Steady State Load Shedding to Prevent Blackout in the Power System using Artificial Bee Colony Algorithm

Transcription

1 Jurnal Teknolog Full paper Steady State Load Sheddng to Prevent Blackout n the Power System usng Artfcal Bee Colony Algorthm R. Mageshvaran a*, T. Jayabarath b a School of Electrcal Engneerng. VIT Unversty. Vellore , Taml Nadu, Inda b School of Electrcal Engneerng. VIT Unversty. Vellore , Taml Nadu, Inda * Correspondng author: rmageshvaran@vt.ac.n Artcle hstory Receved :26 June 2014 Receved n revsed form : 15 February 2015 Accepted :15 March 2015 Graphcal abstract Intalze food source poston, the algorthm parameters Calculate the nectar amount Determne the new food postons for the employed bees Calculate the nectar amount All onlooker dstrbuted Yes Memorze the poston of best food source Fnd the abandoned food source (e., the ndex of the food source whose tral value exceed the lmt and the correspondng employee bee wll behave as scout bee)of best food source No Determne the new food postons for the employed bees Select a food source for the onlooker Abstract Real and reactve power defcences due to generaton and overload contngences n a power system may declne the system frequency and the system voltage. Durng these contngences cascaded falures may occur whch wll lead to complete blackout of certan parts of the power system. Under such stuatons load sheddng s consdered as an emergency control acton that s necessary to prevent a blackout n the power system by relevng overload n some parts of the system. The am of ths paper s to mnmze the amount of load shed durng generaton and overload contngences usng a new meta-heurstc optmzaton algorthm known as artfcal bee colony algorthm (ABC). The optmal soluton for the problem of steady state load sheddng s done by takng squares of the dfference between the connected and suppled real and reactve power. The suppled actve and reactve powers are treated as dependent varables modeled as functons of bus voltages only. The proposed algorthm s tested on IEEE 14, 30, 57, and 118 bus test systems. The applcablty of the proposed method s demonstrated by comparson wth the other conventonal methods reported earler n terms of soluton qualty and convergence propertes. The comparson shows that the proposed algorthm gves better solutons and can be recommended as one of the optmzaton algorthms that can be used for optmal load sheddng. Keywords: Optmal load sheddng; artfcal bee colony algorthm; overload contngency; generaton contngency; voltage dependent load model 2015 Penerbt UTM Press. All rghts reserved. Produce new poston for the exhausted food source All onlooker dstrbuted No Yes Fnal food source poston 1.0 INTRODUCTION Durng normal condtons and those due to small perturbaton, power systems are well desgned to operate and meet the load requrements wthout volatng the constrants of the system. Even under emergency condtons, the dsturbed system state can be made to regan ts normal state wth the help of the control loops lke automatc voltage regulator (AVR) and automatc load frequency control (ALFC). But under extreme emergency condtons lke sudden ncrease n the system demand or unexpected outages, the system constrans and operatonal lmts are volated. Load sheddng s consdered as the ultmate measure to restore the system back to ts normal operatng condtons. Load sheddng s defned as coordnated sets of controls that decrease the electrc load n the system. By carryng out load sheddng, the perturbed system can be forced to settle to a new equlbrum state. Dfferent methods of load sheddng ether n steady state or n transent state have been proposed. An optmal load sheddng program fnds a best steady-state stable operatng pont for a post fault system wth a mnmum amount of load shed. Ref. [1] has formulated the optmal load sheddng problem whch uses the sum of the squares of the dfferences between connected and suppled real and reactve power. The optmzaton package MINOS [11], developed to solve large scale dense or sparse lnearly or nonlnearly constraned or unconstraned optmzaton problems s used to smulate the algorthm. An algorthm to mnmze the amount of load curtalment whch s based on Newton-Raphson (NR) method for solvng the power flow equatons, and Kuhn-Tucker theorem for the optmzaton has been descrbed n [2]. Here, the load sheddng polcy, defnng the prorty schedules s obtaned frst, and then the mnmum load to be shed at each bus s calculated. In the problem formulaton of ths work the system reactve power and losses are not consdered. Also the actve and reactve powers of loads are assumed to be ndependent of bus voltages. 74:1 (2015) eissn

2 114 R. Mageshvaran & T. Jayabarath / Jurnal Teknolog (Scences & Engneerng) 74:1 (2015), A method for optmal load curtalment that consders generator control effects, voltage and frequency characterstcs of the load has been proposed n [3]. Second-order gradent technque s used here to solve the resultng nonlnear optmzaton problem. Ths method s presumed to be an mprovement on the method of [2]. Inablty to curtal system loads durng an emergency s the major drawback of the formulaton n [3]. Moreover ths algorthm does not converge under emergency condtons snce the system generaton s over defned through governor acton and does not suffcently reconcle frequency varatons appled to the load model equatons. Ref. [4] has presented a reformulated optmal load sheddng polcy that takes nto account generator control effects and voltage and frequency characterstcs of loads. Ref. [5] has presented another work of optmal load sheddng problem that uses the sum of squares of the dfference between the connected actve and reactve load and the suppled actve and reactve power. In the formulaton, the suppled actve and reactve power s consdered as dependent varables modeled as a functon of bus voltages only. Mnmzaton of load loss usng a senstvty based approach has been proposed n [6]. In order to lmt the sze of the load beng dropped, dfferent prortes to loads are assgned usng a weghted error crteron. Ref. [7] and [8] have formulated a non-lnear optmzaton problem for the optmal load sheddng and reschedulng of generators durng an emergency state. The non-lnear problem has been approxmated by an accurate senstvty model whch takes nto account the real and reactve nodal njectons, voltage magntudes and angles and loads senstvty to voltage magntudes. The accuracy of the soluton n both these papers s affected by the lnearzaton approach. In [9] and [10] two dfferent methods for generaton reschedulng and load sheddng to allevate lne overloads, based on the senstvty of lne overloads to bus power ncrements have been developed. In [11] a mesh approach has been developed for the formulaton of the network equatons n the load flow analyss. A hybrd approach usng a combnaton of an mpedance matrx method and a nodal-admttance matrx method whch explots the salent characterstcs of the mpedance and admttance method s also developed. In [12] dfferental evoluton algorthm has been mplemented for optmal allocaton o repar tmes and falure rates to segments of a meshed dstrbuton system. An optmal under voltage load sheddng scheme to provde long term voltage stablty usng a new hybrd partcle swarm based smulated annealng optmzaton technque has been presented n [13]. The techncal and economcal aspects of each load are consdered by ncludng the senstvtes of voltage stablty margn n to the cost functon. In [14] a new voltage stablty margn ndex consderng load characterstcs has been ntroduced n under voltage centralzed load sheddng scheme. In [15] quantum nspred evolutonary programmng has been mplemented for the optmal locaton and szng of DG n radal dstrbuton system. In the present paper the optmal load sheddng problem to mnmze the sum of squares of the dfference between the connected loads and the suppled power has been formulated. The ABC algorthm s mplemented to solve the formulated optmzaton problem. The performance of the proposed algorthm for generaton and overload contngences are analyzed. Testng s done usng IEEE 14, 30, representng small and 57, 118, representng medum power system. Currently only conventonal methods have consdered both real and reactve power loads to be shed. Evolutonary computaton has been used already for dfferent load sheddng strateges that have consdered sheddng of real power loads only [12] [15]. However there has been no work reported n the lterature that consders both real and reactve power loads for sheddng. Therefore n ths work both real and reactve power loads are consdered for sheddng and solved by one of the meta-heurstc algorthms vz. ABC algorthm. The optmal solutons obtaned wth the proposed algorthm are compared wth those reported n [1]-[3] and [5]. 2.0 PROBLEM FORMULATION Durng emergency condtons an operatonal objectve s to mnmze the dfference between the connected load and the suppled power subjected to equalty and nequalty constrants [1]. The objectve functon can be expressed as F NB P Pd Q (1) d d Q d where NB s the number of buses n a system, the actve and reactve powers suppled to the load. P, and Q are d d P d, and Q d are the connected actve and reactve load. The weghtng factors and are the parameters related to prorty assgned to the demand at each bus. Flat values are assgned to the prortes of the loads. The objectve functon gven n Eq. (1) s subjected to both network and system lmts constrants resultng n a non-lnear optmzaton problem. 2.1 Equalty Constrants The power flow equatons of the networks are the equalty constrants. These equatons of a network wth NB number of nodes can be wrtten as P V P G P d for V V, for 1,... NB P 0 Q Q V V, Q V where G 1,... NB P and G G d power generatons at bus. Q 0 (2) (3) Q represents the respectve actve and reactve P and Q represents the actve and reactve power njectons at bus. The actve and reactve power njectons at bus n terms of bus voltage magntude and phase angle s expressed as P Q V NB V 1 j Y j V, cos (4) NB V V 1 j Y j V, sn (5) 2.2 Inequalty Constrants The nequalty constrants consdered are the lmts of real and reactve power generatons, bus voltage magntudes and angles, and lne flows. The lmts of real and reactve power generatons of the system are j j j j

3 115 R. Mageshvaran & T. Jayabarath / Jurnal Teknolog (Scences & Engneerng) 74:1 (2015), P P P 1,... NG (6) mn max G G G Q Q Q 1,... NB (7) mn max G G G mn mn where P and G Q are the mnmum real and reactve power G max max generatons and P and G Q are the maxmum avalable real G and reactve power generatons. The lmts of bus voltages of the system are mn max V V V 1,... NB (8) mn max where V and V are the mnmum and maxmum lmts of bus voltages of the system. Ether current magntude constrant due to thermal consderatons or electrcal angle (dfference n voltage angle across a lne) constrant due to stablty consderatons, can be consdered for transmsson lne loadng lmts. In the present formulaton the electrcal angle nequalty constrant s used, whch can be expressed as LF 1,... NB 1; j 1,... NB (9) j j where and j and j. j are the voltage angles at bus and bus j, and s the maxmum voltage phase angle dfference between 2.3 Load Model There are dfferent load models to express the system actve and reactve power demands n terms of bus voltage and system frequency. Here a polynomal functon of the bus voltage s used to express the actve and reactve power demands at any gven bus as N1 N2 V V Pd Pd Pp Pc P z (10) V V N3 N4 V V Qd Q d Qq Qc Q z (11) V V where P, P, p c P, z Q, Q and q c Q are constants assocated wth z ths voltage dependent load model (VDLM) and N 1, N 2, N 3 and N 4 are the powers of polynomal. 2.4 Modfed Objectve Functon The optmal load curtalment problem can be descrbed by Equatons (1)-(11). Substtutng Equatons (2) and (3) n to Equaton (1) results n a modfed objectve functon n terms of PG and P as NB 2 2 [ ( G d ) ( G d ) (12) 1 J P P P Q Q Q 3.0 IMPLEMNTATION OF ARTIFICIAL BEE COLONY ALGORITHM (ABC) FOR OPTIMAL LOAD SHED bees. The flow chart for the artfcal bee colony algorthm [19] s shown n Fgure 1.Ths algorthm s mplemented n the followng steps. Step-1: Intalze the artfcal bee colony algorthm parameters CS : Colony sze = Number of employed bees + Number of onlooker bees SN : Number of food sources (e., Number of solutons) = Number of employee bee = CS / 2 D : Dmenson of the problem (e., Number of parameters of the problem) Lmt: Lmt for scout bee [lm t CS / 2* D] Tral : It s a vector of dmenson equal to [1,Number of food source] Intally ts value s set to zero. Maxmum cycle: Gves the total number of teratons. Intal food source of dmenson [ SN, D] s randomly generated wthn the gven range and the objectve functon f s calculated from Equaton (12) and the ftness of each food source s evaluated usng Equaton (13) and Equaton (14) ( ftness) 1 f f 0 (13) 1 f ( ftness) 1 abs( f ) f f 0 (14) Then the teraton counter starts. Step-2: Employee Bee Phase: New food source s determned usng Equaton (15) v x ( x x ) (15), j, j, j, j k, j Where '' s the th employee bee, ' j ' s the random ndex 'k' s the random ndex based on the dmenson D of the problem. neghbour to ''. ', j ' s the randomly generated number between [ 1,1 ] For each employee bee the objectve functon f & ( ftness ) value s evaluated and compared wth prevous (old) food source and the best one s replaced by the worst. For each dscard of new food source 'v', the tral counter s ncremented. The probablty of all the food sources s determned usng Equaton (16). SN P ft / ft (16) where j j1 ft, ft s the ftness value of j respectvely. th th, j employee bee Step-3: Onlooker Bee Phase: Each onlooker bee selects a food source to explot wth the probablty. The search for the best new source s done n the same manner as that of Step-2 and the best source replaces the worst. Here also for each dscard of new food source 'v', the tral counter s ncremented. The ABC algorthm was formed by observng the actvtes and behavor of the real bees, whle they were lookng for the nectar resources and sharng the amount of the resources wth the other

4 116 R. Mageshvaran & T. Jayabarath / Jurnal Teknolog (Scences & Engneerng) 74:1 (2015), Intalze food source poston, the algorthm parameters Calculate the nectar amount Determne the new food postons for the employed bees Calculate the nectar amount All onlooker dstrbuted Yes No Memorze the poston of best food source Determne the new food postons for the employed bees Select a food source for the onlooker gradent technque based on Kuhn-Tucker theorem [2] and second order gradent technque [3]. The sngle lne dagram and the detaled data of IEEE-14, 30, 57 and 118-bus systems are gven n [11]. The software was wrtten n Matlab and executed on 2.4 GHz, Intel 3 processor wth 2 GB RAM PC. The decson varables of ths problem are the real and reactve power loads to be shed at each bus. Thus for a 14-bus system the number of decson varables wll be 28. The permssble amount of load shed n each bus s assumed as 10 % to 80 % of the total load connected at each bus. The rest 20 % of the load s reserved for emergency condtons. The volaton of the nequalty constrants are penalzed n the objectve functon. The constants and the powers of the polynomal assocated wth the load model gven n Equaton (10) and (11) were assumed as follows: P =0.2, p P =0.3, c P =0.5, z Q =0.2, q Q =0.3 and c Q =0.5. z N1 =1, N 2 =2, N 3 =1 and N 4 = Applcaton to Small Sze Systems Fnd the abandoned food source (e., the ndex of the food source whose tral value exceed the lmt and the correspondng employee bee wll behave as scout bee)of best food source Produce new poston for the exhausted food source No All onlooker dstrbuted Yes Fnal food source poston Fgure 1 Flow chart for artfcal bee colony algorthm Step-4: The selecton of whch employee bee wll behave as scout bee depends on the ndex of the food source (whch s not mproved) whose tral value s exceeded the lmt and abandoned. For that ndex the scout bee randomly search for a food source ndependent of prevous hstory usng Equaton (17) and teraton counter s ncremented. x x r x x mn max mn, d d ( d d ) (17) where 'r' s a random real number wthn the range [ 0,1] mn max x d and x d are the lower and upper borders n the dmenson of the problem space. th d Step-5: Best food source whch s havng the hghest ftness value s prnted. 4.0 SIMULATION RESULTS AND ANALYSIS The proposed ABC approach has been verfed on two small systems IEEE 14-bus and 30-bus, two medum systems IEEE 57- bus and 118-bus test systems. The results obtaned by the proposed approach are compared wth those obtaned by usng conventonal methods reported earler, such as projected augmented lagrangan method mplemented usng MINOS an optmzaton package [1], IEEE 14, 30-bus test systems [11] are consdered here. The two cases of contngences analysed are loss of generaton and overload. The food number of the proposed ABC algorthm for these test systems s IEEE 14-bus System Ths system conssts of 20 lnes, two generators, three synchronous condensers, three transformers and one statc capactor. The generated reactve power lmts are: 150 Q G1 150, 0 Q G 2 140, 0 Q G 3 140, 0 Q G and 0 Q G The generated actve power lmts are: 0 P G 1 200, 0 P G The connected load for ths test system s 259 MW. Under normal operatng condtons the suppled power to the connected load usng NR method wth VDLM s MW. The reactve power suppled by the method used here s MVAR. The suppled powers n Refs. [2], [3] and [5] are MW, MW and MW respectvely for a connected load of 259 MW. For the same connected load the suppled power In [1] s MW. The reactve power suppled by the methods reported n Refs. [2], [3] and [5] are 73.5 MVAR, MVAR and MVAR respectvely. The defct n the suppled power obtaned n ths paper and n Refs. [1], [3] and [5] represents the effect of usng a voltage dependent load model (VDLM) to express the actve power. The total actve and reactve power generaton obtaned n ths paper under normal operatng condton s MW and MVAR respectvely. The total real power loss obtaned here s 13.2 MW. The total actve power generaton obtaned by the method reported n Refs. [2], [3] and [5] for the normal operatng condtons were MW, 270 MW and MW respectvely. The correspondng reactve power generaton reported n these Refs. [2], [3] and [5] were 8.56 MVAR, MVAR and MVAR respectvely. The total actve power loss presented n the Refs. [2], [3] and [5] were MW, MW and MW respectvely. The bus voltages vary between 1.01 pu and 1.08 pu n the NR method wth VDLM, whereas the voltages vary from 0.98 pu to 1.07 pu n Ref. [1,5], 0.93 pu to pu n [2] and pu to pu n [3].

5 117 R. Mageshvaran & T. Jayabarath / Jurnal Teknolog (Scences & Engneerng) 74:1 (2015), The am of optmal load sheddng s to restore normal operatng condtons followng generaton and overload contngences by mnmum load sheddng Loss of Generaton Contngency An abnormal operatng condton representng the loss of generatng unt-2 generatng 72.0 MW or 26% of normal generaton s consdered n ths secton. The amount of load shed usng the proposed ABC approach s MW and the actve power suppled s MW. Whereas the load shed and the actve power suppled reported by Mostafa n Refs. [1] and [5] are MW and MW respectvely. It can be observed that the proposed approach has yelded lower amount of load shed and hgher suppled actve power demand when compared wth other methods. The total actve power suppled reported n Refs. [2] and [3] for ths contngences were 192 MW and MW respectvely. Reactve powers suppled by the proposed method and by the methods used n the Refs. [2], [3] and [5] are MVAR, MVAR, 65.2 MVAR and MVAR respectvely. The total actve and reactve power generaton obtaned by the proposed ABC approach for ths abnormal condton s MW and 80 MVAR respectvely. The correspondng system loss obtaned by ths approach s MW. Whereas the total actve power generaton obtaned by the method reported n Refs. [2], [3] and [5] for ths loss of generaton contngency were 200 MW, MW and MW respectvely. The correspondng reactve power generaton reported n these Refs. [2], [3] and [5] were MVAR, MVAR and MVAR respectvely. The correspondng actve power losses reported n the Refs. [2], [3] and [5] are MW, MW and MW respectvely. From the above stated data t can be observed that the proposed approach has yelded lower amount of load shed and hgher suppled actve power when compared wth other methods reported n [2], [1] and [5]. In [1] t s reported that the method of [3] fals to converge for ths contngency. At the end of the optmzaton the actve power suppled s MW wth a system generaton of MW. Ths shows that the system generaton s less than the suppled power. Therefore the actve power loss becomes negatve n ths work. The bus voltages vary between 1.01 pu and 1.09 pu n the proposed ABC approach. Whereas the voltages vary from pu to pu n Refs. [1, 5] and pu to 1.1pu n [2]. The proposed approaches yelds better bus voltage profle as compared wth those reported n other approaches. Fgure 2 shows the convergence characterstcs of the proposed ABC algorthm for the test system operated under the generaton contngency consdered here. The maxmum teratons to converge for the proposed approach s 19 teratons. Objectve functon Number of teratons Fgure 2 Convergence characterstcs of ABC approach for IEEE 14-bus system under loss of generaton of 72 MW Range of Generaton Defct Contngences The test system s also subjected to certan range of generaton defct contngences. The range of generaton s vared from 260 MW to 160 MW, wth a connected load of 259 MW, whch means, the resultng generaton defct vares from 0 to 99 MW. Fgure 3 shows that the mnmum teratons to converge for the proposed ABC algorthm s 26 correspondng to 160 MW generaton. Snce the severty of the contngency consdered n ths case s ncreased as compared wth prevous case (Generaton loss of 72 MW), the number of teratons needed to converge s ncreased. Fgure 4 (a) shows the total suppled power obtaned by the proposed ABC approach decreases from MW at 260 MW generatons to MW at 160 MW generatons. Fgure 4 (b) shows the correspondng actve power loss decrease from 10.6 MW to 5.91 MW. Whereas the total suppled power n Refs. [1] and [5] decreases from MW at 260 MW generaton to MW at 160 MW generaton wth correspondng actve power loss decrease from MW to 6.22 MW and n [2] the suppled load decreases from MW to MW wth the correspondng actve power loss decrease from 7.08 MW to 2.78 MW for the same range of generaton defcts. Objectve functon Number of teratons Fgure 3 Convergence characterstcs of ABC approach for IEEE 14-bus system under generaton defcts contngency

6 118 R. Mageshvaran & T. Jayabarath / Jurnal Teknolog (Scences & Engneerng) 74:1 (2015), Suppled power n MW MW at 240% overload. Whereas for the same range of overload contngences, n Refs. [1, 5] and [2] the suppled power decreases from MW to MW and from 383.3MW to MW respectvely. Fgure 6 a shows the decrease n suppled power from MW at 150% overload to MW at 240% overload for the proposed ABC approach. The correspondng ncrease n the system losses s shown n Fgure 6b. For ths range of overload contngences the system losses obtaned by the proposed method ncreases from MW to MW. Whereas n Refs. [1, 5] and [2] the system losses ncreases from MW to MW and from 16.7 MW to MW respectvely. 160 System losses n MW Generated power n MW (a) 160 Objectve functon Number of teratons Fgure 4 IEEE 14-bus system under generaton defct contngences usng ABC approach a- Optmal suppled load, b- System losses (b) For ths generaton defct contngences the maxmum voltage obtaned by the proposed ABC method remans constant at 1.03 pu and the mnmum voltage vares between 1.00 pu and pu. Whereas n Refs. [1] and [5] the maxmum voltage decreases from pu to pu and the mnmum voltage magntude decreases from pu to 0.77 pu. For IEEE 14 bus system, bus 3 and bus 4 are the frst and second heavest load buses respectvely. The suppled powers at bus 3 and bus 4 by the proposed ABC approach are 89.2 MW and MW respectvely. In Refs. [1] and [5] the suppled powers at bus 3 and bus 4 are MW and MW respectvely. The suppled powers at bus 3 n [2] s MW and at bus 4 t s MW. The proposed approach supples more power at the heavest loaded buses- bus 3 and bus 4- as compared to Refs. [1], [2] and [5]. 200 Generated power n MW 160 Fgure 5 Convergence characterstcs of ABC approach for 14-bus system under overload contngency Suppled power n MW Connected load n MW (a) Overload Contngences In ths contngency t s consdered overloadng up to 55.4% above the maxmum avalable generaton of 400 MW. Ths corresponds to a connected load between MW (150% of the nomnal load ) to MW (240% of the nomnal load). Fgure 5 shows the maxmum number teratons requred for the proposed approach s 27 teratons correspondng to connected load of MW. For ths contngency the suppled power obtaned usng the proposed method decreases from MW at 150% overload to

7 119 R. Mageshvaran & T. Jayabarath / Jurnal Teknolog (Scences & Engneerng) 74:1 (2015), System losses n MW (b) Fgure 6 IEEE 14-bus system under overload contngences usng ABC Approach a - Optmal suppled power, b - System losses The proposed approach supples MW to bus 3 and MW to bus 4. Whereas Refs. [1,5] supples to bus 3 MW and MW to bus 4. Ref [2] supples MW and MW to buses 3 and 4 respectvely. So, durng the overload contngency consdered the proposed method supples more power to these heavest load buses as compared to the power suppled by the other methods to these buses. A better voltage profle s obtaned by the proposed method durng ths contngency. Maxmum voltage obtaned usng the proposed approach s constant at pu and the mnmum voltage ncreases from to pu. In Refs [1, 5] the maxmum voltages vary between pu and pu. and the mnmum voltage ncreases from 0.77 pu to 0.95 pu. The maxmum voltage reported n [2] s constant at 1.2 pu and the mnmum voltage ncrease from pu to pu IEEE 30-bus System Connected load n MW Ths system conssts of 41 lnes, three generators, three synchronous condensers, two statc capactor and three transformers. The generated reactve power lmts are: 20 G1 43, 10 Q G8 30, 20 G2 43, 10 Q G11 45, 20 G5 50, 10 Q G13 50, The generated actve power lmts are: [3] and [5] are MVAR, MVAR and MVAR respectvely. The defct n the suppled power obtaned n ths paper and n Refs. [1], [3] and [5] represents the effect of usng a VDLM to express the actve power. The total actve and reactve power generaton obtaned n ths paper under normal operatng condton s MW and MVAR respectvely. The total real power loss obtaned here s MW. Whereas the total actve power generaton obtaned by the methods reported n Refs [2], [3] and [5] for the normal operatng condtons were MW, MW and MW respectvely. The correspondng reactve power generaton reported n these Refs [2], [3] and [5] were MVAR, MVAR and MVAR respectvely MW, MW and MW are the respectve total actve power losses reported n the Refs. [2], [3] and [5]. The bus voltages vary between pu and pu n the proposed approach whereas the voltages vary from pu to 1.10 pu n Ref. [1,5], pu to 1.10 pu n [2] and pu to pu n [3] Loss of Generaton Contngency An abnormal operatng condton representng the loss of 60 MW or 20.35% of normal generaton s consdered here. The amount of load shed and the suppled actve power demand obtaned usng the proposed ABC method s MW or % of the nomnal load and MW respectvely. Whereas the load shed and the actve suppled power n Refs. [1] and [5] are MW or % of the nomnal load and MW respectvely. For the same generaton loss, the amount of load shed and the suppled power n [2] are MW or 14.38% of the nomnal load and MW respectvely. It can be observed that the proposed approach has yelded lower amount of load shed when compared wth the other methods. Reactve powers suppled by the proposed ABC approach and by the others methods used n the Refs. [2], [3] and [5] are MVAR, MVAR, MVAR and MVAR respectvely. The total actve and reactve power generaton obtaned by the proposed ABC approach for ths case s 250 MW and MVAR respectvely. The correspondng actve power loss obtaned by ths approach s MW. Whereas the total actve power generaton obtaned by all the methods reported n Refs. [2], [3] and [5] was 250 MW. The correspondng reactve power generaton reported n these Refs. [2], [3] and [5] were MVAR, MVAR and MVAR respectvely. The correspondng actve power losses reported n the Refs. [2], [3] and [5] are MW, MW and MW respectvely. Fgure 7 shows the convergence characterstcs of the proposed ABC approach for the test system operated under ths contngency representng loss of generaton of 60 MW. The maxmum teratons to converge for the proposed approach s 17 teratons. 0 P G 1 175, 0 P G P G 5 75 The suppled power by the NR method wth VDLM used n ths paper under normal operatng condtons s MW for a connected load of MW. The reactve power suppled by the method used n ths paper s MVAR. The suppled powers n Refs. [2], [3] and [5] are MW, MW and MW respectvely for a connected load of MW. In [1] the suppled power s MW for the same connected load. The reactve power suppled by the methods reported n Refs [2],

8 120 R. Mageshvaran & T. Jayabarath / Jurnal Teknolog (Scences & Engneerng) 74:1 (2015), Objectve functon Number of teratons Fgure 7 Convergence characterstcs of ABC approach for the IEEE 30- bus system under loss of generaton of 60 MW The bus voltages vary between pu and pu n the proposed ABC approach.whereas the voltages vary from pu to pu n Refs. [1,5], pu to 1.10 pu n [2] Range of Generaton Defct Contngences The test system s also subjected to a range of generaton defct contngences. The range of generaton s vared from 300 MW to 190 MW, wth a connected load of MW, whch means, the resultng generaton defct vares from 0 to 93.3 MW. Fgure 8 shows the convergence characterstcs of the proposed ABC approach for the generaton of 190 MW and the mnmum teratons beng 20. The number of teratons requred s ncreased n ths case because the severty of the contngency consdered here s more than the prevous case representng loss of generaton of 60 MW. Fgure 9(a) shows the total suppled power obtaned by the proposed ABC approach decreases from MW at 300 MW generatons to MW at 190 MW generatons and Fgure 9(b) shows the correspondng actve power loss decreases from 9.75 MW to MW. Whereas the total suppled power n Refs. [1] and [5] decreases from MW at 300 MW generaton to MW at 190 MW generaton wth correspondng actve power loss decrease from MW to 6.76 MW and n [2] the suppled power decreases from MW at 300 MW generaton to MW at 190 MW generaton wth the correspondng actve power loss decrease from 9.87 MW to 3.94 MW for the same range of generaton defcts. For ths generaton defct contngences the maxmum bus voltage obtaned by the proposed ABC method remans constant at pu and the mnmum voltage vares between 1.01 pu and pu. Whereas n Refs. [1] and [5] the maxmum voltage decreases from 1.1 pu to pu and the mnmum voltage magntude vares from pu to 0.77 pu and n [3] the maxmum voltage s constant at 1.1 pu and mnmum voltage magntude ncreases from pu to pu. Objectve functon Fgure 8 Convergence characterstcs of ABC approach for IEEE 30-bus system under generaton defcts contngency Suppled power n MW System losses n MW Number of teratons 260 Generated power n MW (a) 260 Generated power n MW (b) Fgure 9 IEEE 30-bus system under generaton defct contngences usng ABC approach a- Optmal suppled power, b- System losses For IEEE 30 bus system, bus 5 s the bus wth heavest load and bus 8 s the bus wth second heavest load. The suppled powers by the proposed ABC approach at bus 5 and bus 8 are MW and MW respectvely at a generaton of 250 MW. In Refs. [1] and [5] the suppled powers at bus 5 and at bus 8 are MW and MW respectvely. The suppled power at bus 5 n [2] s MW and at bus 8 t s MW. The proposed approach supples more power at the heavest loaded buses- bus 5 as compared to Refs. [2]

9 121 R. Mageshvaran & T. Jayabarath / Jurnal Teknolog (Scences & Engneerng) 74:1 (2015), Overload Contngences Overloadng up to % above the maxmum avalable generaton of 320 MW s consdered here. Ths corresponds to a connected load between MW (110% of the nomnal load ) to MW (160 % of the nomnal load). Fgure 10 shows the mnmum teratons to converge s 73 correspondng to connected load of MW. For ths contngency the suppled load obtaned usng the proposed method decreases from MW at 110% overload to MW at 160 % overload. Whereas for the same range of overload contngences, the suppled power decreases from MW to MW and from MW to MW n Refs. [1, 5] and [2] respectvely. Fgure 11 (a) shows the decrease n suppled power from MW at 110% overload to MW at 160 % overload for the proposed ABC approach. For ths range of overload contngences the system losses obtaned by the proposed method ncreases from MW to MW whch s shown n Fgure 11(b). Whereas the system losses for ths condton reported n Refs. [1, 5] and [2] ncreases from MW to MW and from MW to MW respectvely. The proposed approach supples MW to bus 5 and MW to bus 8. Whereas Refs. [1, 5] supples to bus 5 MW and 34.6 MW to bus 8. Ref. [2] supples MW and MW to buses 5 and 8 respectvely. So, durng the overload contngences consdered the proposed method supples more power to these heavest load buses as compared to the power suppled by the other methods to these buses. A better voltage profle s obtaned by the proposed method durng ths contngency. Maxmum voltage obtaned usng the proposed approach s constant at pu and the mnmum voltage ncreases from to pu. In Refs. [1, 5] the maxmum voltages vary between pu and pu. and the mnmum voltage ncreases from 0.77 pu to 0.93 pu. The maxmum voltage reported n [2] s constant at 1.1 pu and the mnmum voltage ncrease from pu to pu. Suppled power n MW Objectve functon Connected load n MW (a) Number of teratons (b) Fgure 11 IEEE 30-bus system under overload contngences usng ABC approach a - Optmal suppled power, b - System losses 38.6 Objectve functon Number of teratons Fgure 10 Convergence of ABC approach for 30-bus system under overload contngency 4.2 Applcaton to Medum Sze Systems IEEE 57 and 118-bus test systems [11] are consdered here. In ths secton the results obtaned by the proposed approach under normal and abnormal operatng condtons - generaton contngences - are compared wth those results obtaned n Refs. [1] and [2]. The food number of the proposed ABC algorthm appled to these test systems s assumed as IEEE 57-bus System The total connected actve load for the 57 bus system s MW wth maxmum avalable power generaton of 1440 MW ncludng spnnng reserve. Under normal operatng condtons, the total actve power suppled to the connected load and the correspondng system losses obtaned usng NR method wth VDLM used n ths paper are MW and 1.76% of the nomnal load respectvely. Whereas the power suppled to the connected load by the methods reported n Refs. [1] and [2] were MW and 1251 MW respectvely. The defct n the suppled power obtaned n ths paper and n [1] represents the effect of usng VDLM to express the actve power. The total system losses under the normal operatng condtons obtaned by the methods presented n Refs. [1] and [2] were 1.521% and 1.835% of the system nomnal load respectvely.

10 122 R. Mageshvaran & T. Jayabarath / Jurnal Teknolog (Scences & Engneerng) 74:1 (2015), Objectve functon Better voltage profle has been obtaned usng the NR method wth VDLM used here. The bus voltage vary between 0.99 pu and 1.04 pu. The bus voltages obtaned by the methods reported n [1] vary between 0.81 pu and 1.03 pu. In [2] the bus voltages under normal operatng condtons vary between 0.9 pu and 1.14 pu Loss of Generaton Contngency An abnormal operatng condtons representng the loss of generatng unt-3 has been consdered here as a generaton contngency. The total amount of load shed obtaned by the ABC approach durng ths contngency s.2805 MW, whch s 14.42% of the nomnal load. Whereas for the same contngency, the amount of load shed obtaned by the methods presented n [1] and [2] were MW or 15.23% of the nomnal load and MW (or) % of the nomnal load respectvely. The total load shed obtaned by the proposed approach s lower when compared wth those reported n [1] and [2]. The total system losses obtaned durng ths contngency usng the proposed method s 1.39% of the nomnal load. Whereas for the same contngency the total system losses obtaned by the methods used n [1] and [2] were 1.554% and 0.98% of the system nomnal load. The convergence characterstcs of the proposed ABC approach for ths generaton contngency s shown n Fgure 12 and from ths fgure t can be observed that the maxmum number of teratons requred to converge s Fgure 12 Convergence characterstcs of ABC approach for 57-bus system under generaton loss contngency Under ths abnormal condton also the proposed ABC approach yelds a better voltage profle. The bus voltage vary between pu and 1.07 pu. The bus voltages obtaned by the method reported n [1] vary between 0.80 pu and 0.96 pu. In [2] the bus voltages under normal operatng condtons vary between pu and 1.2 pu IEEE 118-bus System Number of teratons The total connected load for the 118- bus system s 3668 MW wth maxmum avalable power generaton of 4080 MW ncludng spnnng reserve. Under normal operatng condtons the total suppled power to the connected load and the correspondng system losses obtaned n ths paper are MW and 3.95% of the nomnal load respectvely. Whereas the suppled power to the connected load obtaned by the methods reported n Refs. [1] and [2] were MW and 3668 MW. In ths case also the defct n the suppled power obtaned n ths paper and n [1] represents the effect of usng a VDLM to express the actve power. The total system losses obtaned by the methods presented n Refs. [1] and [2] were 2.67% and 4.706% of the system nomnal load. For the proposed method the bus voltage vary between 0.95 pu and 1.17 pu. The bus voltages obtaned by the methods reported n [1] vary between 0.92 pu and 1.2 pu. In [2] the bus voltages under normal operatng condtons vary between pu and 1.2 pu Loss of Generaton Contngences Here, two cases of generaton contngences are consdered. In the frst case, loss of generatng unt - 54 generatng 300 MW along wth decrease n the avalable generaton at unt - 12 from 300 MW to 120 MW, whch means the loss of 480 MW or % of the avalable power s consdered. In the second case the loss of generatng unts 12, 54 and 111, whch means loss of 900 MW or % of the avalable power, s consdered. For the frst case of generaton contngency, the total amount of load shed obtaned by the proposed ABC approach s or 5.36% of the nomnal load. Whereas the amount of load shed obtaned by the methods presented n Refs. [1] and [2] were MW or 6.20% of the nomnal load and MW or 5.17 % of the nomnal load respectvely. Therefore the total load shed obtaned by the proposed method s lower than that of reported n [1] and slghtly greater than that of presented n [2]. The system losses, obtaned by the proposed approach for ths case s 2.841% of the nomnal load and obtaned by the methods used n the Refs. [1] an [2] were 4.34% and 3.32% of the nomnal load respectvely. For the proposed ABC approach the bus voltage vary between pu and pu for ths case. Whereas the bus voltages obtaned by the method reported n [1] vary between 0.9 pu and 1.08 pu. In [2] the varaton of the bus voltages for ths case s between 1.1 pu and 1.2 pu. The convergence characterstc of the proposed ABC approach for ths case s shown n Fgure 13(a) and from the ths fgure t can be observed that the maxmum number of teratons requred by the proposed approach to converge s 50 teratons. The second case of generaton contngency consdered for ths test system represents a large dsturbance where three unts n the system are lost. For ths second case of generaton contngency, the total amount of load shed obtaned by the proposed ABC approach s MW or % of the nomnal load. Whereas the amount of load shed obtaned by the methods presented n Refs. [1] and [2] were MW or 16.24% of the nomnal load and MW or % of the nomnal load respectvely. The system losses, obtaned by the proposed approach for ths case s 3.01 % of the nomnal load and obtaned by the methods used n the Refs. [1] an [2] were 2.93% and 2.05% of the nomnal load respectvely. The system losses obtaned by the proposed method for ths case s slghtly lower than that of those reported n [1]. For the proposed ABC approach the bus voltage vary between pu and pu for ths case. Whereas the bus voltages obtaned by the method reported n [1] vary between 0.90 pu and 1.08 pu. In [2] the varaton of the bus voltages for ths case s between 1.1 pu and 1.2 pu. The convergence characterstc of the proposed ABC approach for ths case s shown n Fgure 13(b). From the fgure t can be observed that ths approach took a maxmum of 78 teratons to converge. As the severty of generaton contngency consdered n the second case s more than that of the frst case, the proposed algorthm requres more number of teratons to converge n ths case as compared to the prevous case.

11 123 R. Mageshvaran & T. Jayabarath / Jurnal Teknolog (Scences & Engneerng) 74:1 (2015), Objectve functon Objectve functon Number of teratons (a) (b) Fgure 13 Convergence characterstcs of ABC approach for 118-bus system under generaton loss contngences (a)- frst case, (b) - second case 5.0 CONCLUSION Number of teratons In ths paper an optmal load sheddng strategy usng a metaheurstc algorthm-abc approach has been presented. The proposed approach has been tested on IEEE 14, 30, 57 and 118 bus test systems. The results obtaned by the proposed approach are compared wth the conventonal methods, namely, projected augmented Lagrangan method (PALM), gradent technque based on Kuhn-Tucker theorem (GTBKTT) and second order gradent technque (SOGT). The comparson s done on the bass of suppled power, system losses, total load shed and the mnmum and maxmum bus voltages. The results presented show that the proposed approach provdes more suppled power and better voltage profle as compared wth those of other methods. Also, the proposed method supples more power to the heavest load buses n the case of IEEE 14 and 30 bus test systems, as compared wth the power suppled by the other methods. In the ABC algorthm durng the employed bees stage, wthout dependng on the qualty of the solutons, a tral soluton s produced for each soluton n the populaton. Whereas on onlooker bees stage, n order to produce tral solutons, the solutons wth the hghest ftness value were used than those wth less ftness. It means that the promsng regons of the search space are searched n shorter tme and n detal. The dversty n the populaton of ABC algorthm are controlled by two types of mechansm, () The tral soluton s obtaned by modfyng a randomly chosen part of a parent usng a magntude determned randomly. Ths modfcaton s relatvely small and useful for local search and fne tunng. () Instead of changng a part of a soluton, a whole soluton n the populaton s removed and then a new one produced randomly s nserted n to the populaton by a scout. Ths mechansm of the algorthm mproves the global search ablty of the algorthm and avods the premature convergence. Hence there s a good balance between the local search process carred out by employed bees and onlooker bees and the global search process carred by artfcal scouts. Ths mproves the exploraton and explotaton characterstcs of the algorthm. Therefore the ABC algorthm has the ablty to perform well on the addressed problem and also has better convergence characterstcs. Based on these outcomes, t s concluded that the proposed ABC algorthm can be consdered as an effectve alternatve approach for optmal load sheddng. Acknowledgement The authors are extremely grateful to the Chancellor, Vce- Chancellor and Vce-Presdents, of VIT Unversty, Vellore, for provdng the excellent nfrastructure facltes and encouragement whch have made ths research work possble. References [1] Mosatafa, M. A., El-Harwary, M. E., Mbamalu, G. A. N., Mansour, M. M., El-Nagar, K. M., and El-Arabaty A. M A Computatonal Comparson of Steady State Load Sheddng Approaches n Electrc Power Systems. IEEE Transactons on Power Systems. 12(1). [2] Hajdu, L. P., Peschon, J., Tnney, W. F., and Percy, D. S Optmal Load-Sheddng Polcy for Power Systems. IEEE Trans. PAS-87(3): [3] Palanswamy, K. A., Msra, K. B., and Sharma, J Optmum Load Sheddng Takng nto Account Voltage and Frequency Characterstcs of Loads. IEEE Trans. PAS-104(6): [4] Mosatafa, M. A., El-Harwary, M. E., Mbamalu, G. A. N., Mansour, M. M., El-Nagar, K. M., and El-Arabaty A. M Optmal Dynamc Load Sheddng Usng a Newton Based Dynamc Algorthm. Electrc Power Systems Research. 34(1995): [5] Mosatafa, M. A., El-Harwary, M. E., Mbamalu, G. A. N., Mansour, M. M., El-Nagar, K. M., and El-Arabaty A. M Steady-state Load Sheddng Schemes: A Performance Comparson. Electrc Power Systems Research. 38(1996): [6] Subramanan, D. K Optmum Load Sheddng Through Programmng Technques. IEEE Trans. PAS-90(1): [7] Chan, S. M., and Schweppe, F. C A Generaton Reallocaton and Load Sheddng Algorthm. IEEE Trans. PAS-98(1): [8] Chan, S. M., and Yp, E. A Soluton of the Transmsson Lmted Dspatch Problem By Sparse Lnear Programmng. IEEE Trans. PAS-98(3): [9] Medcherla, T. K. P., Bllnton R., and Sachdev, M. S Generaton Reschedulng and Load Sheddng to Allevate Lne Overloads-Analyss. IEEE Trans. PAS-98: [10] Medcherla, T. K. P., Bllnton, R., and Sachdev, M. S Generaton Reschedulng and Load Sheddng to Allevate Lne Overloads-System Studes. IEEE Trans. PAS-100(1): [11] Frers, L. L., and Sasson, A. M Investgaton of Load Flow Problem. Proc. IEEE. 115: [12] L. D. Arya, Pushpendra Sngh, L. S. Ttare Dfferental Evoluton Appled for Antcpatory Load Sheddng wth Voltage Stablty Consderatons. Electrcal Power and Energy Systems. 42(2012): [13] N. Sadat, T. Amraee, A.M. Ranjbar A Global Partcle Swarm- Based-Smulated Annealng Optmzaton technque for Under-voltage Load Sheddng Problem. Appled Soft Computng. 9(2009):

12 124 R. Mageshvaran & T. Jayabarath / Jurnal Teknolog (Scences & Engneerng) 74:1 (2015), [14] Jyu Deng, Junyong Lu A Study on a Centralzed Under-Voltage Load Sheddng Scheme Consderng the Load Characterstcs. Internatonal Conference on Appled Physcs and Industral Engneerng, Physcs Proceda. 24(2012): [15] Zuhala Mat Yasn, Ttk Khawa Abdul Rahman, Zuhana Zakara Multobjectve Quantum-Inspred Evolutonary Programmng for Optmal Load Sheddng. IEEE Control and System Graduate Research Colloquum (ICSGRC 2012). [16] C. Sumpavakup, I. Srkun, and S. Chusanapputt A Soluton to the Optmal Power Flow usng Artfcal Bee Colony Algorthm Internatonal Conference on Power System Technology.