Simulation Of Unified Static VAR Compensator And Power System

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Simulation of Unified Static VAR Compensator and Power System Stabilizer
for arresting- Subsynchronous Resonance
S. A. Khaparde
IEEE, Senior Member, Dept. of Electrical Engineering
Indian Institute of Technology, Bombay, India
V. Krishna
IEEE, Student Member, Dept. of ECE
Illinois Institute of Technology, Chicago.
Abstrac+- In the literature, co-ordination of Static Var
Compensator (SVC) and Power System Stabilizer (PSS) using
generator speed deviation or modal speeds as stabilizing signals
is shown to damp the system oscillations. Though such schemes
are able to damp the SSR modes for small disturbances, they
are unable to damp transient SSR due to large disturbances.
Here in this report improvement in the control aspect of the
SVC at the midpoint of the transmission line is suggested. This
scheme attempts different auxiliary signals that include Line
Current, Computed Internal Frequency, Bus Angle deviations.
A system of configuration similar to IEEE First Bench Mark
model is considered, eigen value analysis has been carried out,
and results indicate that Bus Angle deviation signal as auxiliary
control signal for SVC was able to damp most of the modes
leaving some of them still oscillatory. The main feature of the
proposed work is to use combination of deviation in speed and
electrical power output of the generator as input signals to PSS
which operates simultaneously along with SVC. Such
simultaneous PSS and SVC scheme is found to improve the
damping under large disturbances i.e. the growth of system
oscillations is arrested. The simulations are carried out on
PSCAD. The efficacy of controllers to damp SSR under steady
state and faulted conditions where one of the torsional modes
gets excited is presented and discussed.
self excitation have been proposed using composite speed
signals and torsional monitoring devices. It was concluded
that the control strategies are unable to damp other modes of
oscillations. In [71, a new simple concept was introduced
where generator speed deviation was used as auxiliary
stabilizing signal for SVC, in addition to voltage control
action. It was shown later in [SI that the generator speed
signal as auxiliary stabilizing signal will actually undamp the
torsional modes when the system is subjected ‘to large
disturbances.
In[9]. SVC has been used at the midpoint of the
transmission line for damping SSR and for the improvement
in the power transfer capability. A few stabilizing signals
have been shown to damp SSR through linearized eigen
value analysis. But it was not shown whether the signals are
capable of damping torsional modes through time domain
analysis.
Power System Stabilizers(PSS) have been used in Power
Systems to damp the inertial modes of oscillations of turbinegenerators[ 101. h[I I] generator speed based PSS has been
used and it was shown that torsional oscillations are damped,
but the disturbances considered are small. In[ 121, D. C. Lee
et al. have proposed a new scheme for PSS, which uses
deviation in generator speed and electrical power output of
the generator as input signals. It was shown that the inherent
disadvantages of using speed based stabilizers can be
eliminated with this scheme. The coordinated scheme
proposed in [SI,based on modal speeds, has been shown to
damp the torsional oscillations effectively for small
disturbances, however €or large disturbances the scheme can
arrest only the growth of oscillations and satisfactory
damping is not achieved.
Here in this paper a new simple concept is introduced with
simultaneous operation of PSS and SVC. The SVC is at the
midpoint of the transmission line. The PSS model that has
been used is similar to the one presented in [ 121. The
auxiliary signal used for the SVC is the angle deviation at the
SVC bus and has been derived locally. As customary, to
alleviate the damping, the measured signals are passed
through torsional filters before they are input to the
controller. The study has been canied out on the system
considered in[9], which is similar to IEEE FBM. This
configuration has been taken because the results presented in
this paper can be validated with that model as it has shunt
compensation at the midpoint of the transmission line. The
investigations carried out indicate that the proposed scheme
can effectively arrest the growth of the oscillations under
I. INTRODUCTION
Subsynchronous
Resonance is a Power System
phenomenon where the electric power system exchanges its
energy with turbines at one or more frequencies below the
synchronous frequency, when the electric network is
compensated with series capacitors. The problem of torsional
interaction has been [ 1,2,3] identified to take place when the
electric resonant frequency is near the complement of one of
the torsional mode frequencies of the turbine-generator shaft
system. In addition to torsional modes the inertial mode is
also excited as a result of disturbances.
In recent years, great deal of attention has been focused on
mitigating SSR with the use of Static Var Compensators
(SVC), which were previously used only for voltage
regulation purposes and for damping the inertial mode of
oscillations[4,5]. In [6] two new methods to damp SSR by
0-7803-3713-1/97 $10.00 0 1997 IEEE
302
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,
faulted conditions also. The analytical results have been
verified by the time domain simulations with the use of
Manitoba HVDC center's PSCAD. The proposed concept has
been implemented also on IEEE FBM and the results of the
test case 1 -T[ 13]are presented.
11. SYSTEM MODEL
A. Power System Description.
The network configuration that has been used for study
purpose is given in Fig.1. Figure 1 shows a steam turbine
driven synchronous generator supplying power to an infinite
bus through a long distance series compensated transmission
line. A Fixed Capacitor -Thyristor Controlled Rectifier (FCTCR) combination which works as Static Var Compensatory
system is considered at the mid point of the transmission line.
The total system model can be derived by clubbing the
individual subsystem models, which are explained later.
Fig. I. System Configuration used for study.
B. Mechanical System model
The mechanical system has been described using the
'multiresonant mass model' (all modes model)[ 121. This
model is considered because it includes the effect of the
zeroth mode and accounts for the coupling between different
modes. Each major rotating element is modeled as a massless
rotational spring with its stiffness expressed by a spring
constant. Viscous damping of each mass and shaft is
represented by a dash pot damping.
The equation of the i' mass of the n-mass rotating system
is given by
where M is Inertia constant, D is damping, K is spring
constant, T, and T, are mechanical and electrical torque.
Equations for all the masses can be written and can be
linearized around the operating point, and are transformed to
D-Q axis[9], which is synchronously rotating reference
frame.
The state and output equations in the state space form can
bq given as
XM = AM. XM + BMI. UMI +BM2. UM2
YM = CM. XM
(2)
where
XM =[AS, AZi2 Aa3 AS4 AS5 A66 A o , A o 2 A o 3 Ao, A o s
A%
1'
303
UMl = [AID AIQIt, UM2 = [A& Ab ]I, YM = [ A& A u 5 1'
where A6s and Aos are angle deviations and speed deviations
of masses 1 to 6 respectively. The variables in UMl and
UM2 are explained later in Rotor model.
C. Synchronous machine model.
Synchronous machines can be modeled in varying degrees
of complexity depending upon the purpose of the model and
usage. The model reported in [9] has been used in this paper
and is found to be suitable for torsional dynamic studies. The
machine is split at the air gap which is its natural boundary. It
includes a field winding and a damper winding on d axis and
two damper windings on the q axis.
1). Stator Circuit model.
In this model, the stator of the synchronous generator is
represented by a dependent current source (I, ) in parallel
with the subtransient inductance L,' [9]. This stator model is
combined directly with the transmission network model
which is explained later.
I, =[ I, I, I, 1' = I, c + I, s
(3)
where
c'=:fi [ cos(e) cos(e-2~13) cos(e+ 21113) 1
st = fi [ sin(e) Sin(e-2~0) sin(e +2n13) J
&,I, are components of dependent current source along d
and q axis ,respectively. 8 is the rotor angle. Superscript t
indicates transpose.
2). Rotor circuit model.
The flux linkages in the rotor associated with the different
windings are defined as follows
$f
=alWf+%Whfblvf+b2id
$h
=a3Yf +a4Wh+b3id
q g
=
Wg
\Vk
E
Wg + %
%Wk+
bSfq
Wk+ b61q
(4)
where vf is field excitation voltage.
id,iq are d and q components of the machine terminal
currents. All the constants a and b are defined in [9]. Then
the currents have to be transformed to D-Qframe. The state
equation of rotor circuit can be obtained after linearizing as
follows
XR = AR.XR + BRl.UR1 +BR2.UR2 + B W . U W
(5)
where
XR = [ AWf AWh
AWk 1'
URI = [A6 Ao UR2 = A V , uR3 = [AiD AiQ]'
6 and o are the angle and angular speed of the generator
respectively.
The components of the dependent current source, along d-q
axes respectively expressed as
Id=CIWf +C2\11h' r q = c 3 Y g +c4\11k
(6)
The currents are transformed to D-Q frame as r0, I ~ The
.
linearized output equations of rotor circuits is obtained as
YRI- CR1.XR +DRl.URl
r,
YR2=CR2,XR +DW.URl+DEU.UR2 +DR4.UR3
(7)
where
YR1= [AID AIQ]', YR2= Ykl
D.Excitation System
IEEE type 1 excitation system [14] has been used for
studies. The system is based on dc rotating machine and is
consistent with the model provided for the IEEE FBM. The
terminal voltage of the generator is the input to the excitation
system.
transmission line is modeled as a lumped parameter PI circuit
on both sides of FC, and the symmetric nature of network
facilitates its representations in terms of a and p components.
The a and p network configurations have been presented
in[9].
The differential equations of the RLC network can be
written and are to be transformed to synchronous reference
frame D-Q. The linearized state equation and output
equations of the network model can be derived as
Xh=AN.XN+BN2.UN2+BN3
.UN3
YNl=CNl.XN+DN2.UN2+DN3.UN3
YN2=CN2.XN
YN3=CN3.XN
(10)
Where
XN = [AX, A%]'
xD = [ iID
i4D iD
U
xQ
Fig.2 PSS linearized model used for eigenvalue analysis.
In the literature generator speed deviation (conventional
PSS) and modal speeds have been taken as input signals for
the PSS. A small signal model is derived for the system and
the Hephron-Philips constants will be found. From this the
required gain and phase lead to make the speed signal to be
in phase with the electric torque will be found. The output of
the PSS has been added at the Vref summer of excitation
model.
Here the improved model for the PSS[12] has been used
and is given in the Fig.2. The inputs to this model are
generator speed deviation and the deviation in electrical
power output of the synchronous machine. The equivaIent
speed deviation is obtained from these input signals and is
gain and phase adjusted. Parameters of the blocks G(s),Q(s)
and K are given in appendix B.
The state equation of the PSS can be given as follows
XPSS = APSS. XPSS CBPSS.UPSS
YPSS = CPSS. XPSS
(8)
where
UPSS = [U,,, Upss21f= [ Am AP, 1' ,YPSS= [ypss]
The state and output equation of the linearized excitation
system can be derived as
= [ iIQ iZQ i4Q
'2D '3D '4D '5D '6D I'
6 V2QV3QV4QV5QV6Qlf
UN2= [AIIDAb]', UN3= UN2, YN1= AV,, YN2= [Ai, AiQ]'
YN3= [ A V ~AV,*
~ 1'
The outputs of the networks are generator terminal voltage,
currents at the generator end and the voltage at the mid point,
which are the inputs to exciter and SVC system respectively.
F. Static Var System
The SVC system considered is a combination of Fixed
Capacitor (FC) and Thyristor Controlled Reactor(TCR). TCR
provides continuous control of reactive power and in
conjunction with the parallel FC. Fig.3. shows the schematic
of the SVC system with auxiliary feedback. The terminal
voltage perturbation and SVC incremental current, weighted
by a factor &, representing current droop, are fed to the Vref
junction. The voltage regulator is assumed to be PI controller.
Thyristor control action is represented by average dead time
Td and firing angle time delay Ts. The output of the control
block is susceptance(B) variation. Parameters of the above
block diagram are given in appendix B.
The a and p axis currents entering TCR from the Network
are given by the equations
XE =AE.XE +BE.UE
YE =CE.UE
Where
XE = [ AV, AV, AV,1'. YE = [AV, 1, UE = [Avg ypss]'
(9)
E. Network Model.
The network that is considered is shown in the Fig.1. and
the transmission line is compensated by series capacitors. The
SVC has been placed at the midpoint of the network, which is
the concept of compensation by sectioning to improve the
power transfer capability of the line. For the linearized
analysis the whole of SVC is represented as a fixed capacitor
giving reactive power support at the midpoint. The
Fig.3 Linearized SVC control block diagram.
304
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TABLE 1. Real parts of Eigenvalues related to torsional modes.
I
I
I1
I
ITT
I A- without PSS and SVC, I1 A- with SVC at midpoint performing voltage control action, I1 B- with torsional filters in SVC
voltage measurement loop, I1 C- with LC controller, I1 D- with CIF controller, I1 E- with SVC bus angle deviation control,
111 A- with generator speed based PSS acting simultaneously with SVC, 111 B- proposed scheme.
where R and L, represent the resistance and inductance of
the TCR respectively.
The state and output equations of SVC model can be written
as
X'S = AS.XS + BSl.US1 + BS2.US2 + BS3.US3
YS = CS.XS + DS.US1
(12)
where
xs = [ Ai3D AijQ z1 22 23 AB]'
US 1 = [ AV,, AV,, 1' ,US2 = [Av,~]
u s 3 = [AV,], Y s = [A& A&Q]'
G. Auxiliary Control of SVC.
The auxiliary stabilizer signal Avf is added to the main
input of SVC controller to damp the oscillations. Different
auxiliary control signals have been considered in [9]. In[9]
linearized analysis has been carried out and it was shown that
auxiliary signals Computed Intemal Frequency (CIF), and
Line Current (LC) work better to damp oscillations. But the
performance of the controllers for disturbances was not
shown with simulations.
Here in this study it is found that auxiliary signal based on
the deviation of the bus angle at the SVC bus.
The angle of the voltage at the SVC bus is given by
-I
9
(13)
Y1=tan
where D and Q refer to D-Q frame of reference.
Equation 13 is linearized around the operating point and can
be obtained as
Ay3 = ?AVIQ
VI0
- *AVID
Second order transfer function is taken for the auxiliary
signal path. The state and output equations of the auxiliary
control can be given by
XC = AC.XC + BC.UC
YC = CC.XC + DC.UC
(14)
Now the control signal (U, ) will be Ay3.Again which can be
expressed as
U, = FCR.XR + FCM.XM + FCN.XN + FCS.XS
(15)
in terms of the total system state variables. The output of the
control block will be AV,.
H. Overall System
The state and output equations of overall system can be
w.ritten as follows:
XT = AT.XT + BT.UT + B.US2
YT = CT.XT + DT.UT
(16)
where
XT = [ XR XN XE XM XS XPSS XC]*,
YT = [YRl YR2 YR3 YNl YN2 YN3 YN4 YE YMI Yh42
YSI YS2 YPSS YC]',
UT = [URl UR2 UR3 UN1 UN2 UN3 UE UM1 UM2 US1
u s 3 UPSS ucy
The ineterconnectivity between models can be expressed as
UT=FT.YT
(17)
substituting equation (17) in equation (16) and setting US2
to zero, we get the system equations in a reduced form as
follows:
(18)
f T = AA. XT
where AA = [AT + BT[I-FT.DT]' FT.CT]
AT,BT,CT,DT are combined A,B,C,D independent model
matrices.
v30
305
111. ANALYSIS METHODS AND RESULTS
A. Eigenvalue analysis
From the overall system transformation matrix AA
obtained as above, the eigenvalues of the system can be
found. The stability of the system can be estimated from the
real parts of the eigenvalues. If they are positive they
represent an unstable operating condition and the growth of
oscillations.
The resulting eigen values with the use of Line
Current(LC)[9], as auxiliary control signal are given in I1 C.
LC controller improves the damping of mode 1 but the zeroth
mode gets destabilized. The Computed Internal
Frequency(CIF)[S)],as auxiliary signal has resulted in (I1 D),
where it can be seen that damping of mode 1 gets worse. I1
E gives the eigenvalues with bus angle deviation as auxiliary
stabilizing signal. It can be seen that all the modes negative
real parts, but the damping of few torsional modes is still less.
Then PSS , with generator speed deviation signal as the
input signal(conventionai PSS) has been operated
simultaneously along with SVC. The result ,111 A, shows that
a few modes have become unstable, which were oscillatory
(I1 E)with SVC alone. This, once again shows that the
generator speed based stabilizers actually undamp the system
oscillations. The results of the proposed scheme are given in
111 B. Comparing IIE and I11 B shows that the simultaneous
operation of SVC and PSS has improved the damping of all
modes.
0.m
I
3.0
2.0
:10
L
0.0
.LO
40
0.1
mn4r4
-0-0-
:
;
-
withut any contm&rs.
with proposed scheme in operation.
0.0
OS
Fig. 4. Mode 1 Instability and damping with the proposed
scheme.
For brevity only the eigenvalues related to torsional
frequencies are given in Table 1. The eigen values have been
obtained for the system in Fig. 1, with generator generating
800 MW and the compensation level being 50%. From I A, it
can be seen that few modes have positive real parts and this
represents the case SSR being set in. In I1 A, SVC is
incorporated at the midpoint of the transmission line, which
performs only voltage control action. From I A and I1 A it
can be seen that the damping of mode 0 has increased.
Which confirms the fact that SVC can be used in the
damping of mode 0. The measured signal (voltage) contains
subsynchronous components and as it is fed at the summing
point Vref, Fig. 3. ,the reference voltage oscillates with
subsynchronous frequency leading to instability. This has
resulted in a unstable eigenvalue(one of the SVC modes) of
the system with oscillating frequency of 287.0radsec. This
instability is eliminated by the insertion of a torsional filter in
the measurement loop, and the result is presented in I1 B,
from which the improvement in the damping of mode 1 &o
can be seen.
306
0.N
U.@
aa
4.15
420
Rz5
tbnelsel
Fig. 5 . Damping effect of the proposed scheme for 10%
change in mechanical torque.
B. Time Domain Simulations
Digital simulation studies have been carried out to check the
validity of the results of eigenvalue studies and to test the
efficacy of the proposed scheme with large disturbances. All
the independent components of the system, as explained
above have been modeled in PSCAD. The variables that have
been plotted are: Aw is the change in generated speed in
p.u, AT(LPB-GEN) the change in torque transmitted from
the second Low pressure turbine to the Generator, P is the
electric power generated by the generator in p.u, Qc - is the
reactive power supplied by the SVC at the mid point of the
transmission line.
In PSCAD, simulation is started with generator as a voltage
source and is ramped upto the required power and is switched
to the generator-turbine setup. In the present simulations the
ramping is done for 0.3 secs and switchover takes place at 1.1
seconds. Different compensation levels are considered in
different cases so that the efficacy of the proposed scheme
can be tested for different mode instabilities. Derivation of
SVC bus angle in the PSCAD simulation is explained in
appendix A.
-
-
-
oscillations being damped out with the proposed scheme in
operation. From Fig.4, the time taken by the masses to settle
(which is approximately 3 secs), when they are brought into
operation can be seen, which is not present in the system
without the proposed scheme in operation. This is because of
the interaction of the controllers with the masses when they
are initialized.
Case 2: Fig.5, presents a the result of a case where 10%
change in mechanical torque has been applied for 4 cycles at
7th second when masses have settled. The generator is
generating 0.9 pu , and the compensation of the transmission
line being 75%. It can be seen that the growth of oscillations
is arrested though the complete damping is not achieved.
Case 3: Here two, 3 phase faults have been considered. Fig.
6. presents the results with fault inductance being 0.2075H ,
and Fig. 7. with fault inductance 0.004H, which tune mode-3
and mode-2 respectively and make these modes unstable. The
3 phase fault has been created at 7th second. Fig. 7 presents
the result for the test case I-T given in [I31 by IEEE
Subsynchronous Resonance Task force. The results show that
the scheme has positive damping affect on large disturbances
though complete damping is not achieved.
,o 10
8
0.0
E
---
;4.m
451
,025
4.05.
nm
".W
6
t
.;am
:au.
at54
Fig.6. Damping of 3phase fault-mode 3 instability.
Case 1: In Fig. 4., the generator is generating 0.9 p.u. of
power with the line compensation being 85% . This case has
been selected to show the mode 1 instability. The figure
shows the growth of oscillations without controllers and the
* 520
42s
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IV. CONCLUSIONS
Loop Control of Static Var Sources on EHV Transmission
lines,” Paper A 78 135-6 presented at the IEEE PES Winter
Meeting, NewYork, 1978.
R. Mathur, P. Dash and A. Hammad, “Transient and Small
signal Stability of a Superconducting Turbogenerator
Operating with Thyristor Controlled Static Compensator,“
IEEE Trans. Vol. PAS-98, pp. 1937-1946, 1979.
0. Wasynczuk, “Damping Subsynchronous Resonance
Using Reactive Power Control,” IEEE Trans. Vol. PAS100, pp. 1096-1 104, 1981.
A. E. Hammad and M. El-Sadek, “Application of a
Thyristor controlled VAR Compensator for damping
Subsynchronous Oscillations in Power Systems,” IEEE
Trans., Vol. PAS-103, pp. 198-212, 1984.
R. M. Hamouda, M. R. Irwani, and R. Hackam, “Coordinated Static Var Compensator and Power System
Stabilizer for damping PS Oscillations,” IEEE Trans., Vol.
PWRS -2, pp. 1059-1067, 1987.
K. R. Padiyar and R. K Varma, “Static Var system auxiliary
controllers for damping Torsional Oscillations,” Electric
Power Energy Systems, Vol. 12, No.12, pp. 271-285, 1990
P. A. Larsen and D.A. Swann, “Applying Power System
Stabilizers, Part I, General Concept,” IEEE Trans., Vol.
PAS -100, pp. 3017-3024, 1981.
A. A. Fouad and K. T . Khu, “Damping of Torsional
Oscillations in Power Systems with series Compensated
lines ,” IEEE Trans., Vol. PAS-97, No.3, pp. 744-752,
1978.
D. C. Lee, R. E. Beaulieu and J. R. R. Service, “A Power
System Stabilizer using Speed and Electrical Power inputs - design and field experience,” IEEE Trans., Vol. PAS -100,
NO. 9, pp. 4151-4157, 1981.
IEEE Subsynchronous Working Group, “First Bench Mark
Model for Computer Simulation of Subsynchronous
Resonance,” IEEE Trans., PAS-96, No. 5 , pp. 1565-1672,
1977.
IEEE Committee Report, “Computer Representation of
Excitation Systems,” IEEE Trans., Vol. PAS-87, pp. 14601464. 1968.
In this study, unified operation of PSS and SVC at the
midpoint of the transmission line for arresting the growth of
SSR has been presented. The study has been carried out on
modified IEEE FBM model, presented in [9], using the eigen
value analysis and the analytical results have been verified by
time domain simulations. The conclusions can be
summarized as:
1. Deviation in voltage angle of SVC bus as the auxiliary
stabilizing signal damps the SSR better than existing
stabilizing signals.
2. Simultaneous operation of SVC(with proposed auxiliary
control signal) and conventional PSS destabilizes the system.
3. The proposed scheme arrests the growth of oscillations at
critical compensation levels at small as well as large
disturbances.
Further study has to be done to achieve complete damping
and to improve the initial settling time that has been observed
with the proposed scheme in operation.
APPENDIX A
Derivation of SVC bus voltage angle with the quantities
that can be measured at the SVC bus (Fig. 1).
VI = I+j.O
IV31 = 1.O, angle of the SVC bus, w.r.t infmite bus ,say, 6,
1
(e3d
where
P, is power flow from bus 3 to bus 1.
z3i,-e3,is impedance between bus 3 and bus 1.
APPENDIX B
Data for the PSS block parameters:
BIOGRAPHIES
S. A. Kbaparde: was bom at Amravati of Maharashtra state
in India, received his B.E. in 1971, M.Tech. in 1973 and
Ph.D. in 1980 from Indian Institute of Technology,
Kharagpur. He is currently an associate professor of electrical
engineering at IIT Bombay. He has several publications to his
credit and his research interests include pattern recognition,
Data for the SVC block parameters:
K, = 1200, K, = 1.0, K,, =0.01, T, =5.0e-3
T,
=
1.667e-3, T,
= 0.02,
G(s) =
-5
( l+s0.02)2
V. REFERENCES
U1
E21
[31
141
power
IEEE Power System Engineering Committee, “Analysis and
Control of Subsynchronous Resonance,” IEEE Power
Engineering Society Winter Meeting and Tesla Symposium,
1976.
R. G . Farmer, A. L. Schwalb and E. Katz, “Navajo Project
Report on Subsynchronous Analysis and Solution,” IEEE
Trans., Vol. PAS-96, pp. 1226-1232, 1977.
P. M. Anderson, B. L. Aganval and J. E. Van Ness, “Sub
synchronous Resonance in Power Systems,” IEEE Press.
H. Schweickardt, G. Romegialai and K. Reichert, “Closed
308
system
security,
Artificial
Intelligence
and
applications, parallel processing and neural networks. He is
senior member of IEEE and International Neural Network
society. Email: eesakia@ee.iitb.ernet.in.
V. Krishna: was born in Narsapur of Andhra Pradesh state
in India on May 4, 1972. He is currently working towards his
Ph.D degree in Power Systems at Illinois Institute of
Technology, Chicago. Email: kvuppala@ece.iit.edu.
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