2003

II
National Power and Energy Conference (PECon) Proceedings, Bangi, Malaysia

Simulation and Modeling of Stator Flux

Estimator for Induction Motor using Artificial
Neural Network Technique

Yushaizad Yusof, Abdul Halim Mohd. Yatim, Senior Member. IEEE

To ease such task, some assumptions and agreements is

Abslruc/--Accul'ate stator nux estimation for high implemented [ll These assumptions and agreements are as
performance induction motor drives is very important to ensure follows:
I)roper drive operation and stab i l i t y . Unfortunately, there is i. Co nsta nt air gap exists in between smooth surface
some problems occurred when estimating stator flux especially
of stator and rotor. These surfaces contains three
at zero s pe ed and at low frequency. Hence a simple open loop
phase winding depth that can be neglected.
controller of pulse widtll modulation voltage source inverter
ii. Stator an d rotor iron permeability is assumed to be
(PWM-VSI) fed ind uction motor configuration is presented. By
s e lecti on of volt age model-based of stator nux e stimation, infinite and iron loss and saturation is neglected.

a
a a

simp le method USing artificial neural network (ANN) technique iii. Synunetrical stator winding is star-connected with
is proposed to es t i m te stator n ux by means of feed forward neutral that approximately isolated electrically.
back propagation algorithm. In motor drives applications, iv. Air gap spac e harmonics mechanical motive and
artificial neural network has several advantages such as faster flux density can be neglected. Stator winding real
execution speed, harmonic ripple immunity and fanlt tolerance axis is equal to phase-A winding axis.
characteristics that will result in a significant improvement in v. Rotation is positive for anti-clockwise.
the steady state performances. Thus, to simulate and model
Flux vector is flux magnitude for flux feedback control
stator fluX' esti mator, Matlab/Simulillk software package
and information of vector uni t is for vector transformation.
particularly power system cblock set and neural network
toolbox is implemented. A structure of three-layered artificial In order to control stator flux and torque precisely, stator
neural network techniquc has becn app lied to the proposed flux esti mation must be accurate and precise. Calculation of
s tator flux estimator. As a result, this technique gives good torque is depending on stator flux estimation. There are two

and
iml}rovement in estimating stator flux which the estimated distinction models in stato r flux estimation, which are
stator flux is very similar in terms of magnitude and phase voltage model current model respectively. The easiest
angle if compared to the real stator flux. way to estimate stator flux is using voltage model, or
primary circuit equation, where the voltage is integrated.

flux rotor orientation.

K£ylVords--Stator flu X, stator nux estimator, artificial neural
H owev er stator flux oriented implementation is more
network, feed fonvard back propagation, ind uction motor.
complex than
Flux stator is estimated based upon voltage stator open
I. INTRODUCTION

flux
loop integration behind stator resistance drops. So the

(fJs is written like this,

equation in the stationary a-f3 reference frame for stator

F
lux sensors such as Hall's effect devices and tracking

<l>s JCv,-Rsi,)dt (1)

coils are not very suitable in motor drives motor

Rs
control system due to several defect factors like higher
==

cost, bigger size, noise existence, drifts and not so reliable.

Where Vs = stator voltage, = stator resistanc e and
However, in the recent years with the invention of powerful
is stator current. The magnitude and phase equation for
microprocessors, almost all feedback sign al from motor's
'"

stator flux is given below.

(2)
parameter such as fluxes, torque, active and reactive power,

HBn'(:::J
power factor, speed etc. can be calculate and estimate
extremely well. For the purpose of estimating flux stator , it's
I¢ 1== �(<D�s + (fJ�J
s

(3)
important to build a dynamic ind uc tion motor model. This
mathematical model must contain all dynami c aspects that
are occurred during transient and steady state conditions.

This estimation method is .common for voltage model and

is far less sensitive, except for stator resistance, which gives
affects in estimation accuracy due to vanallon of
Y Yusuf is with the Department of Electrical, Electronics and System temperature in the motor. It will be very sensitive at low
Engineering. Nation�1 University of Malaysia (UKM), 43600 Ban gi, speed and zero speed, as a result back electromotive
Selangor. Malaysia (e-mail: yushaiza@cllg.ukm.my).
decreases suddenly and causing a complexity of integration.
A H M Yal;m is currently with the Faculty or Electrical Engineering,
Technology University or Malaysia (UTM), 81310 Skudai, Johor, Malaysia Beside that, estimation technique also raises saturation
(email: halim@ieee.org) problem and integration drift during initial condition and dc

0-7803-8208-0103/$17 cOO «)2003 IEEE.

 12

offset. To overcome saturati o n problem for integrator, low

weakness by
pass filter (LPF) is implemented. However implementation ��i -1{ g�i)

In the o per ation, if sigmoid is used as ac t i vation function,

=

magnitude
of LPF still has its discovering of estimation
error due to and phase error. Its impact is bigger

result in errors of selecting voltage vector.

at frequency that is near to cut-off frequency, which may hence output relation between layers,

Iz: 1 (7)
very low cut-off frequency, but still leave integrat i o n
Thus its need to

drift problem that caused by larger LPF constant time.

select a o�i = + e -nFI.,

Significant improvement for flux s talor estimation with LPF

amj
Equation (5) can be summarize like this,

(8)
in steady state performance for direct to rq u e control
-- == Oki(1 - Ok;)
induction motor is using phase and magnitude compensation
onetk; -
[2]. Others flux stator estimation techniques implementing
For respective output element and hidden layer element,
voltage model including programmable-cascaded LPF,
gives
correction and adjustment of stator resistance using fuzzy

(3-4].
controller or pure integrator, artificial neural network
controller and hybrid flux estimator ( 9)

(10)
u. ARTIFICIAL NEURAL NETWORK
Resilient back propagation (Rprop) is chosen as trai nin g
Artificial neural network (ANN) are successfully algorithm since it is an adaptive learning algorithm that

behaviour. Its we i ght update �w

implemente d in power electronics and motor drives areas considers local topology of the error function to change its
such as in motor control sysiem, early detection of electrical between jth and Jth

(51·
machine faults, digital signal processing of motor's neurons is ba s e d on the so-called 'Manhattan learning rule'

-!!.ij or - �ij or
parameter etc. Back propagation-training algorithm that was
introduce d by Rumelhart, Hinton, and Williams in 1986 �Wij = 0 depending on whether,

(II)
commonly trains the feed forward ANN. The distributed
oE(t) oE(t) E
OWij aWij
a (t)
&vij
weights in the network contribute to the distributed >Oor <Oor =0

untrained network, for instance, weights selection in random

associative memory property of the network. Initially the
The basic idea for improvement realized by the Rprop
manner, the output signal pattern will totally mismatch the algorithm was to obtain more information about topology of
desired output pattern for a given input pattern. The actual error function so that the weight update can be done

pattern by adj usting the weights, using supervised back 6ij which evolves during learning process according
output pattern then is being compared to the desired output appropriately. For each weight introduced it ' s own update

l ocal view of the error function. Thus, second learning

value,
propagation algorithm until the pattern matching occurs or to its

provided
the p ro du c ed pattern error relatively small. rule is as follows,

by "Neural N e twork Toolbox" package in Matlab software. (12)

Back propag ation algorithm and its variables are
I) aE(t)
OWii OWij
!!.ii=n.�(H),ifaE(t- .
ANN lea rnin g consist of two types of network that is
>0
u

Au . A(�-l),if aE(t -1) . oE(t)

implements
supervised and unsupervised network. For proposed ANN <
== n+ 0
stator flux estimator supervised network shown .
OWij OWij
in Figure 1. Time its takes for training purposes depends on
data set size and training algorithm. following equation

1
shows the classical error back propagation algorithm.
where 0 < n < I < 11 +

B
•

l+e-ne"
Oi = !(lIeti) ::: => net; = i: WijOi + (4)

weighl nmlrix ,
i

e: bias.
where 0: inpu t or output vector, W: and

t "
Ok)
+

)---
• .

Ek - �(tJJ - Ok) (fk) - Oki)

2
== ¢:> (5) inpul largel

Subscrip ts i, j, k re fer to any UlIit in the input, hidden and

.
=

output layer, and E, t, 0 are error vector, target vector Error

and update error vector respectively. Whereas sign 17 is
refers to learning rate. Fig, I i\ NN supervised network

(6)
Owkj
Llwk)::: -17(�)
 13

ilL PWM-VSI

For a balanced three-phase system, the two axes or d-q

theory is normally used for dynamic modeling of induction

orthogonal decoupled direct (d) and quadrature (q)

motor. According to this theory, variables are expressed in

components. This d-q dynamic model can be expressed in

stationary reference frame is used where d' and q' axes are
either stationary or rotating reference frame, for the project a

fixed on the stator as shown in figure 2.

Fig. 3. PWM-VSI model

III)

1·:fjTII[HII:Ht�i•••·.t •· I·.HHllmIUHHI.IU
15 .---.----e--,--.---.--�--_r--_,--,

. .
: '
• •• : : : :
{l,60 0001 O_OOl 1),003 0.00( OCU O.OCS 0.00' Q,D OLW • oo�
Ill)

Fig. 2. Stationary reference frame for d-q dynamic model

The model of pulse width modulation-voltage source

inverter is build using Simulink' environment shown in
Figure 3. An open loop control of induction motor is
introduced using sinusoidal PWM to control the switching Fig4. PWM signal
scheme. The generation of gating signal with sinusoidal

reference signal waves (va, Vb, and vo) each shifted by 21f/3.
PWM is shown in Figure 4. There are three 60 Hz sinusoidal
IV. ANN STATOR FLUX ESTIMATOR TRAINING
A carrier wave with frequency 3 kHz is then compared to the ANDTESTlNG

reference signal corresponding to a phase to generate the

gating signal for switching purpose of six pulse MOSFET The ANN stator flux model is developed from motor
devices. The input dc voltage for inverter is set to 380V. parameters such as speed w, electrical torque T., stator
These switches are connected anti-parallel with feedback current and stator voltage in d-q quantity id" iqs, v,I" v,/s
diodes. Eliminating the condition that two switching devices respectively. These four quantities are used as an input for
in the same arm cannot conduct at the same time generates neural network structure; besides real data of stator flux $,
the output voltage. also in d-q quantity is taken as target. Sampling time is 0.6s,
The induction motor used for the simulation studies has the time when steady state condition is reached. From
the following parameters: Three-phase, 3 hp, 220 V, 60 Hz, Simulink environment all these data quantities is saved and
2 pole wound induction motor. then loaded to Neural Network Toolbox for processing
procedures. Since the objective is to estimate stator flux at
Stator resistance, R,: O.80n low speed and zero sp eed, sampling time for processing and
Rotor resistance R,: 1.00 n training of neural network is shorted to O.Ol s only. Total
Stator leakage reactance, Ls: 2.00mH data set points for each quantity is 11886 points . Al1 this
Rotor leakage reactance, LT: 2.00 mR quantities is calculated in an array environment where its
Magnetizing reactance, Lm: 70.0 mH needs to be transposed first before being al10wed to be
Combine rotor and load inertia, J: 0.089 kg/m process in the toolbox. A three layers structure of neural
• Load torque, Tm: 11.87 Nm network is selected, that implies numbers of neurons in each
layers, iteration numbers, bias, type of activation function,
training algoritlun and so on is sel. Neural network structure
implemented is given .as follows:
• Configuration: Three layers
Number of neurons: 4-8-8-1
Activation function: Tansig
Training algoritlun: Resilient back
propagation
 14

Iterations: 897 (d) 1720 (q)

This build-in three layers s tructu re is constructed from two

hidden layers and one output layer and for each layer has a
single activation function. Prior to train the network, all
inputs data and target data needs to normalize first before its
j:CJII r �j =1
� � � �
qtJ
--
M
-
M "

unnormalized back to real data at the end of the training

process. Relati on between output and target is set, after that
this network structure is trained u sing resilient back
propagation algorithm (Rprop).
To make things easy, processing for each quantity of
stator nux d-q c o m po nen t is done separately. Neural
network structure training always t akes a lot of time, which
depends on numher of ne urons, training algorithm lIsed, datn
set numbers and so on. Methodology for training the I{I)

net wo rkis expressed by Figure I. The proposed network,

takes around 2-3 minu tes to complete tmining. At the
begi nning its pro duces undesirable phase and magnitude,
,

which the error is so big and entirely different with the

target Next, this error is feed back into the network to
compensate error re peatedly until the error becoming
considerable small and fulfilled the objective.
During training simulation, a fi gure is appeared
automatically showin g the characteristics performance and
conj ugate gradient movement of proposed network. Goal
for this network is set to le-4. If the gradie nt reaches the
g o a l l ine the training will be terminated After completing
, .

Ihe traini ng procedure, the fresh network then is tested to

verify it performance.

V. RESULT AND DISCUSSION

(b)
Testing for developed ANN s tator nux estimator is done
b y connected all four inputs of motor parameter shown in

l,- -�--�-- �--:-. -:�.�- �- : J

Figure 2 into the estimator block and then verifies the result.
At zero speed and low speed the simulation of stator flux

5.(a)
estimator per formances are considerable well developed.
Figure top shows that
constantly from start up until i ts reaches steady state
motor speed accelerate
! D om1 OWl 0'-003 DIIJoII Oa:li
1(.)
DIJIj 0001 OOO!l
-
Dtm
.
DOl

condition for 188.5 radls at 5.5s. From 0 10 0.00385 the

Il�:�>\:"-, , :l
m id dl e figur e is show ing characteristics of zero speed and
low speed which below 6 radls is point oul from 0.0038 to
0.012s. And lastly characteristics for electrical torque
indicate at the bottom figure
,
. o 1 2' J • '50 ,
;(1) 110"

J�[�lli�d�'-'--J�-- ,-'� -�-'�UUUJ�ill

IJ 4':QI em IIDl
0#�.1..,1lIt" ...
o:m 1rm:J' 1m

(e)
Figure 5. Simulation result, (0) Speed and torque characteristics, (h)
Curnparisoll helween cstinmtcd allll renl value in Ii axis, (e) Comparison
belwccn estim"led ond reol volue in q axis.

While figure 5.{b) mainly poi nt out the result and

performance of estimated stator flux in d axis. From the top
figure the e sti ma ted stator flux s uits the real stator flux well.
It can be seen more clearly that the estimat ed value is ind ee d
pursuing the desired value with a very small margin. If this
 15

figure is zooming in, there is a significant difference Systems Engineering, UKM, bangi, Malaysia. His research i n terests arC in
power electronics and motor drives.
between these two values. Finally the bottom figure indicates

0.017
·
the error produced after comparing the two values. · Its A H M V.tim received his B. Sc. Degree in electrical and electronics
maximum error is about pu at around pairs 10400 engineering from Portsmouth Polytechnic, Portsmouth, U.K., and M. Sc.

whilst minimum error is nearly 0 pu at several pairs. And Ph. D. degrees in power electronics from Bradford University in 1981,
1984, 1990 respectively. Since 1982 he has been a member oC the faculty at
While figure 5.(c) mainly point Ollt the result and the Vniversiti Teknologi M ala ysi a , Skudai, Malays ia where he is currently
performance of estimated stator flux in q axis. From the top a Professor and Deputy Dean of Electrical Engineering Fatuity. He has

figure the estimated stator flux suits the real stator flux well been in v olvedin several research projects in the area of power eleclronics
application and drives. He was Commonwealth fellow 1994-1995 at
in d axis . It can be seen more clearly that the estimated value
Heriot- Watt University, U.K., and visiting scholar at the Yirginia Power
is indeed pursuing the desired villue with a very small Electronics Center in 1993. Dr. yatim is active member of IEEE Malaysian

margin. If this figure is zooming in, there is a significant Section and cO'1'orate member of Institution of Engineers Malaysia. He is
Registered Enginee r with Malaysia Board of Engineers . .
difference between these two values. Finally the bottom
figure indicates the error produced after comparing the two

11100 whilst minimum error is nearly 0 pu at several pairs.

values. Its maximum error is about 0.013 pu at around pairs

VI. CONCLUSION

From the result, the ANN stator flux estimator verifies

good improvement in estimating stator flux at low speed and
zero speed. Its shows the ability not to be influenced by
defects such as drift, dc offset and so on. The
implementation of ANN technique reduces calculation and
designing complexity of an estimator, besides save a lot of
time. It also improves delay time and phase better than
common estimator. On the other hand, ANN stator flux
estimator increases time . response because no time
consuming routine is required. There is a plan to use ANN
stator flux estima tor in vector control and direct torque
control of induction motor in the future.

VII. REFERENCES

[I] N. Mohan, T. M. Undeland,.and W. P, Robbins, "Power Electronics

Converters, Applications and Design", 3,d Ed., 2003, John Wiley &
Sons, Inc.
N. N.

", 3S'h
[2] R- Idris and A. H. M. Yatim, " An Improved Stator Flux
Estimalion in Steady State Operation for Direct Torque Control of
Induction M achine IEEE- Industry Applications Society
An nual Meeting, Rome, Italy.
P] S. Mir, M. E. Elbuluk and D. S. Zinger, "PJ and Fuzzy Estimator for
Tuning the Stator Resistance in Direc t Torque Controlled Induction
MOlor Drives", IEEE Trans. On Power Electronics, Vol. 13, No.2,
pp.279-287.
[4] L. A. Cabrera, M. E. Elbuluk and I. l I us ain , "Tuning the Stator
Resistance of Induction Motor Using Neural Network", IEEE Tr.ans
On Power Electronics, Yol. 12, No.5, p p. 779-787.
[5/ }. Nanda et. aI., A ppl iution of Artificial Neural
" Network to
Economic Load Dispatch", Proc. of the 4'h Int. Conr on Adv. in
Power Systenl Control, Op era tion and Management, APSCOM-97,
1I0ng Kong, Nov. 1997.

VIII. BIOGRAPHIES

Y Yusof rec ei ved his B. Eng fronl K agoshima University, Japan in 1999
and j oined VKM as a tut or aftcr graduation. He obtained his M. Eng from
Universiti Te knologi Malaysia (UTM), Skudai, Malaysia in 2002 and he
is currently a lecturer at the Department of Electrical, Elec t ro ni cs and