is to solve the speed observer equation*/ /* using the 2nd Runge-Kutta method for integration */ #include <stdio.h> #include <stdlib.h> #include <math.h> #include < string.h> #include <malloc.h> double ids [3], iqs [3], vds [3], t [3]; double sigma_ls; double rs, rr, lr, lm, ls; double lds [3[, lqa [3], ldest [3], lqest [3], w [3]; double K1, K2; double T2; double *k1, *k2, *k3, *k4; int n; void main () void getK (double *y, int j, double *kx); double d1 (int j); double d2(int j); double y [6], y1[6] double I; int j, m; FILE* vds_p, *vqs_ p, *ids _ p, *output_p; char vds_file[]=”f_vds.txt”, vqs_file[] = “f_vqs.txt”; char ids_file[] = “ f_ids.txt”,iqs_ file[] = “ f_iqs.txt”; char output_file [] = “ out.txt”; vds_p =fopen (vds_file, “r”); vqs_p= fopen) vqs_file, “r”); ids_lp = fopen (ids_file, “r”) iqs_p = fopen (iqs_file, “r”)
B1
lxxxviii
k1= (double*) malloc (sizeof (double)*6); k2=(double*) malloc(sizeof(double)*6) k3=(double*) malloc(sizeof(double)*6) k4=(double*) malloc(sizeof(double)*6) output_p = fopen(output_file, “w”); rs= 3.35; rr= 1.99; ls =0. 17067; lm =0.16373; sigma_ls=9lm*lm/lr)-ls; K1= 152.3; K2= 2284.8; T2 = lr/rr; /*read data and call rk2 function */ /*read data*/ i=0; while (feof( vds_p)) fscanf(vds_p, “%le%le”, &t, &vds[0]); i++ printf(“total no of points is %le/n”, I); fclose (vds_p) /* counted the total number of points. Going back*/ /*to the beginning of file by closing and opening*/ vds_p =fopen(vds_file, “r”); /*Initialize y values*/ for(j=0;j<6;++j)y[j]=0 /*end of initialization*/ /*Begin j-loop*/ for(j=0; j<(I-3)/2;++j) /*reading first 3 points without invoking rk2*/ if(j<3)