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Critical Clearing Time and Transient Stability

Analysis of SCIG based Wind Farm

with STATCOM

P.Sravanthi, K. Radha Rani, Dr. J. Amarnath, Dr. S.Kamakshaiah

Abstract—In recent years generation of electricity using wind

power has received considerable attention worldwide. Induction

machines are mostly used as generators in wind power based

generations. Since induction machines have a stability problem

as they draw very large reactive currents during fault condition,

reactive power compensation can be provided to improve

stability. This paper deals with the Impact of STATCOM on the

Wind Farm performance. The essential feature of the

STATCOM is that it has the ability to absorb or inject fastly the

reactive power with power grid entirely by means of electronic

processing of the voltage and current waveforms in a voltage

source converter (VSC). This function is identical to the

synchronous condenser with rotating mass. In the present work

transient stability improvement and critical clearing time(CCT)

analysis using STATCOM under faults is proposed.

Improvement of transient stability with and without STATCOM

and reactive power injection by STATCOM is studied.

Simulation results are given, commented and discussed. The test

results prove the effectiveness of the proposed STATCOM

controller in terms of fast damping the power system oscillations

and restoring the power system stability.

Index Terms-- Transient Stability, Critical Clearing Time,

Active Power, Reactive Power, FACTS, STATCOM and Wind

Farm

I. INTRODUCTION

ith the increase in demand of power and decrease of

fossil fuels, mankind has been forced to search

alternative sources for the generation of electricity[1].

Nowadays wind as a significant proportion of non-pollutant

energy generation, is widely used[2]. Wind power in spite of

being stochastic in nature has proved itself as a viable solution

to this problem. As the wind turbine technology is developing

at a good pace, more and more wind power plants are being

integrated with the conventional form of generation.

With the increase in the ratio of wind generation to

conventional generation, several problems related with

integration of wind farms have emerged[1]. In addition, power

transmission and distribution systems face increasing demands

for more power, better quality and higher reliability at lower

cost, as well as low environmental effect. Under these

conditions, transmission networks are called upon to operate

at high transmission levels, and thus power engineers have

had to confront some major operating problems such as

transient stability, damping of oscillations and voltage

regulation etc [3].These problems are due to distinct properties

of the generators used with the conventional form (Thermal &

Hydro) of generation and wind based generation. In thermal

and hydro power based generation synchronous generators are

W

used while in wind based generation mostly induction

generators are used[1].

One of the simple methods of running a wind generating

system is to use the induction generator connected directly to

the grid system The induction generator has inherent

advantages of cost effectiveness and robustness. However

induction generators require reactive power for magnetization.

When the generated active power of an induction generator is

varied due to wind, absorbed reactive power and terminal

voltage of an induction generator can be significantly affected

[4].

Flexible AC Transmission Systems are represented by a

group of power electronic devices. This technology was

developed to perform the same functions as traditional power

system controllers such as transformer tap changers, phase

shifting transformers, passive reactive compensators,

synchronous condensers, etc. Particularly FACTS devices

allow controlling all parameters that determine active and

reactive power transmission, nodal voltages magnitudes,

phase angles and line reactance. Replacement of the

mechanical switches by semi conductor switches allowed

much faster response times without the need for limiting

number of control actions. However, FACTS technology is

much more expensive from the mechanical one. FACTS

devices can be divided into two generations. Older generation

bases on the thyristor valve, where newer uses Voltage Source

Converters (VSC)[5].

Flexible AC Transmission Systems (FACTS) are used

extensively in power systems because of their ability to

provide flexible power control. Examples of such devices are

the Static Synchronous Compensator (STATCOM) and the

Unified Power Flow Controller (UPFC). STATCOM is

preferred in wind farms due to its ability to provide bus bar

voltage support either by supplying and/or absorbing reactive

power in to the system[6].

II. WIND TURBINE MODEL

A. Squirrel Cage Induction Generator

The fixed speed wind generator systems have been used

with a multiple-stage gearbox and a SCIG directly connected

to the grid through a transformer. Therefore, rotor speed

variations are very small, because the only speed variations

that can occur are changes in the rotor slip, because the

operating slip variation is generally less than 1%, this type of

wind generation is normally referred to as fixed speed. A

SCIG consumes reactive power. Therefore, in case of large

978-1-4799-4103-2/14/$31.00©2014 IEEE

2

wind turbines and/or weak grids, often capacitors are added to

generate the induction generator magnetizing current, thus

improving the power factor of the system as a whole. The slip

is generally considered positive in the motor operation mode

and negative in the generator mode. In both operation modes,

higher rotor slips result in higher current in the rotor and

higher electromechanical power conversion. If the machine is

operated at slips greater than unity by turning it backwards, it

absorbs power without delivering anything out i.e. it works as

a brake[3]

The block diagram of wind turbine induction generator is

shown in Fig 1. The stator winding is connected directly to the

60 HZ grid and the rotor is driven by a variable-pitch wind

turbine. The power captured by the wind turbine is converted

into electrical power by the induction generator and is

transmitted to the grid by the stator winding. The pitch angle

is controlled in order to limit the generator output power to its

nominal value for high wind speeds. In order to generate

power the induction generator speed must be slightly above

the synchronous speed. The pitch angle controller regulates

the wind turbine blade pitch angle β, according to the wind

speed variations. A Proportional-Integral (PI) controller is

used to control the blade pitch angle in order to limit the

electric output power to the nominal mechanical power. The

pitch angle is kept constant at zero degree when the measured

electric output power is under its nominal value. When it

increases above its nominal value the PI controller increases

the pitch angle to bring back the measured power to its

nominal value. The pitch angle control system is illustrated in

the Fig 2.[7]

turbine is aggregated with these quantities of the electric

generator coupled with the turbine [3].

(1)

Here Pm= mechanical power developed by the wind

turbine, Cp= power coefficient of the turbine, ρ is the density

of air striking the turbine blades (kg/m3, A is the swept area of

the rotor blades of the turbine (m2), λ is the tip-speed ratio, β

is the pitch angle (degrees)[1] ,[2], [3], [7], [8].

(2)

The relation between Cp, β and λ is shown in Fig 3.

Fig. 3. Aerodynamic power coefficient variation Cp_ against tip speedratio λ

and pitch angle β.

B. Induction Machine

In the present study, the electrical part of the machine is

represented by a fourth-order state-space model and the

mechanical part by a second-order system. All electrical

variables and parameters are referred to the stator. All stator

and rotor quantities are in the arbitrary two-axis reference

frame (d-q frame).

III. STATCOM

Fig. 1. Wind Turbine Induction Generator

Fig. 2. Control System for pitch angle control

The model of wind turbine used for the purpose of

simulation is a per unit model based on the steady state power

equation of a wind turbine. The gear train used for coupling

the generator with the grid is assumed to have infinite stiffness

while the friction factor component and the inertia of the

Shunt compensators are primarily used for bus voltage

regulation by means of providing or absorbing reactive power.

They are effective for damping electromechanical oscillations.

Different kinds of shunt compensators are currently being

used in power systems, of which the most popular ones are

Static Var Compensator SVC and STATCOM . In this work,

only the STATCOM, which has a more complicated topology

than SVC, is studied. Static Synchronous Compensator

(STATCOM) is a shunt controller mainly used to regulate

voltage by generating/absorbing reactive power. The

schematic diagram of STATCOM is shown in Fig 4.

3

transformer and VSC losses and to keep the capacitor

charged.[7]

B. V-I Characteristics of STATCOM

Fig. 4. STATCOM

A. Operating Principle of STATCOM

Fig. 6. V-I Characteristics of STATCOM

Fig. 5. Operating Principle of STATCOM

The resulting STATCOM can inject or absorb reactive

power to or from the bus to which it is connected and thus

regulate bus voltage magnitudes. The main advantage of a

STATCOM over SVC is its reduced size, which results from

the elimination of ac capacitor banks and reactors; moreover,

STATCOM response is about 10 times faster than that of SVC

due to its turn-on and turn-off capabilities. The active and

reactive power exchange between the VSC and the system is

shown in Fig 5 are a function of the converter output voltage

denoted as Vout, i.e,

(3)

Where

V1=line to line voltage of source V1

V2=line to line voltage of V2

X=Reactance of interconnection Transformer and filters

δ= angle of V1 with respect to V2

In steady state operation, the voltage V2 generated by the

VSC is in phase with V1 (=0), so that only reactive power is

flowing (P=0). If V2 is lower than V1, Q is flowing from V1

to V2 (STATCOM is absorbing reactive power).

On the reverse, if V2 is higher than V1, Q is flowing from

V2 to V1 (STATCOM is generating reactive power). The

amount of reactive power is given by

(4)

A capacitor connected on the DC side of the VSC acts as a

DC voltage source. In steady state the voltage V2 has to be

phase shifted slightly behind V1 in order to compensate for

As long as the reactive current stays within the minimum

and minimum current values (-Imax, Imax) imposed by the

converter rating, the voltage is regulated at the reference

voltage Vref. However, a voltage droop is normally used

(usually between 1% and 4% at maximum reactive power

output), and the V-I characteristic has the slope indicated in

the fig 6. In the voltage regulation mode, the V-I characteristic

is described by the following equation:

V=Vref + Xs I

(5)

Where V : Positive Sequence Voltage (pu)

I : Reactive Current (I>0 indicates an Inductive Current)

Xs: Slope or Droop Reactance[9]

IV. OVERVIEW OF POWER SYSTEM STABILITY ANALYSIS

The following definitions from[8] provide the foundation

for transient stability and small-signal stability analysis.

1) Disturbance in a Power System. A disturbance in a

power system is a sudden change or a sequence of changes in

one or more of the operating parameters of the system, or in

one or more of the operating quantities.

2) Small Disturbance in a Power System. A small

disturbance is disturbance for which the equations that

describe the dynamics of the power system may be linearized

for the purpose of analysis.

3) Large Disturbance in a Power System. A large

disturbance is a disturbance for which the equations that

describe the dynamics of the power system cannot be

linearized for the purpose of analysis.

4) Steady-State Stability of a Power System. A power

system is steady-state stable for a particular steady-state

operating condition if, following any small disturbance, it

reaches a steady-state operating condition which is identical or

close to the pre-disturbance operating condition. This is also

known as small disturbance stability of a power system.

5) Transient Stability of a Power System. A power system

is transiently stable for a particular steady-state operating

condition and for a particular disturbance if, following that

disturbance, it reaches an acceptable steady-state operating

condition.

From the above definitions, one observes that the transient

stability problem encompasses the small-disturbance stability

problem. The transient stability analysis involves more

4

detailed non linear models, solution techniques, and includes

steady-state stability analysis of the operating condition that

will be reached following the transient. The stability problem

is concerned with the behavior of the synchronous machines

after a disturbance. For convenience of analysis, stability

problems are generally divided into two major categoriessteady state stability and transient state stability[9].

A. Swing Equation

The relative position of the resultant magnetic field axis

and rotor axis is fixed under normal conditions. Power angle

and torque angle are the angle between the two axes. During

disturbance, a relative motion begins because of the

deceleration or acceleration with respect to the synchronously

rotating air gap mmf. Swing equation is the mathematical

structure to describe relative motion.

d

2

dt

δ

m

2

= P

m

− P

e

Runge-Kutta method

The swing equation can be transformed into state variable

form as[9]

dδ

= Δω

dt

(9)

dΔω πf o

=

Pα

dt

H

Now apply modified Euler’s method to the above equations

as below

dδ

dt

dδ

dt

Δω pi +1

δ ip+1

= Δω pi +1, where Δω pi +1 = Δω i +

=

πf 0

H

Pα

where

δ ip+1

δ ip+1

dΔ ω

dt

dδ

= δi +

dt

Δωi

Δt

δi

(10)

Δt

Then the average value of the two derivatives is used to

find the corrected values.

Swing equation in terms of inertial constant M ,

M

(iii)

(6)

Relationship between electrical power angle δ and

mechanical power angle δm and electrical speed &

mechanical speed of synchronous machine ,

(7)

Where P is the pole number.

Swing equation in terms of electrical power angle δ :

(8)

V. TRANSIENT STABILITY

The transient stability studies involve the determination of

whether or not synchronism is maintained after the machine

has been subjected to severe disturbance. This may be sudden

application of load, loss of generation, loss of large load, or a

fault on the system. In most disturbances, oscillations are of

such magnitude that linearization is not permissible and the

nonlinear swing equation must be solved.

A. Numerical Solution of Swing Equation

The transient stability analysis requires the solution of a

system of coupled non-linear differential equations. In

general, no analytical solution of these equations exists.

However, techniques are available to obtain approximate

solution of such differential equations by numerical methods

and one must therefore resort to numerical computation

techniques commonly known as digital simulation. Some of

the commonly used numerical techniques for the solution of

the swing equation are:

(i)

Point by point method

(ii)

Euler modified method

δic+1

⎛ dδ

= δi + ⎜⎜

⎝ dt

dδ

Δωi

dt

⎛ dΔω

⎜

⎞

c

⎜ dt

p ⎟Δt, Δωi +1 = Δωi +

Δωi ⎟

⎜

⎠

⎜

⎝

dΔω

dt

2

δi +

δip

⎞

⎟

⎟Δt

⎟

⎟

⎠

(11)

B. Point by Point Method

It is always required to know the critical clearing time

corresponding to critical clearing angle so as to design the

operating times of the relay and circuit breaker so that time

taken by them should be less than the critical clearing time for

stable operation of the system.

So the point-by-point method is used for the solution of

critical clearing time associated with critical clearing angle

and also for the solution of multi machine system. The stepby-step or point-by-point method is the conventional,

approximate but proven method. This involves the calculation

of the rotor angle as time is incremented. The accuracy of the

solution depends upon the time increment used in the analysis.

The following parameters are evaluated for each interval (n)

The accelerating power Pa (n-1)=Ps - Pe(n-1)

From the swing equation α(n-1)=Pa(n-1)/M

(12)

5

VI. CRITICAL CLEARING TIME ANALYSIS(CCT)

CCT is defined as maximal fault duration for which the

system remains transiently stable. Mathematically, CCT is a

complex function of pre-fault system conditions(operating

point, topology, system parameters), fault structure (type and

location) and post fault conditions that themselves depend on

the protective relaying plan employed. It would be highly

desirable to define this relation analytically. But, diversity of

variables involved makes this task extremely complicated.

In practice, CCT can be obtained in one of two ways: by

trial and error analysis of system post disturbance equations or

by integrating fault-on equations and checking the value of

Lyapunov energy function until it reaches a previously

determined critical level. For the first approach, many

integration processes are necessary. But, for the second

approach we can evaluate the CCT in just one integration

process. The major problem for the second approach is to find

an analytical energy function which considers a precise model

of generator and the effect of new Flexible AC Transmission

System (FACTS) devices added to improve the transient

behaviour of power system like STATCOM.

The CCT With the continuous increase in the diffusion of

the wind farms in the electric systems is important to be

analyzed.. During severe faults as a three phase fault, the

electromagnetic torque decrease when the mechanical torque

related to wind speed is considered to be constant. In this case

the rotor shaft accelerates; hence it is important to analyze the

speed impact. Critical clearing time CCT and critical speed

CS

The slip factor determines the wind generator stability.

During faults, the increase in slip point at which the

electromagnetic torque corresponds to the same amount as

before disturbance is known as the critical slip. If the

disturbance is cleared beyond the stable point, a continuous

increase in the rotor speed will be encountered whereas, the

electromagnetic torque decreases. In this case runaway slip is

denoted. The time duration starting from the fault time until

the critical slip point is the CCT. Hence the CCT can be

determined from the torque and rotor speed characteristic of

the induction machine. For this purpose, the CCT of a single

induction generator wind turbine was simulated using

Matlab\Simulink.

Fig. 7. Test System

The first objective of this paper is to evaluate the specific

needs of the system to restore to its initial state as quickly as

possible after fault clearing.

A. Effect of Phase-Phase to Ground Fault on Wind Turbine2

The effect of a phase-Phase to ground fault at Wind

Turbine2 is studied. The ground fault is initiated at t=15s and

cleared at t=15.1s. The system is studied under different

conditions at the load bus as chosen below.

(i)

Without Statcom:

Fig 8(a) and 9(a) shows the active and reactive power at the

load bus, it can be seen that the active power curve reached

8.5MW in transient state operation and with the presence of

fault both the curves takes more time to reach stable state of

operation.

Fig 10(a) and 11(a) shows the active and reactive power of

each wind turbine. It is clear according to these results that the

active and reactive power of wind farm takes more oscillations

to reach stable state of operation with the appearance of fault.

(ii)

With Statcom:

According to the previous simulation results, STATCOM

at bus2 is added to view the STATCOM effects.

Fig 8(b) and 9(b) shows the active and reactive power at

the load bus, it can be seen that in both the curves the active

and reactive powers are stabilized faster with less oscillations

compared with the preceding case in the transient state and

even after the fault.

Fig 10(b) and 11(b) shows the active and reactive power

for each wind turbine. According to the simulation results, the

curves presented below shows the importance of the

compensation when the wind farm recovers its operation after

the fault and takes its stability with some oscillation by the

intervention of STATCOM at bus bar 2.

VII. SIMULATION RESULTS

The proposed test system has a wind farm of three wind

turbiness each having two equal wind turbines connected to a

network of 2 bus bars. The type of generator is a Squirrel

Cage Induction Generator(SCIG). Under normal operating

conditions, the wind farm provide 9MW, the bank condenser

used to offer a reactive power to the IG, as presents in the

following Fig 7.

Fig. 8(a). Without STATCOM

6

Fig. 8(b). With STATCOM

Fig. 8. Active power at 33kv bus2

Fig. 11(b). With STATCOM

Fig. 11. Reactive Power of Wind Farm

B. Effect of Three Phase To Ground Fault on Wind Turbine2

(i)

Fig. 9(a). Without STATCOM

Without Statcom:

Fig 12(a) and 13(a) shows the active and reactive power at

the load bus, it can be seen that the active power curve

reached 8.5MW in transient state operation and with the

presence of fault both the curves takes more time to reach

stable state of operation.

Fig 14(a) and 15(a) shows the active and reactive power of

each wind turbine. It is clear according to these results that the

active and reactive power of wind farm takes more oscillations

to reach stable state of operation with the appearance of fault.

(ii)

Fig. 9(b). With STATCOM

Fig. 9. Reactive power at 33kv bus2

With Statcom:

According to the previous simulation results, STATCOM

at bus2 is added to view the STATCOM effects.

Fig 12(b) and 13(b) shows the active and reactive power at

the load bus, it can be seen that in both the curves the active

and reactive powers are stabilized faster with less oscillations

compared with the preceding case in the transient state and

even after the fault.

Fig 14(b) and 15(b) shows the active and reactive power

for each wind turbine. According to the simulation results, the

curves presented below shows the importance of the

compensation when the wind farm recovers its operation after

the fault and takes its stability with some oscillation by the

intervention of STATCOM at bus bar 2.

Fig. 10(a). Without STATCOM

Fig. 10(b). With STATCOM

Fig. 10. Active Power of Wind Farm

Fig. 12(a). Without STATCOM

Fig. 12(b). With STATCOM

Fig. 12. Active Power at 33kv bus2

Fig. 11(a). Without STATCOM

7

Fig. 13(a). Without STATCOM

Fig. 13(b). With STATCOM

Fig. 13. Reactive Power at 33kv bus2

Fig. 14(a). Without STATCOM

Fig. 14(b). With STATCOM

C. Transient Stability Criteria

The wind farm delivers 9MW output power at

steady-state. A phase-phase ground fault was induced at wind

turbine2. The STATCOM is disconnected. The simulation

time is 20seconds which is enough to investigate the transient

behavior of the rotor speed.

Fault is induced at t=15sec and the rotor speed is

shown in pu for various fault clearance time t= 15.1 s, 15.4 s

and 15.41 s. Fig. 16(a), (b), (c). Shows the response on the

rotor speed for phase-phase fault induced at the terminal of the

wind turbine2 and cleared for different time. It is obvious

from the Fig. 16(c) at the fault clearing t=15.41s the machine

is unable to remain stable. Thus, the CCT is 0.41seconds.

Above this critical point the rotor will continue to accelerate

indicating a runaway slip. This means that the CCT of an

induction generator can be calculated, which will be useful to

increase the transient stability criteria.

Fig. 16(a). Rotor Speed vs. Time for Fault Clearing Time t=15.1s

Fig. 16(b). Rotor Speed vs. Time for Fault Clearing Time t=15.4s

Fig. 14. Active Power of Wind Farm

Fig. 16(c). Rotor Speed vs. Time for Fault Clearing Time t=15.41s

Fig. 15(a). Without STATCOM

Fig. 15(b). With STATCOM

Fig. 15. Reactive Power of Wind Farm

The simulation is repeated when the STATCOM is

connected in order to investigate its impact on the transient

stability margin.

To observe the effect of the STATCOM on the critical

clearing time (CCT), the STATCOM is connected and the

phase-phase fault was induced at bus2. By investigating the

fault clearing time it is found that when the STATCOM is

connected, the CCT becomes CCT=0.5sec. It is obvious that

the STATCOM had increased the critical clearing time CCT

by 90ms. Hence giving the machine more time to right

through fault and remains connected and re-establish a stable

operating point after the fault is cleared.

8

power swings damping, voltage regulation, increase of power

transmission and chiefly as a supplier of controllable reactive

power to accelerate voltage recovery after fault occurrence.

IX. REFERENCES

[1]

Fig. 16(c). Rotor Speed vs. Time for Fault Clearing Time t=15.5s

[2]

During fault, the STATCOM have the capacity to control

the reactive power transfer at its terminal. Hence it achieves a

voltage regulation mode. Fig 17. shows the voltage at

STATCOM’s terminal (top) and the reactive power generated

by the STATCOM all along the simulation (bottom).

[3]

[4]

[5]

[6]

[7]

[8]

Fig. 17. Voltage and generated reactive power by STATCOM

[9]

VIII. CONCLUSIONS

FACTS devices are power electronics based reactive

compensators that are connected in a power system and are

capable of improving the power system transient performance

and the quality of supply. In this paper system stability of

SCIG wind farms has been investigated. Power system with

wind farms performance can be improved using FACTS

devices such as STATCOM. The dynamic model of the

studied power system is simulated using Simulink Matlab

package software. Wind farm is compared with and without

the presence of STATCOM under various faults like phasephase to ground fault and three phase to ground fault. Test

system contains three wind farms, each wind farm has two

equal wind turbines. To validate the effect of the STATCOM

controller of power system operation , the system is subjected

to different disturbances such as faults and power operating

conditions.

Solutions for enhancing transient stability margin or

increasing the CCT were proposed. Simulation results proved

that the SATCOM can increase the CCT. Moreover, the

STATCOM contributed in restoring the voltage to its initial

reference point following a disturbance. However, power

electronics converters that use forced-commutated electronic

devices implemented succeed in controlling the voltage and

the reactive power remarkably.

The digital results prove the powerfulness of the proposed

STATCOM controller in terms of stability improvement,

Rajiv Singh, “Transient Stability Improvement of a FSIG Based Grid

Connected wind Farm with the help of a SVC and a STATCOM:A

Comparison”, International Journal of Computer and Electrical

Engineering, Vol.4, No.1, February 2012.

G. Elsady, “STATCOM for Improved Dynamic Performance of Wind

Farms in Power Grid” , 14th International Middle East Power Systems

Conference (MEPCON’10), Cairo University, Egypt, December 19-21,

2010.

Bouhadouza Boubekeur, “Application of STATCOM to Increase

Transient Stability of Wind Farm”, American Journal of Electrical

Power and Energy Systems. Vol. 2, No. 2, 2013.

CH.AppalaNarayana, “Application of STATCOM for Transient

Stability Improvement and Performance Enhancement for a Wind

Turbine Based Induction Generator” , International Journal of Soft

Computing and Engineering (IJSCE) ISSN: 2231-2307, Volume-2,

Issue-6, January 2013.

Naimul Hasan , “ Dynamic Performance Analysis Of DFIG Bases Wind

Farm with Statcom and SVC” ,International Journal of Emerging

Technology and Advanced Engineering.

Valarmathi, “Power Quality Analysis in 6 MW Wind Turbine Using

Static Synchronous Compensator” , American Journal of Applied

Sciences 9 (1): 111-116, 2012.

Pradeep Kumar, “Dynamic Performance of STATCOM on the Induction

Generator based Wind Farm”, International Conference on Global

Scenario in Environment and Energy ICGSEE-2013[14th – 16th March

2013].

Amit Garg, “Dynamic Performance Analysis of IG based Wind Farm

with STATCOM and SVC in MATLAB / SIMULINK”, International

Journal of Computer Applications Volume 71– No.23, June 2013.

K. Radha Rani, J. Amarnath, S. Kamakshaiah, “Transient Stability and

Contingency Analysis of Power System in Deregulated Environment” in

International Review on Modelling and Simulations (IREMOS), Vol.4,

N.3, June 2011, pp.1257-1265.

P.Sravanthi has obtained B.Tech degree in Electrical

& Electronics Engineering from Malineni Lakshmaiah

Women’s Engineering college ,Guntur, A.P, India in

the year 2012.She is presently a post graduate student

in Power System Engineering at R.V.R & J.C. College

of Engineering, Guntur, Andhra Pradesh, India.

K. Radha Rani has obtained B.Tech degree in

Electrical & Electronics Engineering from JNTU

College of Engineering, Kakinada, A.P, India in the

year 1998 and Post Graduation M.E. Electrical Power

Engineering from M.S.university, Vadodara in the year

2001. She has submitted Ph.D. thesis in EE Dept. at

JNTU, Hyderabad and currently associated with

R.V.R&J.C. College of Engineering, Guntur, Andhra Pradesh, India. Her

research interests include power system security and control, FACTS.

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