Journal of Automation and Control Engineering Vol. 1, No. 4, December 2013
Evaluating the Dynamic Stability of Power
System Using UPFC based on Indirect Matrix
Converter
Farzad Mohammadzadeh Shahir and Ebrahim Babaei
Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iran
Email: f-mohammadzadeh@iau-ahar.ac.ir, e-babaei@tabrizu.ac.ir

disadvantageous of prevalent UPFC. Therefore, several
new structures are presented to overcome such
disadvantageous [6-8]. One of the best-presented
structures is the matrix converter based UPFC [9]. The
matrix converter structure is based on 9 bidirectional
switches contain two IGBTs accompanied by two parallelreverse diodes, which can be switched in high frequencies
and directly transmit the energy in ac/ac mode applying no
electrolyte capacitor. The matrix converter structure has
the advantageous such as adjustable power factor, high
qualitative input and output currents, high operation speed,
and lower size, in addition to possessing no electrolyte
capacitor in dc link. It also possesses disadvantageous
such as restricted voltage transfer ratio by 0.86 and
requiring numerous high power semiconductor devices
capable of high frequency switching. According to the
considerable advantageous of matrix converter structure,
in compare with its disadvantageous, it quickly supersedes
ac/dc/ac converters in scientific researches. The most
distinctive restriction of utilizing UPFC-IMC falls in its
switching pattern, which just holds 27 permitted modes
out of 29  512 possible modes. This refers to the nature
of matrix converter structure, which is due to impossibility
of short circuiting input phases and impossibility of open
circuiting output phases during each switching period.
Two common Venturini [10] and SVM [11] are presented
to control 27 permitted switching modes of UPFC-IMC.
The SVM algorithm is based on three-phase input current
of line and three-phase output voltage. Each output is
connected to a single input according to the switching
modes. In [12], the UPFC-IMC switching is carried out by
indirect technique. The operation of UPFC-IMC is
modeled in two voltage source rectifier (VSR) and voltage
source inverter (VSI) sides by switching through ISVM
technique.
In [13], a dynamic modeling of UPFC-IMC was
presented. In this paper, the impacts of UPFC-IMC
presented in [12] are evaluated on the power system
dynamic stability and on the electromechanical
oscillations damping. In order to achieve such aim, it is
assumed that the UPFC-IMC presented in [12] is
connected to the sample power system. The analyses
begin by deriving non-linear equations of the investigated
power system. The linear equations are obtained
linearizing the non-linear equations around the operating
Abstract—In this paper, the affects of the newly presented
structures of unified power flow controller (UPFC) on
power system dynamic stability are investigated. The newly
presented UPFC structure is based on indirect matrix
converter (IMC) controlled by the space vector method
(SVM). A non-linear modeling is accomplished for a sample
power system possessing UPFC-IMC in order to investigate
the affects of it on the dynamic stability. The linear model of
the power system is then mentioned in state equations form
defining system elements and linearizing the non-linear
model around the operation point. A Heffron-Philips model
is presented according to the mentioned state equations for
the sample power system possesses UPFC-IMC. The
accuracy of the mentioned theoretical cases is reconfirmed
through the simulation results in MATLAB/Simulink.
Index Terms—UPFC-IMC, FACTS device, low frequency
oscillations, modified Heffron-Philips model
I.
INTRODUCTION
The generator electromechanical oscillations are one of
the most important problems propounded in power
systems, which occurs during the large distortions as the
input mechanical power and the output electric power
balance is obviated and the damping torque is decreased
[1]. The conventional technique of generator
electromechanical oscillations damping in power system
is to add a power system stabilizer (PSS) to the generator
exciting system [2-3]. Installing PSS in power system
increases the stability margin of the power system against
the electromechanical oscillations in addition to the
system ability enhancement in electromechanical
oscillations damping. Recent progresses in power
electronics field and high power semiconductors
manufacturing magnificently change the compensation
and power transmission fields in power systems. The main
idea supports the FACTS concept is to improve the ability
of transmission system activating its several elements at
components. UPFC is a member of the FACTS family [4].
Prevalent UPFC structure introduced by Gyugyi in 1991
[5], consists of two two-level three-phase series and shunt
converters connected to each other through a back-to-back
dc link. Increasing the converter weight, cost, size, and
power losses are some of the most important
Manuscript received December 11, 2012; revised April 15, 2013.
©2013 Engineering and Technology Publishing
doi: 10.12720/joace.1.4.279-284
279
Journal of Automation and Control Engineering Vol. 1, No. 4, December 2013
point and the modified Heffron-Philips model is proposed
in continuous. The system is then simulated in
MATLAB/Simulink and the most effective signal is
introduced to optimum control of UPFC-IMC in power
system and attenuates rotor oscillations of synchronous
generator.
I t ,1
Series
Ib
Transformer
IE
Vt
Pe  V t ,d I t ,d V t ,q I t ,q , Eq  Eq  ( X d  X d ) I t , d
Vt  Vt , d  jVt , q , Vt , d  X q I t , q , Vt , q  Eq  X d I t , d
Vb
X bv
Parallel
X te

where the follows are valid in (1)-(4):
XT
Transformer
It
E fd  K a (V ref V t )

E fd 
Ta

I t , d  I t ,1, d  I E , d  I B , d , I t , q  I t ,1, q  I E , q  I B , q
Sparse
Converter Matrix

UPFC
V dc
E q
I t ,1, d 
XE
1 mEVdc
1
I E ,d 
cos  E 
Vb cos 
XT
XT 2
XT
It ,1, q 
XE
1 mEVdc
1
I E,q 
sin  E 
Vb sin 
XT
XT 2
XT

V SR

V SI
u k
damping
controller
Figure 1. Single line diagram of investigated system
I E ,d 
II.
( X dT  X BB X b,3 )Vb cos 
INVESTIGATED SYSTEM

In this paper, the IEEE-St1A sample power system is
used to investigate dynamic stability. The evaluated power
system structure is shown in Fig. 1. It is assumed that the
buses are ideal and R E and R B are neglected against X E
and XB . In this paper, E and B subscripts are used for
VSR side and VSI side, respectively, and subscript g
refers to the side of converter ( E and B ). In Fig. 1, X bv ,
I E ,q 

X tE , and X T are transmission line, Equivalent
transformer, and transmission line 1 reactance,
respectively. Also, Vt , Vdc , and Vb are generator terminal,
artificial dc link, and infinite bus voltages, and I t , I t ,1&2 ,
I B,d 
X d ,E

( X dT  X BB X b ,2 ) mEVdc
X d ,E
2
cos  E
X mV
X BB
Eq  dT B dc cos  B
X d ,E
X d ,E 2
( X qT  X BB X a ,3 )
X q,E
Vb sin  
( X qT  X BB X a ,2 ) mEVdc
X q,E
2
sin  E
X qT mBVdc
sin  B
X q,B 2
1
X d ,E

 mEVdc

cos  E 
 X E Eq  ( X b ,1  X E X b ,2 ) 
2



m V

( X b ,3 X E  X b ,1 )Vb cos   X b ,1  B dc cos  B  
 2

Ib and I g show terminal output, transmission line 1 & 2,
infinite bus, and passing on g side currents. So,  is
system load angle.
III.
I B,q 


  0 (  1) 
 
Pm  Pe  Dm 

M
Eq 
E q  E fd
T do
©2013 Engineering and Technology Publishing

 mBVdc

sin  B  
( X a ,1  X B X a ,2 ) 
2



m V

( X a ,3 X B  X a ,1 )Vb sin   X a ,1  B dc sin  B  
 2

DYNAMIC MODELING OF POWER SYSTEM
A. Non-linear Dynamic Model
All components of the investigated power system such
as all reactances and resistances of generator, transformer,
transmission line, series and parallel transformers, along
with transient states of transmission line and UPFC-IMC
transformer are under consider in non-linear modeling
process. The following non-linear equations are obtained
for investigated system:

1
X q,E
X dT  X tE  X d , X qT  X tE  X q , X d , E  X tE  X d  X E
X q , E  X tE  X q  X E , X BB  X bv  X B
X a ,1 


X b,1 
( X q , E X T  X qT X E )
XT
( X d , E X T  X dT X E )
XT
, X a ,2  1 
X qT
, X b,2  1 
X dT
X
, X b,3   dT
XT
XT
XT
, X a ,3  
X qT
XT
In the aforementioned equations, M , X d , X q , and


280
X d show inertia constant, generator reactance on d axis,
generator reactance on q axis, generator transient
Journal of Automation and Control Engineering Vol. 1, No. 4, December 2013

reactance on d axis, respectively, and I t , w , I t ,1, w , I t ,2, w ,
K v ,uk  [K v , E
K v , E
and Vt , w ( w  d , q,0 ) define terminal output current,
current in transmission line 1, current in transmission line
2, generator terminal voltage on w axis, respectively.
Also, Pm , Pe ,  g , and m g ( g  E , B ) mechanical power
  T  
e

B. Linear Dynamic Model
The linear dynamic model is obtained from the nonlinear dynamic model of the system determined by (1)-(4)
[1]. In order to achieve such aim, the non-linear equations
(1)-(4) are linearized around the operation point of the
investigated system and consequently, the system linear
equations are derived. The obtained linear equations are as
follows:



 



SYETEM OPERATION CONDITION IN  (  )
Vt
Vb
Pe
1
1.0 pu
1.0 pu
0.1pu
2
1.0 pu
1.0 pu
1.0 pu
Operation conditions
Pe  K1  K 2 Eq  K p , E mE
 K p , E  E  K p , B mB  K p , B  B
Eq  K 4   K 3 Eq  K q , E mE
 K q , E  E  K q , B mB  K q , B  B
Vt  K 5   K 6 Eq  K v , E mE
 K v , E  E  K v , B mB  K v , B  B



 
D. The State Equations of the Investigated System
The dynamic model of the investigated system can be
defined on (5)-(8) bases and in state space equations form
as follows:
X  AX  BU 
C. The Proposed Modified Heffron-Philips Model
The modified Heffron-Philips model could be proposed
for the investigated system considering (5)-(8) linear
equations. Fig. 2 shows the proposed modified HeffronPhilips block diagram, in which the operation of UPFCIMC is controlled by the linearized m E , m B ,  E ,
and  B control signals. The block diagram of the
proposed modified Heffron-Philips model shown in Fig. 2,
holds 18 constants. These constants can be considered as
the row input vectors to decrease the calculations
complexity. The input row vectors are defined as follows:
K p ,uk  [K p , E K p , E K p , B K p , B ]  

K q ,B
©2013 Engineering and Technology Publishing
K q , B ] 

281

A and B matrices of (16) can be defined as follows:
 
The constant values are defined in details in appendix
K q , E
 B ]T 
m B

E fd  K a (V ref  V t )

E fd 
Ta
K q ,uk  [K q , E
ref

K v ,uk
 E
 U  [m E
A.

 
The row vectors of (12)-(14) are applied on the
proposed modified Heffron-Philips system as the
following input vector according to the UPFC-IMC input
signal:
where the followings are valid in (5)-(8):


 V

1
1  ST a

K6
TABLE I.

K5
Figure 2. The proposed modified Heffron-Philips model
Pm  Pe  Dm 

M
T do
S

1
K 3  ST do
uk

Eq 
 0 
K q ,uk
  0  
E q  E fd

1
MS  D m
K4
E q

K1
K2
K p ,uk
of generator, electric power of generator, phase angle on
g side, and modulation index on g side, respectively.

T m


K v , B ] 
K v ,B


 0

  K1

M
A   K4
 
 T d0
 K K
 a 5
 T a
0

 K
  p ,E

M

B   K q ,E

 T d0

 K a K v ,E
 T
a




0
0
K
 2
M
K3

T d0
0
0

0
K aK 6
Ta
0
0
K p , E
K p ,B
M
K q , E


T d0
K a K v , E
Ta

M
K q ,B
T d0
K a K v ,B
Ta
0 

0 

1   

T d0  
1
 
T a 
0

K p , B 


M
K q , B  


T d0 

K K

 a v , B 
Ta 
In addition, X and U matrices of (16) are considered
as follows:
Journal of Automation and Control Engineering Vol. 1, No. 4, December 2013

X  [

U  [m E
IV.
 E q
 E
E fd ]T 
m B
 B ]T 


SIMULATION RESULTS
As shown in Fig. 1, the probable oscillation states are
recognized by UPFC-IMC using  error signal. The
non-linear analysis of the investigated system is
accomplished using non-linear equations (1)-(4). It is
assumed in simulations that a three-phase to ground fault
is occurred in t  1sec on transmission line 1. This fault is
occurred under ( ) system operation region shown in
Table I, considering other power system parameters
presented in appendix B. Fig. 3(a) shows the simulation
results under 1 operation condition. The stability of the
investigated system faces with drawbacks as the
oscillation occurs. Under 1 operation condition, the
system responds to the oscillations with u k   E fast.
However, the system attenuates the electromechanical
oscillations with lower speed considering u k   B . Fig.
3(b) illustrates the simulation results under  2 operation
condition. Based on the simulation results shown in Fig.
3(b), the system is able to maintain the stability and to
attenuate the oscillations with u k  m E and maintain the
stability of the investigated system with u k   E and it
might undamaged the protective systems and other power
system connected devices.
APPENDIX A
K1  s1 b2  d 2  ( s4  1)b2  s5 sin    b1 s4  d1 
  ( g1Vb cos  )  s4 (e1Vb cos  )  s5 cos  ) 
K 2  I t , q  s1 (b1 s4  d1 ) , K3  1  s3 (b1s4  d1 )
K4  s3 (b2 s4  d2  s5 sin  )
K5  X qVb s6  g1 cos   s4 (e1 cos  )  s8 cos  
 s7 X d  b2 s4  d 2  s5 sin  
K6  s7 [1  X d (b1s4  d1 )]
K p , E  s1 (b3 s4  d3  0.5Vdc s8 cos  E )
9
 s2  0.5Vdc sin  E  (e2  g 2 )  Vb sin  [( s4  1)e2  s8 ]
8
K p , E  s1 (b4 s4  d 4  0.5mEVdc s8 sin  E )  s2 (0.5e2 mEVdc s4
7
 cos  E  0.5 g 2 mEVdc cos  E  0.5mEVdc s8 cos  E )
6
5
without UPFC
0
2
4
K p , B  s1 (b5 s4  d5 )  s2
u k  E
u k  B
uk  mE
uk  mB
4 damping controller
3
Philips model is proposed. According to results, under 1
and  2 operation condition, u k   E and uk  mE
improve dynamic stability. It can be claimed that the
selected signal is persistent if it has a uniform
performance in total ( ) region and is able to attenuate
the electromechanical oscillations of the power system.
The
control
signal
persistence
against
the
electromechanical oscillations in total ( ) region
causes optimum control and maximum system capacity
utilization. Therefore, the persistent signal selection is
particularly important. Also, according to simulation
results, with u k   E improve dynamic stability in
all ( ) .
6
8

  0.5Vdc sin  B  (e3  g3 )  Vb cos  ( s4  1)e1  s8
10
K p , B  s1 (b6 s4  d 6 )  0.5s2 mBVdc ( s4 e3 cos  B  g3 cos  B )
(a)
70
K q , E  s3 (b3 s4  d 3  0.5Vdc s8 cos  E )
60
K q , E  s3 (b4 s4  d 4  0.5mEVdc s8 sin  E )
50
without UPFC
40
0
2
4
K q , B  s3 (b5 s4  d 5 ) , K q , B  s1 (b6 s4  d 6 )
u k  E
u k  B
uk  mE
uk  mB
damping controller
6
8
K v , E  0.5 X qVdc s6 ( s4 e2 sin  E  g 2 sin  E  s8 sin  E )
10
(b)
Figure 3. Simulation results, (a) under
under
2
1
 s7 X d (b3 s4  d3  0.5s8Vdc cos  E )
operation condition, (b)
K v , E  0.5 X q mEVdc s6 (e2 s4  g 2 cos  E  s8 cos  E )
operation condition
 s7 X d  b4 s4  d 4  0.5mEVdc s8 sin  E 
V.
CONCLUSION
Kv, B  0.5 X qVdc s6  e3 s4  g3 sin  B   s7 X d  b5 s4  d5 
In this paper, non-linear and linear modeling is
presented for UPFC-IMC, and the modified Heffron©2013 Engineering and Technology Publishing
282

Journal of Automation and Control Engineering Vol. 1, No. 4, December 2013
Kv , B  0.5 X q s6  e3 s4  g3 cos  B   s7 X d (b6 s4  d6 )
s4 
X bv  X B
( X tE  X d )
, a4  
X tE  X d  X E
( X tE  X d  X E )
a1 
APPENDIX B
Other details of the investigated power system used in
simulations are as follows:
X T ( X tE  X d  X E )  ( X bv  X B )( X tE  X d )
( X tE  X d  X E )
a2 
Vt , q
Vt , d
V
XE
1
, s7 
, s8 
 1 , s5  b , s6 
Vt
Vt
XT
XT
XT
 E  30 ,  B  25 , X E  X B  X tE  X bv  X d  0.1 pu
X T  1.3 pu , X q  2 X d  0.6 , Vdc  Eq  0.5Vb  2.0 pu
X ( X  X d )  ( X bv  X B )( X T  X tE  X d )
a3   T tE
X T ( X tE  X d  X E )
mE  mB  1 , M  8.0s , f s , E  f s , B  50 Hz , Tdo  5.044s
b1  a1 , b2  a2V b cos( ) , b3  0.5a3Vdc cos( E )
Ta  0.05s , Ka  50 , Dm  0
b5  0.5a4Vdc cos( E ) , b6  0.5a4 mBVdc sin( B )
REFERENCES
[1]
X d  X E
XE
, c2 
c1 

X tE  X d  X E
X tE  X d  X E
[2]
X T  X tE  X d  X E X T ( X tE  X d  X E )  X E 2 ( X tE  X d )
X T ( X tE  X d  X E )
c3 
[3]
[4]
X ( X  X d  X E )  X E ( X tE  X d )
c4  T tE
X T ( X tE  X d  X E )
[5]
d 1  c1 , d 2  c 2V b sin( ) , d3  0.5c3Vdc cos( E )
[6]
d4  0.5c3 mEVdc sin( E ) , d5  0.5c4Vdc cos( B )
[7]
d6  0.5c4 mBVdc sin( B )
[8]
e1  
e2  
X tE  X q  ( X tE  X q )( X bv  X B )
g2 
[10]
X tE  X q  ( X T  X tE  X q )( X bv  X B )
X T ( X tE  X q  X E )
e3 
g1 
[9]
X T ( X tE  X q  X E )
[11]
X tE  X q
X tE  X q  X E
[12]
 X E X tE  X q  X T ( X tE  X q  X E )  X E ( X tE  X q )
[13]
X T ( X tE  X q  X E )
X T ( X tE  X q  X E )  X E ( X tE  X q )  X E ( X T  X tE  X q )
Farzad Mohammadzadeh Shahir was born in
Tabriz, Iran, in 1985. He received the B.S. degree in
electronic engineering from Islamic Azad
University, Mianeh, Iran, the M.S. degree in
electrical engineering from Islamic Azad University,
Ahar, Iran, in 2008 and 2011, respectively. In 2004,
he joined the Iran Tractor Manufacturing Company,
Tabriz, Iran, where he has been an electrical
engineering in there. His current research interests include power
system dynamic and power electronic converters.
X T ( X tE  X q  X E )
g3 
X T ( X tE  X q  X E )  X E ( X tE  X q )
X T ( X tE  X q  X E )
s1  Vt , d  X d I t , q , s2  Vt , q  X q I t , d , s3  X d  X d
©2013 Engineering and Technology Publishing
P. Kundor, Power System Stability and Control, Mc. Graw Hill,
New York, 1994.
F. M. Shahir and E. Babaei, “Evaluating the dynamic stability of
power system using upfc based on indirect matrix converter,” in
Proc. ICECT, 2012, pp. 548-553.
H. J. Wang, J. Min, J. Ma, H.Y. Wang, H. J. Fu, and Y. Y. Hu, “A
study on PSS parameters optimizing for multiple low frequency
oscillation modes,” in Proc. APPEEC, 2011, pp. 1-4.
F. M. Shahir and E. Babaei, “Evaluation of power system stability
by UPFC via two shunt voltage-source converters and a series
capacitor,” in Proc. ICEE, 2012.
L. Gyugyi, “Unified power flow control concept for flexible ac
transmission systems,” in Proc. Inst. Elect. Eng., 1991, pp. 19-26.
A. K. Sdigh, M. T. Hagh, and M. Sabahi, “Unified power flow
controller based on two shunt converters and a series capacitor,”
Elsevier Journal of Electric Power System Research, vol. 80, no. 2,
pp. 1511-1519, 2010.
F. M. Shahir and E. Babaei, “Dynamic modeling of UPFC by two
shunt voltage-source converters and a series capacitor,” in Proc.
ICECT, 2012, pp. 554-558.
B. T. Ooi and M. Kazerani, “Unified power flow controller based
on matrix converter,” in Proc. PESC, 1996, pp. 502-507.
F. M. Shahir, E. Babaei, S. Ranjbar, and S. Torabzad, “New
control methods for matrix converter based UPFC under
unbalanced load,” in Proc. IICPE, 2012.
A. Alesina and M. Venturini, “Analysis and design of optimum
amplitude nine-switch direct AC–AC converters,” IEEE Trans.
Power Electron., vol. 4, no. 1, pp. 101-112, 1989.
L. Huber and D. Borojevic, “Space vector modulated three phase
to three phase matrix converter with input power factor
correction,” IEEE Trans. Ind. Appl., vol. 31, no. 6, pp. 1234-1246,
1995.
A. R. Marami Iranaq, M. Tarafdar Haque, and E. Babaei, “A
UPFC based on matrix converter,” in Proc. PEDSTC, 2010, pp.
95-100.
F. M. Shahir, E. Babaei, S. Ranjbar, and S. Torabzad, “Dynamic
modeling of UPFC based on indirect matrix converter,” in Proc.
IICPE, 2012.
283
Journal of Automation and Control Engineering Vol. 1, No. 4, December 2013
Ebrahim Babaei was born in Ahar, Iran in 1970. He
received his B.S. and M.S. in Electrical Engineering
from the Department of Engineering, University of
Tabriz, Tabriz, Iran, in 1992 and 2001, respectively,
graduating with first class honors. He received his
Ph.D. in Electrical Engineering from the Department
of Electrical and Computer Engineering, University
of Tabriz, Tabriz, Iran, in 2007. In 2004, he joined
©2013 Engineering and Technology Publishing
the Faculty of Electrical and Computer Engineering, University of
Tabriz. He was an Assistant Professor from 2007 to 2011 and has been
an Associate Professor since 2011. He is the author of more than 170
journal and conference papers. His current research interests include the
analysis and control of power electronic converters, matrix converters,
multilevel converters, FACTS devices, power system transients, and
power system dynamics.
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