Optimal Locations and Sizing of Capacitors for Voltage Stability Enhancement in Distribution Systems

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1 Optimal catins and Sizing f Capacitrs fr ltage Stability Enhancement in Distributin Systems Mhan. G Reader in Electrical Engineering Annamalai University Annamalainagar , Tamil Nadu, India. Aravindhababu. P Prfessr f Electrical Engineering, Annamalai University Annamalainagar , Tamil Nadu, India. ABSTRACT ltage instability ccurs in pwer s when the is unable t maintain an acceptable vltage prfile under an increasing lad demand and/r cnfiguratin changes. The perating cnditins f the present day distributin s are clser t the vltage stability bundaries due t the ever increasing lad demand. This paper presents a new algrithm fr ptimal lcatins and sizing f static and/r switched shunt capacitrs in rder t enhance vltage stability in additin t imprving the vltage prfile and minimising lsses. Test results n 33 and 69-nde distributin s reveal the superirity f this algrithm. Key wrds: vltage stability, radial distributin s, capacitr placement. Nmenclature l distributin line cnnected between ndes k and m resistance and reactance f linel nn r km jx km pwer lad at nde-m CP M S SI m number f ndes in the real and reactive capacitr placement vltage magnitude vltage stability vltage stability index SI f line- l r nde- m t threshld value fr SI est value f SI in the PA prpsed algrithm P km sum f real pwer lads f all the ndes beynd nde-m plus the real pwer lad f nde-m itself plus the sum f the real pwer lsses f all the branches beynd nde-m. Q km sum f reactive pwer lads f all the ndes beynd nde-m plus the reactive pwer lad f nde-m itself plus the sum f the reactive pwer lsses f all the branches beynd nde-m. Q m reactive pwer delivered by nde-m Q m reactive pwer delivered by nde-m befre cmpensatin Q Q min and max minimum and maximum reactive pwer demands repectively m net reactive pwer cmpensatin at nde- m m initial value f m k vltage magnitude at nde-k est value f M in the k km m vltage angle at nde-k k m t m m, mismatch f SI at nde- Q m additinal reactive pwer cmpensatin required at nde- m 1. INTRODUCTION Mdern pwer s are mre heavily laded than ever befre t meet the grwing demand and ne f the majr prblems assciated with such a stressed is vltage cllapse r vltage instability. ltage cllapse is characterized by a s variatin in perating pint due t increase in lads in such a way that the vltage magnitude gradually decreases until a sharp accelerated change ccurs [1]. The prblem f vltage cllapse may simply be explained as the inability f the pwer t supply the required reactive pwer r because f an excessive absrptin f the reactive pwer by the itself [2]. The prblem f vltage instability r cllapse has becme a matter f great cncern t the utilities in view f its predictin, preventin and necessary crrectins t ensure stable peratin. In recent years, the lad demand in distributin 7

2 s are sharply increasing due t ecnmical and envirnmental pressures. The perating cnditins are thus clser t the vltage stability bundaries. In additin, distributin netwrks experience frequent distinct lad changes. In certain industrial areas, it is bserved that under certain critical lading cnditins, the distributin suffers frm vltage cllapse. In 1997, the vltage instability prblem in a distributin that spread t a crrespnding transmissin caused a majr blackut in S/SE Brazilian [3]. Recently, the vltage stability (S) f radial distributin has been studied and varius vltage stability indices have been develped [-7]. Capacitrs are cmmnly used t prvide reactive pwer supprt in distributin s. The amunt f reactive cmpensatin prvided is very much linked t the placement f capacitrs in distributin feeders in the sense that it essentially determines the lcatin, size, number and type f capacitrs t be placed, as it reduces pwer and energy lsses, increases the available capacity f the feeders and imprves the feeder vltage prfile. Numerus capacitr placement (CP) methds with a view f minimising lsses have been suggested in the literature [-13]. Optimal allcatin and sizing f capacitr banks fr prfitability and vltage enhancement f P n feeders has been suggested [1]. The effect f lcatin and capacity f distributed generatin n vltage stability f distributin s has been studied [15]. Algrithms fr enhancing vltage stability f transmissin s by ptimal CP have been discussed [16-17]. A relatinship between vltage stability and lss minimisatin has been develped and the cncept f maximising vltage stability thrugh lss minimisatin has been utlined [1-19]. Measures fr enhancing vltage stability f distributin s by netwrk recnfiguratin that alters the tplgical structure f the distributin feeders by rearranging the status f switches have been suggested [20-23]. Thugh several attempts have been made t use capacitr banks fr lss minimisatin, vltage prfile imprvement, imprvement f pwer factr, etc, hardly any wrk has been reprted invlving them with a view f enhancing vltage stability f distributin s. The rapid grwth f size and expnentially increasing pwer demand at distributin level necessitate efficient and effective methdlgies t avid vltage cllapse and the cnsequent ccurrence f black-uts. This paper is thus directed twards enhancing S f distributin s thrugh the use f capacitr banks. A new algrithm that uses the SI suggested in [7], fr ptimal lcatins and sizing f static and/r switched shunt capacitrs in radial distributin fr vltage stability enhancement is prpsed in this paper. This methd imprves vltage prfile and reduces lsses in additin t enhancing vltage stability. The methd is tested n 33 and 69-nde radial distributin s and the results are presented. 2. Prpsed CP Algrithm The aim f the present wrk is t place capacitr banks at ptimal lcatins with a view t enhance vltage stability f radial distributin s. The methd uses SI suggested in [7] and ffers reactive pwer supprt at the apprpriate ndes t imprve SI values twards a fixed threshld value, which is chsen based n cnfiguratin and the perating state. The prpsed algrithm (PA) determines the number, sizes, lcatins and types fr capacitrs t be placed n a distributin in rder t enhance vltage stability. Fig. 1 Sample Distributin ine The SI, which varies between unity at n lad and zer at vltage cllapse pint, fr line-l r fr nde-m can be determined by inearising Eq. (1) and neglecting the higher rder terms (1) (2)

3 where (3) The net reactive pwer delivered by nde- m can be written as () inearising Eq. () and neglecting the higher rder terms where (5) (6) Rearranging Eq. (2) and substituting it in Eq. (5), (7) The SI at all ndes are cmputed using Eq. (1). If all these values are greater than a fixed threshld value, it indicates that the is away frm the vltage instability pint and the des nt require any reactive pwer cmpensatin; else the ndes, whse SI values are er than the threshld value, are chsen as the candidate ndes fr cmpensatin. m Hwever, the nde- having the est SI value is chsen fr CP and the additinal reactive pwer Q cmpensatin, m, t be prvided at this nde can be btained by slving Eq. (7). The calculated reactive pwer supprt is prvided at nde- m and the abve prcess is cntinued till all the SI values becme less than the threshld value. The chsen nde- m is said t be ptimal as it is the mst vulnerable nde frm vltage stability pint f view and reactive supprt at that nde ensures the t be far away frm the vltage instability pint when cmpared t prviding reactive supprt at all ther ndes ne at a time. The maximum cmpensatin at each nde is limited t the initial reactive pwer delivered by the respective nde prir t cmpensatin fr aviding ver-dimensining f the capacitr banks as, The capacitr t be installed at a specific nde may be either fixed r switched type, which is based n the minimum and maximum reactive pwer demands, and Q max () Q min in a defined perid. They are chsen t be fixed capacitrs when and switched capacitrs when have t prvide AR supprt. The algrithm f the prpsed methd is summarized as fls: 1. Read the data. 2. t Chse a fixed threshld value,. 3. Set flag 0 and m = 0 fr all the ndes. 9

4 . fr all the ndes. 5. Carryut distributin pwer f. 6. Cmpute SI values, m, at all ndes using Eq. (1). 7. Chse the nde having est value f SI,, as the sensitive nde- m fr CP. t. If, r if flag 1 fr all the candidate ndes, then g t step (10). Q 9. Slve Eq. (7) fr m and then cmpute the net cmpensatin at nde - m 10. Check fr reactive pwer cmpensatin limit: 11. If m Q m, then m Q m and set flag 1 fr nde-m t avid this nde in the subsequent cmputatins. and g t step (). 12. The ptimal lcatins fr CP are btained. Chse the nearest available value f capacitr frm the cmputed values f m. 13. Stp. Table-1 Requirement f AR cmpensatin fr 33 nde ad evel Nde-6 Nde- ight ad Medium ad 50 kar --- Full lad 1200 kar 150 kar Overlad 1350 kar 300 kar Table-2 Type and Size f Capacitr placed fr 33 nde Type Size (kar) Nde-6 Nde- Fixed N N N 1 N Switched N Table-3 Perfrmance f the PM fr 33 nde 3. Simulatin The prpsed algrithm is tested n 33 and 69-nde distributin s. The line and lad data fr these tw s are btained frm the references [2] and [22]. The pwer f suggested in [25] is used in this study. The size f the capacitr banks cnsidered in this study are 150, 300, 50, 600 and 900 kar. The results are btained fr light, medium, full and ver lad cnditins by multiplying the base-lad by a factr 0.5, 0., 1.0 and 1.1 respectively. The threshld value fr SI is taken as 0.95 fr bth s. The threshld value depends n the pwer cnfiguratin and the perating state. If this value is fixed t, it des nt ensure that the pwer will be maintained in a stable state. If this value is fixed t high, the reactive pwer t be prvided will be t excessive. 33 nde test : The minimum reactive pwer cmpensatin required t enhance vltage stability fr different lading cnditins fr 33 nde are given in Table-1. The minimum and maximum reactive pwer demands are 1150 kar and 2530 kar respectively. The size and type f capacitr banks required fr 33 nde based n the variatin f reactive pwer demands are given in Table-2. Tw fixed type f capacitr banks with a net rating f 1050 kar are permanently cnnected at nde-6 and nde- t supply reactive pwer at all lading cnditins. Switched capacitr banks ranging frm 150 kar t 300 kar are cnnected, as shwn in Table-2, t ffer additinal reactive pwer. Table-3 cmpares, and lsses befre and after CP fr different ad evel ight ad Medium ad Full lad Overla d Befre CP ss (kw ) After CP ss (kw )

5 Table- Requirement f AR cmpensatin fr 69 nde ad evel Nde-57 Nde-5 ight ad 50 kar --- Medium ad 900 kar --- Full lad 1200 kar 1050 kar Overlad 1350 kar 1350 kar Table-5 Type and Size f Capacitrs placed fr 69 nde Type Size Nde-57 Nde-5 (kar) Fixed 50 1 N N N Switched N 1 N ad evel ight ad Medium ad N Table-6 Perfrmance f the PM fr 69 nde Befre CP ss (kw) After CP ss (kw) Full lad ading cnditins: The tw fixed capacitrs, given in Table-2, thugh are nt required at lad cnditins t meet the reactive pwer demand, still serve t er the reactive burden f the and reduce the lsses frm.7 kw t 3.0 kw in additin t imprving the vltage prfile. At full lad cnditin, the est SI f befre CP is enhanced t the safe level f 0.96 besides reducing the lses frm t kw and imprving the vltage prfile. This perfrmance is btained in medium as well as ver lad cnditins as seen frm Table-3. It is therefre clear that the ptimal CP enhances vltage stability, imprves vltage prfile and reduces the lsses. 69 nde : The minimum and maximum reactive pwer demands fr 69 nde are 137 kar and 296 kar respectively. 6 The required reactive pwer cmpensatin, size and type f capacitr banks, perfrmance befre and after CP are given in Tables, 5 and 6 respectively. These results als reveal that there is significant imprvement in perfrmance in terms f vltage stability, vltage prfile and lsses.. CONCUSION A CP algrithm fr vltage stability enhancement f radial distributin has been develped. This methd finds the ptimal lcatins and determines the size and type f capacitr banks t be placed t enhance the vltage stability besides imprving the vltage prfile and reducing the lsses. The algrithm selects nly ne nde at a time Q irrespective f the size and cmpute m at the chsen nde during the iterative prcess, which invlves very simple cmputatins and hence is suitable fr practical implementatin n s f any size. 5. Acknwledgements The authrs gratefully acknwledge the authrities f Annamalai University fr the facilities ffered t carry ut this wrk. 6. REFERENCES 1. C. W. Taylr, Pwer System ltage Stability, McGraw-Hill, Inc., P. Kessel and M. Glavitch, Estimating the vltage stability f a pwer, IEEE Trans. Pwer Delivery, 196, PWRD-I (3), pp R. B. Prada.,..J. Suza, ltage stability and thermal limit: cnstraints n the maximum lading f electrical energy distributin feeders, IEE Prc. Gen. Trans and Dist., 199, l. 15 (5), pp G.B.Jasmn and.h.c.c.ee, Distributin netwrk reductin fr vltage stability analysis and lad f calculatins, Internatinal Jurnal f Electrical Pwer and Energy Systems, 1991, l. 13, N. 1, pp F. Gubina and B. Strmenik, A simple apprach t vltage stability assessment in radial netwrks, IEEE Trans. n Pwer Systems, 1997, l.12, N. 3, pp M. Chakravrty and D. Das, ltage stability analysis f radial distributin netwrks, Internatinal Jurnal f Electrical Pwer and Energy Systems, 2001, l. 23, N. 2, pp M. H. Haque, A linear vltage stability margin fr radial distributin s, Prc. IEEE PES General Meeting, Mntreal, Canada, June-2006, pp B. enkatesh and B. Ranjan, Fuzzy EP algrithm and dynamic data structure fr ptimal capacitr allcatin in radial distributin s, IEE Prc. Gen. Trans and Dist., 2006, l. 153, N. 5, pp

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