ESTABLISHING TRADE-OFFS BETWEEN SUSTAINED AND MOMENTARY RELIABILITY INDICES IN ELECTRIC DISTRIBUTION PROTECTION DESIGN: A GOAL PROGRAMMING APPROACH

Transcription

1 ESTABLISHIG TRADE-OFFS BETWEE SUSTAIED AD MOMETARY RELIABILITY IDICES I ELECTRIC DISTRIBUTIO PROTECTIO DESIG: A GOAL PROGRAMMIG APPROACH Gustavo D. Ferrera, Arturo S. Bretas, Maro O. Olvera Federal Unversty of Ro Grande do Sul Porto Alegre, Ro Grande do Sul, Bral gustavoferrera@ece.ufrgs.br, abretas@ece.ufrgs.br, molvera@ece.ufrgs.br Abstract In ths paper, electrc dstrbuton relablty s consdered under both aspects of customer nterruptons: sustaned and momentary. A contngency smulaton-based technque s used to develop nonlnear models for the SAIFI and MAIFI relablty ndces, takng nto account the protectve devces locatons and reclosng schemes used n the substaton breaker and lne reclosers. The models are aggregated to a set of lnear constrants to consttute a nonlnear goal programmng model, used to establsh the tradeoff between SAIFI and MAIFI relablty ndces. As a result, the methodology enables determnstc optmaton of dstrbuton feeder protecton desgn by dentfyng types and locatons for protectve devces, and the protecton schemes to be employed n the lne reclosers and substaton breaker: fuse savng or fuse blowng. A case study consderng a real dstrbuton feeder wth 51 buses s presented to llustrate the applcaton and evaluate the performance of the proposed optmaton methodology. Keywords: Power dstrbuton relablty, power dstrbuton protecton, dstrbuton relablty ndces, goal programmng. 1 ITRODUCTIO Overcurrent protecton system desgn has drect mpact on electrc dstrbuton relablty. Tradtonally, procedures for protectve devces utlaton vary accordng to the relablty rules developed by electrc energy companes [1]. Snce the ncepton of the electrc power ndustry, the utltes protecton practces have focused on reducng the frequency of sustaned nterruptons [2]. Relablty ndces such as SAIFI (System Average Interrupton Frequency Index) have been commonly used by utltes and regulatory agences to evaluate the system performance and establsh servce contnuty crtera. Today, the ncreasng senstvty of customer loads to bref dsturbances has forced the utltes to fnd ways to reduce the number of momentary nterruptons that occur on ther systems [3]. Ths has resulted n ncreasng popularty of the assocated ndces, such as MAIFI (Momentary Average Interrupton Frequency Index) [4]. Dstrbuton protecton system desgn must now consder the mpact of momentary n addton to the permanent nterruptons. The systematc selecton and allocaton of protectve devces allows lmtng the effect of faults on the dstrbuton feeder, mnmng the number of customers affected by protectve devce operaton and, thereby, mnmng the feeder relablty ndces [1, 5]. Ths apples not only to the sustaned nterruptons-related relablty ndces used by the utlty ndustry, but also a reducton n momentary relablty ndces [2]. Addtonally, reclosng schemes have a substantal mpact on relablty ndces, and utltes must consder them n the desgn of the feeder protecton system [3]. Some papers are found n the lterature addressng determnstc optmaton of relablty, by dentfyng types and locatons of protectve devces n dstrbuton systems. Ref. [6] presented the frst lnear bnary programmng (LBP) model n order to mnme the SAIFI ndex. To smplfy the model, the formulaton defnes the dvson of the dstrbuton feeder n one man feeder and laterals, whch were heurstcally classfed n one of three categores. The shortcomng of the model s that t does not consder the effects of falures between the man feeder and the laterals, whch can lead to suboptmal solutons [1], [5], [7]. Addtonally, the model requres that the man feeder and laterals do not have branches, whch must be subsumed at the tap ponts, resultng n the loss of nformaton about the feeder topology. In [8], the authors present a smlar model to [6], to mnme the cost of protectve devces acquston, subect to relablty constrants. Also based n [6], [4] presented a goal programmng technque n order to fnd the trade-off between the SAIFI and ASIFI (Average System Interrupton Frequency Index) ndces. From the soluton obtaned are selected the reclosers where a fuse savng scheme should be appled, based on the trade-offs between a decrease n the SAIFI ndex and an ncrease n the MAIFI. In [5] and [9] nonlnear bnary programmng (LBP) models are presented to mnme the total cost of relablty. Smlar to [6], the authors employ the dvson of dstrbuton feeder n one man feeder and laterals, whch cannot have branches. Ref. [1] presented an mproved LBP model compared to [6], n order to mnme the SAIFI ndex of a feeder. Although usng the same form of feeder dvson of [6], the model takes nto account the effects of falures between the man feeder and the laterals. Fnally, n [7] a more generaled LBP model s presented to mnme the SAIFI or SAIDI ndex. By departng from the feeder dvson adopted n the models prevously presented, the model can represent wth more fdelty the nteractons between the protectve devces, resultng n a more accurate model for the SAIFI ndex. 17 th Power Systems Computaton Conference Stockholm Sweden - August 22-26, 2011

2 Except for [4], all the approaches prevously presented are sngle obectve models that address the optmaton of relablty ndces or economc costs, takng nto account ust the mpact of sustaned nterruptons. In ths paper, dstrbuton relablty s consdered under both aspects of customer nterruptons: sustaned and momentary. A contngency smulaton-based technque s used n the SAIFI and MAIFI models formulaton, to accurately reproduce the protecton system response to faults accordng to the protectve devces locatons and reclosng schemes used n the substaton breaker and lne reclosers. The nonlnear models are aggregated to a set of lnear constrants, and the resultant LBP models are ndependently solved. The numercal results (lower bounds of the ndces) are then stated as goals to a nonlnear goal programmng (LGP) model, used to establsh the trade-off between SAIFI and MAIFI relablty ndces. As a result, the methodology enables determnstc optmaton of dstrbuton feeder protecton desgn by dentfyng types and locatons for protectve devces, and the protecton schemes to be employed n the reclosers and substaton breaker: fuse savng or fuse blowng. A case study consderng a real dstrbuton feeder wth 51 buses s presented to llustrate the applcaton and evaluate the performance of the proposed optmaton methodology. 2 PROBLEM FORMULATIO 2.1 Dstrbuton Feeder Topology Model Fg. 1 shows the one-lne dagram of a radal dstrbuton feeder, consstng of man feeder and lateral branches. The feeder s dvded n sectons arbtrarly numbered, each one correspondng to a canddate pont for the placement of protectve devces. The nstallaton of a devce n a secton s defned as beng at the begnnng of that secton. For the purposes of ths paper, nterconnecton ponts (te ponts) wth adacent feeders or alternatve sources are not consdered. The dstrbuton feeder can be represented by a tree graph, where nodes represent tap connectons or load ponts. Snce each edge has a unque end node n the tree graph, the system can be represented n terms of edges, or feeder sectons. The feeder topology modelng s based on sets, whch composton process s defned as follows: let G be the set of edges of the tree graph that represents the dstrbuton feeder, and p() be the mmedate predecessor of edge on set G. Set U s defned by (1): { () ( ()) ( ( ())) } U =, p, p p, p p p,..., 1. (1) Set U contans secton and all the feeder sectons that precede (upstream ) to secton 1, whch by defnton, s the substaton. For example, consderng Fgure 1: U 1 = {1}, U 4 = {1, 3, 4}, and U 7 = {1, 3, 6, 7}. 2.2 Faults and Interruptons The faults that occur n dstrbuton systems can be classfed as temporary or permanent. A temporary fault Fgure 1: One-lne dagram of a radal dstrbuton feeder. wll clear up f de-energed and then re-energed, and a permanent fault wll persst untl repared by human nterventon [10]. An nterrupton s the loss of servce (power supply) to one or more customers, and s classfed as momentary or sustaned. Despte the use of the term momentary nterrupton, n ths work wll be consdered the concept of momentary nterrupton event. A momentary nterrupton event s one or more nterruptons of total duraton lmted to the tme perod of 5 mnutes. A sustaned nterrupton s any nterrupton not classfed as a part of a momentary event [11]. 2.3 Dstrbuton Feeder Overcurrent Protecton In ths secton the most relevant aspects of feeder overcurrent protecton consdered n the problem formulaton are descrbed. In general, protecton of a dstrbuton system conssts of a crcut breaker wth overcurrent relays and an automatc reclosng relay at the substaton, and lne reclosers and fuses placed at strategc ponts along the feeder. Sectonalers are also used, but they wll not be consdered n ths paper. Due to ther operatonal smlartes, substaton breaker and relays can be represented as a recloser allocated n the frst feeder secton. The recloser has fault current nterruptng and automatc reclosng capabltes, operatng wth a predetermned sequence of openng and reclosng followed by ts lockout. The fuse does not have automatc reclosng capablty. It can only perform open-crcut functon, separatng the faulted crcut by meltng ts fuse-lnk. Hence, the fuse s not able to clear the momentary faults by tself. Two basc reclosng practces are commonly used n recloser-fuse coordnaton: fuse savng and fuse blowng. Fuse savng (also referred to as feeder selectve relayng) s usually mplemented wth the fast curve on a recloser (or the nstantaneous relay on a breaker) so that the recloser (or breaker) operates before the downstream lateral fuses for faults on the laterals. For a temporary fault n a fused lateral, all customers downstream the recloser experence a momentary nterrupton. If the fault s permanent, customers downstream the recloser experence a momentary nterrupton and customers downstream the fuse experence a sustaned nterrupton. Fuse savng scheme results n fewer sustaned nterruptons, but more momentary nterruptons. In the fuse blowng (or fuse clearng) scheme, the fast curve of recloser (or the breaker nstantaneous relay) s blocked. The fuse operates for both temporary and permanent 17 th Power Systems Computaton Conference Stockholm Sweden - August 22-26, 2011

3 faults, wth the customers downstream the fuse experencng a sustaned nterrupton, and the rest of the feeder s prevented from experencng an nterrupton. Ths results n fewer momentary nterruptons but more sustaned nterruptons. In ths paper, we use the termnology fuse savng recloser and fuse blowng recloser, n references to the breaker and reclosers operatng under the fuse savng and fuse blowng reclosng schemes, respectvely. 3 PROPOSED METHOLOGY 3.1 SAIFI and MAIFI Models In ths paper a contngency smulaton-based technque s used n the SAIFI and MAIFI models formulaton to accurately reproduce the protecton system response to faults. The followng assumptons must be consdered n the models formulaton: 1) the falures are ndependent and mutually exclusve; 2) the protectve devces are perfectly coordnated; 3) the falure rates of protectve devces are neglected; and 4) the feeder s operated as a radal feeder. The bnary decson vectors ndcatng the feeder sectons where fuse savng reclosers, fuse blowng reclosers, and fuses are nstalled are defned accordng to (2): x y 0, f a fuse savng recloser s nstalled = on secton. 1, otherwse. 0, f a fuse blowng recloser s nstalled = on secton. (2) 1, otherwse. 0, f a fuse s nstalled on secton. = 1, otherwse. x x, y y,, = 1...G. Where the vertcal bars denote the cardnalty (number of elements) of set G. SAIFI s the most used ndex by electrc utltes to evaluate the frequency of sustaned nterrupton n dstrbuton systems [11]. Currently, MAIFI s becomng more prevalent because some publc servce commssons are requrng utltes to report nformaton on momentary nterruptons, and customers are complanng about shutdown of electronc loads [12]. As mentoned n Secton 2.2, t s used the concept of momentary nterrupton event, whose ndex corresponds to the MAIFI E (Momentary Average Interrupton Event Frequency Index). For sake of notaton, despte the use of the term MAIFI, ths work has consdered the MAIFI E defnton. SAIFI and MAIFI E ndces are formally defned n [11]. For a gven feeder, the ndces estmaton can be calculated by (3) and (4), respectvely. MAIFI = G I M T (4) Where G s the set of feeder sectons, I S and I M are respectvely, the expected number of sustaned and momentary nterruptons for secton, s the number of customers wthn the boundares of secton, and T s the total number of customers on the feeder. Consderng the SAIFI estmaton as a functon of decson vectors x, y and defned n (2), the numerator of (3) s rewrtten as: SAIFI xy = λ x y x y G U k ( U U ),, k k k + γ xkykk x l. G U k ( U U ) (5) Where: λ and γ are the permanent and temporary falure rates of secton [falures/km.year]; s the total number of customers downstream secton, ncludng customers n secton ; U U s the complement of U n U, and results n a set formed by the elements of U that are not elements of U. Equaton (5) evaluates the expected annual frequency of sustaned nterruptons of a feeder, gven the locatons of fuse savng reclosers, fuse blowng reclosers and fuses. The frst term of (5) corresponds to the mpact of permanent faults n secton when a recloser or fuse s nstalled n secton, upstream to secton, and there s not a recloser or fuse nstalled n sectons k, between sectons and. In ths case, the protectve devce n secton (the frst devce upstream the faulted secton ) operates to clear the fault n secton, and customers downstream secton ( ncluded) experence a sustaned nterrupton. The second term of (5) represents the mpact of temporary faults n secton when a fuse s nstalled n secton, there s no other devce n sectons k, and there s not a fuse savng recloser n sectons l, upstream the fuse. If = then U U = Ø (empty set). Snce 1 s the neutral element of multplcaton, we defne the product operators over empty sets equal to 1. In the same manner, snce 0 s the neutral element of addton, the sum over empty sets s defned as equal to 0. The opposte value complements of the decson varables n (5) are expressed by (6) and (7): x y = 3 x y (6) = 1 (7) SAIFI = G I S T (3) Replacng (6), (7) and groupng the frst and second terms of (5), ts fnal form s expressed by (8): 17 th Power Systems Computaton Conference Stockholm Sweden - August 22-26, 2011

4 ( ) SAIFI = λ 3 x y xy,, G U γ ( 1 ) xl xkyk k. k ( U U ) (8) The numerator of (4) s rewrtten as (9), to express the proposed MAIFI estmaton as a functon of decson vectors x, y and : MAIFIxy,, = γ x xk G U k ( U U ) + γ y xkykk xl G U k ( U U ) + λ x x k 1 l G U k ( U U ) l ( U U ) λ xkykk 1 x l. G U k ( U U ) (9) Equaton (9) evaluates the expected annual frequency of momentary nterruptons events of a feeder. Frst and second terms represent the mpact of temporary faults n a secton. The former represents the fault clearng by a fuse savng recloser nstalled n secton upstream faulted secton, and there s no other fuse savng recloser nstalled n sectons k, between sectons and. The second term represents the temporary fault clearng by a fuse blowng recloser nstalled n secton, when there s no other devce n sectons k, and there s not a fuse savng recloser upstream secton. The thrd and fourth terms of (9) represent the mpact of permanent faults n a secton located downstream a fuse, when a fuse savng recloser s nstalled upstream the fuse. In ths case, the customers between the recloser and the fuse experence a momentary nterrupton. The thrd term s actve f there s a fuse savng recloser n secton, there s no other fuse savng recloser n sectons k (between sectons and ), and there s a fuse nstalled n sectons l, also between sectons and. The forth term s actve f a fuse s nstalled n secton, there s no other devce n sectons k, and there s a fuse savng recloser n sectons l, upstream secton. Customers downstream the fuse (determned by the fourth term) wll experence a sustaned nterrupton, so they are subtracted from the customers downstream the fuse savng recloser (determned by the thrd term). The followng equatons are used to elmnate the opposte value complements of the decson varables n (9): x = 1 x (10) y = 1 y (11) By replacng (7), (10) and (11) and groupng the terms of (9), t yelds: MAIFI xy,, = ( )) { (( γ λ γ λ ) + y x l G U ( ) λ 1 y λ 1 x k ( U U ) k ( U U ) + λ + γ 1 x x k k ( )( )} k ( U U ) k (12) 3.2 Constrants A set of lnear constrants s defned n ths secton to ensure the solutons feasblty from the LGP model. Snce the nstallaton of a crcut breaker n the substaton s mandatory, and fuses are not nstalled n the man feeder sectons, constrants (13) and (14) must hold: x1 + y1 = 1 (13) = 1, Q (14) where Q s the set of man feeder sectons. In an attempt to ensure proper coordnaton of protectve devces, the number of devces of the same type that can be nstalled n seres s lmted. In ths paper, the number of reclosers and fuses placed n seres s set n 3 at the most, accordng to (15) and (16): x + y 2 U 3, G (15) U U 3, G (16) U Economc lmtatons are consdered by lmtng the maxmum number of reclosers and fuses avalable for the nstallaton on the feeder, as expressed by (17) and (18): x + y 2 G ( nr + 1) (17) G G nf, (18) G Where nr and nf are the number of avalable reclosers (excludng the substaton breaker) and fuses, respectvely. Fnally, constrants (19) are added to ensure that no more than one devce wll be nstalled n each feeder secton. Also, they ensure the valdty of (6). x + y + 2, G. (19) 17 th Power Systems Computaton Conference Stockholm Sweden - August 22-26, 2011

5 3.3 Goal Programmng Goal Programmng (GP) s a mult-obectve programmng technque based on the concept of satsfyng a number of obectves, tryng to acheve a set of goals (or targets) as close as possble [13]. In the GP method used n ths paper, the basc dea s that the decson maker specfes (optmstc) aspraton levels for the obectve functons and the weghted sum of devatons from these aspraton levels s mnmed. Ths s known as weghted GP (WGP). An obectve functon ontly wth an aspraton level forms a goal. Aspraton levels are assumed to be selected so that they are not achevable smultaneously. The algebrac formulaton of a WGP s gven as [14]: mn s.t. k + + w δ + w δ = 1 + ( ) δ δ f x + = g, = 1...k + δ, δ 0, = 1...k x C s (20) Where: k s the number of obectves; f (x) s the achevement level of obectve ; g s the aspraton level for obectve ; δ - and δ + are respectvely the negatve and postve devatons of f (x) n relaton to aspraton level g. w - and w + are weghtng factors; and C s s the set of hard constrants. In the proposed formulaton, the two LBP models consttuted by (8), (12) and constrants (13-19) are solved ndependently to obtan the aspraton levels for the SAIFI and MAIFI ndces. As they correspond to the lower bounds for the obectves, the negatve devatons and assocated weghts n (20) can be elmnated. Weghts are selected to ensure approprate tradeoffs between obectves and to perform an approprate scalng of the devatonal varables. The latter s mportant to overcome the unntentonal bas towards the obectves wth a larger magntude (ncommensurablty) [13]. Weghts n (20) are then redefned to normale the devatonal varables over the range between the maxmum and mnmum values of the aspraton levels: w w =, = 1,2. + max mn ( g g ) (21) By elmnatng the negatve devatons and weghts, makng δ = δ + ( = 1,2), and usng (21), the WGP problem (20) s redefned to the scope of the proposed dstrbuton relablty optmaton problem as (22): mn w δ + w δ s.t mn SAIFIxy,, δ 1= g1 mn MAIFIxy,, δ 2= g2 δ1, δ2 0 xy,, C s (22) ow, the set of hard constrants C s comprses the constrants defned by (13-19). 4 CASE STUDY The proposed methodology was mplemented n MATLAB envronment [15]. The applcaton receves as nputs the requred feeder topology and relablty data and returns the SAIFI and MAIFI LBP models, as well as the LGP model (22), both n the General Algebrac Modelng System (GAMS) representaton [16]. GAMS s a hgh-level language for mathematcal programmng problems, and serves as an nterface to the Branch And Reduce Optmaton avgator (BARO) solver [17]. BARO mplements determnstc algorthms of the branch-and-bound type enhanced wth a varety of constrant propagaton and dualty technques. The BARO solver can be used onlne, through the EOS server for optmaton [18]. The real dstrbuton feeder shown n Fgure 2 s used to llustrate the applcaton and evaluate the performance of the proposed optmaton methodology. The overhead three-wre dstrbuton feeder has 51 sectons, and serves 3958 customers wth total load of kva. Permanent (λ) and temporary falure rates (γ) n falures/km.year, and the number of customers () of each feeder secton are lsted n the Appendx. Orgnally, the feeder overcurrent protecton system conssts of a substaton crcut breaker, 2 lne reclosers and 18 fuses. We consder the crcut breaker and reclosers operatng under the fuse blowng reclosng scheme. The tests were performed consderng the relocaton of the exstng protectve devces. The frst step s to solve the two LBP problems of mnmng SAIFI and MAIFI ndces to obtan the aspraton levels for the ndces. The base case whch corresponds to the orgnal locatons of protectve devces on the feeder and the solutons obtaned by mnmng SAIFI and MAIFI ndces are shown n Table 1, where SAIFI s n nterruptons per customer per year, and MAIFI s n momentary nterruptons events per customer per year. Case Sectons FBR FSR Fuses SAIFI MAIFI Base 1, 8, 39 4, 6, 10, 12, 16, 18, 20, 24, 27, 29, 34, 37, 40, 42, 44, 46, 48, Mn. SAIFI 1, 23, 38 4, 6, 8, 11, 12, 16, 18, 20, 24, 27, 32, 37, 39, 41, 44, 46, 48, Mn. MAIFI 1, 23, 31 4, 6, 8, 16, 18, 20, 24, 25, 27, 29, 32, 37, 39, 42, 44, 46, 48, FBR = fuse blowng recloser, FSR = fuse savng recloser. Table 1: Base case and solutons obtaned by solvng the SAIFI and MAIFI LBP models. 17 th Power Systems Computaton Conference Stockholm Sweden - August 22-26, 2011

6 Fgure 2: Overhead three-wre dstrbuton feeder used n the case study wth devces locatons determned from the LGP model for w 1 = 0.6 and w 2 = 0.4. w 1 w 2 Sectons FBR FSR Fuses SAIFI MAIFI , 23, 31 4, 6, 8, 12, 16, 18, 20, 24, 27, 32, 37, 39, 40, 41, 44, 46, 48, , , 6, 8, 11, 12, 16, 18, 20, 24, 32, 37, 40, 41, 42, 44, 46, 48, , 43 4, 6, 8, 11, 12, 16, 18, 20, 24, 32, 37, 39, 40, 41, 44, 46, 48, , 38 4, 6, 8, 11, 12, 16, 18, 20, 24, 27, 32, 37, 40, 41, 44, 46, 48, , 36 4, 6, 8, 11, 12, 16, 18, 20, 24, 27, 32, 37, 40, 41, 44, 46, 48, , 38 4, 6, 8, 11, 12, 16, 18, 20, 24, 27, 32, 37, 39, 41, 44, 46, 48, , 23, 36 4, 6, 8, 11, 12, 16, 18, 20, 24, 27, 32, 37, 39, 41, 44, 46, 48, FBR = fuse blowng recloser, FSR = fuse savng recloser. Table 2: Solutons obtaned from the proposed LGP model wth dfferent weghts. From the LBP models solutons, the aspraton levels for the SAIFI s g 1 = nterrup- mn tons/customer.year, and for the MAIFI s g mn 2 = momentary nterruptons events/customer.year. As the obectves of mnmng SAIFI and MAIFI are conflctng, the soluton that mnmes an ndex wll result n the maxmum value for the other ndex. We consder these maxmum values equal to the maxmum values of the aspraton levels for the ndces. Thus, g max 1 = and g max 2 = n Equaton (21). The second step s to fnd the optmal trade-off between the SAIFI and MAIFI ndces. The goal s to fnd a soluton that acheves the establshed goals as close as possble. Dfferent solutons can be obtaned by usng dfferent weghts n (21), makng t possble for the engneer or planner to select one of the solutons, whch satsfes the obectve functons based mostly on hs or her professonal pont of vew. Table 2 shows the set of solutons obtaned from the proposed LGP model, when weghts are vared n steps of 0.1, such that w 1 + w 2 = 1. For w 1 greater than 0.7, the solutons are equal to the Mn. SAIFI case. Then these solutons are excluded from Table 2. Fgure 3 shows the graphcal representaton of the solutons from Table 2 wth labels ndcatng the assocated weghts (w 1, w 2 ), as well as the solutons from the mnmaton of SAIFI and MAIFI ndces. As t can be seen, the soluton (0.5, 0.5) s domnated by solutons (0.6, 0.4) and (0.4, 0.6), ndcatng that no Pareto optmal soluton s avalable n that MAIFI SAIFI Fgure 3: Solutons obtaned from the mnmaton of SAIFI and MAIFI ndces, and the LGP model wth dfferent weghts. regon of solutons space. Protectve devces locatons determned by soluton (0.6, 0.4) are shown n Fgure 2. Ths soluton ndcates a possble reducton to 57.3% and 76.4% of the orgnal SAIFI and MAIFI ndces, wth devatons of 6.9% and 67.5% from the establshed aspraton levels, respectvely. In the presented case study, the LGP model comprsed 169 constrants and 155 varables. As nearly all optmal solutons are usually found n the frst mnutes of solver executon [7], we lmted the BARO solver CPU executon tme to 5 mnutes. 17 th Power Systems Computaton Conference Stockholm Sweden - August 22-26, 2011

7 Powered by TCPDF ( 5 COCLUSIO Ths paper presented a methodology to mprove dstrbuton systems relablty whle establshng the tradeoff between sustaned and momentary nterruptonsrelated ndces. onlnear models were developed for SAIFI and MAIFI ndces that accurately reproduce the protecton system response to faults, takng nto account the protectve devces locatons and reclosng schemes used n the substaton breaker and lne reclosers, fuse savng and fuse blowng. The LBP models were solved ndependently to determne the lower bounds for the relablty ndces, stated as goals to a LGP model. A case study consderng a real dstrbuton feeder has shown that determnng types and locatons of protectve devces, and a better overcurrent protecton scheme to be employed n protectve devces wth reclosng capabltes can greatly reduce the number of customers affected by both temporary and permanent faults and thereby, mnme the dstrbuton relablty ndces. APPEDIX Secton λ γ Secton λ γ 1 0,544 0, ,306 0, ,125 0, ,470 0, ,028 0, ,224 0, ,108 0, ,736 0, ,145 0, ,868 0, ,270 0, ,525 0, ,240 0, ,390 0, ,810 0, ,222 0, ,155 0, ,155 0, ,078 0, ,031 0, ,444 0, ,725 0, ,340 0, ,960 0, ,320 0, ,256 0, ,048 0, ,050 0, ,609 0, ,972 0, ,810 0, ,020 0, ,340 0, ,325 1, ,338 0, ,015 0, ,520 0, ,336 0, ,392 0, ,660 0, ,280 0, ,198 0, ,116 0, ,442 0, ,460 0, ,377 0, ,360 0, ,700 0, ,189 0, ,620 0, ,450 0, Table 3: Permanent (λ) and temporary (γ) falure rates, and number of customers () n each secton of the test feeder. REFERECES [1] L. G. W. Slva, R. A. F. Perera, and J. R. S. Mantovan, Allocaton of Protectve Devces n Dstrbuton Crcuts Usng onlnear Programmng Models and Genetc Algorthms, Elect. Power Syst. Res., vol. 69, no. 1, pp , Apr [2] M. T. Bshop, C. A. McCarthy, V. G. Rose, and E. K. Stanek, Consderng Momentary and Sustaned Relablty Indces n the Desgn of Dstrbuton Feeder Overcurrent Protecton, IEEE Transm. and Dst. Conf. Proceedngs, pp , Apr [3] C. M. Warren, The Effect of Reducng Momentary Outages on Dstrbuton Relablty Indces, IEEE Trans. Power Del., vol. 7, no. 3, pp , Jul [4] F. Soud and K. Tomsovc, Optmal Trade-offs n Dstrbuton Protecton Desgn, IEEE Trans. Power Del., vol. 16, no. 2, pp , Apr [5] J.-M. Sohn, S.-R. am, and J.-K. Park, Value- Based Radal Dstrbuton System Relablty Optmaton, IEEE Trans. Power Syst., vol. 21, no. 2, pp , May [6] F. Soud and K. Tomsovc, Optmed Dstrbuton Protecton Usng Bnary Programmng, IEEE Trans. Power Del., vol. 13, no. 1, pp , Jan [7] E. Zambon, D. Z. Bossos, B. B. Garca, and E. F. Aeredo, A ovel onlnear Programmng Model for Dstrbuton Protecton Optmaton, IEEE Trans. Power Del., vol. 24, no. 4, pp , Oct [8] F. Soud and K. Tomsovc, Towards Optmed Dstrbuton Protecton Desgn, Proceedngs of the 3rd Int. Conf. Power System Plannng Operatons, pp , Jan [9] R. Bupasr,. Wattanapongsakorn, J. Hokert, and D. W. Cot, Optmal Electrc Power Dstrbuton System Relablty Indces Usng Bnary Programmng, Proceedngs of the IEEE Annual Relablty Mantanablty Symp., pp , Jan [10]R. E. Brown, Electrc Power Dstrbuton Relablty, 2nd ed., FL., CRC Press, 2009, pp. 49. [11]IEEE Standard 1366, IEEE Gude for Electrc Power Dstrbuton Relablty Indces, [12]C. A. Warren, R. Ammon, and G. Welch, A Survey of Relablty Measurement Practces n the U.S., IEEE Trans. Power Del., vol. 14, no. 1, Jan [13]M. Tam, D. Jones, C. Romero, Goal Programmng for Decson Makng: An Overvew of the Current State-of-the-art, European Journal of Operatonal Research, pp , no 111, [14]K. M. Mettnen, onlnear Multobectve Optmaton, orwell, Kluwer Academc Publshers, 1999, pp [15]The Mathworks Inc., Mathworks Matlab. [Onlne]. Avalable: [16] GAMS General Algebrac Modelng System. [Onlne]. Avalable: [17] Baron Global Optmaton Software. [Onlne]. Avalable: baron.html. [18] EOS Server for Optmaton. [Onlne]. Avalable: 17 th Power Systems Computaton Conference Stockholm Sweden - August 22-26, 2011