Research ArticleApplication of Firefly Algorithm in Voltage StabilityEnvironment Incorporating Circuit Element Model of SSSC withVariable Susceptance Model of SVC

Luke Jebaraj1 Charles Christober Asir Rajan2 and Kumar Sriram1

1 Department of Electrical and Electronics Engineering StAnnersquos College of Engineering and Technology PanrutiTamil Nadu 607 110 India

2Department of Electrical and Electronics Engineering Pondicherry Engineering College Puducherry 605 014 India

Correspondence should be addressed to Luke Jebaraj jeba mepsyahoocoin

Received 31 January 2014 Revised 2 April 2014 Accepted 3 April 2014 Published 24 April 2014

Academic Editor Jose R C Piqueira

Copyright copy 2014 Luke Jebaraj et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper proposes an application of firefly algorithm (FA) based extended voltage stability margin andminimization of active (or)real power loss incorporating Series-Shunt flexible AC transmission system (FACTS) controller named as static synchronous seriescompensator (SSSC) combined with static var compensator (SVC) A circuit model of SSSC and variable susceptancemodel of SVCare utilized to control the line power flows and bus voltage magnitudes respectively for real power loss minimization and voltagestability limit improvement The line quality proximity index (LQP) is used to assess the voltage stability of a power system Thevalues of voltage profile improvement real power loss minimization and the location and size of FACTS devices were optimizedby FAThe results are obtained from the IEEE 14- and 30-bus test case systems under different operating conditions and comparedwith other leading evolutionary techniques such as shuffled frog leaping algorithm (SFLA) differential evolution (DE) and particleswarm optimization (PSO)

1 Introduction

Voltage stability is concerned with the ability of a powersystem to maintain acceptable voltage at all buses in thesystem under normal conditions and after being subjectedto a disturbance [1] The recent day power systems areundergoing numerous changes and becoming more complexfrom the standpoints of operation control and stabilitymaintenance when they meet ever-increasing load demand[2] A system enters a state of voltage instability when adisturbance increase in load demand or change in systemcondition causes a progressive and uncontrollable declinein voltage The main factor causing voltage instability is theinability of the power system tomeet the demand for reactivepower [3 4] The authors [5 6] discuss methods to assessvoltage stability of a power system to find possible ways toimprove the voltage stability

Abnormal voltages and voltage collapse pose a primarythreat to power system stability security and reliability

Moreover with the fast development of restructuring theproblem of voltage stability has become a major concernin deregulated power systems To maintain security of suchsystems it is desirable to plan suitable measures to improvepower system security and increase voltage stability margins[7] Voltage instability is one of the phenomena whichhave resulted in major blackouts Recently several networkblackouts have been related to voltage collapse [8] The onlyway to counteract this problem is by reducing the reactivepower load in the system or by adding new reactive powergeneration systems in the weakest points of the systemthereby increasing the voltage at those points

The flexible AC transmission system (FACTS) controllersare capable of supplying or absorbing reactive power atfaster rates [9] The introduction of FACTS controllers areincreasingly used to provide voltage and power flow controls[10] Insertion of FACTSdevices is found to be highly effectivein preventing voltage instability and minimize the active orreal power loss on transmission lines [11 12] Series and shunt

Hindawi Publishing CorporationAdvances in Electrical EngineeringVolume 2014 Article ID 349787 11 pageshttpdxdoiorg1011552014349787

2 Advances in Electrical Engineering

compensating devices are used to enhance the static voltagestability margin and reduce the real power loss appreciably[13 14]

The generalized power injection model of SSSC needsmodification of the Jacobianmatrix andmakes quite complexin coding In the SSSC control parameters voltage mag-nitude and angle of the series converters are presented asindependent variables and their values are found throughthe traditional load flow iterative process [15] In this casethe size of the Jacobian matrix increases to incorporate theadditional independent variablesThe newmodel of the SSSCchanges only the bus admittance matrix and consequentlyreduces the coding of load flow problem incorporating SSSCsimple The SSSC control parameters voltage magnitude andangle of the series converters are presented as independentvariables and their values are found through the traditionalload flow iterative process In this case the size of the Jacobianmatrix increases to incorporate the additional independentvariables Hence a simple and easy way to implement SSSCmodel based on the circuit elements is used in this work [16]

Voltage stability assessment with appropriate representa-tions of FACTS devices is investigated and compared underbase case of study [17ndash19] One of the shortcomings of thosemethods only considered the normal state of the system[20] The author [21] presented the different computationaltechniques for voltage stability assessment and control Theauthor [22] focused on the contingency ranking obtainedwith respect to overloads in large power systems Abdelaziz etal [23] proposed the process of contingency ranking throughfuzzy logic approach However voltage collapses are mostlyinitiated by a disturbance like line outages Voltage stabilitylimit improvement needs to be addressed during networkcontingencies So to locate FACTS devices consideration ofcontingency conditions ismore important than considerationof normal state of system and some approaches are proposedto locate FACTS devices with considerations of contingenciestoo [24 25]

Line stability indices provide important informationabout the proximity of the system to voltage instability andcan be used to identify the weakest bus as well as the criticalline with respect to the bus of the system [26] Differenttypes of line stability indices are proposed to evaluate theproximity of the system to voltage instability [27 28] Theline quality proximity index is used in this work for stabilityassessment [29 30] From the family of bioluminescenceinspired computation FA is used to solve the problem of realpower loss minimization and voltage stability maximizationof the system In the firefly algorithm the objective functionof a given optimization problem is based on differences inlight intensity It helps the fireflies to move towards brighterand more attractive locations in order to obtain optimalsolutions All fireflies are characterized by their light intensityassociated with the objective function [31ndash33]

Because of higher cost of the FACTS devices the installa-tion is not recommended to all possible line outages Henceline outage contingency screening and ranking were carriedout to identify the most critical line during which outageFACTS controllers can be positioned and system can beoperated under stable condition [34ndash36]The prime objective

+C

Series couplingtransformer

Voltage sourceconverter

Energy source(optional)

Bus 2VR

Bus 1VS

minus

Figure 1 SSSC configuration

ZLVseang120574 Vjang120575jViang120575i

Figure 2 Circuit element model of SSSC

of this work is to obtain the results from standard IEEE14- and 30-bus test cases through FA incorporating circuitelement model of SSSC combined with variable susceptancemodel of SVC and to compare the results of these series-shunt FACTS controllers with other important evolutionarytechniques such as SFLADE and PSO under normal criticalloading and single-line outage conditions

2 Static Model of FACTS Devices

21 Circuit ElementModel of SSSC TheSSSC can be operatedwithout an external energy source as reactive power sourceand is fully controllable and independent of transmission linecurrent for the purpose of increasing or decreasing the overallreactive voltage drop across the transmission line and therebycontrolling the electric power flow The widely used powerinjectionmodel of SSSC requiresmodification of the Jacobianmatrix and makes the Newton-Raphson load flow (NRLF)coding more complex A new circuit elements based modelof SSSC is utilized to control the line power flows and busvoltage magnitudes for voltage stability limit improvementThe new model of the SSSC changes only the bus admittancematrix and consequently reduces the coding of load flowproblem incorporating SSSC simpleThis converter performsthe main function of injecting a controllable series voltageThe basic configuration of SSSC is depicted in Figure 1 Thecircuit element model of SSSC is also shown in Figure 2

The real and reactive powers exchanged with the line bythe series voltage inserted by SSSC are modeled as a negativeresistance and reactance connected in parallel The negativeresistance represents injection of real power and the reactancemay be either capacitive or inductive depending on whetherreactive power is delivered or absorbed

Advances in Electrical Engineering 3

The complex power exchanged by the series converterwith the line is expressed as

119878119890= 119881se119868 (1)

where119881se is the complex voltage injected by the converter and119868 the current through the line given by

119868 =119881119894ang120575119894+ 119881seang120574 minus 119881119895ang120575119895

119885119871

(2)

The active and reactive powers exchanged with the line aremodeled as resistance and reactance associated as representedby

119877 =1198812

se119875se

119883 =1198812

se119876se

(3)

The elements 119877 and119883 can be calculated by directly using thefollowing equations

119877 =119881se119885119871

119881119894sin (120575

119894minus 120575119895minus 120574) + 119881

119895sin 120574

119883 =119881se119885119871

119881119894cos (120575

119894minus 120575119895minus 120574) minus 119881

119895cos 120574 + 119881se

(4)

The resistance 119877 and the reactance 119883 representing the effectof series voltage are transformed into their equivalent seriescombination This makes the line simple with only series-connected elements of the line (119885

119871) and the 119877SSSC and 119883SSSC

denoting the resistance and reactance of SSSC

119877SSSC =1198771198832

1198772 + 1198832

119883SSSC =1198831198772

1198772 + 1198832

(5)

22 Variable Susceptance Model of SVC A variable suscep-tance 119861SVC represents the fundamental frequency equivalentsusceptance of all shunt modules making up the SVC Thismodel is an improved version of SVCmodels Figure 3 showsthe variable susceptancemodel of SVCwhich is used to deriveits nonlinear power equations and the linearised equationsrequired by Newtonrsquos load flow method

In general the transfer admittance equation for thevariable shunt compensator is

119868SVC = 119895119861SVC119881119895 (6)

And the reactive power of SVC is

119876SVC = minus1198812

119895119861SVC (7)

ViXline

Vj

BSVC

QSVC

Figure 3 Variable susceptance model of SVC

Sj Pj QjSi Pi Qi

VjVi

Bus jBus i

Z = R + jX

Figure 4 Single-line concept of power transmission

13

12 14

1110

9

4

7

1

2 3

5

8

6G

G

G

GG

C

(a) 14-bus system

1

30

29 2827

20

21

22

2324

26 25

1918

17

16

15

14

13 1211

109

8

7

6

5

43

2

G

G

G

G

G G

(b) 30-bus system

Figure 5 One-line diagram of IEEE test system

4 Advances in Electrical Engineering

056

04

120

69

081

06

016

64

062

21

054

52

033

9

079

94

057

6

031

12

069

08

058

52

039

17 070

24

065

03

002040608

11214

Case 1 Case 2 Case 3

Sum

of L

QP

valu

es

(a) For 14-bus system

InitialFASFLA

DEPSO

148

22

255

36

170

31

128

06

222

51

140

27

129

73

242

3

159

5

145

55

225

47

141

74

133

93

241

16

158

53

005

115

225

3

Sum

of L

QP

valu

es

Case 1 Case 2 Case 3

(b) For 30-bus system

Figure 6 Sum of LQP index values comparison

In SVC susceptance model the total susceptance 119861SVC istaken to be the state variable therefore the linearised equationof the SVC is given by

[Δ119875119895

Δ119876119895

] = [0 0

0 120579119895

][[

[

Δ120579119895

Δ119861svc119861svc

]]

]

(8)

where Δ119875119895 Δ119876119895 and Δ120579

119895are the change in real reactive

power and voltage angle at 119895th busAt the end of iteration 119894 the variable shunt susceptance

119861SVC is updated according to

119861(119894)

SVC = 119861(119894minus1)

SVC + (Δ119861SVC119861SVC

)

(119894)

119861(119894minus1)

SVC (9)

This changing susceptance value represents the total SVCsusceptance which is necessary to maintain the nodal voltagemagnitude at the specified value (10 pu in this paper)

3 Line Quality Proximity Index

Voltage stability can be assessed in a system by calculating theline based voltage stability index The LQP index based on apower transmission concept is used in this paperThe value ofline index shows the voltage stability of the systemThe valueclose to unity indicates that the respective line is close to itsstability limit and valuemuch close to zero indicates light loadin the line The formulation begins with the power equationin a power system Figure 4 illustrates a single line of a powertransmission concept

The power equation can be derived as

119875119894= radic

1198812

119894

119883(119876119894minus 119876119895) minus 1198762

119894 (10)

The line stability factor isobtained by setting the discriminantof the reactive power roots at bus 1 to be greater than or equalto zero thus defining the line stability factor LQP as

LQP = 4( 1198831198812

119894

)(119883

1198812

119894

1198752

119894+ 119876119895) (11)

4 Problem Formulation

The objective function of this work is to find the optimalrating and location of FACTS devices combination whichminimizes the real power loss minimizes voltage deviationandmaximizes the voltage stability limit Hence the objectivefunction can be expressed as

119865 = min 119875119871+ 119908VD + (1 minus 119908) LQP (12)

where119908 is the weighing factor for voltage deviation and is setto 10

41 Minimization of Real Power Loss (119875119871) The total real

power of the system can be calculated as follows

119875loss =

119873119871

sum

119896=1

119866119896[1198812

119894+ 1198812

119895minus 2

10038161003816100381610038161198811198941003816100381610038161003816

10038161003816100381610038161003816119881119895

10038161003816100381610038161003816cos (120575

119894minus 120575119895)] (13)

where119873119871is the total number of lines in the system 119866

119896is the

conductance of the line ldquo119896rdquo 119881119894and 119881

119895are the magnitudes of

the sending end and receiving end voltages of the line and 120575119894

and 120575119895are angles of the end voltages

42 Minimization of Load Bus Voltage Deviation (VD) Busvoltagemagnitude should bemaintainedwithin the allowablerange to ensure quality service Voltage profile is improvedby minimizing the deviation of the load bus voltage from thereference value (it is taken as 10 pu in this work)

VD =

119873PQ

sum

119896=1

1003816100381610038161003816119881119868 minus 119881ref1003816100381610038161003816

(14)

where 119881119894is the voltage at 119894th bus and 119881ref is the reference

voltage

43 Minimization of Line Quality Proximity Index (LQP)Voltage stability limit of a power system is increased byminimizing voltage stability index value The indicator takesvalues between 0 (no load) and 1 (full load) The line basedstability index (LQP) is given as

LQP =119873119871

sum

119895=1

LQP119895 (15)

Advances in Electrical Engineering 5

(i) Case 1

(ii) Case 2

(iii) Case 3

1102104106108

11

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Volta

ge v

alue

s in

pu

Bus number

InitialFASFLA

DEPSO

095097099101103105107

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Volta

ge v

alue

s in

pu

Bus number

0981

102104106108

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Volta

ge v

alue

s in

pu

Bus number

(a)

(i) Case 1

(ii) Case 2

098

101

104

107

11

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Volta

ge v

alue

s in

pu

Bus number

088092096

1104108

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Volta

ge v

alue

s in

pu

Bus number

094

098

102

106

11

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Volta

ge v

alue

s in

pu

Bus number

(iii) Case 3

InitialFASFLA

DEPSO

(b)

Figure 7 (a) Voltage profile values comparison for 14-bus system (b) Voltage profile values comparison for 30-bus system

44 Constraints Theminimization problem is subject to thefollowing equality and inequality constraints

441 Equality Constraints

Load Flow Constraints Consider

119875Gi minus 119875Di minus

119873119861

sum

119895=1

119881119894119881119895119884119894119895cos (120575

119894119895+ 120574119895minus 120574119894) = 0

119876Gi minus 119876Di minus

119873119861

sum

119895=1

119881119894119881119895119884119894119895sin (120575

119894119895+ 120574119895minus 120574119894) = 0

(16)

where 119875Gi and 119876Gi are the active and reactive powers of 119894thgenerator and 119875Di and119876Di are the active and reactive powersof 119894th load bus

442 Inequality Constraints

Reactive Power Generation Limit of SVCs By choosing small-sized compensator capital cost involved can be minimum

The size limit of SVC has been taken from minimum of 5MVAR to maximum of 20 MVAR

119876minSVCi le 119876SVCi le 119876

maxSVCi 119894 isin 119873SVC (17)

where119876minSVCi and119876

maxSVCi are theminimum andmaximumVAR

injection limits of 119894th shunt capacitor

Voltage Constraints The acceptable voltage limits in all loadbuses are taken from 095 pu to 105 pu to avoid voltageinstability

119881min119894

le 119881119894le 119881

max119894

119894 isin 119873119861 (18)

where 119881min119894

and119881max119894

are the minimum and maximum valuevoltage of bus ldquo119894rdquo

Transmission Line Flow Limit Consider

119878119894le 119878

max119894 119894 isin 119873

119897 (19)

where 119878119894is the apparent power flow of 119894th branch and 119878max

119894is

the maximum apparent power flow limit of 119894th branch

6 Advances in Electrical Engineering

0 5 10 15 20 25 30

Case 1

Case 2

Case 3

Loss ()

PSODE

SFLAFA

(a) For 14-bus system

0 5 10 15 20 25 30

PSODE

SFLAFA

Case 1

Case 2

Case 3

Loss ()

(b) For 30-bus system

Figure 8 Percentage of real power loss reduction under all cases

Table 1 Optimal values of FA parameters

Parameters Optimal ValuesNumber of fireflies 301205730

01120574 02120572 025119898 40119889 20Maximum iterations 100

5 Firefly Algorithm

51 Overview The firefly algorithm (FA) is a metaheuristicnature-inspired optimization algorithm which is based onthe social (flashing) behavior of fireflies or lighting bugsin the summer sky in the tropical temperature regions Itwas developed by Dr Xin-She Yang at Cambridge Universityin 2007 and it is based on the swarm behavior such asfish insects or bird schooling in nature In particularalthough the firefly algorithm has many similarities withother algorithms which are based on the so-called swarmintelligence such as the famous particle swarm optimization(PSO) artificial bee colony optimization (ABC) and bacterialforaging algorithms (BFA) it is indeed much simpler inboth concept and implementation Furthermore accordingto recent bibliography the algorithm is very efficient and canoutperform other conventional algorithms such as geneticalgorithms for solving many optimization problems a factthat has been justified in a recent research where the statisti-cal performance of the firefly algorithmwasmeasured againstother well-known optimization algorithms using variousstandard stochastic test functions Its main advantage is thefact that it uses mainly real random numbers and it is basedon the global communication among the swarming particles(ie the fireflies) and as a result it seems more effective inmultiobjective optimization such as the economic emissionsload dispatch problem in our case

The firefly algorithm has three particular idealized ruleswhich are based on some of the major flashing characteristicsof real fireflies These rules are the following

(i) All fireflies are unisex and they will move towardsmore attractive and brighter ones regardless their sex

(ii) The degree of attractiveness of a firefly is proportionalto its brightness which decreases as the distance fromthe other firefly increases due to the fact that theair absorbs light If there is no brighter or moreattractive firefly than a particular one it will thenmove randomly

(iii) The brightness or light intensity of a firefly is deter-mined by the value of the objective function of agiven problem For maximization problems the lightintensity is proportional to the value of the objectivefunction

52 Implementation

521 Attractiveness In the firefly algorithm the form ofattractiveness functions of a firefly is the following monoton-ically decreasing function

120573 (119903) = 1205730lowast exp (minus120574119903119898) with 119898 ge 1 (20)

where 119903 is the distance between any two fireflies 1205730is the

initial attractiveness at 119903 = 0 and 120574 is an absorptioncoefficient which controls the decrease of the light intensity

522 Distance The distance between any two fireflies 119894 and119895 at positions 119909

119894and 119909

119895 respectively can be defined as a

Cartesian or Euclidean distance as follows

119903119894119895=10038171003817100381710038171003817119909119894minus 119909119895

10038171003817100381710038171003817= radic

119889

sum

119896=1

(119909119894119896minus 119909119895119896)2

(21)

where 119909119894119896

is the 119896th component of the spatial coordinate 119909119894

of the 119894th firefly and 119889 is the number of dimensions we havefor 119889 = 2 we have

119903119894119895= radic(119909

119894minus 119909119895)2

+ (119910119894minus 119910119895)2

(22)

However the calculation of distance r can also be definedusing other distance metrics based on the nature of theproblem such as Manhattan distance

Advances in Electrical Engineering 7

Table 2 Voltage stability index values of most stressed lines

(a) For 14-bus system

Cases Line number Preinsertion of FACTS Postinsertion of FACTSFA SFLA DE PSO

Case 1

14 01122 00714 00818 00807 0082920 00776 00582 00537 00544 006171 00688 00447 00511 00491 0051917 00593 00310 00388 00408 005039 00515 00291 00346 00307 00401

Case 2

10 02580 01106 01722 01651 0199514 01815 00994 00991 01012 0124420 01494 00912 00941 01109 012869 01393 00833 00994 01081 011201 00799 00517 00604 00597 00661

Case 3

10 01904 01014 00941 01057 0112915 01160 00809 00802 00914 009566 00914 00529 00317 00441 005824 00793 00447 00406 00533 005519 00648 00361 00304 00369 00408

(b) For 30-bus system

Cases Line number Preinsertion of FACTS Postinsertion of FACTSFA SFLA DE PSO

Case 1

12 03691 03664 03687 03700 036835 01284 00695 01264 00987 0128213 01226 00722 00114 01169 0109515 00749 00713 00748 00752 0074914 00678 00667 00674 00676 00672

Case 2

12 03899 03861 03877 03874 038815 03596 00884 03310 00793 0331213 02549 02115 02355 02351 0239016 01687 01241 01735 01767 0161015 01255 01167 01245 01244 01249

Case 3

12 03851 03688 03864 03686 0379313 01732 01159 01766 01152 0171116 00836 00445 00855 00475 008331 00786 00540 00810 00568 0069415 00775 00741 00776 00749 00771

523 Movement The movement of a firefly 119894 which isattracted by a more attractive (ie brighter) firefly 119895 is givenby the following equation

119909119894= 119909119894+ 1205730lowast exp (minus1205741199032

119894119895) lowast (119909

119894minus 119909119895) + 120572 lowast (rand minus 1

2)

(23)

where the first term is the current position of a firefly thesecond term is used for considering a fireflyrsquos attractivenessto light intensity seen by adjacent fireflies and the third termissued for the random movement of a firefly in case there areno any brighter ones The coefficient 120572 is a randomizationparameter determined by the problem of interest while randis a random number generator uniformly distributed in the

space (01) As we will see in this implementation of thealgorithm we use 120573

0= 01 120572 isin [0 1] and the attractiveness

or absorption coefficient 120574 = 02 which guarantees a quickconvergence of the algorithm to the optimal solution Theoptimal values of firefly parameters are in Table 1

6 Results and Discussion

The proposed work is coded in MATLAB 76 platform using28GHz Intel Core 2 Duo processor based PC The methodis tested in the IEEE 14- and 30-bus test systems shownin Figure 5 The line data and bus data are taken from thestandard power system test case archive The 14-bus systemhas 5 generator buses 9 load buses and 20 transmission lines

8 Advances in Electrical Engineering

Table 3 Contingency ranking

Rank 14-bus system 30-bus systemLine number LQP values Line number LQP values

1 1 05795 5 094952 3 03826 9 060503 10 03449 2 049934 2 03157 4 049685 15 01984 7 04693

Table 4 Average load bus voltage values in pu

(a) For 14-bus system

Cases Preinsertion of FACTS Postinsertion of FACTSFA SFLA DE PSO

Case 1 10438 10517 10494 10483 10460Case 2 09890 10082 10013 10051 09966Case 3 10243 10409 10363 10331 10308

(b) For 30-bus system

Cases Preinsertion of FACTS Postinsertion of FACTSFA SFLA DE PSO

Case 1 10260 10296 10306 10288 10265Case 2 09520 09961 09664 09626 09602Case 3 10109 10380 10108 10298 10222

The 30-bus system has 6 generator buses 24 load buses and41 transmission lines System data and results are based on100 MVA and bus number 1 is the reference bus In order toverify the presentedmodels and illustrate the impact of circuitelement model of SSSC with variable susceptance model ofSVC combination study three different operating conditionsare considered as mentioned below

Case 1 The system with normal load in all the load busesis considered as normal condition and the Newton-Raphsonload flow is carried out with loading factor value equal to 1

Case 2 The system with 50 increased load in all the loadbuses is considered as a critical condition Loading of thesystem went beyond this level and results in poor voltageprofile in the load buses and unacceptable real power losslevel

Case 3 Contingency is imposed by considering the mostcritical line outage in the system This is the most suitablecondition for voltage stability analysis of a power system asvoltage stability is usually triggered by line outages

Newton-Raphson program is repeatedly run with theabsence and presence of FACTS device combination Thevoltage stability limit improvement is assessed by the valueof LQP index The voltage stability index values of topfive stressed lines under all cases with preinsertion andpostinsertion of FACTS devices are shown in Table 2 Itis evident from the table that LQP values of the stressedlines are reduced after placement of FACTS devices inthe system

For quick assessment of voltage stability limit improve-ment of the system under the three different operatingconditions sum of the LQP index values of all the linesbefore and after the insertion of FACTS devices combinationis compared in Figure 6 The reduction in the index valuethrough the proposed method indicates the best voltagestability limit improvement

The line outage is ranked according to the severity andthe severity is taken on the basis of the line quality proximityindex values and such values are arranged in descendingorder The maximum value of index indicates most criticalline for outage Line outage contingency screening andranking are carried out on the test systems and the results areshown in Table 3

It is clear from Table 3 that outage of lines numbers 1 and5 are the most critical line outages of 14- and 30-bus systemsrespectively This situation is considered for voltage stabilityimprovement Outage of other lines has not much impact onthe system and therefore they are not given importance Loadflow is run on the system with the lines that have outagesOutage of these lines results in large real power loss andvoltage profile reduction inmost of the load busesThe systemis under stressed conditions and needs to be relieved by somemeans Installation of FACTS devices at suitable locations canrelieve the system much from stressed conditions (reducedline losses)

FACTS devices help the system to maintain acceptablevoltage profile in the load buses Under normal operatingconditions most of the bus voltagemagnitudes are within thenormal value During critical and contingency conditionsvoltagemagnitude of remote load buses are below 095 (lower

Advances in Electrical Engineering 9

Table 5 Minimum-maximum load bus voltage values in pu

(a) For 14-bus system

Cases119881MIN 119881MAX

Preinsertionof FACTS Bus number Postinsertion of FACTS Preinsertion

of FACTS Bus number Postinsertion of FACTSFA SFLA DE PSO FA SFLA DE PSO

Case 1 10173 4 10252 10211 10203 10143 10604 7 10696 10673 10642 10617Case 2 09656 14 10004 09884 09933 09824 10101 7 10211 10176 10199 10155Case 3 09913 5 10264 10208 10104 10111 10350 13 10496 10490 10460 10438

(b) For 30-bus system

Cases119881MIN 119881MAX

Preinsertionof FACTS Bus number Postinsertion of FACTS Preinsertion

of FACTS Bus number Postinsertion of FACTSFA SFLA DE PSO FA SFLA DE PSO

Case 1 09953 30 09978 09976 09959 09954 10576 11 10820 10820 10820 10822Case 2 08915 30 09662 09035 09415 09410 10004 11 10667 10620 10520 10550Case 3 09661 5 10121 09600 09600 09607 10495 11 10820 10820 10820 10820

Table 6 Real power loss values comparison (in MW)

(a) For 14-bus system

Conditions Preinsertion of FACTS (initial) Postinsertion of FACTSFA SFLA DE PSO

Case 1 13401 11014 11409 11693 12106Case 2 35042 28018 28991 28875 29019Case 3 24183 18046 19255 19389 19771

(b) For 30-bus system

Conditions Preinsertion of FACTS (Initial) Postinsertion of FACTSFA SFLA DE PSO

Case 1 17514 13467 14852 16157 16504Case 2 46900 40990 45797 41258 43272Case 3 32569 22801 29272 23234 25561

bound of allowable value) These bus voltages are improvedafter the FACTS devices are installed Voltage profile valuecomparison under all cases incorporating the series-shuntFACTS devices combination is depicted separately in Figures7(a) and 7(b) under both test cases It is obvious fromthe figure that voltage profile comparison of the system isimproved better with the proposed method incorporatingFACTS devices combination The comparison of averagevalue of load bus voltage also proves the enhancing behaviorof voltage stability limit incorporating with FACTS devices ofall cases shown in Table 4 Table 5 exposes the comparisonof minimum and maximum load bus voltages in both theabsence and presence of FACTS devices under all cases

In real power loss minimization point of view throughinsertion of FACTS devices the real power loss under Case1 is decreased by 2387 and 4047MW respectively for14- and 30-bus systems In Case 2 the reduction in realpower loss rate is 7024 and 5910MW respectively Thereduction rate in real power loss is 6137 and 9768MW

respectively under Case 3 operation The real power lossvalues of proposed method compared with other impor-tant evolutionary techniques under all cases are shownin Table 6

The percentage of reduction in real power loss compari-son under all cases including both combinations is depictedin Figure 8 Obviously from the results shown in Table 6 theproposed method is more efficient than other evolutionarytechniques given here to reduce the real power lossminimiza-tion application The much reduction in real power loss andincrease in voltage magnitudes after the insertion of FACTSdevices are highly efficient in relieving a power network fromstressed condition and improving voltage stability limit Themost suitable size and location of combinations of FACTSdevices to improve the voltage stability limit and real powerloss minimization are also given in Table 7 under all caseswith 14- and 30-bus systems respectively The optimized sizeof SVC inserted with both combinations is not in larger valuewhich helps to reduce in cost

10 Advances in Electrical Engineering

Table 7 Best location and size of FACTS devices

(a) For 14-bus system

Cases Series ShuntLocation (line number) Size (degrees of compensation) Location (bus number) Size (MVar)

Case 1

FA 10 00722 + 11989501464 5 72015SFLA 4 00377 + 11989500916 12 86554DE 15 00461 + 11989501540 10 69988PSO 3 00622 + 11989501067 12 83037

Case 2

FA 12 00823 + 11989500961 13 11211SFLA 1 00536 + 11989501642 11 106217DE 9 00507 + 11989501145 12 99654PSO 11 00727 + 11989500836 10 72510

Case 3

FA 12 00769 + 11989500810 13 96817SFLA 10 00421 + 11989501162 5 106528DE 2 00489 + 11989500773 11 89207PSO 7 00673 + 11989501286 10 114368

(b) For 30-bus system

Cases Series ShuntLocation (line number) Size (degrees of compensation) Location (bus number) Size (MVar)

Case 1

FA 5 00159 + 11989500924 12 86962SFLA 1 00086 + 11989500833 19 69688DE 6 00239 + 11989502664 20 58131PSO 12 00191 + 11989500977 23 150806

Case 2

FA 6 00137 + 11989500384 17 90607SFLA 9 00170 + 11989501243 21 141058DE 5 00289 + 11989500931 30 62554PSO 8 00281 + 11989500447 18 190106

Case 3

FA 11 00311 + 11989501417 26 80115SFLA 9 00115 + 11989501302 28 67499DE 6 00112 + 11989500478 25 58559PSO 8 00291 + 11989501189 3 182640

7 Conclusion

In this paper optimal location and size of series-shunt FACTSdevices for voltage stability limit improvement and lossminimization through firefly algorithm are demonstratedThe voltage stability limit improvement and real power lossminimization are done under three operating cases suchas normal critical loading and line outage contingencyconditions The LQP index is used for voltage stabilityassessment The circuit element model of SSSC is consid-ered to improve the voltage stability limit by controllingpower flows and maintaining voltage profile This modelis easy to incorporate the effect of SSSC into Newton-Raphson load flow program codingThe variable susceptancemodel of SVC is used in a combined manner with SSSCIt is clear from the numerical results that voltage stabilitylimit improvement and real power loss minimization arehighly encouraging The real power loss minimization andvoltage stability limit improvement is remarkable by thecombined action of power flow control of SSSC and reac-tive power compensation by SVC through firefly algorithmover other evolutionary optimization techniques given inthis paper

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] T V Cutsem and C Vournas Voltage Stability of Electric PowerSystems Kluwer Academic New York NY USA 1998

[2] P Kundur Power System Stability and Control McGraw-HillNew York NY USA 1994

[3] CW Taylor Power System Voltage Stability McGraw-Hill NewYork NY USA 1994

[4] T van Cutsem ldquoVoltage instability phenomena countermea-sures and analysis methodsrdquo Proceedings of the IEEE vol 88no 2 pp 208ndash227 2000

[5] P Kessel and H Glavitsch ldquoEstimating the voltage stability ofpower systemrdquo IEEE Transactions on Power Delivery vol 1 no3 pp 346ndash354 1986

[6] H J Wan J D McCalley and V Vittal ldquoRisk based voltagesecurity assessmentrdquo IEEE Transactions on Power Systems vol15 no 4 pp 1247ndash1254 2000

Advances in Electrical Engineering 11

[7] I Dobson and H-D Chiang ldquoTowards a theory of voltagecollapse in electric power systemsrdquo Systems and Control Lettersvol 13 no 3 pp 253ndash262 1989

[8] ldquoTechnical Analysis of the August 14 2003 Blackout WhatHappened Why and What Did We Learnrdquo A report by theNorth American Electrical Reliability Council Steering GroupNew Jersey July 2004

[9] N G Hingorani and L Gyugyi Understanding FACTS Con-cepts and Technology of Flexible AC Transmission Systems IEEEPress 2000

[10] K K Sen and M L Sen Introduction to FACTS ControllersTheory Modeling and Applications IEEE Press 2009

[11] GWu A Okoyama J He and Y Yu ldquoAllocation and control ofFACTS devices for steady state stability enhancement of largescale power systemrdquo International Conference on Power SystemTechnology vol 1 pp 357ndash361 1998

[12] N Yorino E E El-Araby H Sasaki and S Harada ldquoA newformulation for FACTS allocation for security enhancementagainst voltage collapserdquo IEEE Transactions on Power Systemsvol 18 no 1 pp 3ndash10 2003

[13] S Biansoongnern S Chusanapiputt and S PhoomvuthisarnldquoOptimal SVC and TCSC placement for minimization of trans-mission lossesrdquo inProceedings of the International Conference onPower System Technology pp 1ndash5 October 2006

[14] M A Abido ldquoPower system stability enhancement usingFACTS controllers a reviewrdquo The Arabian Journal For Scienceand Engineering vol 34 no 1 pp 153ndash172 2009

[15] O L Bekri ldquoOptimal location of SVC and TCSC for voltagestability enhancementrdquo in Proceedings of the 4th InternationalPower Engineering and Optimization Conference (PEOCO rsquo10)pp 7ndash12 June 2010

[16] Y Zhang and Y Zhang ldquoA novel power injection model ofembedded SSSCwithmulti-control modes for power flow anal-ysis inclusive of practical constraintsrdquo Electric Power SystemsResearch vol 76 no 5 pp 374ndash381 2006

[17] A Sode-Yome N Mithulananthan and K Y Lee ldquoStaticvoltage stability margin enhancement using STATCOM TCSCand SSSCrdquo in Proceedings of the IEEEPES Transmission andDistribution Conference and Exhibition pp 1ndash6 August 2005

[18] C A Canizares and Z T Faur ldquoAnalysis of SVC and TCSCcontrollers in voltage collapserdquo IEEE Transactions on PowerSystems vol 14 no 1 pp 158ndash165 1999

[19] S Musunuri and G Dehnavi ldquoComparison of STAT COMSVC TCSC and SSSC performance in steady state voltagestability improvementrdquo in Proceedings of the North AmericanPower Symposium (NAPS rsquo10) pp 1ndash7 September 2010

[20] P Kundur K Morison and B Gao ldquoPractical considerations involtage stability assessmentrdquo International Journal of ElectricalPower and Energy Systems vol 15 no 4 pp 205ndash215 1993

[21] V Ajjarapu Computational Techniques for Voltage StabilityAssessment and Control Springer Science 2006

[22] S Fliscounakis P Panciatici F Capitanescu and L WehenkelldquoContingency ranking with respect to overloads in large powersystems taking into account uncertainity preventive and correc-tive actionsrdquo IEEE Transactions on Power Systems vol 28 no 4pp 4909ndash4917 2013

[23] A Y Abdelaziz A T M Taha M A Mostafa and A MHassan ldquoPower systen contingency ranking using fuzzy logicbased approachrdquo International Journal of Intelligent Systems andApplications no 2 pp 24ndash28 2013

[24] P S Venkataramu and T Ananthapadmanabha ldquoInstallationof unified power flow controller for voltage stability margin

enhancement under line outage contingenciesrdquo Iranian Journalof Electrical and Computer Engineering vol 5 no 2 pp 90ndash962006

[25] M Jarsquofari and S Afsharnia ldquoVoltage stability enhancementin contingency conditions using shunt FACTS devicesrdquo inProceedings of the EUROCON The International Conference onComputer as a Tool pp 1660ndash1665 September 2007

[26] P-A Loef G Andersson and D J Hill ldquoVoltage stabilityindices for stressed power systemsrdquo IEEE Transactions on PowerSystems vol 8 no 1 pp 326ndash335 1993

[27] M Moghavvemi and F M Omar ldquoTechnique for contingencymonitoring and voltage collapse predictionrdquo IEE Proceedings onGeneration Transmission and Distribution vol 145 no 6 pp634ndash640 1998

[28] M Moghavvemi and O Faruque ldquoReal time contingency eval-uation and ranking techniquerdquo IEE Proceedings on GenerationTransmission and Distribution vol 145 no 5 pp 517ndash524 1998

[29] I Musirin and T K A Rahman ldquoNovel fast voltage stabilityindex (FVSI) for voltage stability analysis in power transmissionsystemrdquo in Proceedings of the Student Conference on Researchand Development Proceedings pp 265ndash268 2002

[30] C Reis A Andrade and F P Maciel ldquoLine stability indicesfor voltage collapse predictionrdquo in Proceedings of the 2nd IEEEInternational Conference on Power Engineering Energy andElectrical Drives pp 239ndash243 March 2009

[31] X S Yang Nature-Inspired Metaheuristic Algorithms LuniverPress 2008

[32] X S Yang ldquoFirefly algorithms for multimodal optimizationrdquo inStochastic Algorithms Foundations and Applications SAGA vol5792 of Lecture Notes in Computer Sciences pp 169ndash178 2009

[33] S Łukasik and S Zak ldquoFirefly algorithm for continuousconstrained optimization task computational collective intel-ligencerdquo in Semantic Web Social Networks and Multi-AgentSystems vol 5796 of Lecture Notes in Computer Science pp 97ndash106 2009

[34] N D Reppen R R Austria J A Uhrin M C Patel and AGalatic ldquoPerformance of methods for ranking a evaluation ofvoltage collapse contingencies applied to a large-scale networkrdquoin Proceedings of the IEEE Joint International Conference pp337ndash343 1993

[35] G C Ejebe G D Irisarri S Mokhtari O Obadina PRistanovic and J Tong ldquoMethods for contingency screeningand ranking for voltage stability analysis of power systemsrdquo inProceedings of the IEEE Power Industry Computer ApplicationConference pp 249ndash255 May 1995

[36] E Vaahedi C FuchsW Xu et al ldquoVoltage stability contingencyscreening and rankingrdquo IEEE Transactions on Power Systemsvol 14 no 1 pp 256ndash265 1999

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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DistributedSensor Networks

International Journal of

2 Advances in Electrical Engineering

compensating devices are used to enhance the static voltagestability margin and reduce the real power loss appreciably[13 14]

The generalized power injection model of SSSC needsmodification of the Jacobianmatrix andmakes quite complexin coding In the SSSC control parameters voltage mag-nitude and angle of the series converters are presented asindependent variables and their values are found throughthe traditional load flow iterative process [15] In this casethe size of the Jacobian matrix increases to incorporate theadditional independent variablesThe newmodel of the SSSCchanges only the bus admittance matrix and consequentlyreduces the coding of load flow problem incorporating SSSCsimple The SSSC control parameters voltage magnitude andangle of the series converters are presented as independentvariables and their values are found through the traditionalload flow iterative process In this case the size of the Jacobianmatrix increases to incorporate the additional independentvariables Hence a simple and easy way to implement SSSCmodel based on the circuit elements is used in this work [16]

Voltage stability assessment with appropriate representa-tions of FACTS devices is investigated and compared underbase case of study [17ndash19] One of the shortcomings of thosemethods only considered the normal state of the system[20] The author [21] presented the different computationaltechniques for voltage stability assessment and control Theauthor [22] focused on the contingency ranking obtainedwith respect to overloads in large power systems Abdelaziz etal [23] proposed the process of contingency ranking throughfuzzy logic approach However voltage collapses are mostlyinitiated by a disturbance like line outages Voltage stabilitylimit improvement needs to be addressed during networkcontingencies So to locate FACTS devices consideration ofcontingency conditions ismore important than considerationof normal state of system and some approaches are proposedto locate FACTS devices with considerations of contingenciestoo [24 25]

Line stability indices provide important informationabout the proximity of the system to voltage instability andcan be used to identify the weakest bus as well as the criticalline with respect to the bus of the system [26] Differenttypes of line stability indices are proposed to evaluate theproximity of the system to voltage instability [27 28] Theline quality proximity index is used in this work for stabilityassessment [29 30] From the family of bioluminescenceinspired computation FA is used to solve the problem of realpower loss minimization and voltage stability maximizationof the system In the firefly algorithm the objective functionof a given optimization problem is based on differences inlight intensity It helps the fireflies to move towards brighterand more attractive locations in order to obtain optimalsolutions All fireflies are characterized by their light intensityassociated with the objective function [31ndash33]

Because of higher cost of the FACTS devices the installa-tion is not recommended to all possible line outages Henceline outage contingency screening and ranking were carriedout to identify the most critical line during which outageFACTS controllers can be positioned and system can beoperated under stable condition [34ndash36]The prime objective

+C

Series couplingtransformer

Voltage sourceconverter

Energy source(optional)

Bus 2VR

Bus 1VS

minus

Figure 1 SSSC configuration

ZLVseang120574 Vjang120575jViang120575i

Figure 2 Circuit element model of SSSC

of this work is to obtain the results from standard IEEE14- and 30-bus test cases through FA incorporating circuitelement model of SSSC combined with variable susceptancemodel of SVC and to compare the results of these series-shunt FACTS controllers with other important evolutionarytechniques such as SFLADE and PSO under normal criticalloading and single-line outage conditions

2 Static Model of FACTS Devices

21 Circuit ElementModel of SSSC TheSSSC can be operatedwithout an external energy source as reactive power sourceand is fully controllable and independent of transmission linecurrent for the purpose of increasing or decreasing the overallreactive voltage drop across the transmission line and therebycontrolling the electric power flow The widely used powerinjectionmodel of SSSC requiresmodification of the Jacobianmatrix and makes the Newton-Raphson load flow (NRLF)coding more complex A new circuit elements based modelof SSSC is utilized to control the line power flows and busvoltage magnitudes for voltage stability limit improvementThe new model of the SSSC changes only the bus admittancematrix and consequently reduces the coding of load flowproblem incorporating SSSC simpleThis converter performsthe main function of injecting a controllable series voltageThe basic configuration of SSSC is depicted in Figure 1 Thecircuit element model of SSSC is also shown in Figure 2

The real and reactive powers exchanged with the line bythe series voltage inserted by SSSC are modeled as a negativeresistance and reactance connected in parallel The negativeresistance represents injection of real power and the reactancemay be either capacitive or inductive depending on whetherreactive power is delivered or absorbed

Advances in Electrical Engineering 3

The complex power exchanged by the series converterwith the line is expressed as

119878119890= 119881se119868 (1)

where119881se is the complex voltage injected by the converter and119868 the current through the line given by

119868 =119881119894ang120575119894+ 119881seang120574 minus 119881119895ang120575119895

119885119871

(2)

The active and reactive powers exchanged with the line aremodeled as resistance and reactance associated as representedby

119877 =1198812

se119875se

119883 =1198812

se119876se

(3)

The elements 119877 and119883 can be calculated by directly using thefollowing equations

119877 =119881se119885119871

119881119894sin (120575

119894minus 120575119895minus 120574) + 119881

119895sin 120574

119883 =119881se119885119871

119881119894cos (120575

119894minus 120575119895minus 120574) minus 119881

119895cos 120574 + 119881se

(4)

The resistance 119877 and the reactance 119883 representing the effectof series voltage are transformed into their equivalent seriescombination This makes the line simple with only series-connected elements of the line (119885

119871) and the 119877SSSC and 119883SSSC

denoting the resistance and reactance of SSSC

119877SSSC =1198771198832

1198772 + 1198832

119883SSSC =1198831198772

1198772 + 1198832

(5)

22 Variable Susceptance Model of SVC A variable suscep-tance 119861SVC represents the fundamental frequency equivalentsusceptance of all shunt modules making up the SVC Thismodel is an improved version of SVCmodels Figure 3 showsthe variable susceptancemodel of SVCwhich is used to deriveits nonlinear power equations and the linearised equationsrequired by Newtonrsquos load flow method

In general the transfer admittance equation for thevariable shunt compensator is

119868SVC = 119895119861SVC119881119895 (6)

And the reactive power of SVC is

119876SVC = minus1198812

119895119861SVC (7)

ViXline

Vj

BSVC

QSVC

Figure 3 Variable susceptance model of SVC

Sj Pj QjSi Pi Qi

VjVi

Bus jBus i

Z = R + jX

Figure 4 Single-line concept of power transmission

13

12 14

1110

9

4

7

1

2 3

5

8

6G

G

G

GG

C

(a) 14-bus system

1

30

29 2827

20

21

22

2324

26 25

1918

17

16

15

14

13 1211

109

8

7

6

5

43

2

G

G

G

G

G G

(b) 30-bus system

Figure 5 One-line diagram of IEEE test system

4 Advances in Electrical Engineering

056

04

120

69

081

06

016

64

062

21

054

52

033

9

079

94

057

6

031

12

069

08

058

52

039

17 070

24

065

03

002040608

11214

Case 1 Case 2 Case 3

Sum

of L

QP

valu

es

(a) For 14-bus system

InitialFASFLA

DEPSO

148

22

255

36

170

31

128

06

222

51

140

27

129

73

242

3

159

5

145

55

225

47

141

74

133

93

241

16

158

53

005

115

225

3

Sum

of L

QP

valu

es

Case 1 Case 2 Case 3

(b) For 30-bus system

Figure 6 Sum of LQP index values comparison

In SVC susceptance model the total susceptance 119861SVC istaken to be the state variable therefore the linearised equationof the SVC is given by

[Δ119875119895

Δ119876119895

] = [0 0

0 120579119895

][[

[

Δ120579119895

Δ119861svc119861svc

]]

]

(8)

where Δ119875119895 Δ119876119895 and Δ120579

119895are the change in real reactive

power and voltage angle at 119895th busAt the end of iteration 119894 the variable shunt susceptance

119861SVC is updated according to

119861(119894)

SVC = 119861(119894minus1)

SVC + (Δ119861SVC119861SVC

)

(119894)

119861(119894minus1)

SVC (9)

This changing susceptance value represents the total SVCsusceptance which is necessary to maintain the nodal voltagemagnitude at the specified value (10 pu in this paper)

3 Line Quality Proximity Index

Voltage stability can be assessed in a system by calculating theline based voltage stability index The LQP index based on apower transmission concept is used in this paperThe value ofline index shows the voltage stability of the systemThe valueclose to unity indicates that the respective line is close to itsstability limit and valuemuch close to zero indicates light loadin the line The formulation begins with the power equationin a power system Figure 4 illustrates a single line of a powertransmission concept

The power equation can be derived as

119875119894= radic

1198812

119894

119883(119876119894minus 119876119895) minus 1198762

119894 (10)

The line stability factor isobtained by setting the discriminantof the reactive power roots at bus 1 to be greater than or equalto zero thus defining the line stability factor LQP as

LQP = 4( 1198831198812

119894

)(119883

1198812

119894

1198752

119894+ 119876119895) (11)

4 Problem Formulation

The objective function of this work is to find the optimalrating and location of FACTS devices combination whichminimizes the real power loss minimizes voltage deviationandmaximizes the voltage stability limit Hence the objectivefunction can be expressed as

119865 = min 119875119871+ 119908VD + (1 minus 119908) LQP (12)

where119908 is the weighing factor for voltage deviation and is setto 10

41 Minimization of Real Power Loss (119875119871) The total real

power of the system can be calculated as follows

119875loss =

119873119871

sum

119896=1

119866119896[1198812

119894+ 1198812

119895minus 2

10038161003816100381610038161198811198941003816100381610038161003816

10038161003816100381610038161003816119881119895

10038161003816100381610038161003816cos (120575

119894minus 120575119895)] (13)

where119873119871is the total number of lines in the system 119866

119896is the

conductance of the line ldquo119896rdquo 119881119894and 119881

119895are the magnitudes of

the sending end and receiving end voltages of the line and 120575119894

and 120575119895are angles of the end voltages

42 Minimization of Load Bus Voltage Deviation (VD) Busvoltagemagnitude should bemaintainedwithin the allowablerange to ensure quality service Voltage profile is improvedby minimizing the deviation of the load bus voltage from thereference value (it is taken as 10 pu in this work)

VD =

119873PQ

sum

119896=1

1003816100381610038161003816119881119868 minus 119881ref1003816100381610038161003816

(14)

where 119881119894is the voltage at 119894th bus and 119881ref is the reference

voltage

43 Minimization of Line Quality Proximity Index (LQP)Voltage stability limit of a power system is increased byminimizing voltage stability index value The indicator takesvalues between 0 (no load) and 1 (full load) The line basedstability index (LQP) is given as

LQP =119873119871

sum

119895=1

LQP119895 (15)

Advances in Electrical Engineering 5

(i) Case 1

(ii) Case 2

(iii) Case 3

1102104106108

11

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Volta

ge v

alue

s in

pu

Bus number

InitialFASFLA

DEPSO

095097099101103105107

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Volta

ge v

alue

s in

pu

Bus number

0981

102104106108

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Volta

ge v

alue

s in

pu

Bus number

(a)

(i) Case 1

(ii) Case 2

098

101

104

107

11

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Volta

ge v

alue

s in

pu

Bus number

088092096

1104108

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Volta

ge v

alue

s in

pu

Bus number

094

098

102

106

11

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Volta

ge v

alue

s in

pu

Bus number

(iii) Case 3

InitialFASFLA

DEPSO

(b)

Figure 7 (a) Voltage profile values comparison for 14-bus system (b) Voltage profile values comparison for 30-bus system

44 Constraints Theminimization problem is subject to thefollowing equality and inequality constraints

441 Equality Constraints

Load Flow Constraints Consider

119875Gi minus 119875Di minus

119873119861

sum

119895=1

119881119894119881119895119884119894119895cos (120575

119894119895+ 120574119895minus 120574119894) = 0

119876Gi minus 119876Di minus

119873119861

sum

119895=1

119881119894119881119895119884119894119895sin (120575

119894119895+ 120574119895minus 120574119894) = 0

(16)

where 119875Gi and 119876Gi are the active and reactive powers of 119894thgenerator and 119875Di and119876Di are the active and reactive powersof 119894th load bus

442 Inequality Constraints

Reactive Power Generation Limit of SVCs By choosing small-sized compensator capital cost involved can be minimum

The size limit of SVC has been taken from minimum of 5MVAR to maximum of 20 MVAR

119876minSVCi le 119876SVCi le 119876

maxSVCi 119894 isin 119873SVC (17)

where119876minSVCi and119876

maxSVCi are theminimum andmaximumVAR

injection limits of 119894th shunt capacitor

Voltage Constraints The acceptable voltage limits in all loadbuses are taken from 095 pu to 105 pu to avoid voltageinstability

119881min119894

le 119881119894le 119881

max119894

119894 isin 119873119861 (18)

where 119881min119894

and119881max119894

are the minimum and maximum valuevoltage of bus ldquo119894rdquo

Transmission Line Flow Limit Consider

119878119894le 119878

max119894 119894 isin 119873

119897 (19)

where 119878119894is the apparent power flow of 119894th branch and 119878max

119894is

the maximum apparent power flow limit of 119894th branch

6 Advances in Electrical Engineering

0 5 10 15 20 25 30

Case 1

Case 2

Case 3

Loss ()

PSODE

SFLAFA

(a) For 14-bus system

0 5 10 15 20 25 30

PSODE

SFLAFA

Case 1

Case 2

Case 3

Loss ()

(b) For 30-bus system

Figure 8 Percentage of real power loss reduction under all cases

Table 1 Optimal values of FA parameters

Parameters Optimal ValuesNumber of fireflies 301205730

01120574 02120572 025119898 40119889 20Maximum iterations 100

5 Firefly Algorithm

51 Overview The firefly algorithm (FA) is a metaheuristicnature-inspired optimization algorithm which is based onthe social (flashing) behavior of fireflies or lighting bugsin the summer sky in the tropical temperature regions Itwas developed by Dr Xin-She Yang at Cambridge Universityin 2007 and it is based on the swarm behavior such asfish insects or bird schooling in nature In particularalthough the firefly algorithm has many similarities withother algorithms which are based on the so-called swarmintelligence such as the famous particle swarm optimization(PSO) artificial bee colony optimization (ABC) and bacterialforaging algorithms (BFA) it is indeed much simpler inboth concept and implementation Furthermore accordingto recent bibliography the algorithm is very efficient and canoutperform other conventional algorithms such as geneticalgorithms for solving many optimization problems a factthat has been justified in a recent research where the statisti-cal performance of the firefly algorithmwasmeasured againstother well-known optimization algorithms using variousstandard stochastic test functions Its main advantage is thefact that it uses mainly real random numbers and it is basedon the global communication among the swarming particles(ie the fireflies) and as a result it seems more effective inmultiobjective optimization such as the economic emissionsload dispatch problem in our case

The firefly algorithm has three particular idealized ruleswhich are based on some of the major flashing characteristicsof real fireflies These rules are the following

(i) All fireflies are unisex and they will move towardsmore attractive and brighter ones regardless their sex

(ii) The degree of attractiveness of a firefly is proportionalto its brightness which decreases as the distance fromthe other firefly increases due to the fact that theair absorbs light If there is no brighter or moreattractive firefly than a particular one it will thenmove randomly

(iii) The brightness or light intensity of a firefly is deter-mined by the value of the objective function of agiven problem For maximization problems the lightintensity is proportional to the value of the objectivefunction

52 Implementation

521 Attractiveness In the firefly algorithm the form ofattractiveness functions of a firefly is the following monoton-ically decreasing function

120573 (119903) = 1205730lowast exp (minus120574119903119898) with 119898 ge 1 (20)

where 119903 is the distance between any two fireflies 1205730is the

initial attractiveness at 119903 = 0 and 120574 is an absorptioncoefficient which controls the decrease of the light intensity

522 Distance The distance between any two fireflies 119894 and119895 at positions 119909

119894and 119909

119895 respectively can be defined as a

Cartesian or Euclidean distance as follows

119903119894119895=10038171003817100381710038171003817119909119894minus 119909119895

10038171003817100381710038171003817= radic

119889

sum

119896=1

(119909119894119896minus 119909119895119896)2

(21)

where 119909119894119896

is the 119896th component of the spatial coordinate 119909119894

of the 119894th firefly and 119889 is the number of dimensions we havefor 119889 = 2 we have

119903119894119895= radic(119909

119894minus 119909119895)2

+ (119910119894minus 119910119895)2

(22)

However the calculation of distance r can also be definedusing other distance metrics based on the nature of theproblem such as Manhattan distance

Advances in Electrical Engineering 7

Table 2 Voltage stability index values of most stressed lines

(a) For 14-bus system

Cases Line number Preinsertion of FACTS Postinsertion of FACTSFA SFLA DE PSO

Case 1

14 01122 00714 00818 00807 0082920 00776 00582 00537 00544 006171 00688 00447 00511 00491 0051917 00593 00310 00388 00408 005039 00515 00291 00346 00307 00401

Case 2

10 02580 01106 01722 01651 0199514 01815 00994 00991 01012 0124420 01494 00912 00941 01109 012869 01393 00833 00994 01081 011201 00799 00517 00604 00597 00661

Case 3

10 01904 01014 00941 01057 0112915 01160 00809 00802 00914 009566 00914 00529 00317 00441 005824 00793 00447 00406 00533 005519 00648 00361 00304 00369 00408

(b) For 30-bus system

Cases Line number Preinsertion of FACTS Postinsertion of FACTSFA SFLA DE PSO

Case 1

12 03691 03664 03687 03700 036835 01284 00695 01264 00987 0128213 01226 00722 00114 01169 0109515 00749 00713 00748 00752 0074914 00678 00667 00674 00676 00672

Case 2

12 03899 03861 03877 03874 038815 03596 00884 03310 00793 0331213 02549 02115 02355 02351 0239016 01687 01241 01735 01767 0161015 01255 01167 01245 01244 01249

Case 3

12 03851 03688 03864 03686 0379313 01732 01159 01766 01152 0171116 00836 00445 00855 00475 008331 00786 00540 00810 00568 0069415 00775 00741 00776 00749 00771

523 Movement The movement of a firefly 119894 which isattracted by a more attractive (ie brighter) firefly 119895 is givenby the following equation

119909119894= 119909119894+ 1205730lowast exp (minus1205741199032

119894119895) lowast (119909

119894minus 119909119895) + 120572 lowast (rand minus 1

2)

(23)

where the first term is the current position of a firefly thesecond term is used for considering a fireflyrsquos attractivenessto light intensity seen by adjacent fireflies and the third termissued for the random movement of a firefly in case there areno any brighter ones The coefficient 120572 is a randomizationparameter determined by the problem of interest while randis a random number generator uniformly distributed in the

space (01) As we will see in this implementation of thealgorithm we use 120573

0= 01 120572 isin [0 1] and the attractiveness

or absorption coefficient 120574 = 02 which guarantees a quickconvergence of the algorithm to the optimal solution Theoptimal values of firefly parameters are in Table 1

6 Results and Discussion

The proposed work is coded in MATLAB 76 platform using28GHz Intel Core 2 Duo processor based PC The methodis tested in the IEEE 14- and 30-bus test systems shownin Figure 5 The line data and bus data are taken from thestandard power system test case archive The 14-bus systemhas 5 generator buses 9 load buses and 20 transmission lines

8 Advances in Electrical Engineering

Table 3 Contingency ranking

Rank 14-bus system 30-bus systemLine number LQP values Line number LQP values

1 1 05795 5 094952 3 03826 9 060503 10 03449 2 049934 2 03157 4 049685 15 01984 7 04693

Table 4 Average load bus voltage values in pu

(a) For 14-bus system

Cases Preinsertion of FACTS Postinsertion of FACTSFA SFLA DE PSO

Case 1 10438 10517 10494 10483 10460Case 2 09890 10082 10013 10051 09966Case 3 10243 10409 10363 10331 10308

(b) For 30-bus system

Cases Preinsertion of FACTS Postinsertion of FACTSFA SFLA DE PSO

Case 1 10260 10296 10306 10288 10265Case 2 09520 09961 09664 09626 09602Case 3 10109 10380 10108 10298 10222

The 30-bus system has 6 generator buses 24 load buses and41 transmission lines System data and results are based on100 MVA and bus number 1 is the reference bus In order toverify the presentedmodels and illustrate the impact of circuitelement model of SSSC with variable susceptance model ofSVC combination study three different operating conditionsare considered as mentioned below

Case 1 The system with normal load in all the load busesis considered as normal condition and the Newton-Raphsonload flow is carried out with loading factor value equal to 1

Case 2 The system with 50 increased load in all the loadbuses is considered as a critical condition Loading of thesystem went beyond this level and results in poor voltageprofile in the load buses and unacceptable real power losslevel

Case 3 Contingency is imposed by considering the mostcritical line outage in the system This is the most suitablecondition for voltage stability analysis of a power system asvoltage stability is usually triggered by line outages

Newton-Raphson program is repeatedly run with theabsence and presence of FACTS device combination Thevoltage stability limit improvement is assessed by the valueof LQP index The voltage stability index values of topfive stressed lines under all cases with preinsertion andpostinsertion of FACTS devices are shown in Table 2 Itis evident from the table that LQP values of the stressedlines are reduced after placement of FACTS devices inthe system

For quick assessment of voltage stability limit improve-ment of the system under the three different operatingconditions sum of the LQP index values of all the linesbefore and after the insertion of FACTS devices combinationis compared in Figure 6 The reduction in the index valuethrough the proposed method indicates the best voltagestability limit improvement

The line outage is ranked according to the severity andthe severity is taken on the basis of the line quality proximityindex values and such values are arranged in descendingorder The maximum value of index indicates most criticalline for outage Line outage contingency screening andranking are carried out on the test systems and the results areshown in Table 3

It is clear from Table 3 that outage of lines numbers 1 and5 are the most critical line outages of 14- and 30-bus systemsrespectively This situation is considered for voltage stabilityimprovement Outage of other lines has not much impact onthe system and therefore they are not given importance Loadflow is run on the system with the lines that have outagesOutage of these lines results in large real power loss andvoltage profile reduction inmost of the load busesThe systemis under stressed conditions and needs to be relieved by somemeans Installation of FACTS devices at suitable locations canrelieve the system much from stressed conditions (reducedline losses)

FACTS devices help the system to maintain acceptablevoltage profile in the load buses Under normal operatingconditions most of the bus voltagemagnitudes are within thenormal value During critical and contingency conditionsvoltagemagnitude of remote load buses are below 095 (lower

Advances in Electrical Engineering 9

Table 5 Minimum-maximum load bus voltage values in pu

(a) For 14-bus system

Cases119881MIN 119881MAX

Preinsertionof FACTS Bus number Postinsertion of FACTS Preinsertion

of FACTS Bus number Postinsertion of FACTSFA SFLA DE PSO FA SFLA DE PSO

Case 1 10173 4 10252 10211 10203 10143 10604 7 10696 10673 10642 10617Case 2 09656 14 10004 09884 09933 09824 10101 7 10211 10176 10199 10155Case 3 09913 5 10264 10208 10104 10111 10350 13 10496 10490 10460 10438

(b) For 30-bus system

Cases119881MIN 119881MAX

Preinsertionof FACTS Bus number Postinsertion of FACTS Preinsertion

of FACTS Bus number Postinsertion of FACTSFA SFLA DE PSO FA SFLA DE PSO

Case 1 09953 30 09978 09976 09959 09954 10576 11 10820 10820 10820 10822Case 2 08915 30 09662 09035 09415 09410 10004 11 10667 10620 10520 10550Case 3 09661 5 10121 09600 09600 09607 10495 11 10820 10820 10820 10820

Table 6 Real power loss values comparison (in MW)

(a) For 14-bus system

Conditions Preinsertion of FACTS (initial) Postinsertion of FACTSFA SFLA DE PSO

Case 1 13401 11014 11409 11693 12106Case 2 35042 28018 28991 28875 29019Case 3 24183 18046 19255 19389 19771

(b) For 30-bus system

Conditions Preinsertion of FACTS (Initial) Postinsertion of FACTSFA SFLA DE PSO

Case 1 17514 13467 14852 16157 16504Case 2 46900 40990 45797 41258 43272Case 3 32569 22801 29272 23234 25561

bound of allowable value) These bus voltages are improvedafter the FACTS devices are installed Voltage profile valuecomparison under all cases incorporating the series-shuntFACTS devices combination is depicted separately in Figures7(a) and 7(b) under both test cases It is obvious fromthe figure that voltage profile comparison of the system isimproved better with the proposed method incorporatingFACTS devices combination The comparison of averagevalue of load bus voltage also proves the enhancing behaviorof voltage stability limit incorporating with FACTS devices ofall cases shown in Table 4 Table 5 exposes the comparisonof minimum and maximum load bus voltages in both theabsence and presence of FACTS devices under all cases

In real power loss minimization point of view throughinsertion of FACTS devices the real power loss under Case1 is decreased by 2387 and 4047MW respectively for14- and 30-bus systems In Case 2 the reduction in realpower loss rate is 7024 and 5910MW respectively Thereduction rate in real power loss is 6137 and 9768MW

respectively under Case 3 operation The real power lossvalues of proposed method compared with other impor-tant evolutionary techniques under all cases are shownin Table 6

The percentage of reduction in real power loss compari-son under all cases including both combinations is depictedin Figure 8 Obviously from the results shown in Table 6 theproposed method is more efficient than other evolutionarytechniques given here to reduce the real power lossminimiza-tion application The much reduction in real power loss andincrease in voltage magnitudes after the insertion of FACTSdevices are highly efficient in relieving a power network fromstressed condition and improving voltage stability limit Themost suitable size and location of combinations of FACTSdevices to improve the voltage stability limit and real powerloss minimization are also given in Table 7 under all caseswith 14- and 30-bus systems respectively The optimized sizeof SVC inserted with both combinations is not in larger valuewhich helps to reduce in cost

10 Advances in Electrical Engineering

Table 7 Best location and size of FACTS devices

(a) For 14-bus system

Cases Series ShuntLocation (line number) Size (degrees of compensation) Location (bus number) Size (MVar)

Case 1

FA 10 00722 + 11989501464 5 72015SFLA 4 00377 + 11989500916 12 86554DE 15 00461 + 11989501540 10 69988PSO 3 00622 + 11989501067 12 83037

Case 2

FA 12 00823 + 11989500961 13 11211SFLA 1 00536 + 11989501642 11 106217DE 9 00507 + 11989501145 12 99654PSO 11 00727 + 11989500836 10 72510

Case 3

FA 12 00769 + 11989500810 13 96817SFLA 10 00421 + 11989501162 5 106528DE 2 00489 + 11989500773 11 89207PSO 7 00673 + 11989501286 10 114368

(b) For 30-bus system

Cases Series ShuntLocation (line number) Size (degrees of compensation) Location (bus number) Size (MVar)

Case 1

FA 5 00159 + 11989500924 12 86962SFLA 1 00086 + 11989500833 19 69688DE 6 00239 + 11989502664 20 58131PSO 12 00191 + 11989500977 23 150806

Case 2

FA 6 00137 + 11989500384 17 90607SFLA 9 00170 + 11989501243 21 141058DE 5 00289 + 11989500931 30 62554PSO 8 00281 + 11989500447 18 190106

Case 3

FA 11 00311 + 11989501417 26 80115SFLA 9 00115 + 11989501302 28 67499DE 6 00112 + 11989500478 25 58559PSO 8 00291 + 11989501189 3 182640

7 Conclusion

In this paper optimal location and size of series-shunt FACTSdevices for voltage stability limit improvement and lossminimization through firefly algorithm are demonstratedThe voltage stability limit improvement and real power lossminimization are done under three operating cases suchas normal critical loading and line outage contingencyconditions The LQP index is used for voltage stabilityassessment The circuit element model of SSSC is consid-ered to improve the voltage stability limit by controllingpower flows and maintaining voltage profile This modelis easy to incorporate the effect of SSSC into Newton-Raphson load flow program codingThe variable susceptancemodel of SVC is used in a combined manner with SSSCIt is clear from the numerical results that voltage stabilitylimit improvement and real power loss minimization arehighly encouraging The real power loss minimization andvoltage stability limit improvement is remarkable by thecombined action of power flow control of SSSC and reac-tive power compensation by SVC through firefly algorithmover other evolutionary optimization techniques given inthis paper

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] T V Cutsem and C Vournas Voltage Stability of Electric PowerSystems Kluwer Academic New York NY USA 1998

[2] P Kundur Power System Stability and Control McGraw-HillNew York NY USA 1994

[3] CW Taylor Power System Voltage Stability McGraw-Hill NewYork NY USA 1994

[4] T van Cutsem ldquoVoltage instability phenomena countermea-sures and analysis methodsrdquo Proceedings of the IEEE vol 88no 2 pp 208ndash227 2000

[5] P Kessel and H Glavitsch ldquoEstimating the voltage stability ofpower systemrdquo IEEE Transactions on Power Delivery vol 1 no3 pp 346ndash354 1986

[6] H J Wan J D McCalley and V Vittal ldquoRisk based voltagesecurity assessmentrdquo IEEE Transactions on Power Systems vol15 no 4 pp 1247ndash1254 2000

Advances in Electrical Engineering 11

[7] I Dobson and H-D Chiang ldquoTowards a theory of voltagecollapse in electric power systemsrdquo Systems and Control Lettersvol 13 no 3 pp 253ndash262 1989

[8] ldquoTechnical Analysis of the August 14 2003 Blackout WhatHappened Why and What Did We Learnrdquo A report by theNorth American Electrical Reliability Council Steering GroupNew Jersey July 2004

[9] N G Hingorani and L Gyugyi Understanding FACTS Con-cepts and Technology of Flexible AC Transmission Systems IEEEPress 2000

[10] K K Sen and M L Sen Introduction to FACTS ControllersTheory Modeling and Applications IEEE Press 2009

[11] GWu A Okoyama J He and Y Yu ldquoAllocation and control ofFACTS devices for steady state stability enhancement of largescale power systemrdquo International Conference on Power SystemTechnology vol 1 pp 357ndash361 1998

[12] N Yorino E E El-Araby H Sasaki and S Harada ldquoA newformulation for FACTS allocation for security enhancementagainst voltage collapserdquo IEEE Transactions on Power Systemsvol 18 no 1 pp 3ndash10 2003

[13] S Biansoongnern S Chusanapiputt and S PhoomvuthisarnldquoOptimal SVC and TCSC placement for minimization of trans-mission lossesrdquo inProceedings of the International Conference onPower System Technology pp 1ndash5 October 2006

[14] M A Abido ldquoPower system stability enhancement usingFACTS controllers a reviewrdquo The Arabian Journal For Scienceand Engineering vol 34 no 1 pp 153ndash172 2009

[15] O L Bekri ldquoOptimal location of SVC and TCSC for voltagestability enhancementrdquo in Proceedings of the 4th InternationalPower Engineering and Optimization Conference (PEOCO rsquo10)pp 7ndash12 June 2010

[16] Y Zhang and Y Zhang ldquoA novel power injection model ofembedded SSSCwithmulti-control modes for power flow anal-ysis inclusive of practical constraintsrdquo Electric Power SystemsResearch vol 76 no 5 pp 374ndash381 2006

[17] A Sode-Yome N Mithulananthan and K Y Lee ldquoStaticvoltage stability margin enhancement using STATCOM TCSCand SSSCrdquo in Proceedings of the IEEEPES Transmission andDistribution Conference and Exhibition pp 1ndash6 August 2005

[18] C A Canizares and Z T Faur ldquoAnalysis of SVC and TCSCcontrollers in voltage collapserdquo IEEE Transactions on PowerSystems vol 14 no 1 pp 158ndash165 1999

[19] S Musunuri and G Dehnavi ldquoComparison of STAT COMSVC TCSC and SSSC performance in steady state voltagestability improvementrdquo in Proceedings of the North AmericanPower Symposium (NAPS rsquo10) pp 1ndash7 September 2010

[20] P Kundur K Morison and B Gao ldquoPractical considerations involtage stability assessmentrdquo International Journal of ElectricalPower and Energy Systems vol 15 no 4 pp 205ndash215 1993

[21] V Ajjarapu Computational Techniques for Voltage StabilityAssessment and Control Springer Science 2006

[22] S Fliscounakis P Panciatici F Capitanescu and L WehenkelldquoContingency ranking with respect to overloads in large powersystems taking into account uncertainity preventive and correc-tive actionsrdquo IEEE Transactions on Power Systems vol 28 no 4pp 4909ndash4917 2013

[23] A Y Abdelaziz A T M Taha M A Mostafa and A MHassan ldquoPower systen contingency ranking using fuzzy logicbased approachrdquo International Journal of Intelligent Systems andApplications no 2 pp 24ndash28 2013

[24] P S Venkataramu and T Ananthapadmanabha ldquoInstallationof unified power flow controller for voltage stability margin

enhancement under line outage contingenciesrdquo Iranian Journalof Electrical and Computer Engineering vol 5 no 2 pp 90ndash962006

[25] M Jarsquofari and S Afsharnia ldquoVoltage stability enhancementin contingency conditions using shunt FACTS devicesrdquo inProceedings of the EUROCON The International Conference onComputer as a Tool pp 1660ndash1665 September 2007

[26] P-A Loef G Andersson and D J Hill ldquoVoltage stabilityindices for stressed power systemsrdquo IEEE Transactions on PowerSystems vol 8 no 1 pp 326ndash335 1993

[27] M Moghavvemi and F M Omar ldquoTechnique for contingencymonitoring and voltage collapse predictionrdquo IEE Proceedings onGeneration Transmission and Distribution vol 145 no 6 pp634ndash640 1998

[28] M Moghavvemi and O Faruque ldquoReal time contingency eval-uation and ranking techniquerdquo IEE Proceedings on GenerationTransmission and Distribution vol 145 no 5 pp 517ndash524 1998

[29] I Musirin and T K A Rahman ldquoNovel fast voltage stabilityindex (FVSI) for voltage stability analysis in power transmissionsystemrdquo in Proceedings of the Student Conference on Researchand Development Proceedings pp 265ndash268 2002

[30] C Reis A Andrade and F P Maciel ldquoLine stability indicesfor voltage collapse predictionrdquo in Proceedings of the 2nd IEEEInternational Conference on Power Engineering Energy andElectrical Drives pp 239ndash243 March 2009

[31] X S Yang Nature-Inspired Metaheuristic Algorithms LuniverPress 2008

[32] X S Yang ldquoFirefly algorithms for multimodal optimizationrdquo inStochastic Algorithms Foundations and Applications SAGA vol5792 of Lecture Notes in Computer Sciences pp 169ndash178 2009

[33] S Łukasik and S Zak ldquoFirefly algorithm for continuousconstrained optimization task computational collective intel-ligencerdquo in Semantic Web Social Networks and Multi-AgentSystems vol 5796 of Lecture Notes in Computer Science pp 97ndash106 2009

[34] N D Reppen R R Austria J A Uhrin M C Patel and AGalatic ldquoPerformance of methods for ranking a evaluation ofvoltage collapse contingencies applied to a large-scale networkrdquoin Proceedings of the IEEE Joint International Conference pp337ndash343 1993

[35] G C Ejebe G D Irisarri S Mokhtari O Obadina PRistanovic and J Tong ldquoMethods for contingency screeningand ranking for voltage stability analysis of power systemsrdquo inProceedings of the IEEE Power Industry Computer ApplicationConference pp 249ndash255 May 1995

[36] E Vaahedi C FuchsW Xu et al ldquoVoltage stability contingencyscreening and rankingrdquo IEEE Transactions on Power Systemsvol 14 no 1 pp 256ndash265 1999

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Advances in Electrical Engineering 3

The complex power exchanged by the series converterwith the line is expressed as

119878119890= 119881se119868 (1)

where119881se is the complex voltage injected by the converter and119868 the current through the line given by

119868 =119881119894ang120575119894+ 119881seang120574 minus 119881119895ang120575119895

119885119871

(2)

The active and reactive powers exchanged with the line aremodeled as resistance and reactance associated as representedby

119877 =1198812

se119875se

119883 =1198812

se119876se

(3)

The elements 119877 and119883 can be calculated by directly using thefollowing equations

119877 =119881se119885119871

119881119894sin (120575

119894minus 120575119895minus 120574) + 119881

119895sin 120574

119883 =119881se119885119871

119881119894cos (120575

119894minus 120575119895minus 120574) minus 119881

119895cos 120574 + 119881se

(4)

The resistance 119877 and the reactance 119883 representing the effectof series voltage are transformed into their equivalent seriescombination This makes the line simple with only series-connected elements of the line (119885

119871) and the 119877SSSC and 119883SSSC

denoting the resistance and reactance of SSSC

119877SSSC =1198771198832

1198772 + 1198832

119883SSSC =1198831198772

1198772 + 1198832

(5)

22 Variable Susceptance Model of SVC A variable suscep-tance 119861SVC represents the fundamental frequency equivalentsusceptance of all shunt modules making up the SVC Thismodel is an improved version of SVCmodels Figure 3 showsthe variable susceptancemodel of SVCwhich is used to deriveits nonlinear power equations and the linearised equationsrequired by Newtonrsquos load flow method

In general the transfer admittance equation for thevariable shunt compensator is

119868SVC = 119895119861SVC119881119895 (6)

And the reactive power of SVC is

119876SVC = minus1198812

119895119861SVC (7)

ViXline

Vj

BSVC

QSVC

Figure 3 Variable susceptance model of SVC

Sj Pj QjSi Pi Qi

VjVi

Bus jBus i

Z = R + jX

Figure 4 Single-line concept of power transmission

13

12 14

1110

9

4

7

1

2 3

5

8

6G

G

G

GG

C

(a) 14-bus system

1

30

29 2827

20

21

22

2324

26 25

1918

17

16

15

14

13 1211

109

8

7

6

5

43

2

G

G

G

G

G G

(b) 30-bus system

Figure 5 One-line diagram of IEEE test system

4 Advances in Electrical Engineering

056

04

120

69

081

06

016

64

062

21

054

52

033

9

079

94

057

6

031

12

069

08

058

52

039

17 070

24

065

03

002040608

11214

Case 1 Case 2 Case 3

Sum

of L

QP

valu

es

(a) For 14-bus system

InitialFASFLA

DEPSO

148

22

255

36

170

31

128

06

222

51

140

27

129

73

242

3

159

5

145

55

225

47

141

74

133

93

241

16

158

53

005

115

225

3

Sum

of L

QP

valu

es

Case 1 Case 2 Case 3

(b) For 30-bus system

Figure 6 Sum of LQP index values comparison

In SVC susceptance model the total susceptance 119861SVC istaken to be the state variable therefore the linearised equationof the SVC is given by

[Δ119875119895

Δ119876119895

] = [0 0

0 120579119895

][[

[

Δ120579119895

Δ119861svc119861svc

]]

]

(8)

where Δ119875119895 Δ119876119895 and Δ120579

119895are the change in real reactive

power and voltage angle at 119895th busAt the end of iteration 119894 the variable shunt susceptance

119861SVC is updated according to

119861(119894)

SVC = 119861(119894minus1)

SVC + (Δ119861SVC119861SVC

)

(119894)

119861(119894minus1)

SVC (9)

This changing susceptance value represents the total SVCsusceptance which is necessary to maintain the nodal voltagemagnitude at the specified value (10 pu in this paper)

3 Line Quality Proximity Index

Voltage stability can be assessed in a system by calculating theline based voltage stability index The LQP index based on apower transmission concept is used in this paperThe value ofline index shows the voltage stability of the systemThe valueclose to unity indicates that the respective line is close to itsstability limit and valuemuch close to zero indicates light loadin the line The formulation begins with the power equationin a power system Figure 4 illustrates a single line of a powertransmission concept

The power equation can be derived as

119875119894= radic

1198812

119894

119883(119876119894minus 119876119895) minus 1198762

119894 (10)

The line stability factor isobtained by setting the discriminantof the reactive power roots at bus 1 to be greater than or equalto zero thus defining the line stability factor LQP as

LQP = 4( 1198831198812

119894

)(119883

1198812

119894

1198752

119894+ 119876119895) (11)

4 Problem Formulation

The objective function of this work is to find the optimalrating and location of FACTS devices combination whichminimizes the real power loss minimizes voltage deviationandmaximizes the voltage stability limit Hence the objectivefunction can be expressed as

119865 = min 119875119871+ 119908VD + (1 minus 119908) LQP (12)

where119908 is the weighing factor for voltage deviation and is setto 10

41 Minimization of Real Power Loss (119875119871) The total real

power of the system can be calculated as follows

119875loss =

119873119871

sum

119896=1

119866119896[1198812

119894+ 1198812

119895minus 2

10038161003816100381610038161198811198941003816100381610038161003816

10038161003816100381610038161003816119881119895

10038161003816100381610038161003816cos (120575

119894minus 120575119895)] (13)

where119873119871is the total number of lines in the system 119866

119896is the

conductance of the line ldquo119896rdquo 119881119894and 119881

119895are the magnitudes of

the sending end and receiving end voltages of the line and 120575119894

and 120575119895are angles of the end voltages

42 Minimization of Load Bus Voltage Deviation (VD) Busvoltagemagnitude should bemaintainedwithin the allowablerange to ensure quality service Voltage profile is improvedby minimizing the deviation of the load bus voltage from thereference value (it is taken as 10 pu in this work)

VD =

119873PQ

sum

119896=1

1003816100381610038161003816119881119868 minus 119881ref1003816100381610038161003816

(14)

where 119881119894is the voltage at 119894th bus and 119881ref is the reference

voltage

43 Minimization of Line Quality Proximity Index (LQP)Voltage stability limit of a power system is increased byminimizing voltage stability index value The indicator takesvalues between 0 (no load) and 1 (full load) The line basedstability index (LQP) is given as

LQP =119873119871

sum

119895=1

LQP119895 (15)

Advances in Electrical Engineering 5

(i) Case 1

(ii) Case 2

(iii) Case 3

1102104106108

11

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Volta

ge v

alue

s in

pu

Bus number

InitialFASFLA

DEPSO

095097099101103105107

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Volta

ge v

alue

s in

pu

Bus number

0981

102104106108

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Volta

ge v

alue

s in

pu

Bus number

(a)

(i) Case 1

(ii) Case 2

098

101

104

107

11

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Volta

ge v

alue

s in

pu

Bus number

088092096

1104108

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Volta

ge v

alue

s in

pu

Bus number

094

098

102

106

11

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Volta

ge v

alue

s in

pu

Bus number

(iii) Case 3

InitialFASFLA

DEPSO

(b)

Figure 7 (a) Voltage profile values comparison for 14-bus system (b) Voltage profile values comparison for 30-bus system

44 Constraints Theminimization problem is subject to thefollowing equality and inequality constraints

441 Equality Constraints

Load Flow Constraints Consider

119875Gi minus 119875Di minus

119873119861

sum

119895=1

119881119894119881119895119884119894119895cos (120575

119894119895+ 120574119895minus 120574119894) = 0

119876Gi minus 119876Di minus

119873119861

sum

119895=1

119881119894119881119895119884119894119895sin (120575

119894119895+ 120574119895minus 120574119894) = 0

(16)

where 119875Gi and 119876Gi are the active and reactive powers of 119894thgenerator and 119875Di and119876Di are the active and reactive powersof 119894th load bus

442 Inequality Constraints

Reactive Power Generation Limit of SVCs By choosing small-sized compensator capital cost involved can be minimum

The size limit of SVC has been taken from minimum of 5MVAR to maximum of 20 MVAR

119876minSVCi le 119876SVCi le 119876

maxSVCi 119894 isin 119873SVC (17)

where119876minSVCi and119876

maxSVCi are theminimum andmaximumVAR

injection limits of 119894th shunt capacitor

Voltage Constraints The acceptable voltage limits in all loadbuses are taken from 095 pu to 105 pu to avoid voltageinstability

119881min119894

le 119881119894le 119881

max119894

119894 isin 119873119861 (18)

where 119881min119894

and119881max119894

are the minimum and maximum valuevoltage of bus ldquo119894rdquo

Transmission Line Flow Limit Consider

119878119894le 119878

max119894 119894 isin 119873

119897 (19)

where 119878119894is the apparent power flow of 119894th branch and 119878max

119894is

the maximum apparent power flow limit of 119894th branch

6 Advances in Electrical Engineering

0 5 10 15 20 25 30

Case 1

Case 2

Case 3

Loss ()

PSODE

SFLAFA

(a) For 14-bus system

0 5 10 15 20 25 30

PSODE

SFLAFA

Case 1

Case 2

Case 3

Loss ()

(b) For 30-bus system

Figure 8 Percentage of real power loss reduction under all cases

Table 1 Optimal values of FA parameters

Parameters Optimal ValuesNumber of fireflies 301205730

01120574 02120572 025119898 40119889 20Maximum iterations 100

5 Firefly Algorithm

51 Overview The firefly algorithm (FA) is a metaheuristicnature-inspired optimization algorithm which is based onthe social (flashing) behavior of fireflies or lighting bugsin the summer sky in the tropical temperature regions Itwas developed by Dr Xin-She Yang at Cambridge Universityin 2007 and it is based on the swarm behavior such asfish insects or bird schooling in nature In particularalthough the firefly algorithm has many similarities withother algorithms which are based on the so-called swarmintelligence such as the famous particle swarm optimization(PSO) artificial bee colony optimization (ABC) and bacterialforaging algorithms (BFA) it is indeed much simpler inboth concept and implementation Furthermore accordingto recent bibliography the algorithm is very efficient and canoutperform other conventional algorithms such as geneticalgorithms for solving many optimization problems a factthat has been justified in a recent research where the statisti-cal performance of the firefly algorithmwasmeasured againstother well-known optimization algorithms using variousstandard stochastic test functions Its main advantage is thefact that it uses mainly real random numbers and it is basedon the global communication among the swarming particles(ie the fireflies) and as a result it seems more effective inmultiobjective optimization such as the economic emissionsload dispatch problem in our case

The firefly algorithm has three particular idealized ruleswhich are based on some of the major flashing characteristicsof real fireflies These rules are the following

(i) All fireflies are unisex and they will move towardsmore attractive and brighter ones regardless their sex

(ii) The degree of attractiveness of a firefly is proportionalto its brightness which decreases as the distance fromthe other firefly increases due to the fact that theair absorbs light If there is no brighter or moreattractive firefly than a particular one it will thenmove randomly

(iii) The brightness or light intensity of a firefly is deter-mined by the value of the objective function of agiven problem For maximization problems the lightintensity is proportional to the value of the objectivefunction

52 Implementation

521 Attractiveness In the firefly algorithm the form ofattractiveness functions of a firefly is the following monoton-ically decreasing function

120573 (119903) = 1205730lowast exp (minus120574119903119898) with 119898 ge 1 (20)

where 119903 is the distance between any two fireflies 1205730is the

initial attractiveness at 119903 = 0 and 120574 is an absorptioncoefficient which controls the decrease of the light intensity

522 Distance The distance between any two fireflies 119894 and119895 at positions 119909

119894and 119909

119895 respectively can be defined as a

Cartesian or Euclidean distance as follows

119903119894119895=10038171003817100381710038171003817119909119894minus 119909119895

10038171003817100381710038171003817= radic

119889

sum

119896=1

(119909119894119896minus 119909119895119896)2

(21)

where 119909119894119896

is the 119896th component of the spatial coordinate 119909119894

of the 119894th firefly and 119889 is the number of dimensions we havefor 119889 = 2 we have

119903119894119895= radic(119909

119894minus 119909119895)2

+ (119910119894minus 119910119895)2

(22)

However the calculation of distance r can also be definedusing other distance metrics based on the nature of theproblem such as Manhattan distance

Advances in Electrical Engineering 7

Table 2 Voltage stability index values of most stressed lines

(a) For 14-bus system

Cases Line number Preinsertion of FACTS Postinsertion of FACTSFA SFLA DE PSO

Case 1

14 01122 00714 00818 00807 0082920 00776 00582 00537 00544 006171 00688 00447 00511 00491 0051917 00593 00310 00388 00408 005039 00515 00291 00346 00307 00401

Case 2

10 02580 01106 01722 01651 0199514 01815 00994 00991 01012 0124420 01494 00912 00941 01109 012869 01393 00833 00994 01081 011201 00799 00517 00604 00597 00661

Case 3

10 01904 01014 00941 01057 0112915 01160 00809 00802 00914 009566 00914 00529 00317 00441 005824 00793 00447 00406 00533 005519 00648 00361 00304 00369 00408

(b) For 30-bus system

Cases Line number Preinsertion of FACTS Postinsertion of FACTSFA SFLA DE PSO

Case 1

12 03691 03664 03687 03700 036835 01284 00695 01264 00987 0128213 01226 00722 00114 01169 0109515 00749 00713 00748 00752 0074914 00678 00667 00674 00676 00672

Case 2

12 03899 03861 03877 03874 038815 03596 00884 03310 00793 0331213 02549 02115 02355 02351 0239016 01687 01241 01735 01767 0161015 01255 01167 01245 01244 01249

Case 3

12 03851 03688 03864 03686 0379313 01732 01159 01766 01152 0171116 00836 00445 00855 00475 008331 00786 00540 00810 00568 0069415 00775 00741 00776 00749 00771

523 Movement The movement of a firefly 119894 which isattracted by a more attractive (ie brighter) firefly 119895 is givenby the following equation

119909119894= 119909119894+ 1205730lowast exp (minus1205741199032

119894119895) lowast (119909

119894minus 119909119895) + 120572 lowast (rand minus 1

2)

(23)

where the first term is the current position of a firefly thesecond term is used for considering a fireflyrsquos attractivenessto light intensity seen by adjacent fireflies and the third termissued for the random movement of a firefly in case there areno any brighter ones The coefficient 120572 is a randomizationparameter determined by the problem of interest while randis a random number generator uniformly distributed in the

space (01) As we will see in this implementation of thealgorithm we use 120573

0= 01 120572 isin [0 1] and the attractiveness

or absorption coefficient 120574 = 02 which guarantees a quickconvergence of the algorithm to the optimal solution Theoptimal values of firefly parameters are in Table 1

6 Results and Discussion

The proposed work is coded in MATLAB 76 platform using28GHz Intel Core 2 Duo processor based PC The methodis tested in the IEEE 14- and 30-bus test systems shownin Figure 5 The line data and bus data are taken from thestandard power system test case archive The 14-bus systemhas 5 generator buses 9 load buses and 20 transmission lines

8 Advances in Electrical Engineering

Table 3 Contingency ranking

Rank 14-bus system 30-bus systemLine number LQP values Line number LQP values

1 1 05795 5 094952 3 03826 9 060503 10 03449 2 049934 2 03157 4 049685 15 01984 7 04693

Table 4 Average load bus voltage values in pu

(a) For 14-bus system

Cases Preinsertion of FACTS Postinsertion of FACTSFA SFLA DE PSO

Case 1 10438 10517 10494 10483 10460Case 2 09890 10082 10013 10051 09966Case 3 10243 10409 10363 10331 10308

(b) For 30-bus system

Cases Preinsertion of FACTS Postinsertion of FACTSFA SFLA DE PSO

Case 1 10260 10296 10306 10288 10265Case 2 09520 09961 09664 09626 09602Case 3 10109 10380 10108 10298 10222

The 30-bus system has 6 generator buses 24 load buses and41 transmission lines System data and results are based on100 MVA and bus number 1 is the reference bus In order toverify the presentedmodels and illustrate the impact of circuitelement model of SSSC with variable susceptance model ofSVC combination study three different operating conditionsare considered as mentioned below

Case 1 The system with normal load in all the load busesis considered as normal condition and the Newton-Raphsonload flow is carried out with loading factor value equal to 1

Case 2 The system with 50 increased load in all the loadbuses is considered as a critical condition Loading of thesystem went beyond this level and results in poor voltageprofile in the load buses and unacceptable real power losslevel

Case 3 Contingency is imposed by considering the mostcritical line outage in the system This is the most suitablecondition for voltage stability analysis of a power system asvoltage stability is usually triggered by line outages

Newton-Raphson program is repeatedly run with theabsence and presence of FACTS device combination Thevoltage stability limit improvement is assessed by the valueof LQP index The voltage stability index values of topfive stressed lines under all cases with preinsertion andpostinsertion of FACTS devices are shown in Table 2 Itis evident from the table that LQP values of the stressedlines are reduced after placement of FACTS devices inthe system

For quick assessment of voltage stability limit improve-ment of the system under the three different operatingconditions sum of the LQP index values of all the linesbefore and after the insertion of FACTS devices combinationis compared in Figure 6 The reduction in the index valuethrough the proposed method indicates the best voltagestability limit improvement

The line outage is ranked according to the severity andthe severity is taken on the basis of the line quality proximityindex values and such values are arranged in descendingorder The maximum value of index indicates most criticalline for outage Line outage contingency screening andranking are carried out on the test systems and the results areshown in Table 3

It is clear from Table 3 that outage of lines numbers 1 and5 are the most critical line outages of 14- and 30-bus systemsrespectively This situation is considered for voltage stabilityimprovement Outage of other lines has not much impact onthe system and therefore they are not given importance Loadflow is run on the system with the lines that have outagesOutage of these lines results in large real power loss andvoltage profile reduction inmost of the load busesThe systemis under stressed conditions and needs to be relieved by somemeans Installation of FACTS devices at suitable locations canrelieve the system much from stressed conditions (reducedline losses)

FACTS devices help the system to maintain acceptablevoltage profile in the load buses Under normal operatingconditions most of the bus voltagemagnitudes are within thenormal value During critical and contingency conditionsvoltagemagnitude of remote load buses are below 095 (lower

Advances in Electrical Engineering 9

Table 5 Minimum-maximum load bus voltage values in pu

(a) For 14-bus system

Cases119881MIN 119881MAX

Preinsertionof FACTS Bus number Postinsertion of FACTS Preinsertion

of FACTS Bus number Postinsertion of FACTSFA SFLA DE PSO FA SFLA DE PSO

Case 1 10173 4 10252 10211 10203 10143 10604 7 10696 10673 10642 10617Case 2 09656 14 10004 09884 09933 09824 10101 7 10211 10176 10199 10155Case 3 09913 5 10264 10208 10104 10111 10350 13 10496 10490 10460 10438

(b) For 30-bus system

Cases119881MIN 119881MAX

Preinsertionof FACTS Bus number Postinsertion of FACTS Preinsertion

of FACTS Bus number Postinsertion of FACTSFA SFLA DE PSO FA SFLA DE PSO

Case 1 09953 30 09978 09976 09959 09954 10576 11 10820 10820 10820 10822Case 2 08915 30 09662 09035 09415 09410 10004 11 10667 10620 10520 10550Case 3 09661 5 10121 09600 09600 09607 10495 11 10820 10820 10820 10820

Table 6 Real power loss values comparison (in MW)

(a) For 14-bus system

Conditions Preinsertion of FACTS (initial) Postinsertion of FACTSFA SFLA DE PSO

Case 1 13401 11014 11409 11693 12106Case 2 35042 28018 28991 28875 29019Case 3 24183 18046 19255 19389 19771

(b) For 30-bus system

Conditions Preinsertion of FACTS (Initial) Postinsertion of FACTSFA SFLA DE PSO

Case 1 17514 13467 14852 16157 16504Case 2 46900 40990 45797 41258 43272Case 3 32569 22801 29272 23234 25561

bound of allowable value) These bus voltages are improvedafter the FACTS devices are installed Voltage profile valuecomparison under all cases incorporating the series-shuntFACTS devices combination is depicted separately in Figures7(a) and 7(b) under both test cases It is obvious fromthe figure that voltage profile comparison of the system isimproved better with the proposed method incorporatingFACTS devices combination The comparison of averagevalue of load bus voltage also proves the enhancing behaviorof voltage stability limit incorporating with FACTS devices ofall cases shown in Table 4 Table 5 exposes the comparisonof minimum and maximum load bus voltages in both theabsence and presence of FACTS devices under all cases

In real power loss minimization point of view throughinsertion of FACTS devices the real power loss under Case1 is decreased by 2387 and 4047MW respectively for14- and 30-bus systems In Case 2 the reduction in realpower loss rate is 7024 and 5910MW respectively Thereduction rate in real power loss is 6137 and 9768MW

respectively under Case 3 operation The real power lossvalues of proposed method compared with other impor-tant evolutionary techniques under all cases are shownin Table 6

The percentage of reduction in real power loss compari-son under all cases including both combinations is depictedin Figure 8 Obviously from the results shown in Table 6 theproposed method is more efficient than other evolutionarytechniques given here to reduce the real power lossminimiza-tion application The much reduction in real power loss andincrease in voltage magnitudes after the insertion of FACTSdevices are highly efficient in relieving a power network fromstressed condition and improving voltage stability limit Themost suitable size and location of combinations of FACTSdevices to improve the voltage stability limit and real powerloss minimization are also given in Table 7 under all caseswith 14- and 30-bus systems respectively The optimized sizeof SVC inserted with both combinations is not in larger valuewhich helps to reduce in cost

10 Advances in Electrical Engineering

Table 7 Best location and size of FACTS devices

(a) For 14-bus system

Cases Series ShuntLocation (line number) Size (degrees of compensation) Location (bus number) Size (MVar)

Case 1

FA 10 00722 + 11989501464 5 72015SFLA 4 00377 + 11989500916 12 86554DE 15 00461 + 11989501540 10 69988PSO 3 00622 + 11989501067 12 83037

Case 2

FA 12 00823 + 11989500961 13 11211SFLA 1 00536 + 11989501642 11 106217DE 9 00507 + 11989501145 12 99654PSO 11 00727 + 11989500836 10 72510

Case 3

FA 12 00769 + 11989500810 13 96817SFLA 10 00421 + 11989501162 5 106528DE 2 00489 + 11989500773 11 89207PSO 7 00673 + 11989501286 10 114368

(b) For 30-bus system

Cases Series ShuntLocation (line number) Size (degrees of compensation) Location (bus number) Size (MVar)

Case 1

FA 5 00159 + 11989500924 12 86962SFLA 1 00086 + 11989500833 19 69688DE 6 00239 + 11989502664 20 58131PSO 12 00191 + 11989500977 23 150806

Case 2

FA 6 00137 + 11989500384 17 90607SFLA 9 00170 + 11989501243 21 141058DE 5 00289 + 11989500931 30 62554PSO 8 00281 + 11989500447 18 190106

Case 3

FA 11 00311 + 11989501417 26 80115SFLA 9 00115 + 11989501302 28 67499DE 6 00112 + 11989500478 25 58559PSO 8 00291 + 11989501189 3 182640

7 Conclusion

In this paper optimal location and size of series-shunt FACTSdevices for voltage stability limit improvement and lossminimization through firefly algorithm are demonstratedThe voltage stability limit improvement and real power lossminimization are done under three operating cases suchas normal critical loading and line outage contingencyconditions The LQP index is used for voltage stabilityassessment The circuit element model of SSSC is consid-ered to improve the voltage stability limit by controllingpower flows and maintaining voltage profile This modelis easy to incorporate the effect of SSSC into Newton-Raphson load flow program codingThe variable susceptancemodel of SVC is used in a combined manner with SSSCIt is clear from the numerical results that voltage stabilitylimit improvement and real power loss minimization arehighly encouraging The real power loss minimization andvoltage stability limit improvement is remarkable by thecombined action of power flow control of SSSC and reac-tive power compensation by SVC through firefly algorithmover other evolutionary optimization techniques given inthis paper

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] T V Cutsem and C Vournas Voltage Stability of Electric PowerSystems Kluwer Academic New York NY USA 1998

[2] P Kundur Power System Stability and Control McGraw-HillNew York NY USA 1994

[3] CW Taylor Power System Voltage Stability McGraw-Hill NewYork NY USA 1994

[4] T van Cutsem ldquoVoltage instability phenomena countermea-sures and analysis methodsrdquo Proceedings of the IEEE vol 88no 2 pp 208ndash227 2000

[5] P Kessel and H Glavitsch ldquoEstimating the voltage stability ofpower systemrdquo IEEE Transactions on Power Delivery vol 1 no3 pp 346ndash354 1986

[6] H J Wan J D McCalley and V Vittal ldquoRisk based voltagesecurity assessmentrdquo IEEE Transactions on Power Systems vol15 no 4 pp 1247ndash1254 2000

Advances in Electrical Engineering 11

[7] I Dobson and H-D Chiang ldquoTowards a theory of voltagecollapse in electric power systemsrdquo Systems and Control Lettersvol 13 no 3 pp 253ndash262 1989

[8] ldquoTechnical Analysis of the August 14 2003 Blackout WhatHappened Why and What Did We Learnrdquo A report by theNorth American Electrical Reliability Council Steering GroupNew Jersey July 2004

[9] N G Hingorani and L Gyugyi Understanding FACTS Con-cepts and Technology of Flexible AC Transmission Systems IEEEPress 2000

[10] K K Sen and M L Sen Introduction to FACTS ControllersTheory Modeling and Applications IEEE Press 2009

[11] GWu A Okoyama J He and Y Yu ldquoAllocation and control ofFACTS devices for steady state stability enhancement of largescale power systemrdquo International Conference on Power SystemTechnology vol 1 pp 357ndash361 1998

[12] N Yorino E E El-Araby H Sasaki and S Harada ldquoA newformulation for FACTS allocation for security enhancementagainst voltage collapserdquo IEEE Transactions on Power Systemsvol 18 no 1 pp 3ndash10 2003

[13] S Biansoongnern S Chusanapiputt and S PhoomvuthisarnldquoOptimal SVC and TCSC placement for minimization of trans-mission lossesrdquo inProceedings of the International Conference onPower System Technology pp 1ndash5 October 2006

[14] M A Abido ldquoPower system stability enhancement usingFACTS controllers a reviewrdquo The Arabian Journal For Scienceand Engineering vol 34 no 1 pp 153ndash172 2009

[15] O L Bekri ldquoOptimal location of SVC and TCSC for voltagestability enhancementrdquo in Proceedings of the 4th InternationalPower Engineering and Optimization Conference (PEOCO rsquo10)pp 7ndash12 June 2010

[16] Y Zhang and Y Zhang ldquoA novel power injection model ofembedded SSSCwithmulti-control modes for power flow anal-ysis inclusive of practical constraintsrdquo Electric Power SystemsResearch vol 76 no 5 pp 374ndash381 2006

[17] A Sode-Yome N Mithulananthan and K Y Lee ldquoStaticvoltage stability margin enhancement using STATCOM TCSCand SSSCrdquo in Proceedings of the IEEEPES Transmission andDistribution Conference and Exhibition pp 1ndash6 August 2005

[18] C A Canizares and Z T Faur ldquoAnalysis of SVC and TCSCcontrollers in voltage collapserdquo IEEE Transactions on PowerSystems vol 14 no 1 pp 158ndash165 1999

[19] S Musunuri and G Dehnavi ldquoComparison of STAT COMSVC TCSC and SSSC performance in steady state voltagestability improvementrdquo in Proceedings of the North AmericanPower Symposium (NAPS rsquo10) pp 1ndash7 September 2010

[20] P Kundur K Morison and B Gao ldquoPractical considerations involtage stability assessmentrdquo International Journal of ElectricalPower and Energy Systems vol 15 no 4 pp 205ndash215 1993

[21] V Ajjarapu Computational Techniques for Voltage StabilityAssessment and Control Springer Science 2006

[22] S Fliscounakis P Panciatici F Capitanescu and L WehenkelldquoContingency ranking with respect to overloads in large powersystems taking into account uncertainity preventive and correc-tive actionsrdquo IEEE Transactions on Power Systems vol 28 no 4pp 4909ndash4917 2013

[23] A Y Abdelaziz A T M Taha M A Mostafa and A MHassan ldquoPower systen contingency ranking using fuzzy logicbased approachrdquo International Journal of Intelligent Systems andApplications no 2 pp 24ndash28 2013

[24] P S Venkataramu and T Ananthapadmanabha ldquoInstallationof unified power flow controller for voltage stability margin

enhancement under line outage contingenciesrdquo Iranian Journalof Electrical and Computer Engineering vol 5 no 2 pp 90ndash962006

[25] M Jarsquofari and S Afsharnia ldquoVoltage stability enhancementin contingency conditions using shunt FACTS devicesrdquo inProceedings of the EUROCON The International Conference onComputer as a Tool pp 1660ndash1665 September 2007

[26] P-A Loef G Andersson and D J Hill ldquoVoltage stabilityindices for stressed power systemsrdquo IEEE Transactions on PowerSystems vol 8 no 1 pp 326ndash335 1993

[27] M Moghavvemi and F M Omar ldquoTechnique for contingencymonitoring and voltage collapse predictionrdquo IEE Proceedings onGeneration Transmission and Distribution vol 145 no 6 pp634ndash640 1998

[28] M Moghavvemi and O Faruque ldquoReal time contingency eval-uation and ranking techniquerdquo IEE Proceedings on GenerationTransmission and Distribution vol 145 no 5 pp 517ndash524 1998

[29] I Musirin and T K A Rahman ldquoNovel fast voltage stabilityindex (FVSI) for voltage stability analysis in power transmissionsystemrdquo in Proceedings of the Student Conference on Researchand Development Proceedings pp 265ndash268 2002

[30] C Reis A Andrade and F P Maciel ldquoLine stability indicesfor voltage collapse predictionrdquo in Proceedings of the 2nd IEEEInternational Conference on Power Engineering Energy andElectrical Drives pp 239ndash243 March 2009

[31] X S Yang Nature-Inspired Metaheuristic Algorithms LuniverPress 2008

[32] X S Yang ldquoFirefly algorithms for multimodal optimizationrdquo inStochastic Algorithms Foundations and Applications SAGA vol5792 of Lecture Notes in Computer Sciences pp 169ndash178 2009

[33] S Łukasik and S Zak ldquoFirefly algorithm for continuousconstrained optimization task computational collective intel-ligencerdquo in Semantic Web Social Networks and Multi-AgentSystems vol 5796 of Lecture Notes in Computer Science pp 97ndash106 2009

[34] N D Reppen R R Austria J A Uhrin M C Patel and AGalatic ldquoPerformance of methods for ranking a evaluation ofvoltage collapse contingencies applied to a large-scale networkrdquoin Proceedings of the IEEE Joint International Conference pp337ndash343 1993

[35] G C Ejebe G D Irisarri S Mokhtari O Obadina PRistanovic and J Tong ldquoMethods for contingency screeningand ranking for voltage stability analysis of power systemsrdquo inProceedings of the IEEE Power Industry Computer ApplicationConference pp 249ndash255 May 1995

[36] E Vaahedi C FuchsW Xu et al ldquoVoltage stability contingencyscreening and rankingrdquo IEEE Transactions on Power Systemsvol 14 no 1 pp 256ndash265 1999

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4 Advances in Electrical Engineering

056

04

120

69

081

06

016

64

062

21

054

52

033

9

079

94

057

6

031

12

069

08

058

52

039

17 070

24

065

03

002040608

11214

Case 1 Case 2 Case 3

Sum

of L

QP

valu

es

(a) For 14-bus system

InitialFASFLA

DEPSO

148

22

255

36

170

31

128

06

222

51

140

27

129

73

242

3

159

5

145

55

225

47

141

74

133

93

241

16

158

53

005

115

225

3

Sum

of L

QP

valu

es

Case 1 Case 2 Case 3

(b) For 30-bus system

Figure 6 Sum of LQP index values comparison

In SVC susceptance model the total susceptance 119861SVC istaken to be the state variable therefore the linearised equationof the SVC is given by

[Δ119875119895

Δ119876119895

] = [0 0

0 120579119895

][[

[

Δ120579119895

Δ119861svc119861svc

]]

]

(8)

where Δ119875119895 Δ119876119895 and Δ120579

119895are the change in real reactive

power and voltage angle at 119895th busAt the end of iteration 119894 the variable shunt susceptance

119861SVC is updated according to

119861(119894)

SVC = 119861(119894minus1)

SVC + (Δ119861SVC119861SVC

)

(119894)

119861(119894minus1)

SVC (9)

This changing susceptance value represents the total SVCsusceptance which is necessary to maintain the nodal voltagemagnitude at the specified value (10 pu in this paper)

3 Line Quality Proximity Index

Voltage stability can be assessed in a system by calculating theline based voltage stability index The LQP index based on apower transmission concept is used in this paperThe value ofline index shows the voltage stability of the systemThe valueclose to unity indicates that the respective line is close to itsstability limit and valuemuch close to zero indicates light loadin the line The formulation begins with the power equationin a power system Figure 4 illustrates a single line of a powertransmission concept

The power equation can be derived as

119875119894= radic

1198812

119894

119883(119876119894minus 119876119895) minus 1198762

119894 (10)

The line stability factor isobtained by setting the discriminantof the reactive power roots at bus 1 to be greater than or equalto zero thus defining the line stability factor LQP as

LQP = 4( 1198831198812

119894

)(119883

1198812

119894

1198752

119894+ 119876119895) (11)

4 Problem Formulation

The objective function of this work is to find the optimalrating and location of FACTS devices combination whichminimizes the real power loss minimizes voltage deviationandmaximizes the voltage stability limit Hence the objectivefunction can be expressed as

119865 = min 119875119871+ 119908VD + (1 minus 119908) LQP (12)

where119908 is the weighing factor for voltage deviation and is setto 10

41 Minimization of Real Power Loss (119875119871) The total real

power of the system can be calculated as follows

119875loss =

119873119871

sum

119896=1

119866119896[1198812

119894+ 1198812

119895minus 2

10038161003816100381610038161198811198941003816100381610038161003816

10038161003816100381610038161003816119881119895

10038161003816100381610038161003816cos (120575

119894minus 120575119895)] (13)

where119873119871is the total number of lines in the system 119866

119896is the

conductance of the line ldquo119896rdquo 119881119894and 119881

119895are the magnitudes of

the sending end and receiving end voltages of the line and 120575119894

and 120575119895are angles of the end voltages

42 Minimization of Load Bus Voltage Deviation (VD) Busvoltagemagnitude should bemaintainedwithin the allowablerange to ensure quality service Voltage profile is improvedby minimizing the deviation of the load bus voltage from thereference value (it is taken as 10 pu in this work)

VD =

119873PQ

sum

119896=1

1003816100381610038161003816119881119868 minus 119881ref1003816100381610038161003816

(14)

where 119881119894is the voltage at 119894th bus and 119881ref is the reference

voltage

43 Minimization of Line Quality Proximity Index (LQP)Voltage stability limit of a power system is increased byminimizing voltage stability index value The indicator takesvalues between 0 (no load) and 1 (full load) The line basedstability index (LQP) is given as

LQP =119873119871

sum

119895=1

LQP119895 (15)

Advances in Electrical Engineering 5

(i) Case 1

(ii) Case 2

(iii) Case 3

1102104106108

11

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Volta

ge v

alue

s in

pu

Bus number

InitialFASFLA

DEPSO

095097099101103105107

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Volta

ge v

alue

s in

pu

Bus number

0981

102104106108

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Volta

ge v

alue

s in

pu

Bus number

(a)

(i) Case 1

(ii) Case 2

098

101

104

107

11

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Volta

ge v

alue

s in

pu

Bus number

088092096

1104108

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Volta

ge v

alue

s in

pu

Bus number

094

098

102

106

11

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Volta

ge v

alue

s in

pu

Bus number

(iii) Case 3

InitialFASFLA

DEPSO

(b)

Figure 7 (a) Voltage profile values comparison for 14-bus system (b) Voltage profile values comparison for 30-bus system

44 Constraints Theminimization problem is subject to thefollowing equality and inequality constraints

441 Equality Constraints

Load Flow Constraints Consider

119875Gi minus 119875Di minus

119873119861

sum

119895=1

119881119894119881119895119884119894119895cos (120575

119894119895+ 120574119895minus 120574119894) = 0

119876Gi minus 119876Di minus

119873119861

sum

119895=1

119881119894119881119895119884119894119895sin (120575

119894119895+ 120574119895minus 120574119894) = 0

(16)

where 119875Gi and 119876Gi are the active and reactive powers of 119894thgenerator and 119875Di and119876Di are the active and reactive powersof 119894th load bus

442 Inequality Constraints

Reactive Power Generation Limit of SVCs By choosing small-sized compensator capital cost involved can be minimum

The size limit of SVC has been taken from minimum of 5MVAR to maximum of 20 MVAR

119876minSVCi le 119876SVCi le 119876

maxSVCi 119894 isin 119873SVC (17)

where119876minSVCi and119876

maxSVCi are theminimum andmaximumVAR

injection limits of 119894th shunt capacitor

Voltage Constraints The acceptable voltage limits in all loadbuses are taken from 095 pu to 105 pu to avoid voltageinstability

119881min119894

le 119881119894le 119881

max119894

119894 isin 119873119861 (18)

where 119881min119894

and119881max119894

are the minimum and maximum valuevoltage of bus ldquo119894rdquo

Transmission Line Flow Limit Consider

119878119894le 119878

max119894 119894 isin 119873

119897 (19)

where 119878119894is the apparent power flow of 119894th branch and 119878max

119894is

the maximum apparent power flow limit of 119894th branch

6 Advances in Electrical Engineering

0 5 10 15 20 25 30

Case 1

Case 2

Case 3

Loss ()

PSODE

SFLAFA

(a) For 14-bus system

0 5 10 15 20 25 30

PSODE

SFLAFA

Case 1

Case 2

Case 3

Loss ()

(b) For 30-bus system

Figure 8 Percentage of real power loss reduction under all cases

Table 1 Optimal values of FA parameters

Parameters Optimal ValuesNumber of fireflies 301205730

01120574 02120572 025119898 40119889 20Maximum iterations 100

5 Firefly Algorithm

51 Overview The firefly algorithm (FA) is a metaheuristicnature-inspired optimization algorithm which is based onthe social (flashing) behavior of fireflies or lighting bugsin the summer sky in the tropical temperature regions Itwas developed by Dr Xin-She Yang at Cambridge Universityin 2007 and it is based on the swarm behavior such asfish insects or bird schooling in nature In particularalthough the firefly algorithm has many similarities withother algorithms which are based on the so-called swarmintelligence such as the famous particle swarm optimization(PSO) artificial bee colony optimization (ABC) and bacterialforaging algorithms (BFA) it is indeed much simpler inboth concept and implementation Furthermore accordingto recent bibliography the algorithm is very efficient and canoutperform other conventional algorithms such as geneticalgorithms for solving many optimization problems a factthat has been justified in a recent research where the statisti-cal performance of the firefly algorithmwasmeasured againstother well-known optimization algorithms using variousstandard stochastic test functions Its main advantage is thefact that it uses mainly real random numbers and it is basedon the global communication among the swarming particles(ie the fireflies) and as a result it seems more effective inmultiobjective optimization such as the economic emissionsload dispatch problem in our case

The firefly algorithm has three particular idealized ruleswhich are based on some of the major flashing characteristicsof real fireflies These rules are the following

(i) All fireflies are unisex and they will move towardsmore attractive and brighter ones regardless their sex

(ii) The degree of attractiveness of a firefly is proportionalto its brightness which decreases as the distance fromthe other firefly increases due to the fact that theair absorbs light If there is no brighter or moreattractive firefly than a particular one it will thenmove randomly

(iii) The brightness or light intensity of a firefly is deter-mined by the value of the objective function of agiven problem For maximization problems the lightintensity is proportional to the value of the objectivefunction

52 Implementation

521 Attractiveness In the firefly algorithm the form ofattractiveness functions of a firefly is the following monoton-ically decreasing function

120573 (119903) = 1205730lowast exp (minus120574119903119898) with 119898 ge 1 (20)

where 119903 is the distance between any two fireflies 1205730is the

initial attractiveness at 119903 = 0 and 120574 is an absorptioncoefficient which controls the decrease of the light intensity

522 Distance The distance between any two fireflies 119894 and119895 at positions 119909

119894and 119909

119895 respectively can be defined as a

Cartesian or Euclidean distance as follows

119903119894119895=10038171003817100381710038171003817119909119894minus 119909119895

10038171003817100381710038171003817= radic

119889

sum

119896=1

(119909119894119896minus 119909119895119896)2

(21)

where 119909119894119896

is the 119896th component of the spatial coordinate 119909119894

of the 119894th firefly and 119889 is the number of dimensions we havefor 119889 = 2 we have

119903119894119895= radic(119909

119894minus 119909119895)2

+ (119910119894minus 119910119895)2

(22)

However the calculation of distance r can also be definedusing other distance metrics based on the nature of theproblem such as Manhattan distance

Advances in Electrical Engineering 7

Table 2 Voltage stability index values of most stressed lines

(a) For 14-bus system

Cases Line number Preinsertion of FACTS Postinsertion of FACTSFA SFLA DE PSO

Case 1

14 01122 00714 00818 00807 0082920 00776 00582 00537 00544 006171 00688 00447 00511 00491 0051917 00593 00310 00388 00408 005039 00515 00291 00346 00307 00401

Case 2

10 02580 01106 01722 01651 0199514 01815 00994 00991 01012 0124420 01494 00912 00941 01109 012869 01393 00833 00994 01081 011201 00799 00517 00604 00597 00661

Case 3

10 01904 01014 00941 01057 0112915 01160 00809 00802 00914 009566 00914 00529 00317 00441 005824 00793 00447 00406 00533 005519 00648 00361 00304 00369 00408

(b) For 30-bus system

Cases Line number Preinsertion of FACTS Postinsertion of FACTSFA SFLA DE PSO

Case 1

12 03691 03664 03687 03700 036835 01284 00695 01264 00987 0128213 01226 00722 00114 01169 0109515 00749 00713 00748 00752 0074914 00678 00667 00674 00676 00672

Case 2

12 03899 03861 03877 03874 038815 03596 00884 03310 00793 0331213 02549 02115 02355 02351 0239016 01687 01241 01735 01767 0161015 01255 01167 01245 01244 01249

Case 3

12 03851 03688 03864 03686 0379313 01732 01159 01766 01152 0171116 00836 00445 00855 00475 008331 00786 00540 00810 00568 0069415 00775 00741 00776 00749 00771

523 Movement The movement of a firefly 119894 which isattracted by a more attractive (ie brighter) firefly 119895 is givenby the following equation

119909119894= 119909119894+ 1205730lowast exp (minus1205741199032

119894119895) lowast (119909

119894minus 119909119895) + 120572 lowast (rand minus 1

2)

(23)

where the first term is the current position of a firefly thesecond term is used for considering a fireflyrsquos attractivenessto light intensity seen by adjacent fireflies and the third termissued for the random movement of a firefly in case there areno any brighter ones The coefficient 120572 is a randomizationparameter determined by the problem of interest while randis a random number generator uniformly distributed in the

space (01) As we will see in this implementation of thealgorithm we use 120573

0= 01 120572 isin [0 1] and the attractiveness

or absorption coefficient 120574 = 02 which guarantees a quickconvergence of the algorithm to the optimal solution Theoptimal values of firefly parameters are in Table 1

6 Results and Discussion

The proposed work is coded in MATLAB 76 platform using28GHz Intel Core 2 Duo processor based PC The methodis tested in the IEEE 14- and 30-bus test systems shownin Figure 5 The line data and bus data are taken from thestandard power system test case archive The 14-bus systemhas 5 generator buses 9 load buses and 20 transmission lines

8 Advances in Electrical Engineering

Table 3 Contingency ranking

Rank 14-bus system 30-bus systemLine number LQP values Line number LQP values

1 1 05795 5 094952 3 03826 9 060503 10 03449 2 049934 2 03157 4 049685 15 01984 7 04693

Table 4 Average load bus voltage values in pu

(a) For 14-bus system

Cases Preinsertion of FACTS Postinsertion of FACTSFA SFLA DE PSO

Case 1 10438 10517 10494 10483 10460Case 2 09890 10082 10013 10051 09966Case 3 10243 10409 10363 10331 10308

(b) For 30-bus system

Cases Preinsertion of FACTS Postinsertion of FACTSFA SFLA DE PSO

Case 1 10260 10296 10306 10288 10265Case 2 09520 09961 09664 09626 09602Case 3 10109 10380 10108 10298 10222

The 30-bus system has 6 generator buses 24 load buses and41 transmission lines System data and results are based on100 MVA and bus number 1 is the reference bus In order toverify the presentedmodels and illustrate the impact of circuitelement model of SSSC with variable susceptance model ofSVC combination study three different operating conditionsare considered as mentioned below

Case 1 The system with normal load in all the load busesis considered as normal condition and the Newton-Raphsonload flow is carried out with loading factor value equal to 1

Case 2 The system with 50 increased load in all the loadbuses is considered as a critical condition Loading of thesystem went beyond this level and results in poor voltageprofile in the load buses and unacceptable real power losslevel

Case 3 Contingency is imposed by considering the mostcritical line outage in the system This is the most suitablecondition for voltage stability analysis of a power system asvoltage stability is usually triggered by line outages

Newton-Raphson program is repeatedly run with theabsence and presence of FACTS device combination Thevoltage stability limit improvement is assessed by the valueof LQP index The voltage stability index values of topfive stressed lines under all cases with preinsertion andpostinsertion of FACTS devices are shown in Table 2 Itis evident from the table that LQP values of the stressedlines are reduced after placement of FACTS devices inthe system

For quick assessment of voltage stability limit improve-ment of the system under the three different operatingconditions sum of the LQP index values of all the linesbefore and after the insertion of FACTS devices combinationis compared in Figure 6 The reduction in the index valuethrough the proposed method indicates the best voltagestability limit improvement

The line outage is ranked according to the severity andthe severity is taken on the basis of the line quality proximityindex values and such values are arranged in descendingorder The maximum value of index indicates most criticalline for outage Line outage contingency screening andranking are carried out on the test systems and the results areshown in Table 3

It is clear from Table 3 that outage of lines numbers 1 and5 are the most critical line outages of 14- and 30-bus systemsrespectively This situation is considered for voltage stabilityimprovement Outage of other lines has not much impact onthe system and therefore they are not given importance Loadflow is run on the system with the lines that have outagesOutage of these lines results in large real power loss andvoltage profile reduction inmost of the load busesThe systemis under stressed conditions and needs to be relieved by somemeans Installation of FACTS devices at suitable locations canrelieve the system much from stressed conditions (reducedline losses)

FACTS devices help the system to maintain acceptablevoltage profile in the load buses Under normal operatingconditions most of the bus voltagemagnitudes are within thenormal value During critical and contingency conditionsvoltagemagnitude of remote load buses are below 095 (lower

Advances in Electrical Engineering 9

Table 5 Minimum-maximum load bus voltage values in pu

(a) For 14-bus system

Cases119881MIN 119881MAX

Preinsertionof FACTS Bus number Postinsertion of FACTS Preinsertion

of FACTS Bus number Postinsertion of FACTSFA SFLA DE PSO FA SFLA DE PSO

Case 1 10173 4 10252 10211 10203 10143 10604 7 10696 10673 10642 10617Case 2 09656 14 10004 09884 09933 09824 10101 7 10211 10176 10199 10155Case 3 09913 5 10264 10208 10104 10111 10350 13 10496 10490 10460 10438

(b) For 30-bus system

Cases119881MIN 119881MAX

Preinsertionof FACTS Bus number Postinsertion of FACTS Preinsertion

of FACTS Bus number Postinsertion of FACTSFA SFLA DE PSO FA SFLA DE PSO

Case 1 09953 30 09978 09976 09959 09954 10576 11 10820 10820 10820 10822Case 2 08915 30 09662 09035 09415 09410 10004 11 10667 10620 10520 10550Case 3 09661 5 10121 09600 09600 09607 10495 11 10820 10820 10820 10820

Table 6 Real power loss values comparison (in MW)

(a) For 14-bus system

Conditions Preinsertion of FACTS (initial) Postinsertion of FACTSFA SFLA DE PSO

Case 1 13401 11014 11409 11693 12106Case 2 35042 28018 28991 28875 29019Case 3 24183 18046 19255 19389 19771

(b) For 30-bus system

Conditions Preinsertion of FACTS (Initial) Postinsertion of FACTSFA SFLA DE PSO

Case 1 17514 13467 14852 16157 16504Case 2 46900 40990 45797 41258 43272Case 3 32569 22801 29272 23234 25561

bound of allowable value) These bus voltages are improvedafter the FACTS devices are installed Voltage profile valuecomparison under all cases incorporating the series-shuntFACTS devices combination is depicted separately in Figures7(a) and 7(b) under both test cases It is obvious fromthe figure that voltage profile comparison of the system isimproved better with the proposed method incorporatingFACTS devices combination The comparison of averagevalue of load bus voltage also proves the enhancing behaviorof voltage stability limit incorporating with FACTS devices ofall cases shown in Table 4 Table 5 exposes the comparisonof minimum and maximum load bus voltages in both theabsence and presence of FACTS devices under all cases

In real power loss minimization point of view throughinsertion of FACTS devices the real power loss under Case1 is decreased by 2387 and 4047MW respectively for14- and 30-bus systems In Case 2 the reduction in realpower loss rate is 7024 and 5910MW respectively Thereduction rate in real power loss is 6137 and 9768MW

respectively under Case 3 operation The real power lossvalues of proposed method compared with other impor-tant evolutionary techniques under all cases are shownin Table 6

The percentage of reduction in real power loss compari-son under all cases including both combinations is depictedin Figure 8 Obviously from the results shown in Table 6 theproposed method is more efficient than other evolutionarytechniques given here to reduce the real power lossminimiza-tion application The much reduction in real power loss andincrease in voltage magnitudes after the insertion of FACTSdevices are highly efficient in relieving a power network fromstressed condition and improving voltage stability limit Themost suitable size and location of combinations of FACTSdevices to improve the voltage stability limit and real powerloss minimization are also given in Table 7 under all caseswith 14- and 30-bus systems respectively The optimized sizeof SVC inserted with both combinations is not in larger valuewhich helps to reduce in cost

10 Advances in Electrical Engineering

Table 7 Best location and size of FACTS devices

(a) For 14-bus system

Cases Series ShuntLocation (line number) Size (degrees of compensation) Location (bus number) Size (MVar)

Case 1

FA 10 00722 + 11989501464 5 72015SFLA 4 00377 + 11989500916 12 86554DE 15 00461 + 11989501540 10 69988PSO 3 00622 + 11989501067 12 83037

Case 2

FA 12 00823 + 11989500961 13 11211SFLA 1 00536 + 11989501642 11 106217DE 9 00507 + 11989501145 12 99654PSO 11 00727 + 11989500836 10 72510

Case 3

FA 12 00769 + 11989500810 13 96817SFLA 10 00421 + 11989501162 5 106528DE 2 00489 + 11989500773 11 89207PSO 7 00673 + 11989501286 10 114368

(b) For 30-bus system

Cases Series ShuntLocation (line number) Size (degrees of compensation) Location (bus number) Size (MVar)

Case 1

FA 5 00159 + 11989500924 12 86962SFLA 1 00086 + 11989500833 19 69688DE 6 00239 + 11989502664 20 58131PSO 12 00191 + 11989500977 23 150806

Case 2

FA 6 00137 + 11989500384 17 90607SFLA 9 00170 + 11989501243 21 141058DE 5 00289 + 11989500931 30 62554PSO 8 00281 + 11989500447 18 190106

Case 3

FA 11 00311 + 11989501417 26 80115SFLA 9 00115 + 11989501302 28 67499DE 6 00112 + 11989500478 25 58559PSO 8 00291 + 11989501189 3 182640

7 Conclusion

In this paper optimal location and size of series-shunt FACTSdevices for voltage stability limit improvement and lossminimization through firefly algorithm are demonstratedThe voltage stability limit improvement and real power lossminimization are done under three operating cases suchas normal critical loading and line outage contingencyconditions The LQP index is used for voltage stabilityassessment The circuit element model of SSSC is consid-ered to improve the voltage stability limit by controllingpower flows and maintaining voltage profile This modelis easy to incorporate the effect of SSSC into Newton-Raphson load flow program codingThe variable susceptancemodel of SVC is used in a combined manner with SSSCIt is clear from the numerical results that voltage stabilitylimit improvement and real power loss minimization arehighly encouraging The real power loss minimization andvoltage stability limit improvement is remarkable by thecombined action of power flow control of SSSC and reac-tive power compensation by SVC through firefly algorithmover other evolutionary optimization techniques given inthis paper

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] T V Cutsem and C Vournas Voltage Stability of Electric PowerSystems Kluwer Academic New York NY USA 1998

[2] P Kundur Power System Stability and Control McGraw-HillNew York NY USA 1994

[3] CW Taylor Power System Voltage Stability McGraw-Hill NewYork NY USA 1994

[4] T van Cutsem ldquoVoltage instability phenomena countermea-sures and analysis methodsrdquo Proceedings of the IEEE vol 88no 2 pp 208ndash227 2000

[5] P Kessel and H Glavitsch ldquoEstimating the voltage stability ofpower systemrdquo IEEE Transactions on Power Delivery vol 1 no3 pp 346ndash354 1986

[6] H J Wan J D McCalley and V Vittal ldquoRisk based voltagesecurity assessmentrdquo IEEE Transactions on Power Systems vol15 no 4 pp 1247ndash1254 2000

Advances in Electrical Engineering 11

[7] I Dobson and H-D Chiang ldquoTowards a theory of voltagecollapse in electric power systemsrdquo Systems and Control Lettersvol 13 no 3 pp 253ndash262 1989

[8] ldquoTechnical Analysis of the August 14 2003 Blackout WhatHappened Why and What Did We Learnrdquo A report by theNorth American Electrical Reliability Council Steering GroupNew Jersey July 2004

[9] N G Hingorani and L Gyugyi Understanding FACTS Con-cepts and Technology of Flexible AC Transmission Systems IEEEPress 2000

[10] K K Sen and M L Sen Introduction to FACTS ControllersTheory Modeling and Applications IEEE Press 2009

[11] GWu A Okoyama J He and Y Yu ldquoAllocation and control ofFACTS devices for steady state stability enhancement of largescale power systemrdquo International Conference on Power SystemTechnology vol 1 pp 357ndash361 1998

[12] N Yorino E E El-Araby H Sasaki and S Harada ldquoA newformulation for FACTS allocation for security enhancementagainst voltage collapserdquo IEEE Transactions on Power Systemsvol 18 no 1 pp 3ndash10 2003

[13] S Biansoongnern S Chusanapiputt and S PhoomvuthisarnldquoOptimal SVC and TCSC placement for minimization of trans-mission lossesrdquo inProceedings of the International Conference onPower System Technology pp 1ndash5 October 2006

[14] M A Abido ldquoPower system stability enhancement usingFACTS controllers a reviewrdquo The Arabian Journal For Scienceand Engineering vol 34 no 1 pp 153ndash172 2009

[15] O L Bekri ldquoOptimal location of SVC and TCSC for voltagestability enhancementrdquo in Proceedings of the 4th InternationalPower Engineering and Optimization Conference (PEOCO rsquo10)pp 7ndash12 June 2010

[16] Y Zhang and Y Zhang ldquoA novel power injection model ofembedded SSSCwithmulti-control modes for power flow anal-ysis inclusive of practical constraintsrdquo Electric Power SystemsResearch vol 76 no 5 pp 374ndash381 2006

[17] A Sode-Yome N Mithulananthan and K Y Lee ldquoStaticvoltage stability margin enhancement using STATCOM TCSCand SSSCrdquo in Proceedings of the IEEEPES Transmission andDistribution Conference and Exhibition pp 1ndash6 August 2005

[18] C A Canizares and Z T Faur ldquoAnalysis of SVC and TCSCcontrollers in voltage collapserdquo IEEE Transactions on PowerSystems vol 14 no 1 pp 158ndash165 1999

[19] S Musunuri and G Dehnavi ldquoComparison of STAT COMSVC TCSC and SSSC performance in steady state voltagestability improvementrdquo in Proceedings of the North AmericanPower Symposium (NAPS rsquo10) pp 1ndash7 September 2010

[20] P Kundur K Morison and B Gao ldquoPractical considerations involtage stability assessmentrdquo International Journal of ElectricalPower and Energy Systems vol 15 no 4 pp 205ndash215 1993

[21] V Ajjarapu Computational Techniques for Voltage StabilityAssessment and Control Springer Science 2006

[22] S Fliscounakis P Panciatici F Capitanescu and L WehenkelldquoContingency ranking with respect to overloads in large powersystems taking into account uncertainity preventive and correc-tive actionsrdquo IEEE Transactions on Power Systems vol 28 no 4pp 4909ndash4917 2013

[23] A Y Abdelaziz A T M Taha M A Mostafa and A MHassan ldquoPower systen contingency ranking using fuzzy logicbased approachrdquo International Journal of Intelligent Systems andApplications no 2 pp 24ndash28 2013

[24] P S Venkataramu and T Ananthapadmanabha ldquoInstallationof unified power flow controller for voltage stability margin

enhancement under line outage contingenciesrdquo Iranian Journalof Electrical and Computer Engineering vol 5 no 2 pp 90ndash962006

[25] M Jarsquofari and S Afsharnia ldquoVoltage stability enhancementin contingency conditions using shunt FACTS devicesrdquo inProceedings of the EUROCON The International Conference onComputer as a Tool pp 1660ndash1665 September 2007

[26] P-A Loef G Andersson and D J Hill ldquoVoltage stabilityindices for stressed power systemsrdquo IEEE Transactions on PowerSystems vol 8 no 1 pp 326ndash335 1993

[27] M Moghavvemi and F M Omar ldquoTechnique for contingencymonitoring and voltage collapse predictionrdquo IEE Proceedings onGeneration Transmission and Distribution vol 145 no 6 pp634ndash640 1998

[28] M Moghavvemi and O Faruque ldquoReal time contingency eval-uation and ranking techniquerdquo IEE Proceedings on GenerationTransmission and Distribution vol 145 no 5 pp 517ndash524 1998

[29] I Musirin and T K A Rahman ldquoNovel fast voltage stabilityindex (FVSI) for voltage stability analysis in power transmissionsystemrdquo in Proceedings of the Student Conference on Researchand Development Proceedings pp 265ndash268 2002

[30] C Reis A Andrade and F P Maciel ldquoLine stability indicesfor voltage collapse predictionrdquo in Proceedings of the 2nd IEEEInternational Conference on Power Engineering Energy andElectrical Drives pp 239ndash243 March 2009

[31] X S Yang Nature-Inspired Metaheuristic Algorithms LuniverPress 2008

[32] X S Yang ldquoFirefly algorithms for multimodal optimizationrdquo inStochastic Algorithms Foundations and Applications SAGA vol5792 of Lecture Notes in Computer Sciences pp 169ndash178 2009

[33] S Łukasik and S Zak ldquoFirefly algorithm for continuousconstrained optimization task computational collective intel-ligencerdquo in Semantic Web Social Networks and Multi-AgentSystems vol 5796 of Lecture Notes in Computer Science pp 97ndash106 2009

[34] N D Reppen R R Austria J A Uhrin M C Patel and AGalatic ldquoPerformance of methods for ranking a evaluation ofvoltage collapse contingencies applied to a large-scale networkrdquoin Proceedings of the IEEE Joint International Conference pp337ndash343 1993

[35] G C Ejebe G D Irisarri S Mokhtari O Obadina PRistanovic and J Tong ldquoMethods for contingency screeningand ranking for voltage stability analysis of power systemsrdquo inProceedings of the IEEE Power Industry Computer ApplicationConference pp 249ndash255 May 1995

[36] E Vaahedi C FuchsW Xu et al ldquoVoltage stability contingencyscreening and rankingrdquo IEEE Transactions on Power Systemsvol 14 no 1 pp 256ndash265 1999

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Advances in Electrical Engineering 5

(i) Case 1

(ii) Case 2

(iii) Case 3

1102104106108

11

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Volta

ge v

alue

s in

pu

Bus number

InitialFASFLA

DEPSO

095097099101103105107

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Volta

ge v

alue

s in

pu

Bus number

0981

102104106108

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Volta

ge v

alue

s in

pu

Bus number

(a)

(i) Case 1

(ii) Case 2

098

101

104

107

11

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Volta

ge v

alue

s in

pu

Bus number

088092096

1104108

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Volta

ge v

alue

s in

pu

Bus number

094

098

102

106

11

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Volta

ge v

alue

s in

pu

Bus number

(iii) Case 3

InitialFASFLA

DEPSO

(b)

Figure 7 (a) Voltage profile values comparison for 14-bus system (b) Voltage profile values comparison for 30-bus system

44 Constraints Theminimization problem is subject to thefollowing equality and inequality constraints

441 Equality Constraints

Load Flow Constraints Consider

119875Gi minus 119875Di minus

119873119861

sum

119895=1

119881119894119881119895119884119894119895cos (120575

119894119895+ 120574119895minus 120574119894) = 0

119876Gi minus 119876Di minus

119873119861

sum

119895=1

119881119894119881119895119884119894119895sin (120575

119894119895+ 120574119895minus 120574119894) = 0

(16)

where 119875Gi and 119876Gi are the active and reactive powers of 119894thgenerator and 119875Di and119876Di are the active and reactive powersof 119894th load bus

442 Inequality Constraints

Reactive Power Generation Limit of SVCs By choosing small-sized compensator capital cost involved can be minimum

The size limit of SVC has been taken from minimum of 5MVAR to maximum of 20 MVAR

119876minSVCi le 119876SVCi le 119876

maxSVCi 119894 isin 119873SVC (17)

where119876minSVCi and119876

maxSVCi are theminimum andmaximumVAR

injection limits of 119894th shunt capacitor

Voltage Constraints The acceptable voltage limits in all loadbuses are taken from 095 pu to 105 pu to avoid voltageinstability

119881min119894

le 119881119894le 119881

max119894

119894 isin 119873119861 (18)

where 119881min119894

and119881max119894

are the minimum and maximum valuevoltage of bus ldquo119894rdquo

Transmission Line Flow Limit Consider

119878119894le 119878

max119894 119894 isin 119873

119897 (19)

where 119878119894is the apparent power flow of 119894th branch and 119878max

119894is

the maximum apparent power flow limit of 119894th branch

6 Advances in Electrical Engineering

0 5 10 15 20 25 30

Case 1

Case 2

Case 3

Loss ()

PSODE

SFLAFA

(a) For 14-bus system

0 5 10 15 20 25 30

PSODE

SFLAFA

Case 1

Case 2

Case 3

Loss ()

(b) For 30-bus system

Figure 8 Percentage of real power loss reduction under all cases

Table 1 Optimal values of FA parameters

Parameters Optimal ValuesNumber of fireflies 301205730

01120574 02120572 025119898 40119889 20Maximum iterations 100

5 Firefly Algorithm

51 Overview The firefly algorithm (FA) is a metaheuristicnature-inspired optimization algorithm which is based onthe social (flashing) behavior of fireflies or lighting bugsin the summer sky in the tropical temperature regions Itwas developed by Dr Xin-She Yang at Cambridge Universityin 2007 and it is based on the swarm behavior such asfish insects or bird schooling in nature In particularalthough the firefly algorithm has many similarities withother algorithms which are based on the so-called swarmintelligence such as the famous particle swarm optimization(PSO) artificial bee colony optimization (ABC) and bacterialforaging algorithms (BFA) it is indeed much simpler inboth concept and implementation Furthermore accordingto recent bibliography the algorithm is very efficient and canoutperform other conventional algorithms such as geneticalgorithms for solving many optimization problems a factthat has been justified in a recent research where the statisti-cal performance of the firefly algorithmwasmeasured againstother well-known optimization algorithms using variousstandard stochastic test functions Its main advantage is thefact that it uses mainly real random numbers and it is basedon the global communication among the swarming particles(ie the fireflies) and as a result it seems more effective inmultiobjective optimization such as the economic emissionsload dispatch problem in our case

The firefly algorithm has three particular idealized ruleswhich are based on some of the major flashing characteristicsof real fireflies These rules are the following

(i) All fireflies are unisex and they will move towardsmore attractive and brighter ones regardless their sex

(ii) The degree of attractiveness of a firefly is proportionalto its brightness which decreases as the distance fromthe other firefly increases due to the fact that theair absorbs light If there is no brighter or moreattractive firefly than a particular one it will thenmove randomly

(iii) The brightness or light intensity of a firefly is deter-mined by the value of the objective function of agiven problem For maximization problems the lightintensity is proportional to the value of the objectivefunction

52 Implementation

521 Attractiveness In the firefly algorithm the form ofattractiveness functions of a firefly is the following monoton-ically decreasing function

120573 (119903) = 1205730lowast exp (minus120574119903119898) with 119898 ge 1 (20)

where 119903 is the distance between any two fireflies 1205730is the

initial attractiveness at 119903 = 0 and 120574 is an absorptioncoefficient which controls the decrease of the light intensity

522 Distance The distance between any two fireflies 119894 and119895 at positions 119909

119894and 119909

119895 respectively can be defined as a

Cartesian or Euclidean distance as follows

119903119894119895=10038171003817100381710038171003817119909119894minus 119909119895

10038171003817100381710038171003817= radic

119889

sum

119896=1

(119909119894119896minus 119909119895119896)2

(21)

where 119909119894119896

is the 119896th component of the spatial coordinate 119909119894

of the 119894th firefly and 119889 is the number of dimensions we havefor 119889 = 2 we have

119903119894119895= radic(119909

119894minus 119909119895)2

+ (119910119894minus 119910119895)2

(22)

However the calculation of distance r can also be definedusing other distance metrics based on the nature of theproblem such as Manhattan distance

Advances in Electrical Engineering 7

Table 2 Voltage stability index values of most stressed lines

(a) For 14-bus system

Cases Line number Preinsertion of FACTS Postinsertion of FACTSFA SFLA DE PSO

Case 1

14 01122 00714 00818 00807 0082920 00776 00582 00537 00544 006171 00688 00447 00511 00491 0051917 00593 00310 00388 00408 005039 00515 00291 00346 00307 00401

Case 2

10 02580 01106 01722 01651 0199514 01815 00994 00991 01012 0124420 01494 00912 00941 01109 012869 01393 00833 00994 01081 011201 00799 00517 00604 00597 00661

Case 3

10 01904 01014 00941 01057 0112915 01160 00809 00802 00914 009566 00914 00529 00317 00441 005824 00793 00447 00406 00533 005519 00648 00361 00304 00369 00408

(b) For 30-bus system

Cases Line number Preinsertion of FACTS Postinsertion of FACTSFA SFLA DE PSO

Case 1

12 03691 03664 03687 03700 036835 01284 00695 01264 00987 0128213 01226 00722 00114 01169 0109515 00749 00713 00748 00752 0074914 00678 00667 00674 00676 00672

Case 2

12 03899 03861 03877 03874 038815 03596 00884 03310 00793 0331213 02549 02115 02355 02351 0239016 01687 01241 01735 01767 0161015 01255 01167 01245 01244 01249

Case 3

12 03851 03688 03864 03686 0379313 01732 01159 01766 01152 0171116 00836 00445 00855 00475 008331 00786 00540 00810 00568 0069415 00775 00741 00776 00749 00771

523 Movement The movement of a firefly 119894 which isattracted by a more attractive (ie brighter) firefly 119895 is givenby the following equation

119909119894= 119909119894+ 1205730lowast exp (minus1205741199032

119894119895) lowast (119909

119894minus 119909119895) + 120572 lowast (rand minus 1

2)

(23)

where the first term is the current position of a firefly thesecond term is used for considering a fireflyrsquos attractivenessto light intensity seen by adjacent fireflies and the third termissued for the random movement of a firefly in case there areno any brighter ones The coefficient 120572 is a randomizationparameter determined by the problem of interest while randis a random number generator uniformly distributed in the

space (01) As we will see in this implementation of thealgorithm we use 120573

0= 01 120572 isin [0 1] and the attractiveness

or absorption coefficient 120574 = 02 which guarantees a quickconvergence of the algorithm to the optimal solution Theoptimal values of firefly parameters are in Table 1

6 Results and Discussion

The proposed work is coded in MATLAB 76 platform using28GHz Intel Core 2 Duo processor based PC The methodis tested in the IEEE 14- and 30-bus test systems shownin Figure 5 The line data and bus data are taken from thestandard power system test case archive The 14-bus systemhas 5 generator buses 9 load buses and 20 transmission lines

8 Advances in Electrical Engineering

Table 3 Contingency ranking

Rank 14-bus system 30-bus systemLine number LQP values Line number LQP values

1 1 05795 5 094952 3 03826 9 060503 10 03449 2 049934 2 03157 4 049685 15 01984 7 04693

Table 4 Average load bus voltage values in pu

(a) For 14-bus system

Cases Preinsertion of FACTS Postinsertion of FACTSFA SFLA DE PSO

Case 1 10438 10517 10494 10483 10460Case 2 09890 10082 10013 10051 09966Case 3 10243 10409 10363 10331 10308

(b) For 30-bus system

Cases Preinsertion of FACTS Postinsertion of FACTSFA SFLA DE PSO

Case 1 10260 10296 10306 10288 10265Case 2 09520 09961 09664 09626 09602Case 3 10109 10380 10108 10298 10222

The 30-bus system has 6 generator buses 24 load buses and41 transmission lines System data and results are based on100 MVA and bus number 1 is the reference bus In order toverify the presentedmodels and illustrate the impact of circuitelement model of SSSC with variable susceptance model ofSVC combination study three different operating conditionsare considered as mentioned below

Case 1 The system with normal load in all the load busesis considered as normal condition and the Newton-Raphsonload flow is carried out with loading factor value equal to 1

Case 2 The system with 50 increased load in all the loadbuses is considered as a critical condition Loading of thesystem went beyond this level and results in poor voltageprofile in the load buses and unacceptable real power losslevel

Case 3 Contingency is imposed by considering the mostcritical line outage in the system This is the most suitablecondition for voltage stability analysis of a power system asvoltage stability is usually triggered by line outages

Newton-Raphson program is repeatedly run with theabsence and presence of FACTS device combination Thevoltage stability limit improvement is assessed by the valueof LQP index The voltage stability index values of topfive stressed lines under all cases with preinsertion andpostinsertion of FACTS devices are shown in Table 2 Itis evident from the table that LQP values of the stressedlines are reduced after placement of FACTS devices inthe system

For quick assessment of voltage stability limit improve-ment of the system under the three different operatingconditions sum of the LQP index values of all the linesbefore and after the insertion of FACTS devices combinationis compared in Figure 6 The reduction in the index valuethrough the proposed method indicates the best voltagestability limit improvement

The line outage is ranked according to the severity andthe severity is taken on the basis of the line quality proximityindex values and such values are arranged in descendingorder The maximum value of index indicates most criticalline for outage Line outage contingency screening andranking are carried out on the test systems and the results areshown in Table 3

It is clear from Table 3 that outage of lines numbers 1 and5 are the most critical line outages of 14- and 30-bus systemsrespectively This situation is considered for voltage stabilityimprovement Outage of other lines has not much impact onthe system and therefore they are not given importance Loadflow is run on the system with the lines that have outagesOutage of these lines results in large real power loss andvoltage profile reduction inmost of the load busesThe systemis under stressed conditions and needs to be relieved by somemeans Installation of FACTS devices at suitable locations canrelieve the system much from stressed conditions (reducedline losses)

FACTS devices help the system to maintain acceptablevoltage profile in the load buses Under normal operatingconditions most of the bus voltagemagnitudes are within thenormal value During critical and contingency conditionsvoltagemagnitude of remote load buses are below 095 (lower

Advances in Electrical Engineering 9

Table 5 Minimum-maximum load bus voltage values in pu

(a) For 14-bus system

Cases119881MIN 119881MAX

Preinsertionof FACTS Bus number Postinsertion of FACTS Preinsertion

of FACTS Bus number Postinsertion of FACTSFA SFLA DE PSO FA SFLA DE PSO

Case 1 10173 4 10252 10211 10203 10143 10604 7 10696 10673 10642 10617Case 2 09656 14 10004 09884 09933 09824 10101 7 10211 10176 10199 10155Case 3 09913 5 10264 10208 10104 10111 10350 13 10496 10490 10460 10438

(b) For 30-bus system

Cases119881MIN 119881MAX

Preinsertionof FACTS Bus number Postinsertion of FACTS Preinsertion

of FACTS Bus number Postinsertion of FACTSFA SFLA DE PSO FA SFLA DE PSO

Case 1 09953 30 09978 09976 09959 09954 10576 11 10820 10820 10820 10822Case 2 08915 30 09662 09035 09415 09410 10004 11 10667 10620 10520 10550Case 3 09661 5 10121 09600 09600 09607 10495 11 10820 10820 10820 10820

Table 6 Real power loss values comparison (in MW)

(a) For 14-bus system

Conditions Preinsertion of FACTS (initial) Postinsertion of FACTSFA SFLA DE PSO

Case 1 13401 11014 11409 11693 12106Case 2 35042 28018 28991 28875 29019Case 3 24183 18046 19255 19389 19771

(b) For 30-bus system

Conditions Preinsertion of FACTS (Initial) Postinsertion of FACTSFA SFLA DE PSO

Case 1 17514 13467 14852 16157 16504Case 2 46900 40990 45797 41258 43272Case 3 32569 22801 29272 23234 25561

bound of allowable value) These bus voltages are improvedafter the FACTS devices are installed Voltage profile valuecomparison under all cases incorporating the series-shuntFACTS devices combination is depicted separately in Figures7(a) and 7(b) under both test cases It is obvious fromthe figure that voltage profile comparison of the system isimproved better with the proposed method incorporatingFACTS devices combination The comparison of averagevalue of load bus voltage also proves the enhancing behaviorof voltage stability limit incorporating with FACTS devices ofall cases shown in Table 4 Table 5 exposes the comparisonof minimum and maximum load bus voltages in both theabsence and presence of FACTS devices under all cases

In real power loss minimization point of view throughinsertion of FACTS devices the real power loss under Case1 is decreased by 2387 and 4047MW respectively for14- and 30-bus systems In Case 2 the reduction in realpower loss rate is 7024 and 5910MW respectively Thereduction rate in real power loss is 6137 and 9768MW

respectively under Case 3 operation The real power lossvalues of proposed method compared with other impor-tant evolutionary techniques under all cases are shownin Table 6

The percentage of reduction in real power loss compari-son under all cases including both combinations is depictedin Figure 8 Obviously from the results shown in Table 6 theproposed method is more efficient than other evolutionarytechniques given here to reduce the real power lossminimiza-tion application The much reduction in real power loss andincrease in voltage magnitudes after the insertion of FACTSdevices are highly efficient in relieving a power network fromstressed condition and improving voltage stability limit Themost suitable size and location of combinations of FACTSdevices to improve the voltage stability limit and real powerloss minimization are also given in Table 7 under all caseswith 14- and 30-bus systems respectively The optimized sizeof SVC inserted with both combinations is not in larger valuewhich helps to reduce in cost

10 Advances in Electrical Engineering

Table 7 Best location and size of FACTS devices

(a) For 14-bus system

Cases Series ShuntLocation (line number) Size (degrees of compensation) Location (bus number) Size (MVar)

Case 1

FA 10 00722 + 11989501464 5 72015SFLA 4 00377 + 11989500916 12 86554DE 15 00461 + 11989501540 10 69988PSO 3 00622 + 11989501067 12 83037

Case 2

FA 12 00823 + 11989500961 13 11211SFLA 1 00536 + 11989501642 11 106217DE 9 00507 + 11989501145 12 99654PSO 11 00727 + 11989500836 10 72510

Case 3

FA 12 00769 + 11989500810 13 96817SFLA 10 00421 + 11989501162 5 106528DE 2 00489 + 11989500773 11 89207PSO 7 00673 + 11989501286 10 114368

(b) For 30-bus system

Cases Series ShuntLocation (line number) Size (degrees of compensation) Location (bus number) Size (MVar)

Case 1

FA 5 00159 + 11989500924 12 86962SFLA 1 00086 + 11989500833 19 69688DE 6 00239 + 11989502664 20 58131PSO 12 00191 + 11989500977 23 150806

Case 2

FA 6 00137 + 11989500384 17 90607SFLA 9 00170 + 11989501243 21 141058DE 5 00289 + 11989500931 30 62554PSO 8 00281 + 11989500447 18 190106

Case 3

FA 11 00311 + 11989501417 26 80115SFLA 9 00115 + 11989501302 28 67499DE 6 00112 + 11989500478 25 58559PSO 8 00291 + 11989501189 3 182640

7 Conclusion

In this paper optimal location and size of series-shunt FACTSdevices for voltage stability limit improvement and lossminimization through firefly algorithm are demonstratedThe voltage stability limit improvement and real power lossminimization are done under three operating cases suchas normal critical loading and line outage contingencyconditions The LQP index is used for voltage stabilityassessment The circuit element model of SSSC is consid-ered to improve the voltage stability limit by controllingpower flows and maintaining voltage profile This modelis easy to incorporate the effect of SSSC into Newton-Raphson load flow program codingThe variable susceptancemodel of SVC is used in a combined manner with SSSCIt is clear from the numerical results that voltage stabilitylimit improvement and real power loss minimization arehighly encouraging The real power loss minimization andvoltage stability limit improvement is remarkable by thecombined action of power flow control of SSSC and reac-tive power compensation by SVC through firefly algorithmover other evolutionary optimization techniques given inthis paper

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] T V Cutsem and C Vournas Voltage Stability of Electric PowerSystems Kluwer Academic New York NY USA 1998

[2] P Kundur Power System Stability and Control McGraw-HillNew York NY USA 1994

[3] CW Taylor Power System Voltage Stability McGraw-Hill NewYork NY USA 1994

[4] T van Cutsem ldquoVoltage instability phenomena countermea-sures and analysis methodsrdquo Proceedings of the IEEE vol 88no 2 pp 208ndash227 2000

[5] P Kessel and H Glavitsch ldquoEstimating the voltage stability ofpower systemrdquo IEEE Transactions on Power Delivery vol 1 no3 pp 346ndash354 1986

[6] H J Wan J D McCalley and V Vittal ldquoRisk based voltagesecurity assessmentrdquo IEEE Transactions on Power Systems vol15 no 4 pp 1247ndash1254 2000

Advances in Electrical Engineering 11

[7] I Dobson and H-D Chiang ldquoTowards a theory of voltagecollapse in electric power systemsrdquo Systems and Control Lettersvol 13 no 3 pp 253ndash262 1989

[8] ldquoTechnical Analysis of the August 14 2003 Blackout WhatHappened Why and What Did We Learnrdquo A report by theNorth American Electrical Reliability Council Steering GroupNew Jersey July 2004

[9] N G Hingorani and L Gyugyi Understanding FACTS Con-cepts and Technology of Flexible AC Transmission Systems IEEEPress 2000

[10] K K Sen and M L Sen Introduction to FACTS ControllersTheory Modeling and Applications IEEE Press 2009

[11] GWu A Okoyama J He and Y Yu ldquoAllocation and control ofFACTS devices for steady state stability enhancement of largescale power systemrdquo International Conference on Power SystemTechnology vol 1 pp 357ndash361 1998

[12] N Yorino E E El-Araby H Sasaki and S Harada ldquoA newformulation for FACTS allocation for security enhancementagainst voltage collapserdquo IEEE Transactions on Power Systemsvol 18 no 1 pp 3ndash10 2003

[13] S Biansoongnern S Chusanapiputt and S PhoomvuthisarnldquoOptimal SVC and TCSC placement for minimization of trans-mission lossesrdquo inProceedings of the International Conference onPower System Technology pp 1ndash5 October 2006

[14] M A Abido ldquoPower system stability enhancement usingFACTS controllers a reviewrdquo The Arabian Journal For Scienceand Engineering vol 34 no 1 pp 153ndash172 2009

[15] O L Bekri ldquoOptimal location of SVC and TCSC for voltagestability enhancementrdquo in Proceedings of the 4th InternationalPower Engineering and Optimization Conference (PEOCO rsquo10)pp 7ndash12 June 2010

[16] Y Zhang and Y Zhang ldquoA novel power injection model ofembedded SSSCwithmulti-control modes for power flow anal-ysis inclusive of practical constraintsrdquo Electric Power SystemsResearch vol 76 no 5 pp 374ndash381 2006

[17] A Sode-Yome N Mithulananthan and K Y Lee ldquoStaticvoltage stability margin enhancement using STATCOM TCSCand SSSCrdquo in Proceedings of the IEEEPES Transmission andDistribution Conference and Exhibition pp 1ndash6 August 2005

[18] C A Canizares and Z T Faur ldquoAnalysis of SVC and TCSCcontrollers in voltage collapserdquo IEEE Transactions on PowerSystems vol 14 no 1 pp 158ndash165 1999

[19] S Musunuri and G Dehnavi ldquoComparison of STAT COMSVC TCSC and SSSC performance in steady state voltagestability improvementrdquo in Proceedings of the North AmericanPower Symposium (NAPS rsquo10) pp 1ndash7 September 2010

[20] P Kundur K Morison and B Gao ldquoPractical considerations involtage stability assessmentrdquo International Journal of ElectricalPower and Energy Systems vol 15 no 4 pp 205ndash215 1993

[21] V Ajjarapu Computational Techniques for Voltage StabilityAssessment and Control Springer Science 2006

[22] S Fliscounakis P Panciatici F Capitanescu and L WehenkelldquoContingency ranking with respect to overloads in large powersystems taking into account uncertainity preventive and correc-tive actionsrdquo IEEE Transactions on Power Systems vol 28 no 4pp 4909ndash4917 2013

[23] A Y Abdelaziz A T M Taha M A Mostafa and A MHassan ldquoPower systen contingency ranking using fuzzy logicbased approachrdquo International Journal of Intelligent Systems andApplications no 2 pp 24ndash28 2013

[24] P S Venkataramu and T Ananthapadmanabha ldquoInstallationof unified power flow controller for voltage stability margin

enhancement under line outage contingenciesrdquo Iranian Journalof Electrical and Computer Engineering vol 5 no 2 pp 90ndash962006

[25] M Jarsquofari and S Afsharnia ldquoVoltage stability enhancementin contingency conditions using shunt FACTS devicesrdquo inProceedings of the EUROCON The International Conference onComputer as a Tool pp 1660ndash1665 September 2007

[26] P-A Loef G Andersson and D J Hill ldquoVoltage stabilityindices for stressed power systemsrdquo IEEE Transactions on PowerSystems vol 8 no 1 pp 326ndash335 1993

[27] M Moghavvemi and F M Omar ldquoTechnique for contingencymonitoring and voltage collapse predictionrdquo IEE Proceedings onGeneration Transmission and Distribution vol 145 no 6 pp634ndash640 1998

[28] M Moghavvemi and O Faruque ldquoReal time contingency eval-uation and ranking techniquerdquo IEE Proceedings on GenerationTransmission and Distribution vol 145 no 5 pp 517ndash524 1998

[29] I Musirin and T K A Rahman ldquoNovel fast voltage stabilityindex (FVSI) for voltage stability analysis in power transmissionsystemrdquo in Proceedings of the Student Conference on Researchand Development Proceedings pp 265ndash268 2002

[30] C Reis A Andrade and F P Maciel ldquoLine stability indicesfor voltage collapse predictionrdquo in Proceedings of the 2nd IEEEInternational Conference on Power Engineering Energy andElectrical Drives pp 239ndash243 March 2009

[31] X S Yang Nature-Inspired Metaheuristic Algorithms LuniverPress 2008

[32] X S Yang ldquoFirefly algorithms for multimodal optimizationrdquo inStochastic Algorithms Foundations and Applications SAGA vol5792 of Lecture Notes in Computer Sciences pp 169ndash178 2009

[33] S Łukasik and S Zak ldquoFirefly algorithm for continuousconstrained optimization task computational collective intel-ligencerdquo in Semantic Web Social Networks and Multi-AgentSystems vol 5796 of Lecture Notes in Computer Science pp 97ndash106 2009

[34] N D Reppen R R Austria J A Uhrin M C Patel and AGalatic ldquoPerformance of methods for ranking a evaluation ofvoltage collapse contingencies applied to a large-scale networkrdquoin Proceedings of the IEEE Joint International Conference pp337ndash343 1993

[35] G C Ejebe G D Irisarri S Mokhtari O Obadina PRistanovic and J Tong ldquoMethods for contingency screeningand ranking for voltage stability analysis of power systemsrdquo inProceedings of the IEEE Power Industry Computer ApplicationConference pp 249ndash255 May 1995

[36] E Vaahedi C FuchsW Xu et al ldquoVoltage stability contingencyscreening and rankingrdquo IEEE Transactions on Power Systemsvol 14 no 1 pp 256ndash265 1999

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

6 Advances in Electrical Engineering

0 5 10 15 20 25 30

Case 1

Case 2

Case 3

Loss ()

PSODE

SFLAFA

(a) For 14-bus system

0 5 10 15 20 25 30

PSODE

SFLAFA

Case 1

Case 2

Case 3

Loss ()

(b) For 30-bus system

Figure 8 Percentage of real power loss reduction under all cases

Table 1 Optimal values of FA parameters

Parameters Optimal ValuesNumber of fireflies 301205730

01120574 02120572 025119898 40119889 20Maximum iterations 100

5 Firefly Algorithm

51 Overview The firefly algorithm (FA) is a metaheuristicnature-inspired optimization algorithm which is based onthe social (flashing) behavior of fireflies or lighting bugsin the summer sky in the tropical temperature regions Itwas developed by Dr Xin-She Yang at Cambridge Universityin 2007 and it is based on the swarm behavior such asfish insects or bird schooling in nature In particularalthough the firefly algorithm has many similarities withother algorithms which are based on the so-called swarmintelligence such as the famous particle swarm optimization(PSO) artificial bee colony optimization (ABC) and bacterialforaging algorithms (BFA) it is indeed much simpler inboth concept and implementation Furthermore accordingto recent bibliography the algorithm is very efficient and canoutperform other conventional algorithms such as geneticalgorithms for solving many optimization problems a factthat has been justified in a recent research where the statisti-cal performance of the firefly algorithmwasmeasured againstother well-known optimization algorithms using variousstandard stochastic test functions Its main advantage is thefact that it uses mainly real random numbers and it is basedon the global communication among the swarming particles(ie the fireflies) and as a result it seems more effective inmultiobjective optimization such as the economic emissionsload dispatch problem in our case

The firefly algorithm has three particular idealized ruleswhich are based on some of the major flashing characteristicsof real fireflies These rules are the following

(i) All fireflies are unisex and they will move towardsmore attractive and brighter ones regardless their sex

(ii) The degree of attractiveness of a firefly is proportionalto its brightness which decreases as the distance fromthe other firefly increases due to the fact that theair absorbs light If there is no brighter or moreattractive firefly than a particular one it will thenmove randomly

(iii) The brightness or light intensity of a firefly is deter-mined by the value of the objective function of agiven problem For maximization problems the lightintensity is proportional to the value of the objectivefunction

52 Implementation

521 Attractiveness In the firefly algorithm the form ofattractiveness functions of a firefly is the following monoton-ically decreasing function

120573 (119903) = 1205730lowast exp (minus120574119903119898) with 119898 ge 1 (20)

where 119903 is the distance between any two fireflies 1205730is the

initial attractiveness at 119903 = 0 and 120574 is an absorptioncoefficient which controls the decrease of the light intensity

522 Distance The distance between any two fireflies 119894 and119895 at positions 119909

119894and 119909

119895 respectively can be defined as a

Cartesian or Euclidean distance as follows

119903119894119895=10038171003817100381710038171003817119909119894minus 119909119895

10038171003817100381710038171003817= radic

119889

sum

119896=1

(119909119894119896minus 119909119895119896)2

(21)

where 119909119894119896

is the 119896th component of the spatial coordinate 119909119894

of the 119894th firefly and 119889 is the number of dimensions we havefor 119889 = 2 we have

119903119894119895= radic(119909

119894minus 119909119895)2

+ (119910119894minus 119910119895)2

(22)

However the calculation of distance r can also be definedusing other distance metrics based on the nature of theproblem such as Manhattan distance

Advances in Electrical Engineering 7

Table 2 Voltage stability index values of most stressed lines

(a) For 14-bus system

Cases Line number Preinsertion of FACTS Postinsertion of FACTSFA SFLA DE PSO

Case 1

14 01122 00714 00818 00807 0082920 00776 00582 00537 00544 006171 00688 00447 00511 00491 0051917 00593 00310 00388 00408 005039 00515 00291 00346 00307 00401

Case 2

10 02580 01106 01722 01651 0199514 01815 00994 00991 01012 0124420 01494 00912 00941 01109 012869 01393 00833 00994 01081 011201 00799 00517 00604 00597 00661

Case 3

10 01904 01014 00941 01057 0112915 01160 00809 00802 00914 009566 00914 00529 00317 00441 005824 00793 00447 00406 00533 005519 00648 00361 00304 00369 00408

(b) For 30-bus system

Cases Line number Preinsertion of FACTS Postinsertion of FACTSFA SFLA DE PSO

Case 1

12 03691 03664 03687 03700 036835 01284 00695 01264 00987 0128213 01226 00722 00114 01169 0109515 00749 00713 00748 00752 0074914 00678 00667 00674 00676 00672

Case 2

12 03899 03861 03877 03874 038815 03596 00884 03310 00793 0331213 02549 02115 02355 02351 0239016 01687 01241 01735 01767 0161015 01255 01167 01245 01244 01249

Case 3

12 03851 03688 03864 03686 0379313 01732 01159 01766 01152 0171116 00836 00445 00855 00475 008331 00786 00540 00810 00568 0069415 00775 00741 00776 00749 00771

523 Movement The movement of a firefly 119894 which isattracted by a more attractive (ie brighter) firefly 119895 is givenby the following equation

119909119894= 119909119894+ 1205730lowast exp (minus1205741199032

119894119895) lowast (119909

119894minus 119909119895) + 120572 lowast (rand minus 1

2)

(23)

where the first term is the current position of a firefly thesecond term is used for considering a fireflyrsquos attractivenessto light intensity seen by adjacent fireflies and the third termissued for the random movement of a firefly in case there areno any brighter ones The coefficient 120572 is a randomizationparameter determined by the problem of interest while randis a random number generator uniformly distributed in the

space (01) As we will see in this implementation of thealgorithm we use 120573

0= 01 120572 isin [0 1] and the attractiveness

or absorption coefficient 120574 = 02 which guarantees a quickconvergence of the algorithm to the optimal solution Theoptimal values of firefly parameters are in Table 1

6 Results and Discussion

The proposed work is coded in MATLAB 76 platform using28GHz Intel Core 2 Duo processor based PC The methodis tested in the IEEE 14- and 30-bus test systems shownin Figure 5 The line data and bus data are taken from thestandard power system test case archive The 14-bus systemhas 5 generator buses 9 load buses and 20 transmission lines

8 Advances in Electrical Engineering

Table 3 Contingency ranking

Rank 14-bus system 30-bus systemLine number LQP values Line number LQP values

1 1 05795 5 094952 3 03826 9 060503 10 03449 2 049934 2 03157 4 049685 15 01984 7 04693

Table 4 Average load bus voltage values in pu

(a) For 14-bus system

Cases Preinsertion of FACTS Postinsertion of FACTSFA SFLA DE PSO

Case 1 10438 10517 10494 10483 10460Case 2 09890 10082 10013 10051 09966Case 3 10243 10409 10363 10331 10308

(b) For 30-bus system

Cases Preinsertion of FACTS Postinsertion of FACTSFA SFLA DE PSO

Case 1 10260 10296 10306 10288 10265Case 2 09520 09961 09664 09626 09602Case 3 10109 10380 10108 10298 10222

The 30-bus system has 6 generator buses 24 load buses and41 transmission lines System data and results are based on100 MVA and bus number 1 is the reference bus In order toverify the presentedmodels and illustrate the impact of circuitelement model of SSSC with variable susceptance model ofSVC combination study three different operating conditionsare considered as mentioned below

Case 1 The system with normal load in all the load busesis considered as normal condition and the Newton-Raphsonload flow is carried out with loading factor value equal to 1

Case 2 The system with 50 increased load in all the loadbuses is considered as a critical condition Loading of thesystem went beyond this level and results in poor voltageprofile in the load buses and unacceptable real power losslevel

Case 3 Contingency is imposed by considering the mostcritical line outage in the system This is the most suitablecondition for voltage stability analysis of a power system asvoltage stability is usually triggered by line outages

Newton-Raphson program is repeatedly run with theabsence and presence of FACTS device combination Thevoltage stability limit improvement is assessed by the valueof LQP index The voltage stability index values of topfive stressed lines under all cases with preinsertion andpostinsertion of FACTS devices are shown in Table 2 Itis evident from the table that LQP values of the stressedlines are reduced after placement of FACTS devices inthe system

For quick assessment of voltage stability limit improve-ment of the system under the three different operatingconditions sum of the LQP index values of all the linesbefore and after the insertion of FACTS devices combinationis compared in Figure 6 The reduction in the index valuethrough the proposed method indicates the best voltagestability limit improvement

The line outage is ranked according to the severity andthe severity is taken on the basis of the line quality proximityindex values and such values are arranged in descendingorder The maximum value of index indicates most criticalline for outage Line outage contingency screening andranking are carried out on the test systems and the results areshown in Table 3

It is clear from Table 3 that outage of lines numbers 1 and5 are the most critical line outages of 14- and 30-bus systemsrespectively This situation is considered for voltage stabilityimprovement Outage of other lines has not much impact onthe system and therefore they are not given importance Loadflow is run on the system with the lines that have outagesOutage of these lines results in large real power loss andvoltage profile reduction inmost of the load busesThe systemis under stressed conditions and needs to be relieved by somemeans Installation of FACTS devices at suitable locations canrelieve the system much from stressed conditions (reducedline losses)

FACTS devices help the system to maintain acceptablevoltage profile in the load buses Under normal operatingconditions most of the bus voltagemagnitudes are within thenormal value During critical and contingency conditionsvoltagemagnitude of remote load buses are below 095 (lower

Advances in Electrical Engineering 9

Table 5 Minimum-maximum load bus voltage values in pu

(a) For 14-bus system

Cases119881MIN 119881MAX

Preinsertionof FACTS Bus number Postinsertion of FACTS Preinsertion

of FACTS Bus number Postinsertion of FACTSFA SFLA DE PSO FA SFLA DE PSO

Case 1 10173 4 10252 10211 10203 10143 10604 7 10696 10673 10642 10617Case 2 09656 14 10004 09884 09933 09824 10101 7 10211 10176 10199 10155Case 3 09913 5 10264 10208 10104 10111 10350 13 10496 10490 10460 10438

(b) For 30-bus system

Cases119881MIN 119881MAX

Preinsertionof FACTS Bus number Postinsertion of FACTS Preinsertion

of FACTS Bus number Postinsertion of FACTSFA SFLA DE PSO FA SFLA DE PSO

Case 1 09953 30 09978 09976 09959 09954 10576 11 10820 10820 10820 10822Case 2 08915 30 09662 09035 09415 09410 10004 11 10667 10620 10520 10550Case 3 09661 5 10121 09600 09600 09607 10495 11 10820 10820 10820 10820

Table 6 Real power loss values comparison (in MW)

(a) For 14-bus system

Conditions Preinsertion of FACTS (initial) Postinsertion of FACTSFA SFLA DE PSO

Case 1 13401 11014 11409 11693 12106Case 2 35042 28018 28991 28875 29019Case 3 24183 18046 19255 19389 19771

(b) For 30-bus system

Conditions Preinsertion of FACTS (Initial) Postinsertion of FACTSFA SFLA DE PSO

Case 1 17514 13467 14852 16157 16504Case 2 46900 40990 45797 41258 43272Case 3 32569 22801 29272 23234 25561

bound of allowable value) These bus voltages are improvedafter the FACTS devices are installed Voltage profile valuecomparison under all cases incorporating the series-shuntFACTS devices combination is depicted separately in Figures7(a) and 7(b) under both test cases It is obvious fromthe figure that voltage profile comparison of the system isimproved better with the proposed method incorporatingFACTS devices combination The comparison of averagevalue of load bus voltage also proves the enhancing behaviorof voltage stability limit incorporating with FACTS devices ofall cases shown in Table 4 Table 5 exposes the comparisonof minimum and maximum load bus voltages in both theabsence and presence of FACTS devices under all cases

In real power loss minimization point of view throughinsertion of FACTS devices the real power loss under Case1 is decreased by 2387 and 4047MW respectively for14- and 30-bus systems In Case 2 the reduction in realpower loss rate is 7024 and 5910MW respectively Thereduction rate in real power loss is 6137 and 9768MW

respectively under Case 3 operation The real power lossvalues of proposed method compared with other impor-tant evolutionary techniques under all cases are shownin Table 6

The percentage of reduction in real power loss compari-son under all cases including both combinations is depictedin Figure 8 Obviously from the results shown in Table 6 theproposed method is more efficient than other evolutionarytechniques given here to reduce the real power lossminimiza-tion application The much reduction in real power loss andincrease in voltage magnitudes after the insertion of FACTSdevices are highly efficient in relieving a power network fromstressed condition and improving voltage stability limit Themost suitable size and location of combinations of FACTSdevices to improve the voltage stability limit and real powerloss minimization are also given in Table 7 under all caseswith 14- and 30-bus systems respectively The optimized sizeof SVC inserted with both combinations is not in larger valuewhich helps to reduce in cost

10 Advances in Electrical Engineering

Table 7 Best location and size of FACTS devices

(a) For 14-bus system

Cases Series ShuntLocation (line number) Size (degrees of compensation) Location (bus number) Size (MVar)

Case 1

FA 10 00722 + 11989501464 5 72015SFLA 4 00377 + 11989500916 12 86554DE 15 00461 + 11989501540 10 69988PSO 3 00622 + 11989501067 12 83037

Case 2

FA 12 00823 + 11989500961 13 11211SFLA 1 00536 + 11989501642 11 106217DE 9 00507 + 11989501145 12 99654PSO 11 00727 + 11989500836 10 72510

Case 3

FA 12 00769 + 11989500810 13 96817SFLA 10 00421 + 11989501162 5 106528DE 2 00489 + 11989500773 11 89207PSO 7 00673 + 11989501286 10 114368

(b) For 30-bus system

Cases Series ShuntLocation (line number) Size (degrees of compensation) Location (bus number) Size (MVar)

Case 1

FA 5 00159 + 11989500924 12 86962SFLA 1 00086 + 11989500833 19 69688DE 6 00239 + 11989502664 20 58131PSO 12 00191 + 11989500977 23 150806

Case 2

FA 6 00137 + 11989500384 17 90607SFLA 9 00170 + 11989501243 21 141058DE 5 00289 + 11989500931 30 62554PSO 8 00281 + 11989500447 18 190106

Case 3

FA 11 00311 + 11989501417 26 80115SFLA 9 00115 + 11989501302 28 67499DE 6 00112 + 11989500478 25 58559PSO 8 00291 + 11989501189 3 182640

7 Conclusion

In this paper optimal location and size of series-shunt FACTSdevices for voltage stability limit improvement and lossminimization through firefly algorithm are demonstratedThe voltage stability limit improvement and real power lossminimization are done under three operating cases suchas normal critical loading and line outage contingencyconditions The LQP index is used for voltage stabilityassessment The circuit element model of SSSC is consid-ered to improve the voltage stability limit by controllingpower flows and maintaining voltage profile This modelis easy to incorporate the effect of SSSC into Newton-Raphson load flow program codingThe variable susceptancemodel of SVC is used in a combined manner with SSSCIt is clear from the numerical results that voltage stabilitylimit improvement and real power loss minimization arehighly encouraging The real power loss minimization andvoltage stability limit improvement is remarkable by thecombined action of power flow control of SSSC and reac-tive power compensation by SVC through firefly algorithmover other evolutionary optimization techniques given inthis paper

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] T V Cutsem and C Vournas Voltage Stability of Electric PowerSystems Kluwer Academic New York NY USA 1998

[2] P Kundur Power System Stability and Control McGraw-HillNew York NY USA 1994

[3] CW Taylor Power System Voltage Stability McGraw-Hill NewYork NY USA 1994

[4] T van Cutsem ldquoVoltage instability phenomena countermea-sures and analysis methodsrdquo Proceedings of the IEEE vol 88no 2 pp 208ndash227 2000

[5] P Kessel and H Glavitsch ldquoEstimating the voltage stability ofpower systemrdquo IEEE Transactions on Power Delivery vol 1 no3 pp 346ndash354 1986

[6] H J Wan J D McCalley and V Vittal ldquoRisk based voltagesecurity assessmentrdquo IEEE Transactions on Power Systems vol15 no 4 pp 1247ndash1254 2000

Advances in Electrical Engineering 11

[7] I Dobson and H-D Chiang ldquoTowards a theory of voltagecollapse in electric power systemsrdquo Systems and Control Lettersvol 13 no 3 pp 253ndash262 1989

[8] ldquoTechnical Analysis of the August 14 2003 Blackout WhatHappened Why and What Did We Learnrdquo A report by theNorth American Electrical Reliability Council Steering GroupNew Jersey July 2004

[9] N G Hingorani and L Gyugyi Understanding FACTS Con-cepts and Technology of Flexible AC Transmission Systems IEEEPress 2000

[10] K K Sen and M L Sen Introduction to FACTS ControllersTheory Modeling and Applications IEEE Press 2009

[11] GWu A Okoyama J He and Y Yu ldquoAllocation and control ofFACTS devices for steady state stability enhancement of largescale power systemrdquo International Conference on Power SystemTechnology vol 1 pp 357ndash361 1998

[12] N Yorino E E El-Araby H Sasaki and S Harada ldquoA newformulation for FACTS allocation for security enhancementagainst voltage collapserdquo IEEE Transactions on Power Systemsvol 18 no 1 pp 3ndash10 2003

[13] S Biansoongnern S Chusanapiputt and S PhoomvuthisarnldquoOptimal SVC and TCSC placement for minimization of trans-mission lossesrdquo inProceedings of the International Conference onPower System Technology pp 1ndash5 October 2006

[14] M A Abido ldquoPower system stability enhancement usingFACTS controllers a reviewrdquo The Arabian Journal For Scienceand Engineering vol 34 no 1 pp 153ndash172 2009

[15] O L Bekri ldquoOptimal location of SVC and TCSC for voltagestability enhancementrdquo in Proceedings of the 4th InternationalPower Engineering and Optimization Conference (PEOCO rsquo10)pp 7ndash12 June 2010

[16] Y Zhang and Y Zhang ldquoA novel power injection model ofembedded SSSCwithmulti-control modes for power flow anal-ysis inclusive of practical constraintsrdquo Electric Power SystemsResearch vol 76 no 5 pp 374ndash381 2006

[17] A Sode-Yome N Mithulananthan and K Y Lee ldquoStaticvoltage stability margin enhancement using STATCOM TCSCand SSSCrdquo in Proceedings of the IEEEPES Transmission andDistribution Conference and Exhibition pp 1ndash6 August 2005

[18] C A Canizares and Z T Faur ldquoAnalysis of SVC and TCSCcontrollers in voltage collapserdquo IEEE Transactions on PowerSystems vol 14 no 1 pp 158ndash165 1999

[19] S Musunuri and G Dehnavi ldquoComparison of STAT COMSVC TCSC and SSSC performance in steady state voltagestability improvementrdquo in Proceedings of the North AmericanPower Symposium (NAPS rsquo10) pp 1ndash7 September 2010

[20] P Kundur K Morison and B Gao ldquoPractical considerations involtage stability assessmentrdquo International Journal of ElectricalPower and Energy Systems vol 15 no 4 pp 205ndash215 1993

[21] V Ajjarapu Computational Techniques for Voltage StabilityAssessment and Control Springer Science 2006

[22] S Fliscounakis P Panciatici F Capitanescu and L WehenkelldquoContingency ranking with respect to overloads in large powersystems taking into account uncertainity preventive and correc-tive actionsrdquo IEEE Transactions on Power Systems vol 28 no 4pp 4909ndash4917 2013

[23] A Y Abdelaziz A T M Taha M A Mostafa and A MHassan ldquoPower systen contingency ranking using fuzzy logicbased approachrdquo International Journal of Intelligent Systems andApplications no 2 pp 24ndash28 2013

[24] P S Venkataramu and T Ananthapadmanabha ldquoInstallationof unified power flow controller for voltage stability margin

enhancement under line outage contingenciesrdquo Iranian Journalof Electrical and Computer Engineering vol 5 no 2 pp 90ndash962006

[25] M Jarsquofari and S Afsharnia ldquoVoltage stability enhancementin contingency conditions using shunt FACTS devicesrdquo inProceedings of the EUROCON The International Conference onComputer as a Tool pp 1660ndash1665 September 2007

[26] P-A Loef G Andersson and D J Hill ldquoVoltage stabilityindices for stressed power systemsrdquo IEEE Transactions on PowerSystems vol 8 no 1 pp 326ndash335 1993

[27] M Moghavvemi and F M Omar ldquoTechnique for contingencymonitoring and voltage collapse predictionrdquo IEE Proceedings onGeneration Transmission and Distribution vol 145 no 6 pp634ndash640 1998

[28] M Moghavvemi and O Faruque ldquoReal time contingency eval-uation and ranking techniquerdquo IEE Proceedings on GenerationTransmission and Distribution vol 145 no 5 pp 517ndash524 1998

[29] I Musirin and T K A Rahman ldquoNovel fast voltage stabilityindex (FVSI) for voltage stability analysis in power transmissionsystemrdquo in Proceedings of the Student Conference on Researchand Development Proceedings pp 265ndash268 2002

[30] C Reis A Andrade and F P Maciel ldquoLine stability indicesfor voltage collapse predictionrdquo in Proceedings of the 2nd IEEEInternational Conference on Power Engineering Energy andElectrical Drives pp 239ndash243 March 2009

[31] X S Yang Nature-Inspired Metaheuristic Algorithms LuniverPress 2008

[32] X S Yang ldquoFirefly algorithms for multimodal optimizationrdquo inStochastic Algorithms Foundations and Applications SAGA vol5792 of Lecture Notes in Computer Sciences pp 169ndash178 2009

[33] S Łukasik and S Zak ldquoFirefly algorithm for continuousconstrained optimization task computational collective intel-ligencerdquo in Semantic Web Social Networks and Multi-AgentSystems vol 5796 of Lecture Notes in Computer Science pp 97ndash106 2009

[34] N D Reppen R R Austria J A Uhrin M C Patel and AGalatic ldquoPerformance of methods for ranking a evaluation ofvoltage collapse contingencies applied to a large-scale networkrdquoin Proceedings of the IEEE Joint International Conference pp337ndash343 1993

[35] G C Ejebe G D Irisarri S Mokhtari O Obadina PRistanovic and J Tong ldquoMethods for contingency screeningand ranking for voltage stability analysis of power systemsrdquo inProceedings of the IEEE Power Industry Computer ApplicationConference pp 249ndash255 May 1995

[36] E Vaahedi C FuchsW Xu et al ldquoVoltage stability contingencyscreening and rankingrdquo IEEE Transactions on Power Systemsvol 14 no 1 pp 256ndash265 1999

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International Journal of

Advances in Electrical Engineering 7

Table 2 Voltage stability index values of most stressed lines

(a) For 14-bus system

Cases Line number Preinsertion of FACTS Postinsertion of FACTSFA SFLA DE PSO

Case 1

14 01122 00714 00818 00807 0082920 00776 00582 00537 00544 006171 00688 00447 00511 00491 0051917 00593 00310 00388 00408 005039 00515 00291 00346 00307 00401

Case 2

10 02580 01106 01722 01651 0199514 01815 00994 00991 01012 0124420 01494 00912 00941 01109 012869 01393 00833 00994 01081 011201 00799 00517 00604 00597 00661

Case 3

10 01904 01014 00941 01057 0112915 01160 00809 00802 00914 009566 00914 00529 00317 00441 005824 00793 00447 00406 00533 005519 00648 00361 00304 00369 00408

(b) For 30-bus system

Cases Line number Preinsertion of FACTS Postinsertion of FACTSFA SFLA DE PSO

Case 1

12 03691 03664 03687 03700 036835 01284 00695 01264 00987 0128213 01226 00722 00114 01169 0109515 00749 00713 00748 00752 0074914 00678 00667 00674 00676 00672

Case 2

12 03899 03861 03877 03874 038815 03596 00884 03310 00793 0331213 02549 02115 02355 02351 0239016 01687 01241 01735 01767 0161015 01255 01167 01245 01244 01249

Case 3

12 03851 03688 03864 03686 0379313 01732 01159 01766 01152 0171116 00836 00445 00855 00475 008331 00786 00540 00810 00568 0069415 00775 00741 00776 00749 00771

523 Movement The movement of a firefly 119894 which isattracted by a more attractive (ie brighter) firefly 119895 is givenby the following equation

119909119894= 119909119894+ 1205730lowast exp (minus1205741199032

119894119895) lowast (119909

119894minus 119909119895) + 120572 lowast (rand minus 1

2)

(23)

where the first term is the current position of a firefly thesecond term is used for considering a fireflyrsquos attractivenessto light intensity seen by adjacent fireflies and the third termissued for the random movement of a firefly in case there areno any brighter ones The coefficient 120572 is a randomizationparameter determined by the problem of interest while randis a random number generator uniformly distributed in the

space (01) As we will see in this implementation of thealgorithm we use 120573

0= 01 120572 isin [0 1] and the attractiveness

or absorption coefficient 120574 = 02 which guarantees a quickconvergence of the algorithm to the optimal solution Theoptimal values of firefly parameters are in Table 1

6 Results and Discussion

The proposed work is coded in MATLAB 76 platform using28GHz Intel Core 2 Duo processor based PC The methodis tested in the IEEE 14- and 30-bus test systems shownin Figure 5 The line data and bus data are taken from thestandard power system test case archive The 14-bus systemhas 5 generator buses 9 load buses and 20 transmission lines

8 Advances in Electrical Engineering

Table 3 Contingency ranking

Rank 14-bus system 30-bus systemLine number LQP values Line number LQP values

1 1 05795 5 094952 3 03826 9 060503 10 03449 2 049934 2 03157 4 049685 15 01984 7 04693

Table 4 Average load bus voltage values in pu

(a) For 14-bus system

Cases Preinsertion of FACTS Postinsertion of FACTSFA SFLA DE PSO

Case 1 10438 10517 10494 10483 10460Case 2 09890 10082 10013 10051 09966Case 3 10243 10409 10363 10331 10308

(b) For 30-bus system

Cases Preinsertion of FACTS Postinsertion of FACTSFA SFLA DE PSO

Case 1 10260 10296 10306 10288 10265Case 2 09520 09961 09664 09626 09602Case 3 10109 10380 10108 10298 10222

The 30-bus system has 6 generator buses 24 load buses and41 transmission lines System data and results are based on100 MVA and bus number 1 is the reference bus In order toverify the presentedmodels and illustrate the impact of circuitelement model of SSSC with variable susceptance model ofSVC combination study three different operating conditionsare considered as mentioned below

Case 1 The system with normal load in all the load busesis considered as normal condition and the Newton-Raphsonload flow is carried out with loading factor value equal to 1

Case 2 The system with 50 increased load in all the loadbuses is considered as a critical condition Loading of thesystem went beyond this level and results in poor voltageprofile in the load buses and unacceptable real power losslevel

Case 3 Contingency is imposed by considering the mostcritical line outage in the system This is the most suitablecondition for voltage stability analysis of a power system asvoltage stability is usually triggered by line outages

Newton-Raphson program is repeatedly run with theabsence and presence of FACTS device combination Thevoltage stability limit improvement is assessed by the valueof LQP index The voltage stability index values of topfive stressed lines under all cases with preinsertion andpostinsertion of FACTS devices are shown in Table 2 Itis evident from the table that LQP values of the stressedlines are reduced after placement of FACTS devices inthe system

For quick assessment of voltage stability limit improve-ment of the system under the three different operatingconditions sum of the LQP index values of all the linesbefore and after the insertion of FACTS devices combinationis compared in Figure 6 The reduction in the index valuethrough the proposed method indicates the best voltagestability limit improvement

The line outage is ranked according to the severity andthe severity is taken on the basis of the line quality proximityindex values and such values are arranged in descendingorder The maximum value of index indicates most criticalline for outage Line outage contingency screening andranking are carried out on the test systems and the results areshown in Table 3

It is clear from Table 3 that outage of lines numbers 1 and5 are the most critical line outages of 14- and 30-bus systemsrespectively This situation is considered for voltage stabilityimprovement Outage of other lines has not much impact onthe system and therefore they are not given importance Loadflow is run on the system with the lines that have outagesOutage of these lines results in large real power loss andvoltage profile reduction inmost of the load busesThe systemis under stressed conditions and needs to be relieved by somemeans Installation of FACTS devices at suitable locations canrelieve the system much from stressed conditions (reducedline losses)

FACTS devices help the system to maintain acceptablevoltage profile in the load buses Under normal operatingconditions most of the bus voltagemagnitudes are within thenormal value During critical and contingency conditionsvoltagemagnitude of remote load buses are below 095 (lower

Advances in Electrical Engineering 9

Table 5 Minimum-maximum load bus voltage values in pu

(a) For 14-bus system

Cases119881MIN 119881MAX

Preinsertionof FACTS Bus number Postinsertion of FACTS Preinsertion

of FACTS Bus number Postinsertion of FACTSFA SFLA DE PSO FA SFLA DE PSO

Case 1 10173 4 10252 10211 10203 10143 10604 7 10696 10673 10642 10617Case 2 09656 14 10004 09884 09933 09824 10101 7 10211 10176 10199 10155Case 3 09913 5 10264 10208 10104 10111 10350 13 10496 10490 10460 10438

(b) For 30-bus system

Cases119881MIN 119881MAX

Preinsertionof FACTS Bus number Postinsertion of FACTS Preinsertion

of FACTS Bus number Postinsertion of FACTSFA SFLA DE PSO FA SFLA DE PSO

Case 1 09953 30 09978 09976 09959 09954 10576 11 10820 10820 10820 10822Case 2 08915 30 09662 09035 09415 09410 10004 11 10667 10620 10520 10550Case 3 09661 5 10121 09600 09600 09607 10495 11 10820 10820 10820 10820

Table 6 Real power loss values comparison (in MW)

(a) For 14-bus system

Conditions Preinsertion of FACTS (initial) Postinsertion of FACTSFA SFLA DE PSO

Case 1 13401 11014 11409 11693 12106Case 2 35042 28018 28991 28875 29019Case 3 24183 18046 19255 19389 19771

(b) For 30-bus system

Conditions Preinsertion of FACTS (Initial) Postinsertion of FACTSFA SFLA DE PSO

Case 1 17514 13467 14852 16157 16504Case 2 46900 40990 45797 41258 43272Case 3 32569 22801 29272 23234 25561

bound of allowable value) These bus voltages are improvedafter the FACTS devices are installed Voltage profile valuecomparison under all cases incorporating the series-shuntFACTS devices combination is depicted separately in Figures7(a) and 7(b) under both test cases It is obvious fromthe figure that voltage profile comparison of the system isimproved better with the proposed method incorporatingFACTS devices combination The comparison of averagevalue of load bus voltage also proves the enhancing behaviorof voltage stability limit incorporating with FACTS devices ofall cases shown in Table 4 Table 5 exposes the comparisonof minimum and maximum load bus voltages in both theabsence and presence of FACTS devices under all cases

In real power loss minimization point of view throughinsertion of FACTS devices the real power loss under Case1 is decreased by 2387 and 4047MW respectively for14- and 30-bus systems In Case 2 the reduction in realpower loss rate is 7024 and 5910MW respectively Thereduction rate in real power loss is 6137 and 9768MW

respectively under Case 3 operation The real power lossvalues of proposed method compared with other impor-tant evolutionary techniques under all cases are shownin Table 6

The percentage of reduction in real power loss compari-son under all cases including both combinations is depictedin Figure 8 Obviously from the results shown in Table 6 theproposed method is more efficient than other evolutionarytechniques given here to reduce the real power lossminimiza-tion application The much reduction in real power loss andincrease in voltage magnitudes after the insertion of FACTSdevices are highly efficient in relieving a power network fromstressed condition and improving voltage stability limit Themost suitable size and location of combinations of FACTSdevices to improve the voltage stability limit and real powerloss minimization are also given in Table 7 under all caseswith 14- and 30-bus systems respectively The optimized sizeof SVC inserted with both combinations is not in larger valuewhich helps to reduce in cost

10 Advances in Electrical Engineering

Table 7 Best location and size of FACTS devices

(a) For 14-bus system

Cases Series ShuntLocation (line number) Size (degrees of compensation) Location (bus number) Size (MVar)

Case 1

FA 10 00722 + 11989501464 5 72015SFLA 4 00377 + 11989500916 12 86554DE 15 00461 + 11989501540 10 69988PSO 3 00622 + 11989501067 12 83037

Case 2

FA 12 00823 + 11989500961 13 11211SFLA 1 00536 + 11989501642 11 106217DE 9 00507 + 11989501145 12 99654PSO 11 00727 + 11989500836 10 72510

Case 3

FA 12 00769 + 11989500810 13 96817SFLA 10 00421 + 11989501162 5 106528DE 2 00489 + 11989500773 11 89207PSO 7 00673 + 11989501286 10 114368

(b) For 30-bus system

Cases Series ShuntLocation (line number) Size (degrees of compensation) Location (bus number) Size (MVar)

Case 1

FA 5 00159 + 11989500924 12 86962SFLA 1 00086 + 11989500833 19 69688DE 6 00239 + 11989502664 20 58131PSO 12 00191 + 11989500977 23 150806

Case 2

FA 6 00137 + 11989500384 17 90607SFLA 9 00170 + 11989501243 21 141058DE 5 00289 + 11989500931 30 62554PSO 8 00281 + 11989500447 18 190106

Case 3

FA 11 00311 + 11989501417 26 80115SFLA 9 00115 + 11989501302 28 67499DE 6 00112 + 11989500478 25 58559PSO 8 00291 + 11989501189 3 182640

7 Conclusion

In this paper optimal location and size of series-shunt FACTSdevices for voltage stability limit improvement and lossminimization through firefly algorithm are demonstratedThe voltage stability limit improvement and real power lossminimization are done under three operating cases suchas normal critical loading and line outage contingencyconditions The LQP index is used for voltage stabilityassessment The circuit element model of SSSC is consid-ered to improve the voltage stability limit by controllingpower flows and maintaining voltage profile This modelis easy to incorporate the effect of SSSC into Newton-Raphson load flow program codingThe variable susceptancemodel of SVC is used in a combined manner with SSSCIt is clear from the numerical results that voltage stabilitylimit improvement and real power loss minimization arehighly encouraging The real power loss minimization andvoltage stability limit improvement is remarkable by thecombined action of power flow control of SSSC and reac-tive power compensation by SVC through firefly algorithmover other evolutionary optimization techniques given inthis paper

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] T V Cutsem and C Vournas Voltage Stability of Electric PowerSystems Kluwer Academic New York NY USA 1998

[2] P Kundur Power System Stability and Control McGraw-HillNew York NY USA 1994

[3] CW Taylor Power System Voltage Stability McGraw-Hill NewYork NY USA 1994

[4] T van Cutsem ldquoVoltage instability phenomena countermea-sures and analysis methodsrdquo Proceedings of the IEEE vol 88no 2 pp 208ndash227 2000

[5] P Kessel and H Glavitsch ldquoEstimating the voltage stability ofpower systemrdquo IEEE Transactions on Power Delivery vol 1 no3 pp 346ndash354 1986

[6] H J Wan J D McCalley and V Vittal ldquoRisk based voltagesecurity assessmentrdquo IEEE Transactions on Power Systems vol15 no 4 pp 1247ndash1254 2000

Advances in Electrical Engineering 11

[7] I Dobson and H-D Chiang ldquoTowards a theory of voltagecollapse in electric power systemsrdquo Systems and Control Lettersvol 13 no 3 pp 253ndash262 1989

[8] ldquoTechnical Analysis of the August 14 2003 Blackout WhatHappened Why and What Did We Learnrdquo A report by theNorth American Electrical Reliability Council Steering GroupNew Jersey July 2004

[9] N G Hingorani and L Gyugyi Understanding FACTS Con-cepts and Technology of Flexible AC Transmission Systems IEEEPress 2000

[10] K K Sen and M L Sen Introduction to FACTS ControllersTheory Modeling and Applications IEEE Press 2009

[11] GWu A Okoyama J He and Y Yu ldquoAllocation and control ofFACTS devices for steady state stability enhancement of largescale power systemrdquo International Conference on Power SystemTechnology vol 1 pp 357ndash361 1998

[12] N Yorino E E El-Araby H Sasaki and S Harada ldquoA newformulation for FACTS allocation for security enhancementagainst voltage collapserdquo IEEE Transactions on Power Systemsvol 18 no 1 pp 3ndash10 2003

[13] S Biansoongnern S Chusanapiputt and S PhoomvuthisarnldquoOptimal SVC and TCSC placement for minimization of trans-mission lossesrdquo inProceedings of the International Conference onPower System Technology pp 1ndash5 October 2006

[14] M A Abido ldquoPower system stability enhancement usingFACTS controllers a reviewrdquo The Arabian Journal For Scienceand Engineering vol 34 no 1 pp 153ndash172 2009

[15] O L Bekri ldquoOptimal location of SVC and TCSC for voltagestability enhancementrdquo in Proceedings of the 4th InternationalPower Engineering and Optimization Conference (PEOCO rsquo10)pp 7ndash12 June 2010

[16] Y Zhang and Y Zhang ldquoA novel power injection model ofembedded SSSCwithmulti-control modes for power flow anal-ysis inclusive of practical constraintsrdquo Electric Power SystemsResearch vol 76 no 5 pp 374ndash381 2006

[17] A Sode-Yome N Mithulananthan and K Y Lee ldquoStaticvoltage stability margin enhancement using STATCOM TCSCand SSSCrdquo in Proceedings of the IEEEPES Transmission andDistribution Conference and Exhibition pp 1ndash6 August 2005

[18] C A Canizares and Z T Faur ldquoAnalysis of SVC and TCSCcontrollers in voltage collapserdquo IEEE Transactions on PowerSystems vol 14 no 1 pp 158ndash165 1999

[19] S Musunuri and G Dehnavi ldquoComparison of STAT COMSVC TCSC and SSSC performance in steady state voltagestability improvementrdquo in Proceedings of the North AmericanPower Symposium (NAPS rsquo10) pp 1ndash7 September 2010

[20] P Kundur K Morison and B Gao ldquoPractical considerations involtage stability assessmentrdquo International Journal of ElectricalPower and Energy Systems vol 15 no 4 pp 205ndash215 1993

[21] V Ajjarapu Computational Techniques for Voltage StabilityAssessment and Control Springer Science 2006

[22] S Fliscounakis P Panciatici F Capitanescu and L WehenkelldquoContingency ranking with respect to overloads in large powersystems taking into account uncertainity preventive and correc-tive actionsrdquo IEEE Transactions on Power Systems vol 28 no 4pp 4909ndash4917 2013

[23] A Y Abdelaziz A T M Taha M A Mostafa and A MHassan ldquoPower systen contingency ranking using fuzzy logicbased approachrdquo International Journal of Intelligent Systems andApplications no 2 pp 24ndash28 2013

[24] P S Venkataramu and T Ananthapadmanabha ldquoInstallationof unified power flow controller for voltage stability margin

enhancement under line outage contingenciesrdquo Iranian Journalof Electrical and Computer Engineering vol 5 no 2 pp 90ndash962006

[25] M Jarsquofari and S Afsharnia ldquoVoltage stability enhancementin contingency conditions using shunt FACTS devicesrdquo inProceedings of the EUROCON The International Conference onComputer as a Tool pp 1660ndash1665 September 2007

[26] P-A Loef G Andersson and D J Hill ldquoVoltage stabilityindices for stressed power systemsrdquo IEEE Transactions on PowerSystems vol 8 no 1 pp 326ndash335 1993

[27] M Moghavvemi and F M Omar ldquoTechnique for contingencymonitoring and voltage collapse predictionrdquo IEE Proceedings onGeneration Transmission and Distribution vol 145 no 6 pp634ndash640 1998

[28] M Moghavvemi and O Faruque ldquoReal time contingency eval-uation and ranking techniquerdquo IEE Proceedings on GenerationTransmission and Distribution vol 145 no 5 pp 517ndash524 1998

[29] I Musirin and T K A Rahman ldquoNovel fast voltage stabilityindex (FVSI) for voltage stability analysis in power transmissionsystemrdquo in Proceedings of the Student Conference on Researchand Development Proceedings pp 265ndash268 2002

[30] C Reis A Andrade and F P Maciel ldquoLine stability indicesfor voltage collapse predictionrdquo in Proceedings of the 2nd IEEEInternational Conference on Power Engineering Energy andElectrical Drives pp 239ndash243 March 2009

[31] X S Yang Nature-Inspired Metaheuristic Algorithms LuniverPress 2008

[32] X S Yang ldquoFirefly algorithms for multimodal optimizationrdquo inStochastic Algorithms Foundations and Applications SAGA vol5792 of Lecture Notes in Computer Sciences pp 169ndash178 2009

[33] S Łukasik and S Zak ldquoFirefly algorithm for continuousconstrained optimization task computational collective intel-ligencerdquo in Semantic Web Social Networks and Multi-AgentSystems vol 5796 of Lecture Notes in Computer Science pp 97ndash106 2009

[34] N D Reppen R R Austria J A Uhrin M C Patel and AGalatic ldquoPerformance of methods for ranking a evaluation ofvoltage collapse contingencies applied to a large-scale networkrdquoin Proceedings of the IEEE Joint International Conference pp337ndash343 1993

[35] G C Ejebe G D Irisarri S Mokhtari O Obadina PRistanovic and J Tong ldquoMethods for contingency screeningand ranking for voltage stability analysis of power systemsrdquo inProceedings of the IEEE Power Industry Computer ApplicationConference pp 249ndash255 May 1995

[36] E Vaahedi C FuchsW Xu et al ldquoVoltage stability contingencyscreening and rankingrdquo IEEE Transactions on Power Systemsvol 14 no 1 pp 256ndash265 1999

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

8 Advances in Electrical Engineering

Table 3 Contingency ranking

Rank 14-bus system 30-bus systemLine number LQP values Line number LQP values

1 1 05795 5 094952 3 03826 9 060503 10 03449 2 049934 2 03157 4 049685 15 01984 7 04693

Table 4 Average load bus voltage values in pu

(a) For 14-bus system

Cases Preinsertion of FACTS Postinsertion of FACTSFA SFLA DE PSO

Case 1 10438 10517 10494 10483 10460Case 2 09890 10082 10013 10051 09966Case 3 10243 10409 10363 10331 10308

(b) For 30-bus system

Cases Preinsertion of FACTS Postinsertion of FACTSFA SFLA DE PSO

Case 1 10260 10296 10306 10288 10265Case 2 09520 09961 09664 09626 09602Case 3 10109 10380 10108 10298 10222

The 30-bus system has 6 generator buses 24 load buses and41 transmission lines System data and results are based on100 MVA and bus number 1 is the reference bus In order toverify the presentedmodels and illustrate the impact of circuitelement model of SSSC with variable susceptance model ofSVC combination study three different operating conditionsare considered as mentioned below

Case 1 The system with normal load in all the load busesis considered as normal condition and the Newton-Raphsonload flow is carried out with loading factor value equal to 1

Case 2 The system with 50 increased load in all the loadbuses is considered as a critical condition Loading of thesystem went beyond this level and results in poor voltageprofile in the load buses and unacceptable real power losslevel

Case 3 Contingency is imposed by considering the mostcritical line outage in the system This is the most suitablecondition for voltage stability analysis of a power system asvoltage stability is usually triggered by line outages

Newton-Raphson program is repeatedly run with theabsence and presence of FACTS device combination Thevoltage stability limit improvement is assessed by the valueof LQP index The voltage stability index values of topfive stressed lines under all cases with preinsertion andpostinsertion of FACTS devices are shown in Table 2 Itis evident from the table that LQP values of the stressedlines are reduced after placement of FACTS devices inthe system

For quick assessment of voltage stability limit improve-ment of the system under the three different operatingconditions sum of the LQP index values of all the linesbefore and after the insertion of FACTS devices combinationis compared in Figure 6 The reduction in the index valuethrough the proposed method indicates the best voltagestability limit improvement

The line outage is ranked according to the severity andthe severity is taken on the basis of the line quality proximityindex values and such values are arranged in descendingorder The maximum value of index indicates most criticalline for outage Line outage contingency screening andranking are carried out on the test systems and the results areshown in Table 3

It is clear from Table 3 that outage of lines numbers 1 and5 are the most critical line outages of 14- and 30-bus systemsrespectively This situation is considered for voltage stabilityimprovement Outage of other lines has not much impact onthe system and therefore they are not given importance Loadflow is run on the system with the lines that have outagesOutage of these lines results in large real power loss andvoltage profile reduction inmost of the load busesThe systemis under stressed conditions and needs to be relieved by somemeans Installation of FACTS devices at suitable locations canrelieve the system much from stressed conditions (reducedline losses)

FACTS devices help the system to maintain acceptablevoltage profile in the load buses Under normal operatingconditions most of the bus voltagemagnitudes are within thenormal value During critical and contingency conditionsvoltagemagnitude of remote load buses are below 095 (lower

Advances in Electrical Engineering 9

Table 5 Minimum-maximum load bus voltage values in pu

(a) For 14-bus system

Cases119881MIN 119881MAX

Preinsertionof FACTS Bus number Postinsertion of FACTS Preinsertion

of FACTS Bus number Postinsertion of FACTSFA SFLA DE PSO FA SFLA DE PSO

Case 1 10173 4 10252 10211 10203 10143 10604 7 10696 10673 10642 10617Case 2 09656 14 10004 09884 09933 09824 10101 7 10211 10176 10199 10155Case 3 09913 5 10264 10208 10104 10111 10350 13 10496 10490 10460 10438

(b) For 30-bus system

Cases119881MIN 119881MAX

Preinsertionof FACTS Bus number Postinsertion of FACTS Preinsertion

of FACTS Bus number Postinsertion of FACTSFA SFLA DE PSO FA SFLA DE PSO

Case 1 09953 30 09978 09976 09959 09954 10576 11 10820 10820 10820 10822Case 2 08915 30 09662 09035 09415 09410 10004 11 10667 10620 10520 10550Case 3 09661 5 10121 09600 09600 09607 10495 11 10820 10820 10820 10820

Table 6 Real power loss values comparison (in MW)

(a) For 14-bus system

Conditions Preinsertion of FACTS (initial) Postinsertion of FACTSFA SFLA DE PSO

Case 1 13401 11014 11409 11693 12106Case 2 35042 28018 28991 28875 29019Case 3 24183 18046 19255 19389 19771

(b) For 30-bus system

Conditions Preinsertion of FACTS (Initial) Postinsertion of FACTSFA SFLA DE PSO

Case 1 17514 13467 14852 16157 16504Case 2 46900 40990 45797 41258 43272Case 3 32569 22801 29272 23234 25561

bound of allowable value) These bus voltages are improvedafter the FACTS devices are installed Voltage profile valuecomparison under all cases incorporating the series-shuntFACTS devices combination is depicted separately in Figures7(a) and 7(b) under both test cases It is obvious fromthe figure that voltage profile comparison of the system isimproved better with the proposed method incorporatingFACTS devices combination The comparison of averagevalue of load bus voltage also proves the enhancing behaviorof voltage stability limit incorporating with FACTS devices ofall cases shown in Table 4 Table 5 exposes the comparisonof minimum and maximum load bus voltages in both theabsence and presence of FACTS devices under all cases

In real power loss minimization point of view throughinsertion of FACTS devices the real power loss under Case1 is decreased by 2387 and 4047MW respectively for14- and 30-bus systems In Case 2 the reduction in realpower loss rate is 7024 and 5910MW respectively Thereduction rate in real power loss is 6137 and 9768MW

respectively under Case 3 operation The real power lossvalues of proposed method compared with other impor-tant evolutionary techniques under all cases are shownin Table 6

The percentage of reduction in real power loss compari-son under all cases including both combinations is depictedin Figure 8 Obviously from the results shown in Table 6 theproposed method is more efficient than other evolutionarytechniques given here to reduce the real power lossminimiza-tion application The much reduction in real power loss andincrease in voltage magnitudes after the insertion of FACTSdevices are highly efficient in relieving a power network fromstressed condition and improving voltage stability limit Themost suitable size and location of combinations of FACTSdevices to improve the voltage stability limit and real powerloss minimization are also given in Table 7 under all caseswith 14- and 30-bus systems respectively The optimized sizeof SVC inserted with both combinations is not in larger valuewhich helps to reduce in cost

10 Advances in Electrical Engineering

Table 7 Best location and size of FACTS devices

(a) For 14-bus system

Cases Series ShuntLocation (line number) Size (degrees of compensation) Location (bus number) Size (MVar)

Case 1

FA 10 00722 + 11989501464 5 72015SFLA 4 00377 + 11989500916 12 86554DE 15 00461 + 11989501540 10 69988PSO 3 00622 + 11989501067 12 83037

Case 2

FA 12 00823 + 11989500961 13 11211SFLA 1 00536 + 11989501642 11 106217DE 9 00507 + 11989501145 12 99654PSO 11 00727 + 11989500836 10 72510

Case 3

FA 12 00769 + 11989500810 13 96817SFLA 10 00421 + 11989501162 5 106528DE 2 00489 + 11989500773 11 89207PSO 7 00673 + 11989501286 10 114368

(b) For 30-bus system

Cases Series ShuntLocation (line number) Size (degrees of compensation) Location (bus number) Size (MVar)

Case 1

FA 5 00159 + 11989500924 12 86962SFLA 1 00086 + 11989500833 19 69688DE 6 00239 + 11989502664 20 58131PSO 12 00191 + 11989500977 23 150806

Case 2

FA 6 00137 + 11989500384 17 90607SFLA 9 00170 + 11989501243 21 141058DE 5 00289 + 11989500931 30 62554PSO 8 00281 + 11989500447 18 190106

Case 3

FA 11 00311 + 11989501417 26 80115SFLA 9 00115 + 11989501302 28 67499DE 6 00112 + 11989500478 25 58559PSO 8 00291 + 11989501189 3 182640

7 Conclusion

In this paper optimal location and size of series-shunt FACTSdevices for voltage stability limit improvement and lossminimization through firefly algorithm are demonstratedThe voltage stability limit improvement and real power lossminimization are done under three operating cases suchas normal critical loading and line outage contingencyconditions The LQP index is used for voltage stabilityassessment The circuit element model of SSSC is consid-ered to improve the voltage stability limit by controllingpower flows and maintaining voltage profile This modelis easy to incorporate the effect of SSSC into Newton-Raphson load flow program codingThe variable susceptancemodel of SVC is used in a combined manner with SSSCIt is clear from the numerical results that voltage stabilitylimit improvement and real power loss minimization arehighly encouraging The real power loss minimization andvoltage stability limit improvement is remarkable by thecombined action of power flow control of SSSC and reac-tive power compensation by SVC through firefly algorithmover other evolutionary optimization techniques given inthis paper

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] T V Cutsem and C Vournas Voltage Stability of Electric PowerSystems Kluwer Academic New York NY USA 1998

[2] P Kundur Power System Stability and Control McGraw-HillNew York NY USA 1994

[3] CW Taylor Power System Voltage Stability McGraw-Hill NewYork NY USA 1994

[4] T van Cutsem ldquoVoltage instability phenomena countermea-sures and analysis methodsrdquo Proceedings of the IEEE vol 88no 2 pp 208ndash227 2000

[5] P Kessel and H Glavitsch ldquoEstimating the voltage stability ofpower systemrdquo IEEE Transactions on Power Delivery vol 1 no3 pp 346ndash354 1986

[6] H J Wan J D McCalley and V Vittal ldquoRisk based voltagesecurity assessmentrdquo IEEE Transactions on Power Systems vol15 no 4 pp 1247ndash1254 2000

Advances in Electrical Engineering 11

[7] I Dobson and H-D Chiang ldquoTowards a theory of voltagecollapse in electric power systemsrdquo Systems and Control Lettersvol 13 no 3 pp 253ndash262 1989

[8] ldquoTechnical Analysis of the August 14 2003 Blackout WhatHappened Why and What Did We Learnrdquo A report by theNorth American Electrical Reliability Council Steering GroupNew Jersey July 2004

[9] N G Hingorani and L Gyugyi Understanding FACTS Con-cepts and Technology of Flexible AC Transmission Systems IEEEPress 2000

[10] K K Sen and M L Sen Introduction to FACTS ControllersTheory Modeling and Applications IEEE Press 2009

[11] GWu A Okoyama J He and Y Yu ldquoAllocation and control ofFACTS devices for steady state stability enhancement of largescale power systemrdquo International Conference on Power SystemTechnology vol 1 pp 357ndash361 1998

[12] N Yorino E E El-Araby H Sasaki and S Harada ldquoA newformulation for FACTS allocation for security enhancementagainst voltage collapserdquo IEEE Transactions on Power Systemsvol 18 no 1 pp 3ndash10 2003

[13] S Biansoongnern S Chusanapiputt and S PhoomvuthisarnldquoOptimal SVC and TCSC placement for minimization of trans-mission lossesrdquo inProceedings of the International Conference onPower System Technology pp 1ndash5 October 2006

[14] M A Abido ldquoPower system stability enhancement usingFACTS controllers a reviewrdquo The Arabian Journal For Scienceand Engineering vol 34 no 1 pp 153ndash172 2009

[15] O L Bekri ldquoOptimal location of SVC and TCSC for voltagestability enhancementrdquo in Proceedings of the 4th InternationalPower Engineering and Optimization Conference (PEOCO rsquo10)pp 7ndash12 June 2010

[16] Y Zhang and Y Zhang ldquoA novel power injection model ofembedded SSSCwithmulti-control modes for power flow anal-ysis inclusive of practical constraintsrdquo Electric Power SystemsResearch vol 76 no 5 pp 374ndash381 2006

[17] A Sode-Yome N Mithulananthan and K Y Lee ldquoStaticvoltage stability margin enhancement using STATCOM TCSCand SSSCrdquo in Proceedings of the IEEEPES Transmission andDistribution Conference and Exhibition pp 1ndash6 August 2005

[18] C A Canizares and Z T Faur ldquoAnalysis of SVC and TCSCcontrollers in voltage collapserdquo IEEE Transactions on PowerSystems vol 14 no 1 pp 158ndash165 1999

[19] S Musunuri and G Dehnavi ldquoComparison of STAT COMSVC TCSC and SSSC performance in steady state voltagestability improvementrdquo in Proceedings of the North AmericanPower Symposium (NAPS rsquo10) pp 1ndash7 September 2010

[20] P Kundur K Morison and B Gao ldquoPractical considerations involtage stability assessmentrdquo International Journal of ElectricalPower and Energy Systems vol 15 no 4 pp 205ndash215 1993

[21] V Ajjarapu Computational Techniques for Voltage StabilityAssessment and Control Springer Science 2006

[22] S Fliscounakis P Panciatici F Capitanescu and L WehenkelldquoContingency ranking with respect to overloads in large powersystems taking into account uncertainity preventive and correc-tive actionsrdquo IEEE Transactions on Power Systems vol 28 no 4pp 4909ndash4917 2013

[23] A Y Abdelaziz A T M Taha M A Mostafa and A MHassan ldquoPower systen contingency ranking using fuzzy logicbased approachrdquo International Journal of Intelligent Systems andApplications no 2 pp 24ndash28 2013

[24] P S Venkataramu and T Ananthapadmanabha ldquoInstallationof unified power flow controller for voltage stability margin

enhancement under line outage contingenciesrdquo Iranian Journalof Electrical and Computer Engineering vol 5 no 2 pp 90ndash962006

[25] M Jarsquofari and S Afsharnia ldquoVoltage stability enhancementin contingency conditions using shunt FACTS devicesrdquo inProceedings of the EUROCON The International Conference onComputer as a Tool pp 1660ndash1665 September 2007

[26] P-A Loef G Andersson and D J Hill ldquoVoltage stabilityindices for stressed power systemsrdquo IEEE Transactions on PowerSystems vol 8 no 1 pp 326ndash335 1993

[27] M Moghavvemi and F M Omar ldquoTechnique for contingencymonitoring and voltage collapse predictionrdquo IEE Proceedings onGeneration Transmission and Distribution vol 145 no 6 pp634ndash640 1998

[28] M Moghavvemi and O Faruque ldquoReal time contingency eval-uation and ranking techniquerdquo IEE Proceedings on GenerationTransmission and Distribution vol 145 no 5 pp 517ndash524 1998

[29] I Musirin and T K A Rahman ldquoNovel fast voltage stabilityindex (FVSI) for voltage stability analysis in power transmissionsystemrdquo in Proceedings of the Student Conference on Researchand Development Proceedings pp 265ndash268 2002

[30] C Reis A Andrade and F P Maciel ldquoLine stability indicesfor voltage collapse predictionrdquo in Proceedings of the 2nd IEEEInternational Conference on Power Engineering Energy andElectrical Drives pp 239ndash243 March 2009

[31] X S Yang Nature-Inspired Metaheuristic Algorithms LuniverPress 2008

[32] X S Yang ldquoFirefly algorithms for multimodal optimizationrdquo inStochastic Algorithms Foundations and Applications SAGA vol5792 of Lecture Notes in Computer Sciences pp 169ndash178 2009

[33] S Łukasik and S Zak ldquoFirefly algorithm for continuousconstrained optimization task computational collective intel-ligencerdquo in Semantic Web Social Networks and Multi-AgentSystems vol 5796 of Lecture Notes in Computer Science pp 97ndash106 2009

[34] N D Reppen R R Austria J A Uhrin M C Patel and AGalatic ldquoPerformance of methods for ranking a evaluation ofvoltage collapse contingencies applied to a large-scale networkrdquoin Proceedings of the IEEE Joint International Conference pp337ndash343 1993

[35] G C Ejebe G D Irisarri S Mokhtari O Obadina PRistanovic and J Tong ldquoMethods for contingency screeningand ranking for voltage stability analysis of power systemsrdquo inProceedings of the IEEE Power Industry Computer ApplicationConference pp 249ndash255 May 1995

[36] E Vaahedi C FuchsW Xu et al ldquoVoltage stability contingencyscreening and rankingrdquo IEEE Transactions on Power Systemsvol 14 no 1 pp 256ndash265 1999

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Advances in Electrical Engineering 9

Table 5 Minimum-maximum load bus voltage values in pu

(a) For 14-bus system

Cases119881MIN 119881MAX

Preinsertionof FACTS Bus number Postinsertion of FACTS Preinsertion

of FACTS Bus number Postinsertion of FACTSFA SFLA DE PSO FA SFLA DE PSO

Case 1 10173 4 10252 10211 10203 10143 10604 7 10696 10673 10642 10617Case 2 09656 14 10004 09884 09933 09824 10101 7 10211 10176 10199 10155Case 3 09913 5 10264 10208 10104 10111 10350 13 10496 10490 10460 10438

(b) For 30-bus system

Cases119881MIN 119881MAX

Preinsertionof FACTS Bus number Postinsertion of FACTS Preinsertion

of FACTS Bus number Postinsertion of FACTSFA SFLA DE PSO FA SFLA DE PSO

Case 1 09953 30 09978 09976 09959 09954 10576 11 10820 10820 10820 10822Case 2 08915 30 09662 09035 09415 09410 10004 11 10667 10620 10520 10550Case 3 09661 5 10121 09600 09600 09607 10495 11 10820 10820 10820 10820

Table 6 Real power loss values comparison (in MW)

(a) For 14-bus system

Conditions Preinsertion of FACTS (initial) Postinsertion of FACTSFA SFLA DE PSO

Case 1 13401 11014 11409 11693 12106Case 2 35042 28018 28991 28875 29019Case 3 24183 18046 19255 19389 19771

(b) For 30-bus system

Conditions Preinsertion of FACTS (Initial) Postinsertion of FACTSFA SFLA DE PSO

Case 1 17514 13467 14852 16157 16504Case 2 46900 40990 45797 41258 43272Case 3 32569 22801 29272 23234 25561

bound of allowable value) These bus voltages are improvedafter the FACTS devices are installed Voltage profile valuecomparison under all cases incorporating the series-shuntFACTS devices combination is depicted separately in Figures7(a) and 7(b) under both test cases It is obvious fromthe figure that voltage profile comparison of the system isimproved better with the proposed method incorporatingFACTS devices combination The comparison of averagevalue of load bus voltage also proves the enhancing behaviorof voltage stability limit incorporating with FACTS devices ofall cases shown in Table 4 Table 5 exposes the comparisonof minimum and maximum load bus voltages in both theabsence and presence of FACTS devices under all cases

In real power loss minimization point of view throughinsertion of FACTS devices the real power loss under Case1 is decreased by 2387 and 4047MW respectively for14- and 30-bus systems In Case 2 the reduction in realpower loss rate is 7024 and 5910MW respectively Thereduction rate in real power loss is 6137 and 9768MW

respectively under Case 3 operation The real power lossvalues of proposed method compared with other impor-tant evolutionary techniques under all cases are shownin Table 6

The percentage of reduction in real power loss compari-son under all cases including both combinations is depictedin Figure 8 Obviously from the results shown in Table 6 theproposed method is more efficient than other evolutionarytechniques given here to reduce the real power lossminimiza-tion application The much reduction in real power loss andincrease in voltage magnitudes after the insertion of FACTSdevices are highly efficient in relieving a power network fromstressed condition and improving voltage stability limit Themost suitable size and location of combinations of FACTSdevices to improve the voltage stability limit and real powerloss minimization are also given in Table 7 under all caseswith 14- and 30-bus systems respectively The optimized sizeof SVC inserted with both combinations is not in larger valuewhich helps to reduce in cost

10 Advances in Electrical Engineering

Table 7 Best location and size of FACTS devices

(a) For 14-bus system

Cases Series ShuntLocation (line number) Size (degrees of compensation) Location (bus number) Size (MVar)

Case 1

FA 10 00722 + 11989501464 5 72015SFLA 4 00377 + 11989500916 12 86554DE 15 00461 + 11989501540 10 69988PSO 3 00622 + 11989501067 12 83037

Case 2

FA 12 00823 + 11989500961 13 11211SFLA 1 00536 + 11989501642 11 106217DE 9 00507 + 11989501145 12 99654PSO 11 00727 + 11989500836 10 72510

Case 3

FA 12 00769 + 11989500810 13 96817SFLA 10 00421 + 11989501162 5 106528DE 2 00489 + 11989500773 11 89207PSO 7 00673 + 11989501286 10 114368

(b) For 30-bus system

Cases Series ShuntLocation (line number) Size (degrees of compensation) Location (bus number) Size (MVar)

Case 1

FA 5 00159 + 11989500924 12 86962SFLA 1 00086 + 11989500833 19 69688DE 6 00239 + 11989502664 20 58131PSO 12 00191 + 11989500977 23 150806

Case 2

FA 6 00137 + 11989500384 17 90607SFLA 9 00170 + 11989501243 21 141058DE 5 00289 + 11989500931 30 62554PSO 8 00281 + 11989500447 18 190106

Case 3

FA 11 00311 + 11989501417 26 80115SFLA 9 00115 + 11989501302 28 67499DE 6 00112 + 11989500478 25 58559PSO 8 00291 + 11989501189 3 182640

7 Conclusion

In this paper optimal location and size of series-shunt FACTSdevices for voltage stability limit improvement and lossminimization through firefly algorithm are demonstratedThe voltage stability limit improvement and real power lossminimization are done under three operating cases suchas normal critical loading and line outage contingencyconditions The LQP index is used for voltage stabilityassessment The circuit element model of SSSC is consid-ered to improve the voltage stability limit by controllingpower flows and maintaining voltage profile This modelis easy to incorporate the effect of SSSC into Newton-Raphson load flow program codingThe variable susceptancemodel of SVC is used in a combined manner with SSSCIt is clear from the numerical results that voltage stabilitylimit improvement and real power loss minimization arehighly encouraging The real power loss minimization andvoltage stability limit improvement is remarkable by thecombined action of power flow control of SSSC and reac-tive power compensation by SVC through firefly algorithmover other evolutionary optimization techniques given inthis paper

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] T V Cutsem and C Vournas Voltage Stability of Electric PowerSystems Kluwer Academic New York NY USA 1998

[2] P Kundur Power System Stability and Control McGraw-HillNew York NY USA 1994

[3] CW Taylor Power System Voltage Stability McGraw-Hill NewYork NY USA 1994

[4] T van Cutsem ldquoVoltage instability phenomena countermea-sures and analysis methodsrdquo Proceedings of the IEEE vol 88no 2 pp 208ndash227 2000

[5] P Kessel and H Glavitsch ldquoEstimating the voltage stability ofpower systemrdquo IEEE Transactions on Power Delivery vol 1 no3 pp 346ndash354 1986

[6] H J Wan J D McCalley and V Vittal ldquoRisk based voltagesecurity assessmentrdquo IEEE Transactions on Power Systems vol15 no 4 pp 1247ndash1254 2000

Advances in Electrical Engineering 11

[7] I Dobson and H-D Chiang ldquoTowards a theory of voltagecollapse in electric power systemsrdquo Systems and Control Lettersvol 13 no 3 pp 253ndash262 1989

[8] ldquoTechnical Analysis of the August 14 2003 Blackout WhatHappened Why and What Did We Learnrdquo A report by theNorth American Electrical Reliability Council Steering GroupNew Jersey July 2004

[9] N G Hingorani and L Gyugyi Understanding FACTS Con-cepts and Technology of Flexible AC Transmission Systems IEEEPress 2000

[10] K K Sen and M L Sen Introduction to FACTS ControllersTheory Modeling and Applications IEEE Press 2009

[11] GWu A Okoyama J He and Y Yu ldquoAllocation and control ofFACTS devices for steady state stability enhancement of largescale power systemrdquo International Conference on Power SystemTechnology vol 1 pp 357ndash361 1998

[12] N Yorino E E El-Araby H Sasaki and S Harada ldquoA newformulation for FACTS allocation for security enhancementagainst voltage collapserdquo IEEE Transactions on Power Systemsvol 18 no 1 pp 3ndash10 2003

[13] S Biansoongnern S Chusanapiputt and S PhoomvuthisarnldquoOptimal SVC and TCSC placement for minimization of trans-mission lossesrdquo inProceedings of the International Conference onPower System Technology pp 1ndash5 October 2006

[14] M A Abido ldquoPower system stability enhancement usingFACTS controllers a reviewrdquo The Arabian Journal For Scienceand Engineering vol 34 no 1 pp 153ndash172 2009

[15] O L Bekri ldquoOptimal location of SVC and TCSC for voltagestability enhancementrdquo in Proceedings of the 4th InternationalPower Engineering and Optimization Conference (PEOCO rsquo10)pp 7ndash12 June 2010

[16] Y Zhang and Y Zhang ldquoA novel power injection model ofembedded SSSCwithmulti-control modes for power flow anal-ysis inclusive of practical constraintsrdquo Electric Power SystemsResearch vol 76 no 5 pp 374ndash381 2006

[17] A Sode-Yome N Mithulananthan and K Y Lee ldquoStaticvoltage stability margin enhancement using STATCOM TCSCand SSSCrdquo in Proceedings of the IEEEPES Transmission andDistribution Conference and Exhibition pp 1ndash6 August 2005

[18] C A Canizares and Z T Faur ldquoAnalysis of SVC and TCSCcontrollers in voltage collapserdquo IEEE Transactions on PowerSystems vol 14 no 1 pp 158ndash165 1999

[19] S Musunuri and G Dehnavi ldquoComparison of STAT COMSVC TCSC and SSSC performance in steady state voltagestability improvementrdquo in Proceedings of the North AmericanPower Symposium (NAPS rsquo10) pp 1ndash7 September 2010

[20] P Kundur K Morison and B Gao ldquoPractical considerations involtage stability assessmentrdquo International Journal of ElectricalPower and Energy Systems vol 15 no 4 pp 205ndash215 1993

[21] V Ajjarapu Computational Techniques for Voltage StabilityAssessment and Control Springer Science 2006

[22] S Fliscounakis P Panciatici F Capitanescu and L WehenkelldquoContingency ranking with respect to overloads in large powersystems taking into account uncertainity preventive and correc-tive actionsrdquo IEEE Transactions on Power Systems vol 28 no 4pp 4909ndash4917 2013

[23] A Y Abdelaziz A T M Taha M A Mostafa and A MHassan ldquoPower systen contingency ranking using fuzzy logicbased approachrdquo International Journal of Intelligent Systems andApplications no 2 pp 24ndash28 2013

[24] P S Venkataramu and T Ananthapadmanabha ldquoInstallationof unified power flow controller for voltage stability margin

enhancement under line outage contingenciesrdquo Iranian Journalof Electrical and Computer Engineering vol 5 no 2 pp 90ndash962006

[25] M Jarsquofari and S Afsharnia ldquoVoltage stability enhancementin contingency conditions using shunt FACTS devicesrdquo inProceedings of the EUROCON The International Conference onComputer as a Tool pp 1660ndash1665 September 2007

[26] P-A Loef G Andersson and D J Hill ldquoVoltage stabilityindices for stressed power systemsrdquo IEEE Transactions on PowerSystems vol 8 no 1 pp 326ndash335 1993

[27] M Moghavvemi and F M Omar ldquoTechnique for contingencymonitoring and voltage collapse predictionrdquo IEE Proceedings onGeneration Transmission and Distribution vol 145 no 6 pp634ndash640 1998

[28] M Moghavvemi and O Faruque ldquoReal time contingency eval-uation and ranking techniquerdquo IEE Proceedings on GenerationTransmission and Distribution vol 145 no 5 pp 517ndash524 1998

[29] I Musirin and T K A Rahman ldquoNovel fast voltage stabilityindex (FVSI) for voltage stability analysis in power transmissionsystemrdquo in Proceedings of the Student Conference on Researchand Development Proceedings pp 265ndash268 2002

[30] C Reis A Andrade and F P Maciel ldquoLine stability indicesfor voltage collapse predictionrdquo in Proceedings of the 2nd IEEEInternational Conference on Power Engineering Energy andElectrical Drives pp 239ndash243 March 2009

[31] X S Yang Nature-Inspired Metaheuristic Algorithms LuniverPress 2008

[32] X S Yang ldquoFirefly algorithms for multimodal optimizationrdquo inStochastic Algorithms Foundations and Applications SAGA vol5792 of Lecture Notes in Computer Sciences pp 169ndash178 2009

[33] S Łukasik and S Zak ldquoFirefly algorithm for continuousconstrained optimization task computational collective intel-ligencerdquo in Semantic Web Social Networks and Multi-AgentSystems vol 5796 of Lecture Notes in Computer Science pp 97ndash106 2009

[34] N D Reppen R R Austria J A Uhrin M C Patel and AGalatic ldquoPerformance of methods for ranking a evaluation ofvoltage collapse contingencies applied to a large-scale networkrdquoin Proceedings of the IEEE Joint International Conference pp337ndash343 1993

[35] G C Ejebe G D Irisarri S Mokhtari O Obadina PRistanovic and J Tong ldquoMethods for contingency screeningand ranking for voltage stability analysis of power systemsrdquo inProceedings of the IEEE Power Industry Computer ApplicationConference pp 249ndash255 May 1995

[36] E Vaahedi C FuchsW Xu et al ldquoVoltage stability contingencyscreening and rankingrdquo IEEE Transactions on Power Systemsvol 14 no 1 pp 256ndash265 1999

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

10 Advances in Electrical Engineering

Table 7 Best location and size of FACTS devices

(a) For 14-bus system

Cases Series ShuntLocation (line number) Size (degrees of compensation) Location (bus number) Size (MVar)

Case 1

FA 10 00722 + 11989501464 5 72015SFLA 4 00377 + 11989500916 12 86554DE 15 00461 + 11989501540 10 69988PSO 3 00622 + 11989501067 12 83037

Case 2

FA 12 00823 + 11989500961 13 11211SFLA 1 00536 + 11989501642 11 106217DE 9 00507 + 11989501145 12 99654PSO 11 00727 + 11989500836 10 72510

Case 3

FA 12 00769 + 11989500810 13 96817SFLA 10 00421 + 11989501162 5 106528DE 2 00489 + 11989500773 11 89207PSO 7 00673 + 11989501286 10 114368

(b) For 30-bus system

Cases Series ShuntLocation (line number) Size (degrees of compensation) Location (bus number) Size (MVar)

Case 1

FA 5 00159 + 11989500924 12 86962SFLA 1 00086 + 11989500833 19 69688DE 6 00239 + 11989502664 20 58131PSO 12 00191 + 11989500977 23 150806

Case 2

FA 6 00137 + 11989500384 17 90607SFLA 9 00170 + 11989501243 21 141058DE 5 00289 + 11989500931 30 62554PSO 8 00281 + 11989500447 18 190106

Case 3

FA 11 00311 + 11989501417 26 80115SFLA 9 00115 + 11989501302 28 67499DE 6 00112 + 11989500478 25 58559PSO 8 00291 + 11989501189 3 182640

7 Conclusion

In this paper optimal location and size of series-shunt FACTSdevices for voltage stability limit improvement and lossminimization through firefly algorithm are demonstratedThe voltage stability limit improvement and real power lossminimization are done under three operating cases suchas normal critical loading and line outage contingencyconditions The LQP index is used for voltage stabilityassessment The circuit element model of SSSC is consid-ered to improve the voltage stability limit by controllingpower flows and maintaining voltage profile This modelis easy to incorporate the effect of SSSC into Newton-Raphson load flow program codingThe variable susceptancemodel of SVC is used in a combined manner with SSSCIt is clear from the numerical results that voltage stabilitylimit improvement and real power loss minimization arehighly encouraging The real power loss minimization andvoltage stability limit improvement is remarkable by thecombined action of power flow control of SSSC and reac-tive power compensation by SVC through firefly algorithmover other evolutionary optimization techniques given inthis paper

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] T V Cutsem and C Vournas Voltage Stability of Electric PowerSystems Kluwer Academic New York NY USA 1998

[2] P Kundur Power System Stability and Control McGraw-HillNew York NY USA 1994

[3] CW Taylor Power System Voltage Stability McGraw-Hill NewYork NY USA 1994

[4] T van Cutsem ldquoVoltage instability phenomena countermea-sures and analysis methodsrdquo Proceedings of the IEEE vol 88no 2 pp 208ndash227 2000

[5] P Kessel and H Glavitsch ldquoEstimating the voltage stability ofpower systemrdquo IEEE Transactions on Power Delivery vol 1 no3 pp 346ndash354 1986

[6] H J Wan J D McCalley and V Vittal ldquoRisk based voltagesecurity assessmentrdquo IEEE Transactions on Power Systems vol15 no 4 pp 1247ndash1254 2000

Advances in Electrical Engineering 11

[7] I Dobson and H-D Chiang ldquoTowards a theory of voltagecollapse in electric power systemsrdquo Systems and Control Lettersvol 13 no 3 pp 253ndash262 1989

[8] ldquoTechnical Analysis of the August 14 2003 Blackout WhatHappened Why and What Did We Learnrdquo A report by theNorth American Electrical Reliability Council Steering GroupNew Jersey July 2004

[9] N G Hingorani and L Gyugyi Understanding FACTS Con-cepts and Technology of Flexible AC Transmission Systems IEEEPress 2000

[10] K K Sen and M L Sen Introduction to FACTS ControllersTheory Modeling and Applications IEEE Press 2009

[11] GWu A Okoyama J He and Y Yu ldquoAllocation and control ofFACTS devices for steady state stability enhancement of largescale power systemrdquo International Conference on Power SystemTechnology vol 1 pp 357ndash361 1998

[12] N Yorino E E El-Araby H Sasaki and S Harada ldquoA newformulation for FACTS allocation for security enhancementagainst voltage collapserdquo IEEE Transactions on Power Systemsvol 18 no 1 pp 3ndash10 2003

[13] S Biansoongnern S Chusanapiputt and S PhoomvuthisarnldquoOptimal SVC and TCSC placement for minimization of trans-mission lossesrdquo inProceedings of the International Conference onPower System Technology pp 1ndash5 October 2006

[14] M A Abido ldquoPower system stability enhancement usingFACTS controllers a reviewrdquo The Arabian Journal For Scienceand Engineering vol 34 no 1 pp 153ndash172 2009

[15] O L Bekri ldquoOptimal location of SVC and TCSC for voltagestability enhancementrdquo in Proceedings of the 4th InternationalPower Engineering and Optimization Conference (PEOCO rsquo10)pp 7ndash12 June 2010

[16] Y Zhang and Y Zhang ldquoA novel power injection model ofembedded SSSCwithmulti-control modes for power flow anal-ysis inclusive of practical constraintsrdquo Electric Power SystemsResearch vol 76 no 5 pp 374ndash381 2006

[17] A Sode-Yome N Mithulananthan and K Y Lee ldquoStaticvoltage stability margin enhancement using STATCOM TCSCand SSSCrdquo in Proceedings of the IEEEPES Transmission andDistribution Conference and Exhibition pp 1ndash6 August 2005

[18] C A Canizares and Z T Faur ldquoAnalysis of SVC and TCSCcontrollers in voltage collapserdquo IEEE Transactions on PowerSystems vol 14 no 1 pp 158ndash165 1999

[19] S Musunuri and G Dehnavi ldquoComparison of STAT COMSVC TCSC and SSSC performance in steady state voltagestability improvementrdquo in Proceedings of the North AmericanPower Symposium (NAPS rsquo10) pp 1ndash7 September 2010

[20] P Kundur K Morison and B Gao ldquoPractical considerations involtage stability assessmentrdquo International Journal of ElectricalPower and Energy Systems vol 15 no 4 pp 205ndash215 1993

[21] V Ajjarapu Computational Techniques for Voltage StabilityAssessment and Control Springer Science 2006

[22] S Fliscounakis P Panciatici F Capitanescu and L WehenkelldquoContingency ranking with respect to overloads in large powersystems taking into account uncertainity preventive and correc-tive actionsrdquo IEEE Transactions on Power Systems vol 28 no 4pp 4909ndash4917 2013

[23] A Y Abdelaziz A T M Taha M A Mostafa and A MHassan ldquoPower systen contingency ranking using fuzzy logicbased approachrdquo International Journal of Intelligent Systems andApplications no 2 pp 24ndash28 2013

[24] P S Venkataramu and T Ananthapadmanabha ldquoInstallationof unified power flow controller for voltage stability margin

enhancement under line outage contingenciesrdquo Iranian Journalof Electrical and Computer Engineering vol 5 no 2 pp 90ndash962006

[25] M Jarsquofari and S Afsharnia ldquoVoltage stability enhancementin contingency conditions using shunt FACTS devicesrdquo inProceedings of the EUROCON The International Conference onComputer as a Tool pp 1660ndash1665 September 2007

[26] P-A Loef G Andersson and D J Hill ldquoVoltage stabilityindices for stressed power systemsrdquo IEEE Transactions on PowerSystems vol 8 no 1 pp 326ndash335 1993

[27] M Moghavvemi and F M Omar ldquoTechnique for contingencymonitoring and voltage collapse predictionrdquo IEE Proceedings onGeneration Transmission and Distribution vol 145 no 6 pp634ndash640 1998

[28] M Moghavvemi and O Faruque ldquoReal time contingency eval-uation and ranking techniquerdquo IEE Proceedings on GenerationTransmission and Distribution vol 145 no 5 pp 517ndash524 1998

[29] I Musirin and T K A Rahman ldquoNovel fast voltage stabilityindex (FVSI) for voltage stability analysis in power transmissionsystemrdquo in Proceedings of the Student Conference on Researchand Development Proceedings pp 265ndash268 2002

[30] C Reis A Andrade and F P Maciel ldquoLine stability indicesfor voltage collapse predictionrdquo in Proceedings of the 2nd IEEEInternational Conference on Power Engineering Energy andElectrical Drives pp 239ndash243 March 2009

[31] X S Yang Nature-Inspired Metaheuristic Algorithms LuniverPress 2008

[32] X S Yang ldquoFirefly algorithms for multimodal optimizationrdquo inStochastic Algorithms Foundations and Applications SAGA vol5792 of Lecture Notes in Computer Sciences pp 169ndash178 2009

[33] S Łukasik and S Zak ldquoFirefly algorithm for continuousconstrained optimization task computational collective intel-ligencerdquo in Semantic Web Social Networks and Multi-AgentSystems vol 5796 of Lecture Notes in Computer Science pp 97ndash106 2009

[34] N D Reppen R R Austria J A Uhrin M C Patel and AGalatic ldquoPerformance of methods for ranking a evaluation ofvoltage collapse contingencies applied to a large-scale networkrdquoin Proceedings of the IEEE Joint International Conference pp337ndash343 1993

[35] G C Ejebe G D Irisarri S Mokhtari O Obadina PRistanovic and J Tong ldquoMethods for contingency screeningand ranking for voltage stability analysis of power systemsrdquo inProceedings of the IEEE Power Industry Computer ApplicationConference pp 249ndash255 May 1995

[36] E Vaahedi C FuchsW Xu et al ldquoVoltage stability contingencyscreening and rankingrdquo IEEE Transactions on Power Systemsvol 14 no 1 pp 256ndash265 1999

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Advances in Electrical Engineering 11

[7] I Dobson and H-D Chiang ldquoTowards a theory of voltagecollapse in electric power systemsrdquo Systems and Control Lettersvol 13 no 3 pp 253ndash262 1989

[8] ldquoTechnical Analysis of the August 14 2003 Blackout WhatHappened Why and What Did We Learnrdquo A report by theNorth American Electrical Reliability Council Steering GroupNew Jersey July 2004

[9] N G Hingorani and L Gyugyi Understanding FACTS Con-cepts and Technology of Flexible AC Transmission Systems IEEEPress 2000

[10] K K Sen and M L Sen Introduction to FACTS ControllersTheory Modeling and Applications IEEE Press 2009

[11] GWu A Okoyama J He and Y Yu ldquoAllocation and control ofFACTS devices for steady state stability enhancement of largescale power systemrdquo International Conference on Power SystemTechnology vol 1 pp 357ndash361 1998

[12] N Yorino E E El-Araby H Sasaki and S Harada ldquoA newformulation for FACTS allocation for security enhancementagainst voltage collapserdquo IEEE Transactions on Power Systemsvol 18 no 1 pp 3ndash10 2003

[13] S Biansoongnern S Chusanapiputt and S PhoomvuthisarnldquoOptimal SVC and TCSC placement for minimization of trans-mission lossesrdquo inProceedings of the International Conference onPower System Technology pp 1ndash5 October 2006

[14] M A Abido ldquoPower system stability enhancement usingFACTS controllers a reviewrdquo The Arabian Journal For Scienceand Engineering vol 34 no 1 pp 153ndash172 2009

[15] O L Bekri ldquoOptimal location of SVC and TCSC for voltagestability enhancementrdquo in Proceedings of the 4th InternationalPower Engineering and Optimization Conference (PEOCO rsquo10)pp 7ndash12 June 2010

[16] Y Zhang and Y Zhang ldquoA novel power injection model ofembedded SSSCwithmulti-control modes for power flow anal-ysis inclusive of practical constraintsrdquo Electric Power SystemsResearch vol 76 no 5 pp 374ndash381 2006

[17] A Sode-Yome N Mithulananthan and K Y Lee ldquoStaticvoltage stability margin enhancement using STATCOM TCSCand SSSCrdquo in Proceedings of the IEEEPES Transmission andDistribution Conference and Exhibition pp 1ndash6 August 2005

[18] C A Canizares and Z T Faur ldquoAnalysis of SVC and TCSCcontrollers in voltage collapserdquo IEEE Transactions on PowerSystems vol 14 no 1 pp 158ndash165 1999

[19] S Musunuri and G Dehnavi ldquoComparison of STAT COMSVC TCSC and SSSC performance in steady state voltagestability improvementrdquo in Proceedings of the North AmericanPower Symposium (NAPS rsquo10) pp 1ndash7 September 2010

[20] P Kundur K Morison and B Gao ldquoPractical considerations involtage stability assessmentrdquo International Journal of ElectricalPower and Energy Systems vol 15 no 4 pp 205ndash215 1993

[21] V Ajjarapu Computational Techniques for Voltage StabilityAssessment and Control Springer Science 2006

[22] S Fliscounakis P Panciatici F Capitanescu and L WehenkelldquoContingency ranking with respect to overloads in large powersystems taking into account uncertainity preventive and correc-tive actionsrdquo IEEE Transactions on Power Systems vol 28 no 4pp 4909ndash4917 2013

[23] A Y Abdelaziz A T M Taha M A Mostafa and A MHassan ldquoPower systen contingency ranking using fuzzy logicbased approachrdquo International Journal of Intelligent Systems andApplications no 2 pp 24ndash28 2013

[24] P S Venkataramu and T Ananthapadmanabha ldquoInstallationof unified power flow controller for voltage stability margin

enhancement under line outage contingenciesrdquo Iranian Journalof Electrical and Computer Engineering vol 5 no 2 pp 90ndash962006

[25] M Jarsquofari and S Afsharnia ldquoVoltage stability enhancementin contingency conditions using shunt FACTS devicesrdquo inProceedings of the EUROCON The International Conference onComputer as a Tool pp 1660ndash1665 September 2007

[26] P-A Loef G Andersson and D J Hill ldquoVoltage stabilityindices for stressed power systemsrdquo IEEE Transactions on PowerSystems vol 8 no 1 pp 326ndash335 1993

[27] M Moghavvemi and F M Omar ldquoTechnique for contingencymonitoring and voltage collapse predictionrdquo IEE Proceedings onGeneration Transmission and Distribution vol 145 no 6 pp634ndash640 1998

[28] M Moghavvemi and O Faruque ldquoReal time contingency eval-uation and ranking techniquerdquo IEE Proceedings on GenerationTransmission and Distribution vol 145 no 5 pp 517ndash524 1998

[29] I Musirin and T K A Rahman ldquoNovel fast voltage stabilityindex (FVSI) for voltage stability analysis in power transmissionsystemrdquo in Proceedings of the Student Conference on Researchand Development Proceedings pp 265ndash268 2002

[30] C Reis A Andrade and F P Maciel ldquoLine stability indicesfor voltage collapse predictionrdquo in Proceedings of the 2nd IEEEInternational Conference on Power Engineering Energy andElectrical Drives pp 239ndash243 March 2009

[31] X S Yang Nature-Inspired Metaheuristic Algorithms LuniverPress 2008

[32] X S Yang ldquoFirefly algorithms for multimodal optimizationrdquo inStochastic Algorithms Foundations and Applications SAGA vol5792 of Lecture Notes in Computer Sciences pp 169ndash178 2009

[33] S Łukasik and S Zak ldquoFirefly algorithm for continuousconstrained optimization task computational collective intel-ligencerdquo in Semantic Web Social Networks and Multi-AgentSystems vol 5796 of Lecture Notes in Computer Science pp 97ndash106 2009

[34] N D Reppen R R Austria J A Uhrin M C Patel and AGalatic ldquoPerformance of methods for ranking a evaluation ofvoltage collapse contingencies applied to a large-scale networkrdquoin Proceedings of the IEEE Joint International Conference pp337ndash343 1993

[35] G C Ejebe G D Irisarri S Mokhtari O Obadina PRistanovic and J Tong ldquoMethods for contingency screeningand ranking for voltage stability analysis of power systemsrdquo inProceedings of the IEEE Power Industry Computer ApplicationConference pp 249ndash255 May 1995

[36] E Vaahedi C FuchsW Xu et al ldquoVoltage stability contingencyscreening and rankingrdquo IEEE Transactions on Power Systemsvol 14 no 1 pp 256ndash265 1999

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of