International Conference on Electrical, Electronics, and Optimization Techniques (ICEEOT) - 2016
PSO-Based Online Vector Controlled Induction
Motor Drives
Bhola Jha, M. K. Panda, Prafull Kumar Pandey, Lokesh Pant
Abstract—Modern motor control drives start increasing
the use of various optimization techniques to tune the
controller because of its accuracy and simplicity. Usually,
the classical controllers used in motor control drives are
not adaptable to the changes such as parameter variation,
voltage unbalances, changes in load etc. So, online control
should be encouraged in order to make the system robust.
In this connection, this paper presents online vector
control of induction motor using Particle Swarm
Optimization (PSO) techniques. The PI controller used in
speed control loop is tuned using PSO. The results
obtained in offline and online modes are compared and
validated using MATLAB. The computational steps to
implement PSO in Online Vector Controlled Induction
Motor Drives are lucidly presented.
Keywords— Modeling, vector control, indirect method,
PSO, online, axis and phase transformation etc.
I. INTRODUCTION
Induction motors also known as asynchronous motors are
robust, less expensive, less maintenance and have high torqueto-weight ratio. Moreover the cost is also lower than dc motor,
as well as the inertia and the weight. Due to no electrical
connection between stationary and rotating parts of the motor,
the industries have taken the benefits of induction motors over
dc motors which were used earlier.
Traditionally, separately excited dc machines were the best
choice for applications in adjustable speed drives, where
independent torque and flux control is possible over a wide a
range of speed by independent variation of field and armature
currents. The dc machines also have the excellent dynamic
performance due to inherent decoupling between field flux
and armature current. But, inherent decoupling between field
(stator) and armature (rotor) is not present in induction motor
drives. To decouple this, a control strategy is developed
known as vector control.
The vector control is based on the principle of field orientation
to realize dc motor characteristics in an induction motor drive.
It is one of the most excellent control strategies of torque and
flux control in induction machine. Independent control of
All Authors are with Department of Electrical Engineering, G. B. Pant
Engineering College, Pauri-Garhwal, Uttarakhand 246194 INDIA.
978-1-4673-9939-5/16/$31.00 ©2016 IEEE
torque (active power) and flux (reactive power) can be
obtained using this technique. Its accuracy can reach the
values such as 0.5% regarding the speed and 2% regarding the
torque, even in standstill. This control is said to be one of the
future ways of controlling the induction machine in four
quadrants. There are two methods of vector control one is
direct method and other is indirect method. In direct method
the field angle is obtained directly by Hall sensors whereas in
indirect method, field angle is obtained by rotor position.
There are many numbers of literatures and books are available
in [1-12]. Every Literature is having its own merits and
demerits. In this paper, implementation of vector control using
indirect method is presented.
Now a day’s induction motor drives start increasing the use of
heuristic search optimization approach to tune the controller.
There are number of search optimization techniques such as
GA, PSO, Ant Colony, Bee Colony etc. But, the PSO is found
more popular due to its simplicity and accuracy. This
algorithm is developed by Kennedy and Eberhart in 1990. The
basic concepts regarding this are available in [13-15]. The
application of this algorithm starts increasing in almost all the
areas of engineering. As per the electrical engineering is
concerned, there are number of literature are found available
in machine drives [16-19] power sector especially smart grid,
sustainable energy etc. [20-22]. In most of the paper, either
PID/PI controller tuning approach or optimization of
membership function of fuzzy logic controller is proposed. In
this paper online tuning approach of PI controller for vector
controlled induction motor is proposed, which is relatively
new approach. In near future, online approach for control of
motor drives may be increasing in order to make the robust
system. In this paper, actually two separate works are carried
out, first one is the development of vector control strategy and
second one is the online implementation of PSO to the vector
controlled induction motor drives. The results are obtained,
compared and validated using MATLAB/SIMULINK.
II. MODELING OF INDUCTION MACHINE
A dynamic model of the machine subjected to control must be
known in order to understand and design vector controlled
drives or direct control drives. The dynamic model considers
the instantaneous effects of varying voltage/currents, stator
frequency, and torque disturbance. We know that per phase
equivalent circuit of the induction motor is only valid in
steady state condition. But in transient response condition the
voltages and currents in three phases are not in balance
condition. It is too much difficult to study the machine
performance of the machine by analyzing with three phases. In
order to reduce this complexity, the transformation of axes
from 3 – Φ to 2 – Φ is necessary. The axis transformation is
shown in Fig.1. The following matrices for 3 – Φ to 2 – Φ and
vice-versa are obtained.
λe qs = Ls i e qs + Lm i e qr
λe ds = Ls i e ds + Lm i e dr
(1)
λe qr = Lr i e qr + Lmi e qs
λe dr = Lr i e dr + Lmi e ds
λe qm = Lm (i e qs + iqre )
(2)
λe dm = Lm (idse + idre )
Since the rotor is short circuited, so rotor equations containing
flux linkages as variables are given by
Rr i e dr + pλe qr + ω sl λe dr = 0
Rr i e qr − ω sl λe qr + pλe dr = 0
ω sl = ω s − ω r
where
(3)
Here,
p=
A resultant rotor flux linkage, λr, is assumed to be on the
direct axes, to reduce the number of variables in the equation
by one. Moreover, it corresponds with the reality that the rotor
flux linkages are a single variable. Hence, aligning the d-axes
with rotor flux phasor yields;
Fig.1: Axis transformation (from 3-phase to 2-phase)
Vqss 
 s 2
Vds  =
 s 3
Vos 
Cos θ

Sin θ
0.5

Cos (θ −120o ) Cos (θ +120o )
Sin (θ −120o ) Sin (θ +120o )
0.5
Cos θ
V as 

V  = Cos (θ − 120 0 )
 bs 

V cs 
Cos (θ + 120 0 )
0.5
Sin θ
1
0
Sin (θ − 120 ) 1
Sin (θ + 120 0 ) 1
d
dt
 Vas
 
 Vbs
 V 
  cs 
V qs s 
 s
V ds 
 s
V os 
λr =λedr
(4)
λeqr= 0
(5)
pλeqr = 0
(6)
Now the new rotor equation
Rr i e dr + ω sl λe r = 0
Vector control is derived from dynamic equation [10-13] of
the induction machine in the synchronously rotating frames by
using superscripts e to denote this electrical synchronously
reference frames.
The stator and rotor d-q voltages in the synchronously
reference frame are defined as below in equation (A)
Rr i e qr + pλe r = 0
(7)
The rotor currents in terms of the stator currents are
iqre = −
idre = −
L e
iqs
Lr
λr
Lr
−
(8)
L e
ids
Lr
Now the field –and torque –producing component;
The stator and rotor flux linkages in the synchronously
reference frame are defined as
i f = idse =
[1 + T p] λ
iT = iqse =
Tr × ω s
λr
Lm
r
Lr
r
(9)
Rotor time constant;
Tr =
2
Lr
Rr
(10)
The electromagnetic torque of an induction machine is given
as:
Te =
3P
Lm (i e qs i e dr − i e ds i e qr )
22
(11)
Or
3 P Lm e
Te =
(i qs λ dr − i e ds λ qr ) = K te λ dr i qse = K te λ r iT
2 2 Lr
(12)
The electromechanical equation of an induction motor drive is
given as:
Te − TL =
III.
2 dω r
J
p dt
Fig.2: Phasor diagram of Vector Control
(13)
The perpendicular component iT is hence the torque producing
component. By writing rotor flux linkages and torque in terms
of these component as
VECTOR CONTROL OF INDUCTION MACHINE
Vector Control made the ac drives equivalent to dc drives in
the independent control of flux and torque. For this purpose
the stator current phasor can be resolved along the rotor flux
linkages, and the component along the rotor flux linkages is
the field producing current. The control is achieved in field
coordinates is possible by inverter control and is known as
field oriented control or vector control because it relates to the
phasor control of the rotor flux linkages. The operating
principle of Vector Control can be understood by the block
diagram shown in Fig.2.
To explain this principle of vector control, an assumption is
made that the position of the flux linkages phasor λr is known.
λr is at θf from a stationary reference, θf is referred to as field
angle hereafter, and the three stator currents can be
transformed into d-q axes currents in the synchronous
reference frames.
λr α if
Te α λr iT α if iT
It can be seen that if and iT have only dc components in steady
state, because the relative speed with respect to the rotor field
is zero. The rotor flux linkage λr is oriented towards
synchronous reference frame hence the flux and torque
producing component of current are dc quantities and are ideal
for use as control variables. Mathematical expressions
involved are mentioned here first followed by an algorithm
computational flow chart shown in Fig.3 and block diagram of
vector control shown in Fig.4.
θ = (ω + ω sl )dt =  ω e dt
Cos (θf −120o ) Cos (θf +120o )  ias e  r

Sin (θf −120o ) Sin (θf +120o )  ibs
L m × iq
 i  ω sl = T × λ r
0.5
0.5
r
  cs 
Cos θf
i qs 2 
 e  = Sin θf
i ds 3 
0.5

e
From which the stator current phasor is is derived as
is =
λr =
(i ) + (i )
e
qs
2
e
ds
2
And the stator phasor angle is
id* =
θ s = tan −1 (iqse ÷ idse )
Where (ieqs=iT and ieds=if) are the q and d axes currents in the
synchronous reference frames that are obtained by projecting
the stator current phasor on the q and d axes, respectively. The
phasor diagram is shown in Fig 2.
The current phasor is produces the rotor flux λr in same phase
and the torque Te. Therefore, resolving the stator current
phasor along λr reveals that the component if is the field
producing component, shown in Fig 3.
i q* =
L m × id
(1 + T r s )
λ* r
Lm
 L × T *e
2
2
×
×  r
P
3
 L m × λr



•These reference currents i*d and i*q are now compared with the
actual measured currents using PI controller for the reference
voltages Vd* and Vq*. This reference voltage Vdq* is converted
to Vabc* for the PWM inverter.
3
•Generated pulse is given to PWM Inverter which supplies to
the stator of induction motor, the commanded rotor flux
linkages and torque are produced. The inverter controls both
the magnitude of the current and its phase, allowing the
machine’s flux and torque channels to be decoupled by
controlling precisely and injecting the flux-and torqueproducing currents in the induction machine to match the
required rotor flux linkages and electromagnetic torque.
IV. PARTICLE SWARM OPTIMIZATION (PSO)
Particle Swarm Optimization is a relatively heuristic
evolutionary search method whose mechanics are inspired by
swarming or collaborative behavior of biological population.
This approach based on probability laws to find an optimal
solution in a given search space. There are many numbers of
optimization algorithm are available like Genetic Algorithm,
Ant Colony, Bee Colony, PSO etc. Among all, PSO is found
little more popular due to its simplicity. The few outstanding
features of PSO are listed below:
• PSO provides more accurate results without using
complex operations.
• Due to the application of probability concept, it is
more flexible and robust.
• It is able to overcome premature convergence which
increases the search action capability.
• Time required for the PSO optimization is less.
• It is easy to use PSO in Online mode.
• Achieving the optimal response from any given initial
search point is almost guaranteed.
The PSO algorithm was invented by Kennedy and Eberhart in
1990, having the idea of flying birds in searching food. In this
algorithm, the search process can be introduced as a group of
birds looking for food in a given search space. It means that
there is one specific area or space where the food is available,
but the birds are not aware of it. But they know the distance of
food at each step of searching process. To get closer to the
location of food, all the birds follow the nearest bird. In this
algorithm, each bird is introduced as a particle and all the
particles form a group or Swarm. Each particle is determined
by two vectors X(t) and V(t) respectively that represent the
location and velocity of that particle at that time. Position of
each particle is considered as a solution of answer of a problem.
To find best position or answer of a particular problem in a
given space, particles changes their velocity and position based
on their own flying experiences, past experiences and friends
flying experiences as well. This collaborative approach
ultimately leads to find a solution. In an n-dimensional search
area, position and velocity of ith particle at time k or iteration
number can be represented as follows:
Fig.3: Computational flow chart for Vector Control
Vi(k) = [Vi1(k) Vi2(k) ………. Vin (k)]T
(14)
Xi(k) = [Xi1(k) Xi2(k) ………. Xin (k)]T
(15)
Each particle remembering its best position for each move and
storing all values from the beginning. The best position of each
particle at time k is a best position termed as local best or
personal best. The local or personal best position of ith particle
up to time k is represented as below:
Pbest (k) = [Pbest, i1 (k), Pbest, i2 (k) …… Pbest, in (k)]
Fig.4: Block diagram of Vector Control
4
(16)
Apart from local best, there is a global best, which is the best
solution of all the particles in the whole group, can be
represented as follows:
Gbest (k) = [Gbest, 1 (k), Gbest, 2 (k) …… Gbest, n (k)]
(17)
Each particle position and velocity at time (k+1) is obtained
from the following equations.
Vij(k+1) = W Vij(k) + C1 Rand1ij (Pbest,ij(k) - Xij(k)) + C2 Rand2ij
(Gbest,j(k) – Xij(k))
(18)
Xij(k+1) = Xij(k) + Vij(k+1)
(19)
Where, Vij and Xij are the ith element of the velocity vector V
and position vector X for ith particle position,
Vij = jth dimension of ith particle velocity.
Pbest,ij = jth dimension of best position of ith particle at time k.
Gbest,i = jth dimension of best global position (i.e. best position
achieved so far by all the particles)
W = inertia weight
Rand1ij and Rand2ij = two random numbers in the interval [0 1].
C1 and C2 = training factors or self confidence (C1) or swarm
confidence (C2).
k = time or iteration number.
Initializations of parameters are very important in order to have
the convergence.
PSO algorithm is summarized below:
Step 1: Set the algorithm parameters such as the number of
particles, dimension, inertia weight, training factors, . Here, the
number of particles = 50, dimension = 3. Training factors 1.2/2,
inertia weight = 0.9.
Step 2: Initialization of all the particles [X(k), V(k)] are done
randomly.
Step 3: Initialization of Pbest vectors for all particles using
random initial values obtained in step 2.
Step 4: Calculating the fitness value i.e. local best position for
each particle.
Step 5: Determine the global best position.
Step 6: Updating the particle velocity vectors and position
vectors using above equations.
Step 7: Updating the Pbest for each particle.
Step 8: Updating Gbest. If the objective value of Gbest (k+1) is
better than the objective value of Gbest (k), then
Gbest (k) = Gbest (k+1).
Step 9: If the condition is met then iteration will stop otherwise
go back to step 6.
The computational flow chart for the proposed online PSO
based vector controlled induction motor drives is shown below
in Fig.5:
This paper proposed an online PI tuning controller approach
using PSO technique to analyze the performance of vector
controlled induction motor drives.
Fig.5: Computational flow chart for PSO
V.
RESULTS AND DISCUSSION
The Fig.6 and Fig.7 shows dynamic performance of speed and
torque respectively. From both the figure, this is clear that the
speed and torque ripples are less in online mode as compared
to offline.
1400
1200
S p e e d (r p m )
1000
Offline PI Controller
Online PSO-Based PI Controller
800
600
400
200
0
0
0.1
0.2
0.3
0.4
0.5
Time (Second)
0.6
Fig.6: Speed versus time
5
0.7
0.8
0.9
1
2000
[5] B. N. Kar et.al “Indirect Vector Control of Induction Motor using sliding
mode controller” IET International Conference on Sustainable Energy and
Intelligent Systems, July 20-22, 2011, Chennai, 507-511.
[6] Liying Liu, Zhenlin Xu, Quieng Mei “Sensorless Vector Control Induction
Motor Drive Based on ADRC and Flux Observer” IEEE Control and Decision
Conference, June 17-19, 2009, 245-248, Guilin.
[7] Zerikat M, Mechernene A, Chekroun S “High Performance Sensorless
Vector Control of Induction Motor Drives using Artificial Intelligence
Technique” IEEE International Conference on Automation and Robotics,
Aug.23-26, 2010, 67-75, Miedzyzdroje.
[8] P .C. Kraus, O. Wasynczuk, Scott. D. Sudhoff “Analysis of Electric
Machinery”, 2nd Edition, 2004, John Wilely and Sons.
[9] G. R. Slemon,"Modelling of Induction Machines for Electric Drives,"
IEEE Trans. on Industry Applications, Vol.25, No. 6, pp. 1126-1131, Nov.
1989.
[10] M. Godoy Simoes and Fellix A. Ferret “Alternate Energy Systems:
Design and Analysis with Induction Generator” 2nd edition, CRC Press-Taylor
and Francis Group.
[11] Dr. P. S. Bhimbra “Generalized Theory of Electrical Machinery” Khanna
Publishers 2012.
[12] K.B. narayan, K.B. Mohanty and M. Singh “Indirect Vector Control of
Induction Motor using Fuzzy Logic Controller” IEEE, 10th International
Conference on Environment and Electrical Engg.(EEEIC), 8-11 May, 2011.
[13] R. C. Eberhart and Yuhui Shi “Comparision between Genetic Algorithm
and PSO”.
[14] Rania Hassan, Babak Cohanim, Oliver de Weck “A Comparision of PSO
and G.A” American Institute of Aeronautics and Astronaautics”.
[15] Sree Bash Chabdra Debnath, Pintu Chandra Shill, K. Murusae “PSO
Based Adative Strategy for tuning of FLC” International Journal of Artificial
Intelligence and Applications, Vol.4, No.1, jan.2013, pp37-50.
[16] Uddin.M, Sang Woo Nam “New Online Loss Minization-Based
Controlled of Induction Motor Drives” IEEE Transactions on Power
Electronics, Vol.23, 2008, pp.926-933.
[17] Waheedabeevi. M, Sukesh Kumar A, Nair N.S “New Online Loss
Minimization of Scalar and Vector Controlled Induction Motor Drives” IEEE
International Conference PEDES 2012.
[18] Boumediene Allaoua et. al “The Efficiency of PSO Applied on Fuzzy
Logic DC Motor Speed Control” Serbian Journal of Electrical Engg. Vol.5,
No.2, 2008, pp 247-262
[19] D. Das and A. Ghosh ”Algorithm for PSO Tuned Fuzzy Controller of a
DC Motor” International Journal of Computer Applications, Vol.77,No.4, July
2013, pp 37-41.
[20] H. Bervani et. al “Intelligent Frequency Control in an AC Micro Grid:
Online PSO-Based Fuzzy Tuning Approach” IEEE Transaction on Smart Grid
Vol.3, No.4, Dec.2012, pp.1935-1944.
[21] Hassan Bervani et. al “Intelligent LFC Concerning High Penetration of
Wind Power: Synthesis and Real Time Application” IEEE Transaction on
Sustainable Energy, Vol.5, No.2, April 2013, pp655-662
[22] Manoj Datta et. al “A Frequency Control Approach by Photovoltaic
Generator in a PV-Diesel Hybrid Power System” IEEE Transaction on Energy
Conversion, Vol.26, No.2, June 2011, pp559-571.
Offline PI Controller
Reference Torque
Online PSO-Based PI Controller
1500
T o rq u e (N -m )
1000
500
0
-500
-1000
0
0.1
0.2
0.3
0.4
0.5
Time (Second)
0.6
0.7
0.8
0.9
1
Fig.7: Torque versus time
A speed of 1200 rpm and torque of 200 N-m are tracked
accurately using online tuning of PI controller as compared to
offline PI controller. Therefore, PSO-Based online tuning of
PI controller for vector controlled induction motor drives is
encouraged. This is to be noted that offline PI controller is
tuned with conventional Ziegler-Nicolas method.
VI. CONCLUSION
Indirect method of Vector Control of Induction Motor is
presented. The computational flow chart for PSO algorithm
and vector are lucidly presented. Online tuning of PI controller
for vector controlled induction motor drives is compared to
offline tuning of PI controller for the same drives. This is
found that PSO-Based online control performance is
satisfactory.
VI. APPENDIX
S. N
1
2
3
4
5
6
7
Parameters
Stator resistance
Stator inductance
Rotor inductance
Rotor resistance
Mutual inductance
Moment of inertia
No of pole pair
Values
0.1830 Ω
0.0533 H
0.0560 H
0.277 Ω
0.0533 H
0.0165 Kg-m2
2
8
9
Frequency
DC Supply
50 Hz
400 V
10
11
Off line PI Controller (Kp and Ki)
On line PI Controller (Kp and Ki)
1 and 500
1.3604&2.4467
All the symbols have their usual meanings.
VII.
REFERENCES
[1] Bimal K Bose “Modern Power Electronics and AC Drives” Prentice Hall
2002.
[2] R. Krishnan “Electric Motor Drives-Modeling, Analysis & Control”
Prentice-Hall, 2001.
[3] D. W. Novotney, et al. "Introduction to Field Orientation and High
Performance AC Drives," IEEE IAS Tutorial Course, 1986.
[4] M. Menna et.al “Speed Sensorless Vector Control of an Induction Motor
using spiral vector model ECKF and ANN controller” IEEE conference on
Electric Machines and Drives EMDC, May3-5, 2007, Antalya, 1165-1167.
6