TCSC PLACEMENT FOR LOSS MINIMISATION USING SELF ADAPTIVE FIREFLY ALGORITHM

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1 Journal of Engineering Science and Technology Vol. 10, No. 3 (2015) School of Engineering, Taylor s University PLACEMENT FOR LOSS MINIMISATION USING SELF ADAPTIVE FIREFLY ALGORITHM R. SELVARASU*, M. SURYA KALAVATHI Departent of EEE, JNTUH, Hyderabad, India *Corresponding Author: selvarasunaveen@gail.co Abstract This paper presents the use of Self Adaptive Firefly Algorith to identify the optial placeent of Thyristor Controlled Series Copensator () in a power syste network. The objective is to iniise the transission loss in power syste network with the placeent of. To validate the proposed algorith, siulations are perfored on three IEEE test syste using MATLAB software package. Siulation results show that the identified location and paraeter of is able to iniise the transission loss in the power syste network. Keywords: Firefly algorith, Loss iniisation, Optial location,. 1. Introduction In last two decades, the deand for electrical energy is exponentially increasing. The construction of new generation syste, power transission networks can solve these deands. However, there are soe liitations to construct new syste. They involve installation cost, environent ipact, political, large displaceent of population and land acquisition. One of the alternative solutions to respond the increasing deand is by iniisation of transission loss using Flexible Alternating Current Transission Systes (FACTS) devices. The FACTS is a concept proposed by N.G.Hingorani [1] as a well-known ter for higher controllability in power syste by eans of power electronic devices. Better utilisation of an existing power syste capacity by installing FACTS devices has becoe essential in the area of ongoing research. FACTS devices have the capability to control the various electrical paraeters in transission network in order to achieve better syste perforance. 21

2 22 R. Selvarasu and M. S. Kalavathi Noenclatures G l Conductance of l th line I Light intensity of the th firefly k Nuber of iterations L M Line location of the th l Nuber of transission of lines M Maxiu nuber of fireflies,n Nuber of fireflies nd Nuber of decision variables P Di Real power drawn by the load at i th bus P Gi Real power generation at i th generator P loss Total real power loss Q Di Reactive power drawn by the load at bus i Q Gi Reactive power generation at i th generator ax Q Gi Maxiu reactive power generation of i th generator in Q Gi Miniu reactive power generation of i th generator r,n Cartesian distance between th and n th firefly V i,v j Voltage agnitudes at bus i and j respectively X line Reactance of the transission line Greek Sybols α Rando oveent factor β,n Attractiveness Paraeter δ ij Voltage angle at bus i and j γ Absorption paraeter Copensation factor of the γ Abbreviations FA Firefly Algorith SAFA Self Adaptive Firefly Algorith Thyristor Controlled Series Copensator FACTS devices can be divided in to Shunt Connected, Series connected and cobination of both [2]. The Static Var Copensator (SVC) and Static Synchronous Copensator (STATCOM) are belongs the shunt connected devices and are in use for a long tie in various places. Consequently, they are variable shunt reactors which inject or absorb reactive power in order to control the voltage at a given bus [3].Both Thyristor Controlled Series Copensator () and Static Synchronous Series Copensator (SSSC) are belongs to the series connected devices. The and SSSC ainly control the active power in a line by varying the line reactance. They are in operation at a few places but are still in the stage of developent [, 5]. Unified Power Flow Controller (UPFC) is belongs to Cobination of Shunt and Series devices. UPFC is able to control active power, reactive power and voltage agnitude siultaneously or separately [6].

3 Placeent for Loss Miniisation using Self Adaptive Firefly Algorith 23 Optial location of various types of FACTS devices in the power syste has been experienced using different Meta-heuristic algorith such as Genetic Algorith (GA), Siulated annealing (SA), Ant Colony Optiisation (ACO), Bees Algoriths (BA), Differential Evolution (DE), and Particle Swar Optiisation (PSO), etc. [7].Optial locations of ulti type FACTS devices in a power syste to iprove the loadability by eans of Genetic Algorith has been successfully ipleented [8]. PSO has been applied to deterine the optial location of FACTS devices considering cost of installation []. PSO has been proposed to select the optial location and setting paraeter of SVC and to itigate sall signal oscillations in ulti achine power syste [10]. PSO has been proposed to iprove the power syste stability by deterining the optial location and controller design of STATCOM [11]. Bees Algorith has been proposed to deterine the optial allocation of FACTS devices for axiising the available transfer capability [12]. Bacterial Foraging algorith has been used to find the optial location of UPFC devices with objectives of iniising the losses [13, 1]. Firefly Algorith has been developed by Xin-She Yang [7, 15], it could handle ulti odal probles of cobinational and nuerical optiisation ore naturally and efficiently. It has been then applied by various researchers for solving various probles, to nae a few: econoic dispatch [16-18], fault identification [1], scheduling [20] and Unit coitent [21], etc. However, the iproper choice of FA paraeters affects the convergence and ay lead to suboptial solutions. There is thus a need for developing better strategies for optially selecting the FA paraeters with a view of obtaining the global best solution besides achieving better convergence. Self-Adaptive FA (SAFA) based strategies have been proposed to iniise the transission loss through placing s [22] and UPFCs [23]. In this paper Self Adaptive Firefly Algorith is proposed to identify the optial location and paraeter of, which iniises the transission loss in the power syste network. Siulations are perfored on IEEE 1-bus IEEE 30-bus and IEEE 57-bus syste using MATLAB software package. Siulations results are presented to deonstrate the effectiveness of the proposed approach. 2. Model The Thyristor Controlled Series Copensator () is a capacitive reactance copensator. It consists of a series capacitor bank shunted by a thyristor controlled reactor in order to provide a soothly variable series capacitive reactance [2]. The can be connected in series with the transission line to copensate the inductive reactance of the transission line. The reactance of the depends on its copensation ratio and the reactance of the transission line where it is located. The odel of is shown in Fig.1. ij The odelled by the reactance, X is given as follows X = X + X (1) X line = γ X (2) line

4 2 R. Selvarasu and M. S. Kalavathi Bus i Bus j X X line Fig. 1. odel. 3. Firefly Algorith Firefly Algorith is a recent nature inspired eta- heuristic algoriths which has been developed by Xin-She Yang at Cabridge University in 2007 [7]. The algorith iics the flashing behaviour of fireflies. This FA is siilar to other optiisation algoriths eploying swar intelligence such as PSO. But Firefly Algorith is found to have superior perforance in any cases [] Classical firefly algorith It eploys three ideal rules. First rule is all fireflies are unisex which eans that one firefly will be attracted to other fireflies regardless of their sex. Second rule is the degree of the attractiveness of a firefly is proportional to its brightness, thus each firefly s oves towards brighter one. More brightness eans less distance between two fireflies. Though if any two flashing fireflies are having sae brightness, then they ove randoly. Final rule is the brightness of a firefly is deterined by the value of the objective function. In case of axiisation proble, the brightness of each firefly is proportional to the value of the objective function. For a iniisation proble, the brightness of each firefly is inversely proportional to the value of the objective function. Firefly Algorith initially produces a swar of fireflies located randoly in the search space. Initial distribution is usually produced fro a unifor rando distribution and the position of each firefly in the search space represents a potential solution of the optiisation proble. Diension of the search space is equal to the nuber of optiising paraeters in the given proble. Fitness function takes the position of a firefly as input and produces a single nuerical output denoting how good the potential solution is. Fitness value is assigned to each firefly. The brightness of each firefly depends on the fitness value of that firefly. Each one firefly is attracted by the brightness of other firefly and tries to ove towards the. The velocity or the drag a firefly towards another firefly depends on the attractiveness. The attractiveness of firefly depends on the relative distance between the fireflies and it can be a function of the brightness of the fireflies as well. In each iterative step, Firefly Algorith coputes the brightness and the relative attractiveness of each firefly. Based on these values, the positions of the fireflies are updated. After a sufficient nuber of iterations, all fireflies will converge to the best possible position on the search space. The nuber of fireflies in the swar is known as the population size, N. The selection of population size depends on the specific optiisation proble. Though, typically a population size of 20 to 50 is used for PSO and Firefly Algorith for ost applications [, 17]. Each th firefly is denoted by a vector x as

5 Placeent for Loss Miniisation using Self Adaptive Firefly Algorith nd x = [ x, x... x ] (3) The search space is liited by the following inequality constraints v v v x (in) x x (ax), v = 1, 2..., nd () Initially, the positions of the fireflies are generated fro a unifor distribution using the following equation x v v v = x (in) + ( x ( ax) x ( in)) rand (5) v Here, rand is a rando nuber between 0 and 1, taken fro a unifor distribution. The initial distribution does not significantly affect the perforance of the algorith. Every tie the algorith is executed and the optiisation process starts with a different set of initial points. However, in each case, the algorith searches for the optiu solution. In the case of ultiple possible sets of solutions, the proposed algorith ay converge on different solutions each tie. Although each of those solutions will be valid as they all will satisfy the requireent. The light intensity of the th firefly, I is given by I =Fitness(x ) (6) The attractiveness between th and n th 2, n ( β ax,, n β in,, n ) exp ( γ r, n ) β in,, n firefly, β,n is given by β = + (7) nd, n = x xn = ) v= 1 r k k 2 ( x xn (8) The value of β in is taken as 0.2 and the value of β ax is taken as 1. γ is another constant whose value is related to the dynaic range of the solution space. The position of firefly is updated in each iterative step. If the light intensity of n th firefly is larger than the light intensity of the th firefly, then the th firefly oves towards the n th firefly and its otion at k th iteration is denoted by the following equation: x ( k) = x ( k 1) + β, ( x ( k 1) x ( k 1)) + α ( rand 0.5) () n n The rando oveent factor α is a constant whose value depends on the dynaic range of the solution space. At each iterative step, the intensity and the attractiveness of each firefly is calculated. The intensity of each firefly is copared with all other fireflies and the positions of the fireflies are updated using Eq. (). After an adequate nuber of iterations, each firefly converges to the sae position in the search space and the global optiu is achieved Self-adaptive firefly algorith In the above narrated FA, each firefly of the swar travel around the proble space taking into account the results obtained by others and still applying its own randoised oves as well. The rando oveent factor (α) is very effective on the perforance of Firefly Algorith. A large value of α akes the oveent to explore the solution through the distance search space and saller value of α tends to facilitate local search. In this paper the rando oveent factor (α) is

6 26 R. Selvarasu and M. S. Kalavathi dynaically tuned in each iteration. The influence of other solutions is controlled by the value of attractiveness (7), which can be adjusted by odifying three paraeters α, β in, and γ. In general the value of β ax should be used fro 0 to1 and two liiting cases can be defined: The algorith perfors cooperative local search with the brightest firefly strongly deterining other fireflies positions, especially in its neighbourhood, when β ax = 1 and only non-cooperative distributed rando search with β ax = 0. On the other hand, the value of γ deterines the variation of attractiveness with increasing distance fro counicated firefly. Setting γ as 0 corresponds to no variation or attractiveness is constant and conversely putting γ as results in attractiveness being close to zero which again is equivalent to the coplete rando search. In general γ in the range of 0 to 10 can be chosen for better perforance. Indeed, the choice of these paraeters affects the final solution and the convergence of the algorith. Each firefly with nd decision variables in the Firefly Algorith will be defined to encopass nd + 3.Firefly Algorith variables in a self-adaptive ethod, where the last three variables represent α, β in and γ. A firefly can be represented as x 1 2 nd = x, x..., x, α, β, γ ] (10) [ in, Each firefly possessing the solution vector, α, β in and γ undergo the whole search process. During iteration, the FA produces better off-springs through Eqs. (7) and () using the paraeters available in the firefly of Eq. (10), thereby enhancing the convergence of the algorith. The basic steps of the Firefly Algorith can be suarised as the pseudo code which is depicted in Appendix A.. Proble Forulation To achieve the better utilisation of an existing power syste, the optial location and paraeter of to be identified in the power transission network to iniise the total real power loss. The objective of this paper is to identify the optial location and paraeter of the which iniise the real power loss..1. Objective function The objective of this paper is to iniise transission loss with the placeent of in power syste network, which can be evaluated fro the power flow solution [13], and written as: Min P = nl loss l= G1 ( Vi + V j 2V iv j cosδ ij ) (11).2. Proble constraints The equality constraints are the load flow equation given by P Q Gi Gi P = P ( V, δ ) (12) Di i Q = Q ( V, δ ) (13) Di i

7 Placeent for Loss Miniisation using Self Adaptive Firefly Algorith 27 Q Two inequality constraints are considered as follows: The first constraint includes reactive power generation at PV buses. in ax Q Q (1) Gi Gi Gi The second constraint represents the rating of 0 8X X 0. X p.u (15). 2 line line The Self Adaptive firefly algorith based optial location of proble is defined as ( L1, γ,1, α, β in,, γ )...( L, γ x =...( LN, γ,, N, α, β, α, β N in in,, γ )..., N, γ N ) The Self Adaptive Firefly Algorith searches for optial solution by axiising light intensity I, like fitness function in any other stochastic optiisation techniques. The light intensity function can be obtained by transforing the power loss function into I function as Max I = /( 1+ ) P loss (16) 1 (17) A population of firefly is randoly generated and their intensity is calculated using Eq. (6). Based on the light intensity, each firefly oved to the optial solution through Eq. () and the iterative process continues till the algorith converges. The flow of the proposed FA based ethod is given through the flow chart of Appendix A. 5. Siulation Results and Discussions The effectiveness of the proposed Self Adaptive Firefly algorith (SAFA) to identify the optial location and paraeter of the devices to iniise the transission loss in the power syste has been ipleented and tested on IEEE 1-bus, IEEE 30-bus and IEEE 57-bus syste using MATLAB 7.5. The line data and bus data for the three test systes are taken fro [2]. The results of the SAFA are copared with that of the Honey Bee Optiisation Algorith (HBOA) and Bacterial Foraging Optiisation Algorith (BFOA) Case 1: IEEE 1- bus syste In this case IEEE 1- bus syste has been considered to identify the optial location and paraeter of the to iniise the real power loss. IEEE 1- bus syste has 20 transission lines, five generator buses (bus no 1,2,3,6 and 8) and rests are load buses. Siulations are carried out for different nuber of without considering the installing cost. The siulation results in ters of the locations and the paraeters and the resulting loss are presented in Table 1. It is observed fro the Table 1 that the identified location of iniises the real power loss. When three is considered real power loss considerably reduced fro MW to MW. If four is considered the real power loss reduction is insignificant fro the installation cost point of view. But the HBOA and BFOA is able to reduce the losses only to MW and MW respectively for placing three devices. This lowest loss value indicates

8 28 R. Selvarasu and M. S. Kalavathi the superior perforance of the proposed SAFA. However when another is added, the loss reduction is insignificant. It is thus concluded that three devices are adequate to achieve the desired goal of iniising the loss. The coparison of real power loss for IEEE 1 bus syste is shown in Fig. 2.The convergence characteristics of SAFA for IEEE 1 bus syste is shown in Fig. 3. No of Table 1. Optial location, paraeter of and real power loss for IEEE 1- bus syste. Proposed Method Honey Bee Bacterial Foraging Real Real Real power L γ M power L γ M power L γ M loss ( p.u) loss (p.u) loss (p.u) (MW) (MW) (MW) Fig. 2. Coparison of real power loss for IEEE 1 bus syste. Fig. 3. Convergence characteristics of SAFA for IEEE 1 bus syste.

9 Placeent for Loss Miniisation using Self Adaptive Firefly Algorith Case 2: IEEE 30- bus syste In this case IEEE 30- bus syste has been considered to identify the optial location and paraeter of the to iniise the real power loss. IEEE 30- bus syste has 1 transission lines, six generator buses (bus no 1, 2, 5, 8, 11 and 13) and rests are load buses. Siulations are carried out for different nuber of without considering the installing cost. The siulation results in ters of the locations and the paraeters and the resulting loss are presented in Table 2. It is observed fro the Table 3 that the identified location of iniises the real power loss. When six is considered real power loss considerably reduced fro MW to MW. But the HBOA and BFOA is able to reduce the losses only to MW and MW respectively for placing six devices. This lowest loss value indicates the superior perforance of the proposed SAFA. It is thus concluded that six devices are adequate to achieve the desired goal of iniising the loss. The coparison of real power loss for IEEE 30 bus syste is shown in Fig..The convergence characteristics of SAFA for IEEE 30 bus syste is shown in Fig. 5. No of Table 2. Optial locations, paraeter of and real power loss for IEEE 30- bus syste. Real power loss (MW) Proposed Method Honey Bee Bacterial Foraging L M γ (p.u) Real power loss (MW) L M γ (p.u) Real power loss (MW) L M γ (p.u) Fig.. Coparison of real power loss for IEEE 30 bus syste.

10 300 R. Selvarasu and M. S. Kalavathi Fig. 5. Convergence characteristics of SAFA for IEEE 30 bus syste Case 3: IEEE 57- bus syste The IEEE 57 bus syste has 80 transission lines and seven generator buses (bus no 1, 2, 3,6,8, and 12). Siulations are carried out for different nuber of without considering the installing cost. The siulation results in ters of the locations and the paraeters and the resulting loss are presented in Table 3. It is observed fro the Table 3 that the identified location of iniises the real power loss. When six is considered real power loss considerably reduced fro MW to 26.7 MW. But the HBOA and BFOA is able to reduce the losses only to MW and MW respectively for placing six devices. This lowest loss value indicates the superior perforance of the proposed SAFA. However when another is added, the loss reduction is insignificant. It is thus concluded that six devices are adequate to achieve the desired goal of iniising the loss. The coparison of real power loss for IEEE 57 bus syste is shown in Fig. 6.The convergence characteristics of SAFA for IEEE 57 bus syste is shown in Fig. 7. Fig. 6. Coparison of real power loss for IEEE 57 bus syste.

11 Placeent for Loss Miniisation using Self Adaptive Firefly Algorith 301 Fig. 7. Convergence characteristics of SAFA for IEEE 57 bus syste. No of Table 3. Optial locations, paraeter of and real power loss for IEEE 30- bus syste. Real Power Loss (MW) Proposed Method Honey Bee Bacterial Foraging L M γ ( p.u) Real Power Loss (MW) L M γ (p.u) Real Power Loss (MW) L M γ (p.u) Paraeter of the Adaptive Firefly Algorith The population size N for three IEEE test syste are taken as 30. The axiu nuber of Iterations considered as 200. The rando oveent factor α are tuned during each iteration. The initial value of α is set to 0.5. The attractiveness paraeter β is varied fro β in to β ax. The value of β in is taken as 0.2 and the value of β ax is taken as 1. The absorption paraeter γ is taken as 1 and it is tuned in all iteration. It has to be pointed out that the perforance of the entire etaheuristic optiisation algorith is very dependent on the tuning of their different paraeters. A sall change in the paraeter ay result in a large change in the

12 302 R. Selvarasu and M. S. Kalavathi solution of these algoriths. Self adaptive Firefly Algorith is a powerful algorith which efficiently tuned all the paraeters to obtain the global or near global optial solution. It is very clear fro the above discussions that the proposed SAFA is able to reduce to the loss to the lowest possible by optially placing and deterining the paraeters when copared to other optiisation algoriths. In addition the selfadaptive nature of the algorith avoids repeated runs for fixing the optial FA paraeters by a trial and error procedure and provides the best possible paraeters values. 6. Conclusion The optial location of FACTS devices play a vital role in achieving the proper functioning of these devices. However this paper ade an attept to identify the optial location and paraeter of which iniises the transission loss in the power syste network using Self Adaptive Firefly algorith. Siulations results are presented for IEEE1-bus IEEE30- bus and IEEE57- bus systes. Results have shown that the identified location of iniise the transission loss in the power syste network. With the above proposed algorith it is possible for utility to place devices in transission network such that proper planning and operation can be achieved with iniu syste losses. References 1. Hingorani, N.G.; and Gyugyi, I. (2000). Understanding FACTS: concepts and technology of flexible AC transission systes. IEEE Press, New York. 2. Mathur, R.M.; and Vara, R.K. (2002). Thyristor-based FACTS Controllers for Electrical Transission Systes. Piscataway: IEEE Press. 3. Abriz-perez, H.; Acha, E.; and Fuerte-Esquivel, C.R. (2000). Advanced SVC odels for Newton Raphson load flow and Newton optial power flow studies. IEEE Transaction on Power Syste, 15(1), Orfanogianni, T. (2000). A flexible software environent for steady state power flow optiisation with series FACTS devices. DSc Tech Diss, ETH, Zurich. 5. Larsen, E.V.; Clark, K.; Miske, S.A.; and Urbanek, J. (1). Characteristic and rating considerations of thyristor controlled series copensation. IEEE Transactions on Power Delivery, (2), Gyugyi, L. (12). Unified power flow controller concept for flexible AC transission syste. IEE proceedings, 13(), Yang, X.S. (2010). Nature-Inspired Meta-Heuristic Algorith. Beckington, Luniver Press. 8. Gerbex, S.; Cherkao, R.; and Gerond, A.J. (2001). Optial location of ulti type FACTS devices in a power systes by eans of genetic algoriths. IEEE Transaction on Power Syste,16(3), Saravanan, M.; Mary, R.S.S.; Venkatesh, P.; and Abraha, J.P.S. (2007). Application of particle swar optiisation technique for optial location of

13 Placeent for Loss Miniisation using Self Adaptive Firefly Algorith 303 FACTS devices considering cost of installation and syste loadability. Electrical Power Systes Research, 77(3-), Mondal, D.; Chakrabarti, A.; and Sengupta, A. (2012). Optial placeent and paraeter setting of SVC and using PSO to itigate sall signal stability proble. International Journal of Electrical Power & Energy Systes, 2(1), Siddhartha, P.; and Narayana, P.P. (2008). Optial location and controller design of STATCOM for power syste stability iproveent using PSO. Journal of the Franklin Institute, 35(2), Mohaid, I.R.; Khairuddin, A.; and Mustafa, M.W. (200). Optial allocation of FACTS devices for ATC enhanceent using Bees algorith. World Acadey of science Engineering and Technology, 3, Tripathy, M.; and Mishra, S. (2007). Bacteria foraging based solution to optiize both real power loss and voltage stability liit. IEEE Transactions on Power Syste, 22(1), Senthil, K.M.; and Renuga, P. (2012). Application of UPFC for enhanceent of voltage profile and iniisation of losses using fast Voltage stability index (FVSI). Archives of Electrical Engineering Journal, 61(2), Yang, X.S. (200). Firefly algoriths for ultiodal optiisation, Stochastic algoriths: Foundations and applications. SAGA 200, LNCS, Berlin, Gerany: Springer-Verlag, 572, Apostolopoulos, T.; and Vlachos, A. (2011). Application of the Firefly Algorith for solving the econoic eissions load dispatch proble. International Journal of Cobinatorics, 2011(523806), Taher, N.; Rasoul, A.A.; and Alireza, R. (2012). Reserve constrained dynaic econoic dispatch: A new fast self-adaptive odified firefly algorith. IEEE Syste Journal, 6(), Yang, X.S.; Hosseini, S.S.; and Gandoi, A.H. (2012). Firefly algorith for solving non-convex econoic dispatch probles with valve loading effect. Applied Soft Coputing, 12(3), Falcon, R.; Aleida, M.; and Nayak, A. (2011). Fault identification with binary adaptive fireflies in parallel and distributed systes. Proceedings of IEEE Congress on Evolutionary Coputation, Chandrasekaran, K.; and Sion, S.P. (2011). Deand response scheduling in SCUC proble for solar integrated theral syste using firefly algorith. Proceedings of IET Conference on Renewable Power Generation (RPG 2011), Chandrasekaran, K.; and Sion, S.P. (2012). Network and reliability Constrained unit coitent proble using binary real coded Firefly Algorith. International Journal of Electrical Power and Energy Systes, 3(1), Selvarasu, R, and Christober, A.R.C. (2013) Self Adaptive Firefly Algorith based transission loss iniisation using. In Proceedings of International Conference on Advanced Nanoaterials and Eerging Engineering Technologies,

14 30 R. Selvarasu and M. S. Kalavathi 23. Selvarasu, R; and Surya, K.M. (2013) Optial placeent of UPFC for voltage constrained loss iniisation using self-adaptive Firefly Algorith. International Review of Electrical Engineering, 8(), University of Washington. (2012). Power systes test case archive. Retrieved May 5, 2012 fro

15 Placeent for Loss Miniisation using Self Adaptive Firefly Algorith 305 Appendix A Figures and their Captions Read the Power Syste Data Select the population size Nand Maxiu nuber of Iterations for convergence check Generate the initial population while (terination requireents are not et) do for =1:N Alter the syste data α, β in, and γ according to th firefly values Run the load flow Copute the Real power loss Calculate I For n=1: N Alter the syste data according to n th firefly values Run the load flow Copute the Real power loss Calculate I If I < I n Copute γ,n using (8) Evaluate β,n using (7) Move th firefly towards n th firefly through () end if end for n end for, Rank the fireflies and find the current best End while End Fig. A-1. Pseudo Code of Firefly Algorith.

16 306 R. Selvarasu and M. S. Kalavathi Start Read power syste data Choose FA paraeters such as population size, Iter ax, α, β in and γ A Calculate the transission loss and copute light intensity I n using equation (6) K=0 Generate initial population and location of fireflies for =1:N B Is I < I n Yes No Move th firefly towards n th firefly using equation () Place the according to th fireflies Obtain the values for α, β in, and r fro th fireflies Run the load flow K= k+1 No n Is k > Iter ax B Calculate the transission loss and copute light intensity I using (6) for n=1:n Yes Optial solution is reached. The fire fly with largest light intensity is the optial solution Place the according to n th fireflies Run the load flow Print the results Stop A Fig. A-2. Flow Chart of the Self Adaptive FA.