Fifteenth National Power Systems Conference (NPSC), IIT Bombay, December 2008
An Approach for Optimal Placement of UPFC to
Enhance Voltage Stability Margin under
Contingencies
Sreekanth Reddy Donapati and M.K.Verma
selection of optimal line. The sensitivity of loading factor with
respect to reactive power generation at buses and reactance of
the lines has been proposed in [4] to decide optimal location
for the placement of Static Var Compensator (SVC) and
TCSC, respectively. Two sets of sensitivity factors have been
utilized together to optimally place the UPFC. The criterion
for placement of UPFC suggested in [4] has ignored phaseshifter action of UPFC which may lead to inaccurate results. A
voltage stability L index of load buses in coordination with
minimum singular value has been proposed in [6]. The index
has been computed to identify optimal location of UPFC for
improving system security. A linear programming based
optimal power flow algorithm for the placement of UPFC has
been proposed in [7] to reduce overloads and voltage
violations. However, reduction of loads and voltage violations
may not always be helpful in improving voltage stability
margin. Particle Swarm Optimization (PSO) technique has
been used [8] to achieve maximum system loadability with
minimum cost of installation. Particle swarm optimization
technique has been employed in [9] to maximize the
loadability of transmission system using Unified Power Flow
Controller under line outages. Optimal placement of UPFC
based on evolutionary programming has been suggested in
[10] to enhance maximum loadability of the system.
The work on UPFC placement has mainly concentrated to
see its impact for the system intact case and under line outage
cases. However, outage of some of the generators may also
cause voltage instability in the power system. In this paper a
sensitivity based approach has been presented to study impact
of UPFC placement in loading margin enhancement under
critical contingencies considering line as well as generator
outage cases. The effectiveness of the proposed method of
UPFC placement has been established on a practical 75-bus
Indian system representing Uttar Pradesh State Power
Corporation Network.
Abstract— This paper proposes a sensitivity based technique
for optimal placement of Unified Power Flow Controller (UPFC)
to enhance voltage stability margin under contingencies. The
sensitivity of system loading factor with respect to the reactive
power flowing through lines computed for the system intact case
and critical contingency cases have been used to decide optimal
location for the placement of UPFC. The proposed sensitivity
factor has been derived from the reactive power flow balance
equation. The effectiveness of the proposed method for the
placement of UPFC in voltage stability margin enhancement has
been validated on a practical 75-bus Indian system representing
Uttar Pradesh State Power Corporation Network.
I. INTRODUCTION
N recent years an instability usually termed voltage
instability has been responsible for several major
network collapses world-wide [1]. The actual cases of
blackouts characterized by voltage depressions reported in the
literature indicate that standard practice procedures such as
transformer tap-changing, capacitor switching, synchronous
condenser adjustment, and load shedding may aggravate an
already unstable voltage profile [2]. The problem of voltage
instability which may sometimes result into voltage collapse
in the system, has become a matter of great concern to the
utilities in view of its prediction, prevention and necessary
corrections to ensure a stable operation.
The advent of Flexible AC Transmission Systems (FACTS)
Controllers [3] has created new opportunities for increasing
power system stability margin including voltage stability
margin. However, due to high cost and, for maximum
enhancement in voltage stability margin, these are to be
optimally placed in the system. Out of different types of
FACTS controllers, Unified Power Flow Controller (UPFC)
seems to be more effective in voltage stability enhancement
[4] due to its ability to control series and shunt variables,
simultaneously. The selection of optimal bus based on
combination of continuation power flow and optimal power
flow for the placement of UPFC has been suggested in [5].
However, no specific criterion has been proposed for the
____________________________
I
II. UPFC MODEL
In the present work, UPFC has been represented by steadystate injection model [5],[11]. The UPFC consists of two
switching converters operated from a common DC link, as
shown in figure-1 [12]. In this figure, the series converter of
UPFC (Converter-2) has been assumed to be connected
between buses i and j having voltages Vi ‘T i and V j ‘T j ,
Sreekanth Reddy Donapati (email: shrykanth@gmail.com) is with Reliance
Infrastructure Limited, Noida, Uttar Pradesh, India. M.K.Verma (e-mail:
mkverma.eee@itbhu.ac.in) is with the Department of Electrical Engineering,
Institute of Technology, Banaras Hindu University,Varanasi, Uttar Pradesh,
India.
541
Fifteenth National Power Systems Conference (NPSC), IIT Bombay, December 2008
In (1), variables r and Ȗ control magnitude and phase angle of
respectively. Converter-2 injects an AC voltage Vs with
injected voltage Vs , rmax represents maximum limit of variable
controllable magnitude and phase angle in series with the
transmission line. Converter-1 (shunt converter) injects or
absorbs an independently controllable reactive power to bus-i.
This is represented by the current, Iq. It also supplies or
absorbs the active power demanded by Converter-2, through
the common DC link. This is represented by the current, Ip.
r. In the present work, rmax has been taken as 0.2 considering it
as a reasonably high value. Vi Vi ‘T i represents complex
voltage at bus-i.
The steady-state injection model of UPFC has been derived
from figure-2 [5] and has been shown in figure-3. In figure -3
UPFC has been represented as controllable loads connected at
buses i and j.
In [4], shunt converter has been represented as a constant
voltage variable reactive power source, whereas series
converter has been considered as a variable reactance in the
line. This model of UPFC ignores phase-shifter action of
series converter. Steady-state injection model of UPFC
overcomes this limitation.
Figure-1: UPFC schematic diagram
The UPFC circuit arrangement has been shown in figure-2.
In this figure, the series converter has been represented by an
AC voltage source Vs in series with a reactance X s . The
shunt converter has been represented as an independently
controllable reactive power Qconv 1 injected to or absorbed
Figure-3: UPFC injection model
III. METHODOLOGY
from bus-i. In addition, this converter also supplies or absorbs
real power Pconv1 to the series converter through the common
DC link.
The proposed sensitivity based approach for determination
of the optimal location of UPFC is described below:
The reactive power balance equation at bus-i can be given
by:
I ij and I ji represent current flowing from bus-i to
'
bus-j and from bus-j to bus-i, respectively. Vi represents
QG i ( QD ib O K Di S ' base sin I i )
complex voltage of a fictitious bus-i'.
n
Q ik ¦ V i V j Yij sin (G i G j T ij )
(2)
j 1
zk
where,
QGi = Reactive power generation at bus –i
QDib = Reactive power demand at bus-i at the base case
operating point
Qik = Reactive power flowing from bus-i to bus-k
Ȝ = Loading factor common to all the buses
KDi= Constant multiplier showing the rate of change of load
at the ith bus
S 'base =Mega Volt Ampere (MVA) base used for scaling to
Figure-2: UPFC circuit arrangement
equivalent Mega Volt Ampere Reactive (MVAR) load
increase.
ĭi = power factor angle of the increased load at ith bus
Vi ‘įi = Complex voltage at bus –i
Yij ‘ = Gij + jBij = ij th element of the bus admittance
matrix
n= Total number of the buses in the system
The series voltage source Vs is controllable in magnitude
and phase and can be given by:
Vs = r Vi e jJ
(1)
B
where, 0 < r < rmax and 0 < Ȗ < 2ʌ
542
Fifteenth National Power Systems Conference (NPSC), IIT Bombay, December 2008
In [4], sensitivity of loading factor with respect to reactive
power generation at bus-i (wO/wQGi), and sensitivity of loading
factor with respect to reactance Xij of a line connected between
buses i and j (wO/wXij), have been derived from reactive power
balance equation (2) as:
wO
w QG i
wO
wX ij
w Vi
ª
«1 2V i w QG Bii
i
«
«
­§ w V j
w Vi ·
¸
«
V j
° ¨¨ V i
QG i ¸¹
QG
w
w
«
i
°
©
1
«
°
K Di S ' base sin I i « n ° Yij sin G i G j T ij
®
«
V V Y cos G i G j T ij
« j 1 ° i j ij
« z i °§ w G
wG j ·
i
°¨
¸
«
¨
°
QG
QG i ¸¹
w
w
i
¯©
¬«
¦
Vi
1
K Di S 'base sinI i X ij2
º
»
»
½»
°»
°»
°»
°»
¾»
°»
°»
°»
°»
¿¼
values (
of sensitivity factors computed for system intact case and
critical contingency cases, priority lines for the placement of
series converter of UPFC have been determined. Depending
upon magnitude of
(3)
placement of shunt converter. If
absolute value compared to
(4)
hand, if
wO
, which relates changes in loading
wQik
point, the
factor with respect to change in reactive power flowing from
bus-i to bus-k has been proposed in this work. This sensitivity
factor has been obtained by differentiating reactive power
balance equation (2) with respect to Qik and is given as:
Y 1 [ Z 1 ( 1 X ) 1 ]
¦
wQik ª wVk
wVi º
Vk
«Vi
» Yik sin (Gi G j Tij )
wQGi ¬ wQGi
wQGi ¼
ª wG
wG º
Vi V j Yik cos(Gi G j Tik ) « i k »
¬ wQGi wQGi ¼
(5)
(6)
(7)
Z
The sensitivity factor
wO
wO
is greater in magnitude compared to
wQki
wQik
wO
sensitivities have been calculated for each
wQ
ik
of the lines at a stressed point close to the maximum
loadability point. The partial derivatives ˜Vi/˜QGi, ˜įi/˜QGi,
(i = 1,…,n) in (6) & (8) can be derived for different buses
from the inverse Jacobian matrix of the full Newton Raphson
Load Flow (NRLF) in polar Form. An additional criterion for
optimal placement of the UPFC in this work has been that
UPFC should not be placed at generator buses.
The placement of UPFC is a planning issue where, accuracy
is important and computational speed is insignificant.
Therefore, critical contingencies have been identified based on
post-contingency loading margins computed using
continuation power flow method [13]. In order to obtain
loading margins, real power generations, real and reactive
power demands have been varied as per following:
PGi PGib 1 O (9)
where,
­ª wV j
½
wVi º
G
G
T
sin
(
)
V
V
Y
°
°
«
»
i
j
ij
i
j
ij
n
wQGi ¼
°¬ wQGi
°
X
®
¾
wG j º°
ª wGi
j 1°
»°
z k ° Vi V j Yij cos( Gi G j Tij ) «
¬ wQGi wQGi ¼¿
¯
Y K Di S 'base sin I i
wO
bus-i is considered as the
wQki
bus-k is considered as the priority bus. The loading margin
(the distance between the base case operating point and the
nose point) can be computed after UPFC placement at each of
the candidate locations for the system intact case and critical
contingency cases. The combination of priority line and
priority bus producing maximum enhancement in loading
margin for majority of the critical contingencies has been
selected as the optimal site for UPFC placement.
Since voltage instability occurs at the maximum loadability
may result in inaccurate selection of priority lines. Therefore,
wO
wQik
wO
is having higher
wQik
priority bus for the placement of shunt converter. On the other
The sensitivity factors wO/wQGi and wO/wXij have been used
in [4] to determine priority buses for the placement of shunt
converter and priority lines for the placement of series
converter, respectively. However, the sensitivity factor wO/wXij
has been obtained by neglecting the sensitivity terms relating
change in complex voltages with respect to line reactance (i.e.
wV k
wG k
and
, k = 1,……., n, have been neglected). This
wX ij
wX ij
a new sensitivity
wO
wO
and
corresponding to priority
wQik
wQki
lines, bus-i or bus-k can be considered as priority buses for the
>Vi V j cosG i G j @
wO
wO
and
). Based on maximum absolute value
wQik
wQki
(8)
where,
PGi = Real power generation at bus-i
PGib = Real power generation at bus-i at the base case
operating point.
PDi PDib 1 O (10)
wO
can be computed using (5) for
wQik
where,
PDi = Real power demand at bus-i
PDib = Real power demand at bus-i at the base case
operating point
each of the lines under system intact case and critical
contingency cases. Each line is having two such sensitivity
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Fifteenth National Power Systems Conference (NPSC), IIT Bombay, December 2008
QDi
QDib 1 O (11), respectively. The loading margins without UPFC and
with UPFC placed in priority locations for the system intact
case & critical contingency cases are shown in Tables II and
III. It is observed from Tables II and III that UPFC placement
in line 29-38 (towards bus-29) causes maximum enhancement
in voltage stability margin for system intact case and for most
of the severe outage cases. Hence, line 29-38 (towards bus-29)
was considered as the optimal location for UPFC placement.
(11)
where
QDi =Reactive power demand at bus-i
IV. CASE STUDIES
The proposed method of placement of UPFC controller has
been tested on a practical 75-bus Indian system representing
Uttar Pradesh State Power Corporation Network.
The 75-bus Indian system has 15 generators (at buses 1-15)
and 98 transmission lines (including 24 transformers). This
system has been taken from [14] with loadings reduced to
90% of original values.
The loading margin for the system intact case &
contingency cases (considering line and generator outages)
were obtained using continuation power flow based software
package UWPFLOW [15]. While running repeated load flows
real power generations, real and reactive power demands were
increased as per equations (9), (10) & (11), respectively. The
critical contingencies were obtained based on post
contingency loading margins. Based on post contingency
loading margins critical contingencies were indentified to be
the outages of lines 29-30, 36-37, 74-73, 23-29, 29-75, 22-25,
55-44, 26-22, 44-15( generator-15) and 16-50 in the order of
relative severity. The proposed sensitivity factors
wO
wQik
TABLE I
ABSOLUTE VALUE OF
wO
wQik
FOR TWO MOST
SENSITIVE
LINES – 75 BUS INDIAN SYSTEM
Outage
Intact
System
(No
outage)
29-30
36-37
74-73
23-29
were calculated for all the lines using (5) at a
29-75
loading value corresponding to 90% of maximum loading
value for the system intact case and for each of the critical
contingencies. The absolute value of these sensitivity factors
for two most sensitive lines for the intact case and critical
contingency cases are shown in Table-I. It is observed from
Table-I that line 29-38 (towards bus-29) has maximum value
of sensitivity factor for outages of lines 23-29, 55-44, 26-22
and 44-15 (generator-15). Line 39-59 (towards bus-39) has
maximum value of sensitivity factor for the system intact case
and for the outage of line 74-73. Line 35-17 (towards bus-35)
has maximum value of sensitivity factor for the outage of line
36-37. Line 54-28 (towards bus-54) has maximum value of
sensitivity factor for the outage of lines 29-75 and 16-50. Line
43-58 (towards bus-43) has maximum value of sensitivity
factor for outage of lines 29-30 and 22-25. Hence, lines 29-38
(towards bus-29), 39-59 (towards bus-39), 35-17 (towards
bus-35), 54-28 (towards bus-54), 43-58 (towards bus-43) were
considered as priority locations for the placement of UPFC.
The loading margin for the intact system and for the critical
contingency cases, with UPFC placed in each of the priority
locations were calculated using repeated load flows. For
obtaining maximum loadability points, starting from the base
case operating point, loads were gradually increased in the
steps of 0.01, until load flow diverged (loads were increased in
the steps of 0.001 near the point of divergence to get more
accurate estimate of loading margins). While running repeated
load flows steady-state injection model of UPFC [5] was
considered and real power generations, real and reactive
power demands were increased as per equations (9), (10) &
22-25
55-44
26-22
44-15
(Generator
-15)
16-50
Line
(Towards bus)
wO
wQik
Line
(Towards bus)
wO
wQik
39-59
(39)
49.1434
18-71
(18)
24.590
43-58
(43)
35-17
(35)
60.388
36-19
(36)
35-41
(35)
36.448
39-59
(39)
29-38
(29)
54-28
(54)
43-58
(43)
29-38
(29)
29-38
(29)
29-38
(29)
33.771
63-55
(63)
44-45
(44)
44-45
(44)
35-17
(35)
44-45
(44)
44-45
(44)
45-44
(45)
28.098
54-28
(54)
111.808
29-38
(29)
50.475
21.331
109.61
44.458
25.244
160.02
106.40
60.21
18.105
97.686
32.495
25.178
34.04
97.686
54.517
The voltage profiles of most critical bus for intact case and
for the critical contingency cases were plotted using
UWPFLOW & MATLAB. Figure-4 shows the voltage profile
of most critical bus for the intact system with and without
UPFC controller placed in the system. The voltage profile of
the most critical bus for the three most severe outage cases
(viz. outage of lines 29-30,36-37,74-73) are shown in figures
5, 6 and 7, respectively. It is observed from figures 4, 5, 6 and
7 that placement of UPFC at the optimal location results in
significant enhancement in voltage stability margins.
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Fifteenth National Power Systems Conference (NPSC), IIT Bombay, December 2008
TABLE III
IMPACT OF UPFC ON LOADING MARGIN (CONTINUED)
(75-BUS INDIAN SYSTEM)
TABLE II
IMPACT OF UPFC ON LOADING MARGIN (75-BUS INDIAN
SYSTEM)
Loading Margin
Outage
Intact
System (No
Outage)
Without
UPFC
Controller
With
UPFC in line
29-38
towards bus29
Loading Margin
With UPFC in line
43-58 towards bus-43
Outage
Without UPFC
Controller
With
UPFC in
line 39-59
towards
bus-39
With
UPFC in
line 54-28
towards
bus-54
With
UPFC in
line 35-17
towards
bus-35
0.169
0.191
0.188
Intact System
(No Outage)
0.17
0.19
0.18
0.18
29-30
0.013
0.029
0.033
29-30
0.01
0.03
0.03
0.01
36-37
0.038
0.045
0.042
36-37
0.04
0.043
*
0.043
74-73
0.051
0.066
0.067
74-73
0.051
0.066
0.065
0.055
23-29
0.053
0.079
0.077
23-29
0.053
0.078
0.072
0.053
29-75
0.053
0.071
0.068
29-75
0.053
0.069
0.062
0.060
22-25
0.058
0.075
0.081
22-25
0.058
0.077
0.078
0.058
55-44
0.064
0.082
0.084
55-44
0.064
0.083
0.075
0.065
26-22
0.065
0.090
0.086
26-22
0.065
0.088
0.077
0.070
0.069
0.084
0.082
0.069
0.081
0.081
0.075
0.091
0.105
0.103
0.091
0.103
0.096
0.085
44-15
(Generator
-15)
16-50
44-15
(Generator-15)
16-50
*Load flow divergence
Figure 5: Voltage profile of the most critical bus under line 29-30 outage for
75 -bus Indian System
Figure 4: Voltage profile of the most critical bus for the intact case for
75 -bus Indian System
545
Fifteenth National Power Systems Conference (NPSC), IIT Bombay, December 2008
[4]
[5]
[6]
[7]
[8]
Figure 6: Voltage profile of the most critical bus under line 36-37 outage
for 75 -bus Indian System
[9]
[10]
[11]
[12]
[13]
[14]
[15]
Figure 7: Voltage profile of the most critical bus under line 74-73 outage
for 75 -bus Indian System
V. CONCLUSION
M.K.Verma and S.C.Srivastava “ Enhancement of voltage stability
margin under contingencies using FACTS controllers” Proc. of the
International Conference on Power System Operation in Deregulated
Regime, IT-BHU, Varanasi (India), pp. 139-149, March 6-7, 2006.
H.A. Abdelsalam, G.E. M. Aly, M. Abdelkrim and K.M. Shebl,
“Optimal location of the Unified Power Flow Controller in electrical
power system,” Proc. of the Large Engineering Systems Conference on
Power Engineering – LESCOPE-2004, Westin Nova Scotian, pp. 41-46,
July 28-30, 2004.
D. Thukaram, L. Jenkins and K. Visakha, “Improvement of system
security with unified-power flow controller at suitable locations under
network contingencies of interconnected systems”, IEE Proc.-Gener.
Transm. Distrib., Vol. 152, No. 5, pp. 682-690, September 2005.
Weishao and Vijay Vittal, “LP based OPF for corrective FACTS control to
relieve overloads and voltage violations”, IEEE Trans on Power Systems,
Vol. 21, No. 4, pp. 1832-1839, November 2006.
M. Saravanan, S. Mary Raja Slochanal, P. Venkatesh, Prince Stephen
Abraham. J “Application of PSO technique for optimal location of
FACTS devices considering system loadability and cost of installation”,
Power Engineering Conference, Singapore, Vol- 2, pp. 716-721, Nov
29- Dec 2, 2005.
S.T.Jaya Christa and P.Venkatesh, “Application of Particle Swarm
Optimization for optimal placement of Unified Power Flow Controllers
in electrical Systems with line outages”, International Conference on
Computational Intelligence and Multimedia Applications,, Sivakasi
(India), Vol. 1, pp. 119-124, Dec.2007.
J. Hao, L.B. Shi and Ch. Chen, “Optimising location of unified power
flow controllers by means of improved evolutionary programming”, IEE
Proc.-Gener. Transm. Distrib., Vol. 151, No. 6, pp.705-712, November
2004.
M. Noroozian, L. Anguist, M. Ghandhari and G. Andersson, “Use of
UPFC for optimal power flow control”, IEEE Trans. on Power Delivery,
Vol. 12, No. 4, pp. 1629-1634, October 1997.
L. Gyugyi, C. D. Schauder, S. L. Williams, T. R. Rietman, D. R.
Togerson and A. Edris, “The Unified Power Flow Controller: A new
approach to power transmission control”, IEEE Trans. on Power
Delivery, Vol. 10, No. 2, pp. 1085-1097, April 1995.
Venkataramana Ajjarapu and Colin Christy, “Continuation Power Flow:
A tool for steady state voltage stability analysis”, IEEE Trans. on
Power Systems, Vol. 7, No. 1, pp.416-423, February 1992.
S.N.Singh and S.C. Srivastava, “Corrective action planning to achieve
optimal power flow solution”, IEE Proceeedings, Part C, Vol. 142, pp.
576-582, November 1995.
Software
Package
UWPFLOW
available
at
http://www.power.uwaterloo.ca/~claudio/software/pflow.html.
Sreekanth Reddy Donapati (b’1984) received B. Tech. degree in Electrical
A sensitivity based approach has been proposed in this
paper for the optimal placement of UPFC in power system to
enhance voltage stability under contingencies. The sensitivity
of loading parameter (O) with respect to reactive power
flowing through lines has been computed to decide optimal
location for the placement of UPFC. From the case studies
carried out on 75-bus Indian system, a considerable increase in
loading margin have been observed after UPFC placement at
the optimal location. These sensitivity factors can be easily
computed and are quite simple to adopt.
Engineering from Bapatla Engineering College, Andhra Pradesh, India in
2006 and M. Tech. Degree from Institute of Technology, Banaras Hindu
University, Varanasi, India in 2008. Presently he is working in Reliance
Infrastructure Limited, Noida, India. His research interests include voltage
stability studies and application of FACTS controllers.
M. K. Verma (b’1965) received B. Tech. degree in Electrical Engineering
from NIT, Rourkela (India) in 1989, M. Tech. degree from BIT, Sindri (India)
in 1994 and Ph.D. degree from Indian Institute of Technology, Kanpur (India)
in 2005. Presently he is a Reader in Electrical Engineering Department at
REFERENCES
[1]
[2]
[3]
Institute of Technology, Banaras Hindu University, Varanasi, India. His
Jaime De La Ree, Yilu Liu, Lamine Mili, Arun G. Phadke, and Luiz
Dasilva, “Catastrophic failures in power systems: Causes, Analyses, and
Countermeasures”, Proceedings of the IEEE, Vol. 93, No. 5, pp. 956964, May 2005.
Clark H.K, “New challenge: voltage stability,” IEEE Power Engineering
Review, pp. 33-37, April 1990.
N G. Hingorani, and L. Gyugyi, “Understanding FACTS: Concepts and
Technology of Flexible AC Transmission Systems”, IEEE Press, NewYork, 2000.
research interests include voltage stability studies, application of FACTS
controllers, power system dynamics and operation and control of modern
power systems.
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