A NEW TECHNIQUE OF LOAD SHEDDING TO STABILIZE VOLTAGE MAGNITUDE AND FAST VOLTAGE STABILITY INDEX BY USING HYBRID OPTIMIZATION

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1 A NEW TECHNIQUE OF LOAD SHEDDING TO STABILIZE VOLTAGE MAGNITUDE AND FAST VOLTAGE STABILITY INDEX BY USING HYBRID OPTIMIZATION Raja Masood Lark 1,2, Mohd. Wazr Mustafa 2, Abdulrahaman Okno Otuoze 2,3, Obalowu Olatunj Mohammed 2,3 and Alyu Hamza Sule 2,4 1 Department of Electrcal Engneerng, NED Unversty of Engneerng and Technology, Sndh, Pakstan 2 Faculty of Electrcal Engneerng, Unverst Teknolog Malaysa Skuda, Johor Bharu, Malaysa 3 Department of Electrcal and Electroncs Engneerng, Faculty of Engneerng and Technology, Unversty of Ilorn, Ilorn, Ngera 4 Department of Electrcal Engneerng, Hassan Usman Katsna Polytechnc, Ngera E-Mal: rmlark@gmal.com ABSTRACT The boundary lmtaton of power systems n terms of generaton and network growth, Owng to lack of generaton or transmsson capacty, due to ths a power system operates near to ts stablty boundares. The growng complexty of heavly loaded power systems stuck through dsturbances and outages makes the problem of voltage uncertanty even worse, a blackout s usually the result of ncreasng load beyond the transmsson capacty of the power system. Therefore, under voltage load sheddng (UVLS) s performed as a fnal remedy to avod larger scale voltage collapse, restore reactve power balance and fnally re-establsh the operatng condtons, so t s consdered, as state of the art to acheve voltage stablty. Weak buses are dentfed usng the Fast Voltage Stablty Index (FVSI). Moreover, t s capable for dentfcaton of crtcal areas n a large power system; determne the pont of voltage collapse, mum permssble load, and the most crtcal lne n an nterconnected system. It s hghlghted that f load shed s conducted at the locaton wth hgh FVSI ndex value, the system would become more voltage stable. Ths paper focuses on optmal load shed as well as enhancng the system voltage profle ths results to stablze fast voltage stablty ndex values by usng a hybrd optmzaton algorthm based on the well-known Genetc Algorthm (GA) and Partcle Swarm Optmzaton (PSO). GA has tradtonally been known for ts accuracy whle the PSO algorthm s popular for ts fast convergence tme. The GAPSO algorthm s utlzed to mnmze the total amount of load shed on the weak buses under the constrant of mantanng the mnmum system voltage profle. The performance of the proposed technque was assessed by smulatons n MATLAB/SIMULINK under the IEEE-30 bus meshed networks. Thus, the proposed technque s not only robust aganst system falures but s also effcent enough for real tme applcatons n power systems. Keywords: fast voltage stablty ndex, voltage collapse, voltage stablty, under voltage load sheddng. 1. INTRODUCTION Modern power systems are very complex, non lnear, heavly stressed and have plentful arrangements of operatng stuatons. The number of dsturbances that need to be nspected has rased massvely. One of the man causes for power blackouts s voltage nstablty whch s attrbuted to nsuffcent generaton as well as transmsson capactes. The ncreasng demand for electrc power has put a lot of pressure on the systems responsble for the operaton and control of the hghly complex power networks that exsts today. The load s consdered the drvng force for voltage stablty, e.g. When the system voltage magntude declnes, motors are used to mprove ts voltage magntude by rsng the amount of reactve power. However, n the extreme contngency condtons the exstng reactve power sources are not suffcent to stablze the decreasng system voltage and ncreasng FVSI values. Furthermore, factors such as unexpected load ncrements or component outage causes a voltage collapse resultng n blackout state. The major challenges faced by power system operators nclude change n the nature of loads, performance of the on load tap changer transformer, the dependency on generaton postoned remotely away from load centers, natural load growth, and the nfluence of protecton and control systems. Contngency condton may be created by overloadng the power system up to a certan lmt leadng to an outage of transmsson lne or a generator. Smlarly, a sudden change n load value or generatons may also gve rse to a contngency stuaton. Contngency analyss gves tools for buldng, analysng, and managng records of contngences and related volatons [1]. The success of UVLS n stablzng a system depends on determnng the optmal amount, tme and locaton for load sheddng. Sheddng lesser or more than requred amount of load does not arrest voltage nstablty and may even lead to a voltage collapse or over frequency problems, respectvely. Smlarly, sheddng load at the wrong place may cause unnecessary nterrupton, loss of customer trust, and the utlty revenue. The tme nstant at whch load sheddng needs to perform s also very crucal as dscussed n [2]. The UVLS scheme has been proven to be robust tool n stablzng systems sufferng from low voltage magntudes and ncreasng FVSI values[3-5], note that voltage nstablty does not only nfluence the local load area but may also spread to the adjacent area n an nterconnected power system, commonly known as cascadng falures. 2734

2 The decreasng magntude of voltage and ncreasng values of FVSI ndex are the sgn of power system nstablty and f remedal acton not taken tmely power system may falls n a blackout condton very quckly. To restore power flow solvablty and mprove voltage magntudes, the load buses are chosen based on (FVSI) value, hgh values of FVSI ndcate weak buses, whch are the most sutable canddate for load shed. Therefore, ths paper focuses on fndng the optmal amount of load shed whch stablze the decreasng magntude of voltage and ncreasng values of FVSI. In order to acheve ths hybrd technque based on the GA and PSO algorthms s proposed. The proposed technque converts UVLS nto an optmzaton problem wth a multobjectve functon ncludng mnmum amount of load shed, at selected weak buses and mnmum voltage drop n order to acheve voltage stablty at all buses, In addton t also stablze the ncreasng FVSI values. Thus the proposed technque has the ablty to stablze the voltage profle and FVSI values. Ths paper s structured as follows secton 2 provdes a revew of the exstng lterature relevant to ths research. Secton 3 explans problem formulaton whle secton 4 ntroduces some prelmnary background. The proposed UVLS technque s presented n secton 5 whereas secton 6 gves the smulaton studes and results. Fnally the concluson s gven n secton LITERATURE REVIEW A concrete approach offerng the least amount and fnest locaton of load sheddng was presented n [6]. The proposed technque uses a mult-stage and non-lnear approach to fnd the mnmum load shed at each stage. Genetc Algorthms were executed n the Hydro-Quebec system to estmate the amount of load shed n[7, 8],but the approach s unable to grp a broader range of load behavor, dfferent scenaros and short-term voltage nstablty problems. GA was utlzed to nvestgatefor optmal supply restoraton approach n the network of dstrbuton system [9]. Lkewsealternatvestudy [10] showedan optmzaton tool bulton GA to estmate and perform load shed. To solve steady State load sheddng problem a novel applcaton of the GA presented n [11]. A new adaptve load sheddng technque usng GA s proposed n [12]. The load buses are ranked from the strongest to the weakest. The weakest bus s consdered the best opton for load sheddng. The voltage stablty margn s hghly nfluence by the weakest buses n an nterconnected power system. Therefore, the dentfcaton of weak buses s necessary for plannng and operaton of power systems n long-term studes. Partcle Swarm Optmzaton was combned wth Smulated Annealng to form a hybrd, was mplemented to tackle UVLS problem more effcently n [13]. The technque was tested on the IEEE 14 and 118 bus test systems. However, ths technque can only be used for long term voltage stablty and s unsutable for short term voltage stablty. Another hybrd scheme consstng of Partcle Swarm Optmsaton (PSO) and Lnear Programmng (LP)was developed to resolve the ssues of low convergence and elmnate transmsson lne overloadng [14]. The technque was mplemented on the IEEE 14 bus system and had a fast convergence tme. However, t was unable to solve non-lnear problems. Modal analyss and PSO were combned to acheve optmal load sheddng and voltage stablty n [15]. However, the proposed technque works well on Transmsson networks only. For the dstrbuton system, a Comprehensve Learnng PSO (CLPSO) was developed to acheve an optmal partton, n case of upstream loss [16]. The proposed technque works successfully on an Egyptan 66kV, 45 bus meshed network and 33-radal bus system. The dynamcs related by voltage stablty are frequently slow [17], therefore, the use of statc based approaches s consdered as a good approxmaton [18-20].An adaptve under-voltage load sheddng scheme usng model predctve control and a technque for load sheddng based on the consderaton of voltage stablty was proposed n [21, 22]. To prevent voltage nstablty a new nteger value modellng of optmal load sheddng was acheved through hybrd dscrete partcle swarm optmzaton by consderng mult objectves, the proposed methodology was employed on IEEE 14 and 30 bus test systems[2]. Probablstc under voltage load sheddng usng pont estmate method was presented n [23]. Estebsar A, Pons [24] show that automatc UVLS s better to manual UVLS wth the Technoeconomc mpacts of automatc Undervoltage load sheddng under emergences. A robust UVLS scheme proposed by combnng GA and PSO to mprove transmsson lne performance wth the ftness of mnmum customer nterrupton cost was presented n[25]. However, the proposed technque does not acheve fast convergence and optmum amount load shed. Another study combnes GA and PSO to get optmal DG szng and locaton n dstrbuton networks[26].it s observed that hybrd technques perform well for large and complex power systems and produce more optmal and qualty solutons than ndvdual technques [27]. 3. PROBLEM FORMULATION The objectve functon s the sum of the weghed dfference between the pre-contngency and postcontngency for the actve power demands and may be formulated to mnmze the total load shed at selected buses and mnmzaton of voltage drop at all buses so that the voltage stablty s mzed. The objectve functon s gven as follows: N BUS 1 P b D P a D mn{ ( P f ( x ) f x ))} V V 2 1 NLS L mn (1) (2) 2735

3 Subject to V and where PL s the th load sheddng bus, mn (3) f ( x ) f ( x ) are the lmts of mnmum and mum load sheddng lmts at th load bus and V s the th bus voltage whch should not be less than 0.9.Equalty constrants of the networks are the power flow equatons. P( V) P P ( V) P( V, ) 0 G d Q( V) Q Q ( V) Q ( V, ) 0 G d NB P( V, ) V V Y cos( ) j j j j 1 NB Q ( V, ) V V Y sn( ) j j j j 1 Lkewse, the change n actve and reactve power generaton value under the base condton and for loadng condton are consdered as nequalty constrant. P P P 1,2,... NG mn G G G P P P mn G G G Q Q Q 1,2,... NG mn G G G Q Q Q mn G G G (4) (5) (6) (7) (8) (9) (10) (11) The magntude of all bus voltages s selected as an nequalty constrant whch s n the current state as well as the load shed condton. V V V N mn, L (12) Notatons used n above mathematcal equatons are explaned n Table-1. Table-1. Notatons used n mathematcal equatons b P D a P D P G Q P Q V G d d V 2 V 1 V V j Y j j j NB N L NG mn G Actve power demand at bus multplyng wth loadng factor before load shed (n stresses condton) Actve power demand at bus after load sheddng (unstressed condton) Actve power generated at th bus Reactve power generated at th bus Actve power demand at th bus Reactve power demand at th bus Bus voltage magntude Voltage after load sheddng (unstressed condton) Voltage before load sheddng (In stressed condton) Phase angle Bus voltage magntude at th bus Bus voltage magntude at bus j Admttance of lne th j th (Ω) Voltage angle at th bus Voltage angle atj th bus Admttance angle of th j th lne Number of buses Number of lnes Number of generators P Mnmum actve power generaton at th bus Maxmum actve power generaton at P th G bus mn Mnmum reactve power generaton at Q th G bus Maxmum reactve power generaton at Q th G bus Mnmum change n actve power at th bus mn P G Maxmum change n actve power at P th G bus mn Mnmum change n reactve power at Q th G bus Maxmum change n reactve power at Q th G bus V Mnmum voltage magntude at th bus mn V Maxmum voltage magntude at th bus 4. PRELIMINARY BACKGROUND 4.1 Genetc algorthm A non-lnear, mult-objectve problems requre a global optmzaton GA whch has obtaned substantal 2736

4 attenton as arobust stochastc search algorthm[28]. Developed algorthm s based on the bology of natural evoluton; GA s performed on a set of the populaton wth the applcaton of survval of the fttest prncple to yeld superor estmates of the soluton n a contnuous cycle on the lmt of predetermned constrants. Based on ndvdual s level of ftness, each generaton (soluton) produces a new set of estmatons and redevelops followng the prncple of operatons as those of natural genetcs. In ths method, the development of populatons of as et of ndvduals results, that are superor matched n terms of ther adaptaton to the gven condtons [29]. Three types of operators are nvolved n the basc form of GA namely, selecton, crossover, and mutaton. A populaton contans k chromosome representng canddate soluton n GA algorthm, the dmenson of each chromosome s m and the number of optmzed parameters s real value vector. Consequently, the dmenson of the space problem s ndcated by every optmzed parameter. Step 1: Intalzaton stage: k number of chromosome s generated randomly and counter t = 0 s set. [X m (0), m= 1,..., k], where x m (0) [x m,1 (0), x m,2 (0),. x m,j (0)]. X m,n (0) s produced n search space [x n mn x n ] randomly. Step 2: Ftness: the objectve functon use m, the best value, m best of the objectve functon, m s sought to evaluate each of the chromosomes n the ntal populaton and then the chromosome assocated wth the global best set as m best. Step 3: Tmng update: The tme counter, t s updated to t = t + 1. Step 4: Fresh populaton: The fresh populaton s created by followng the succeedng steps untl the fresh populaton s ended. Bascally, the followng steps are followed: a) Selecton: Based on ther ftness, two parent chromosomes from the populaton are chosen. b) Crossover: To form a new chld, the parents are then crossed over usng a crossover probablty. c) Mutaton: New chld s mutated at each chromosome usng mutaton probablty d) Acceptance: The new chld s now placed n a fresh populaton Step 5: Replacement: The Newly produced populaton s used to further run the algorthm. Step 6: Stoppng: Stop, f any of the stoppng crtera for next step s fulflled, otherwse go to step Partcle swarm optmzaton In 1995, Kennedy and Eberhardt ntroduced PSO [30]. Inspred by the socal behavour of brds flockng and fsh schoolng, a swarm ntellgence technque, PSO was establsh to be fast and robust n resolvng large-scale nonlnear mult-objectve optmzaton problems. It has been broadly employed n numerous engneerng problems ncludng UVLS. The man ssue s to dentfy collapse pont or mum loadng n the power system, PSO s sutable and fast to dentfy and t s successfully employed n UVLS problem. In developng PSO algorthm, the populaton of k partcles sgnfyng canddate solutons wth m beng the representaton of optmzed parameter are defned. Every partcle s an m dmensonal real-valued vector ndcatng every optmzed constrant gves a dmenson of the problem space. The followng steps explan the PSO technque. Step 1: Intalzaton: Set the tme counter,t = 0 and generate k chromosome randomly,[x m (0), m=1, k], where x m (0) = [x m,1 (0), x m,2 (0),.. x m,j (0)], x m,n (0) s randomly produced n search space, [x n mn, x n ]. V m (0) s randomly produced for estmaton of the objectve functon. For every partcle set x m *(0) = x m (0) and m*m = m m, m = 1,..n. Then, the best value of the objectve functon s sought m best. The partcle related wth m best s set as the global best, x** (0) wth an objectve functon m**. The ntal value of the w (0) s set to Step 2: Tmng update: The tme counter, t s updated tot = t + 1 Step 3: Update of the weght: The nerta weght s updated. Step 4: Update of the velocty: The ndvdual best and the global best s now used to replace the partcle velocty by the followng equaton: v ( t) ( t) v ( t 1) c r ( X ( t 1) x ( t 1) * j, k j, k 1 1 j, k j, k c r ( x x ( t 1))) * 2 2 best j, k Step 5: Poston update: Every partcle change ts poston based on the updated velocty, and may expressed by the followng equaton X m.n (t) = X m,n (t-1) + V m,n (t) Ths helps to set any partcle whch volates ts poston bounds n any dmenson to ts approprate lmt. Step 6: Evaluaton of Partcle: Based on updated poston every partcle s now evaluated. If m mn <m* then updates ndvdual best as x* m (t) = x j (t), m l = m l * Step 7: The mnmum value s now sought for; f mn<m**,then the global best s updated by m** = m mn and x** = x mn (t). Step 8: Stoppng: On the satsfacton of stoppng crtera then stop, otherwse go to step

5 4.3 Fast voltage stablty ndex Orgnatng from the equaton of two bus network shown n Fgure-1, the Fast Voltage Stablty Index can be formulated as Where X j, s lne reactance between lne and j, Z j s the mpedance between lne and j,q j s the reactve power flow at the recevng end and V s the sendng end voltage FVSI j 2 4Z j Q j 2 V X j (13) Bus V Bus j Vj S = P + jq Zj = Rj + jxj Fgure-1. Model of two bus power system.[31]. Sj = Pj + jqj The FVSI j ndex can be estmated for any of the lnes of the network and depends, bascally on the reactve power. In power systems, FVSI s consdered a strong ndex for analysng the voltage stablty condton [32]. FVSI s also useful n determnng power system s mum loadablty, on-lne voltage stablty assessment and dentfcaton of weak buses. Ths shows that FVSI provdes essental nformaton to correctly ndcate the weak buses for load sheddng. Let us consder the IEEE 30 bus system. Fgure-2 shows the trend of voltage and FVSI plotted aganst enhancng values of reactve power for the 30 th bus. It s found that the correlaton between the voltage magntude and FVSI s negatve.e. ncreasng the reactve power demand at Bus 30, results n a decrease n bus voltage magntude whle the correspondng FVSI values ncrease as evdent n Fgure-2. 1 Voltage Magntude V/S Reactve Power Voltage Magntude (pu) V FVSI Fgure-2. Bus voltage and FVSI ndex aganst ncreasng reactve power demand at bus PROPOSED LOAD SHEDDING METHOD In the feld of optmzaton hybrd metaheurstcs have emerged wth superor results n terms of best ftness and computaton tme. The proposed scheme s based on a hybrd approach by combnng GA and PSO. However, both suffer from ther own ndvdual drawbacks for example although GA s popular for producng accurate results but takes a long tme to converge. Smlarly PSO s popular for ts short convergence tme but may not always converge to the best soluton. GA and PSO have been proven to be well suted for generator and lne outage Reactve Power MVAR cases[33]. Therefore, by proposng a hybrd scheme based on GA and PSO n ths work, t s expected to combne the strengths of these technques and produce a better algorthm than ether of the algorthms deployed alone. The proposed algorthm to obtan the optmal amount of load shed for a power system under stress s gven n algorthm 1. ALGORITHM 1: GAPSO Input: Populaton sze, Problem sze, P crossover, P mutaton Output: S best 1 Populaton Intalze Populaton (Populaton sze, Problem sze ); θ: 2738

6 2 P g-best θ ; 3 for each P Populaton do 4 P velocty Update Velocty (P velocty, P l-best, P p-best, ); 5 P poston Update Poston (P poston, P velocty ); 6 f Cost(P poston ) Cost (P p-best ) then 7 P p-best P poston ; 8 f Cost (P p-best ) Cost (P l-best ) then 9 P l-best P p-best ; 10 S best P l-best ; 11 end f 12 end f 13 end for 14 Parents Select Parents (Populaton, Populaton sze ); 15 Chldren θ; 16 for each Parent 1, Parent 2 Parents do 17 Chld 1, Chld 2 Crossover (Parent 1, Parent 2, P crossover ); 18 Chldren Mutate (Chld 1, P mutaton ); 19 Chldren Mutate (Chld 2,P mutaton ); 20 end for 21 Evaluate Populaton (Chldren); 22 S best Get Best Solutons (Chldren); 23 Populaton Replace (Populaton, Chldren); 24 return S best ; 25 end The proposed algorthm replaces the local search mechansm of GA wth the global search mechansm of PSO as shown n lne 3 to 13 of Algorthm 1. After obtanng the global solutons usng PSO, the resultng optmum values are employed by GA to obtan the optmum value of load shed. 6. SIMULATION RESULTS (IEEE 30 BUS) The proposed hybrd GA-PSO algorthm was examned on the IEEE 30bus test system usng the MATPOWER [34, 35] toolbox n MATLAB. The system ncludes 6 generators wth buses located at 1, 2, 5,8,11 and 13 as shown n Fgure-8. It s made of 41 lnes, two Statc VAR sources at buses 10 and 24, and 4 tap changng transformers. The base load of the system s 283.4MW and MVAR. In heavy loadng condton when orgnal real and reactve loads are multpled by a loadng factor of 1.58, the total load s ncreased to MW and MVAR. The power flow analyss s possble and the values are converged but when loadng factor ncreased to 1.59 the power flow s not possble and the values dd not converge. Total mum possble ncrement of load s MW, so the total load ncrease at all buses by 2.834MW whch s 0.01 % of the base load 283.4MW wll lead to non-solvablty so t s consdered as total mum possble load sheddng for ths case. To nvestgate the performance of the proposed method and ts effcency, only sheddng of load on weak buses represents the best opton for restorng solvablty otherwse sheddng on healthy buses creates unnecessary nterrupton and does not restore solvablty. We suppose that the system loadng s ncreased by 1.58 tmes the base case, followng ths dsrupton the voltage profle of the overall system decreases as shown n Fgure-6. Fve weak buses are selected 30, 26, 29, 24 and 7 for load sheddng based on the hghest FVSI values as tabulated n Table-2. Dfferent loadng condtons at selected buses are lsted n Table-3, whch would gve knowledge to generate ther boundary. Table-4 and Fgure-3 shows the voltage magntudes of selected buses before and after load shed. It s clear from Fgures 3, 6 and 9 that voltage profle s mproved sgnfcantly by proposed technque. Table-2. Top fve weak buses selected for load sheddng. Lne Bus FVSI Rank Table-3. Dfferent loadng values for weak buses. loadng factor =1.58 loadng factor=1.59 Bus No. Base loadng P (MW) solvable Unsolvable Table-4. Bus voltage magntudes at weak buses before and after load sheddng. Volts after load Volts before Volts after load Volts after load Bus No shed by load shed shed by GA shed by PSO GAPSO

7 Voltage magntude (pu) Volts profle weak buses Weak buses Fgure-3. Volts magntude weak buses. GAPSO PSO GA Overloadng The proposed method makes a sgnfcant mprovement n the voltage profle of the system as shown n Fgures 3, 6 and 7. It s also observed that when the system s overloaded the voltage of the buses falls below 0.9pu as shown n Fgure-5. However, the proposed technque successfully stablzes these buses and thus the overall system voltage profle as shown n Fgures 3 and 6. Moreover, the proposed GAPSO technque also outperforms the GA and PSO n terms of the voltage profle as shown n Fgures 3 and 6. The proposed technque have also the ablty to stablze the FVSI values and Voltage on ncreasng reactve power demand on bus 30 as shown n Fgures 4 and 5 respectvely. The voltage of bus 30 falls to a very dangerous level 0.6pu (Fgure-5) f load sheddng not perform than t may lead to a system collapse condton. Moreover, the FVSI values of bus 30 are stable at 0.1 as shown n Fgure-4, whle the Voltage magntude s stable at 0.98pu as shown n Fgure-5. These results show that the proposed technque gves the most accurate results n term of stablze the voltage magntude and FVSI ndex values. The power system returns back to a safe and normal operatng condton after load shed. Therefore, the proposed method may be employed for real tme applcatons n power systems. FVSI Values Before load shed After load shed FVSI vs Reactve Power Demand Reactve Power MVAR Fgure-4. FVSI values before and after load shed. 2740

8 Voltage magntude (pu) Voltage Magntude vs Reactve Power Before load shed After load shed Reactve Power MVAR Fgure-5. Voltage magntude before and after load shed. Vpu GA PSO GAPSO Normal Case Overlaod voltage Buses Fgure-6. Voltage profle of IEEE 30 bus test system after load sheddng. 2741

9 Voltage Profle IEEE 30 Bus Voltage PU Buses GAPSO PSO GA Fgure-7. Volts profle of all algorthms. 2742

10 Fgure-8. IEEE 30 bus test system [36, 37]. 7. CONCLUSIONS Ths paper proposed a hybrd GA-PSO based technque for load sheddng n power systems. The proposed methodology explots the advantages of GA and PSO technques by combnng them n a sngle algorthm. The proposed algorthm uses threshold values of FVSI to select the weak buses for load sheddng. The performance was evaluated usng the Matpower envronment n MATLAB and compared wth the performance of GA and PSO algorthms used ndvdually for load sheddng. The results show that the proposed algorthm was mplemented on IEEE 30 bus test systems. The GAPSO algorthm sheds the mnmum amount of load and brngs a sgnfcant mprovement n voltage profle along wth stable FVSI values whch guarantees a secure power system operaton of the collapsng system. Moreover, the proposed algorthm also outperforms the GA and PSO algorthms. The results clearly ndcate the effectveness of proposed method. Thus t can be concluded that proposed technque for load sheddng reduces the FVSI ndex hence reducng the probablty of voltage nstablty, fnally acheved stablzed voltages whch ensures power system relablty. ACKNOWLEDGEMENT The authors are gratefully acknowledgng the Research Facltes provde by Unverst Technolog Malaysa and fnancal support by Human Resource Development under the scheme Strengthenng of NED Unversty of Engneerng and Technology, Mega-M3 of the Hgher Educaton Commsson (HEC), Pakstan. NED Unversty of Engneerng and Technology Sndh, Pakstan. REFERENCES [1] Roy AK, Jan SK Contngency analyss n power system. 2743

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