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Speed Control of Induction Motor by Z-source Indirect Matrix
Converter with PSO PI Controller
Majid salim *, Mohammad sarvi**, and Mohsen rezaei***
*Islamic Azad University Saveh Branch, [email protected]
**Imam Khomeini International University, [email protected]
***Third Author Affiliation, Third Author Email
Abstract: In this paper the results which are produced by
simulating the Z-source indirect Matrix converters for
induction motor speed control are shown. The method used
for this purpose is flux control keeping the V/f ratio and
regulating slippage. For achieving to desirable voltage at
different frequencies with much or less transmitting voltage
ratio, the modulation coefficient at inverter section and the
shoot-through at Z-source has been used. Also, for
optimizing the PI controller coefficient at proposed system
PSO Algorithm and for showing the results of PSO
Algorithm and for showing the results of simulation in
matlab/simulink, the parameters of an induction motor 5HP
has been used. The results show to using the proposed
system and indirect z-source matrix converter, appropriate
velocity and desirable torque are obtained in a short time.
this article, the model of indirect matrix converter that is
made of the direct one having 18 unidirectional switches.
(As shown in fig. 2) so that 12 switches are placed in
the rectifier section while 6 switches are placed in the
Keywords: Z-source indirect matrix converter, Induction
motor, Pso algorithm
1.
Introduction
Experts and engineers in power electronic and
industrial have always paid interested in how to motor
speed control.
Thus; there has always been an attempt to present
effective and useful methods for this important matter. To
change frequency and AC voltage level, Conventional
transformers first convert the input voltage to DC and
then transform it to a desired AC level. The operation can
result in loss and harmonic in the form of voltage wave
and current. On the other hand; this is while we need high
capacity elements to store energy. Direct converters such
as cyclo-converters are not favourable as they cause
harmonic in voltage and current and affect the speed and
torque of motor negatively [1,2,13].
Also, only the output frequency can be a less than input
frequency [3]. The matrix converter (fig.1) and its
controlling method were presented in 1985 by Venturini
and because of some problems it could not find a huge
application in the industry [4]. Matrix converter besides
such advantages as simplicity and integrity, possibility of
adjusting output frequency and voltage in a wide range,
no need to energy storing parts of high capacity and high
coefficient of power[5-8], has also disadvantages such as
the low level of voltage transfer ratio (about 0.866). in
inverter section.
Fig.1: Direct matrix converter
Using the impedance network converter (z-source) [9]in
the indirect matrix converter can solve the problem of the
voltage transfer ratio in the converter and regulate it at a
desirable value. Since in the matrix converter the power
conversion can be done directly, there is no need for
energy storage requirements.
Fig.2: Indirect matrix converter
Moreover, the converter can accommodate the changes
in moment-speed in induction motor in four quarters that
proves advantageous compared to other types of
converters[10]. The control method of motor speed
control here V/F is for the stabilization of flux and
maximum torque for all of the speeds in the offered
system [11] and for a good response, PI controllers have
been optimized by particle swarm optimization( PSO)
algorithm[12].
2.
Z- source Indirect Matrix Converter (ZSIMC)
As it was mentioned before, one of the disadvantages
of matrix converter is the low level of voltage transfer
ratio.The problem however could be resolve by
juxtaposing an impedance network converter with matrix
converter.Fig.3 shows the ZSIMC.
Fig.5[9].
Fig.4:Rectifier stage in Z-source indirect matrix converter
Fig.5:Simple boost control method
Fig.3:Z-source indirect matrix converter
2.1
Configuration and Operating Principle
As shown in fig.3, converter has been formed of three
main sections:
The rectifier section includes 6 bidirectional switches,
the impedance network is a joint between rectifier part
and inverter which Also carries out the function of
increasing the voltage transfer ratio and the inverter
section made up of 6 unidirectional switches and the
converter's output is for connection to the load. PWM
technique has been applied to control the switches in the
rectifier section so that at any time, the highest positive or
negative three-phase input voltages are put in the rectifier
output. The working and switching stages are presented
in Fig.4. The impedance network (Z-Source) operates in
the two operational modes of Active and Shoot-through.
These modes are created by the switches operating in the
inverter section. Simple boost control method is applied
to control the operational modes of the impedance
network alongside inverter. The process is shown in
2.2
The Calculation of Voltage Transfer Ratio
Let’s assume the three-phase input voltage follows the
(1):
v a 
cos( wt )

 
vc 


cos( wt  120 


 
(((((((((((((((((((((((((((((((
vi  vb  vm cos( wt  120 
(1)
As a result of using PWM method to control the
inverter; the calculation of the average voltage in one
stage from fig.4 for example,in first stage includes two
sections Vac and Vab whose share in each one of them in
first stage can be written as follows:
d ab 
 vb
v c
, d ac (((((((((

va
va
(2)
In accordance to fig.5 the average voltage at first
stage can be calculated as follows:
v rec  d abv ab  d ac v ac 
3v m
2 cos wt
(3)
For Z-source to take two equivalent circuit at shoot
through condition in fig.6(a) and active condition in
fig.6(b) into account the voltage transfer ratio can be
calculated like this:
(a)
(b)
Fig.6:Z-source
condition
operation.(a)
shoot-through
condition.(b)
active
At shoot-through condition:
(4)
vl  v c , vi  0
At active condition:
(5)
vl  vrec  vc , vd  vc  vl
To take the time of shoot-through condition with T0 and
the time of active condition with T1 and by considering
that the average voltage of inductor in a period is zero,
we will have:
vl  0 
T0 vc  T1 ( vrec  vc )
T
vd  vc  vl  2vc  vrec 
B
 0,
vc
T1

v rec
T1  T0
T
 vrec  B  vrec
T1  T0
T
1
, D0  0
1  2 D0
T
vo  M
vd
 MB  vrec
2
(6)
(8)
(9)
(10)
By replacing the (10) in (7) and (9) we will have:
3 M  vi
v0 
2( 2 M  1 ) cos( wt )
3.
As:
(7)
M:modulation index
On the other hand, as a result of using simple boost
control method in inverter section the relation between
D0 and M can be written like this:
D0  1  M
The speed error signal will be applied to P1controller
and subsequently to the slip adjuster. This way the Wsl
reference signal will be adjusted. Synchronous speed will
be obtained through addition of Wsl and Wm. The result
could be used to determine the operational frequency of
the converter and motor. Moreover, by Wms, we can
determine the motor’s needed voltage by the flow control
block. Given V is lower than the maximum output
voltage of the matrix converter, in the absence of
impedance network (Z-Source), modulation coefficient
(m) in the block 1 will be applied to adjust the output
voltage of converter. Otherwise, since the amplitude of
the needed voltage is more than the converter’s maximum
generated voltage through the block 1, the block 2 (which
is accompanied by impedance network or Z-Source) will
be used to obtain the needed voltage amplitude. The
structure of Block 1 has been obtained from Equation 11,
and Block 2, from Equation (12). Considering Equation
12, due to dependency of D0 on the quantity of m, the
equation has been written based on m. Use of the
proposed system leads into decrease of voltage stress and
losses in converter switchers since it doesn’t use the zsource converter and Shoot-through state at low
frequencies.
(12)
Where Vcon is control voltage and Vtri is triangular
voltage in Sinusoidal Pulse Wide Modulation, Vd is
output voltage of the rectifier part and Vac is the first
harmonic range and output voltage of the converter.The
process is operated by a selector. In the proposed system
(Fig.8), three PI controllers have been used. Each has two
variables of P and I and six variables are defined for the
system totally. In order to achieve improved quantities for
the system, a primary population consisting of 10
particles was defined. Each comprises all six variables.
Consequently, a matrix of 10 × 6 is defined. After
repetition for three times and according to the target
function, which is minimization of the velocity and
torque error, the improved quantity of controllers has
5.
(11)
The Proposed System
Fig.8 presents the practical circuit of controlling
method of closed loop. Velocity error signal will be
imposed to PI controller and from that also to the slip
regulator.
Particle Swarm Optimization (PSO) Algorithm
Pso is a novel population based optimization method
that was introduced by kennedy and eberhart in 1995 for
simulating bird flock and fish school .it uses a number of
particles that constitute a swarm .that swarm continuously
updates the knowledge of given searching space.
Each particle in the swarm involves a position array and
a velocity array. the position array is a possible solution
to the problem. Let x and v denote a particle coordinates
and its corresponding flight velocity in a search space,
respectively. The particle update their velocities and
positions as:
Figure 9 shows velocity, electric torque, and current in
induction motor and inductor current of the z-source
converter part and load torque in startup condition with
PSO-PI controller. In this state, at 3.2 seconds, a load of
3N.m is devised on the shaft of the motor.
(a)
(b)
Fig.8:Proposed system
V k 1  W k V k  c1 r1 ( Pbest  x k )
(c)
(14)
 c 2 r2 ( Gbest  x k )
x k 1  x k  xV k 1
W k  Wm ax 
Wm ax  Wm in
k
max int eration
(15)
(16)
Where k is current iteration. c1 and c2 are two positive
factors called acceleration coefficients. r1 and r2 are two
random number in range of [0,1] with uniform
distribution. Pbest is the best previous position of particle
and Gbest is the best particle among all the
particles. W k is inertia weight suitable selection of W
provides a balance between global and local explorations.
X is constriction factor to ensure convergence is a
function of c1 , c2 as below:
x
(17)
2
2c
c  4c
Where c  c1  c2 and c 4
Fig.9:Motor starting with no load condition
6.
(d)
Simulation Results
Simulations have been performed to confirm the
theoretical concepts of proposed system, parameters
belonging to a squirrel cage induction motor of 5Hp,
460v and 4poles were taken into consideration. for
simulation studies on computer used matlab program and
switching frequency at rectifier side and inverter side are
20KHZ and 10KHZ,respectively.input voltage for matrix
converter is balanced three phase:180V,50HZ
(e)
Fig.9. Start up condition a) velocity curve b) torque curve c) motor
current d) Z-source inductor current e) load torque
Figure (10) indicates line voltage, three-phase current,
velocity and electric torque of the motor for change in
load torque respectively. In this state, first, load torque is
5 [N.m] to the motor and at t=2 [sec], torque is decreased
to 2.5 [N.m] and at t=5.1 [Sec], the torque equals to zero
and the only load on the shaft of the motor are friction
and inertia. During this process, it is found that motor
velocity enjoys minor fluctuations and finally, it remains
constant at 50 [rad/sec].
(c)
(d)
(e)
Figure 11: changes in motor parameters and converter, compared to
command signal changes in resistive- generator breaking state a)
velocity b) torque c) three-phase current of the motor d) output voltage
of the converter e) output voltage of Z-source converter.
(e)
Fig.10. System parameter response to load torque changes a) line
voltage b) three-phase motor current c) motor velocity d)
electromagnetic torque e) load torque.
Figure (10) shows Command signal indicates the
velocity, induced to the system. Respective results of
changes of motor parameters and converter are shown in
figure (11).
Fig.10. Command signal induced to the system
Figure 11 shows variation in motor parameter compared
to command signal changes.
(a)
7.
Conclusion
in this paper the results simulation of indirect matrix
converter with Z-source was exhibited by matlab/
simulink. In order to study the improvement of
characteristics, corresponding results have been
compared to PI results. Respective characteristics of zsource converter have been used for increase voltage
transfer ratio in the matrix converter. With respect to
study of various break methods and in consideration of
the results obtained in this regard, it has been revealed
that innate characteristic of the converter can be used in
order to establish various break states and extra circuits
can be discarded accordingly. Moreover, use of the
offered system has led to increase and decrease of voltage
in the converter by Shoot-through coefficient and that of
modulation index for various frequencies of management
resulting in decrease of voltage stress and losses in the
switches of the converter. Considering number of PI
controllers in the system, PSO Algorithm has been used
for improvement. Corresponding results have shown that
this method enjoys more desirable reactions compared to
common PI.
References
[1] B.K.Bose,”Modern power electronic and ac drives,” Upper
saddle Rivers,NJ:Prentice-Hall PTR,2002.
P.Nielsen,F.Blaabjerg,and J.k.Pederson,”New protection issues of
Matrix converter:design consideration for adjustable-speed drives”
Ind.App,IEEE Trans.,vol.35,Issue5:1150-1161,1999.
[3] M.H.Rashid,”Power electronics,”2nded:Englewood cliffs,NJ:
Prentice-Hall,1993
[2]
(b)
[4] M.Venturini,”A new sine wave in, sine wave out, conversion
technique elimination reactive component,”Proc.of Power
con.,pp.E3-I-E3-15,1980
[5] J.W.Kolar,M.Baumann,F.Schafmeister,H.Ertl,”Novel three-phase
ac-dc-ac sparse matrix converter,”IEEE APEG02,vol.2,pp.287292,2002.
[6] S.Kwak,H.A.Toliyat,”Development of modulation strategy for
two-phase
ac-ac
matrix
converter,”IEEE
Trans.Energy
conver.,vol.20,pp.493-493,Jun2004.
[7] L.Wei,T.A.Lipo,”A novel matrix converter topology with simple
commutation,”Procceedings
of
the
IEEE-IAS
Annual
meeting,vol.3,pp.1749-1754,2001.
[8] B.G.Lakshmi,P.sanjeevikumar, and P.Dananjayan,”Performance
analysis of ac-dc-ac converter as a matrix converter,”Indian
International
conference
on
power
engineering,IEEEIICPE06,Chennai,pp.no.57-61,2006.
[9] F.Z.peng, “Z-source inverter,” IEEE Trans.Ind.Appl.,Vol.39,no.2,
pp.504-510,Mar.-Apr.2003.
[10] S.Sunter,and J.C.Clare,”A true four quadrant matrix converter
induction motor drive with servo performance”,Power electronic
Specialist conference,PESC99,27th Annual IEEE,vol1:146-151,1996.
[11] G.K.Dubey,”Power semiconductor controlled drives,”Prentice
Hall,1989.
[12] J.Kennedy,R.Eberhart,”Particle swarm optimization”
[13] H.Kara ca, R.Akkaya, A matrix converter controlled whit the
optimum amplitude – direct transfer function approach, 6th international
conference on electrical engineering ICEENG 2008, May 2008 .