Aalborg Universitet. Published in: The 7th International Conference on Renewable Power Generation. Publication date: 2018

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1 Aalborg Unverstet Hybrd Mxed-Integer Non-Lnear Programmng Approach for Drectonal Over-Current Relay Coordnaton Javad, Mohammad Sadegh ; Esmaeel Nezhad, Al ; Moghaddam, Amjad Anvar; Zapata, Josep Mara Guerrero Publshed n: The 7th Internatonal Conference on Renewable Power Generaton Publcaton date: 2018 Document Verson Accepted author manuscrpt, peer revewed verson Lnk to publcaton from Aalborg Unversty Ctaton for publshed verson (APA): Javad, M. S., Esmaeel Nezhad, A., Anvar-Moghaddam, A., & Guerrero, J. M. (2018). Hybrd Mxed-Integer Non-Lnear Programmng Approach for Drectonal Over-Current Relay Coordnaton. In The 7th Internatonal Conference on Renewable Power Generaton (pp. 1-6). IET Conference Proceedng. General rghts Copyrght and moral rghts for the publcatons made accessble n the publc portal are retaned by the authors and/or other copyrght owners and t s a condton of accessng publcatons that users recognse and abde by the legal requrements assocated wth these rghts.? Users may download and prnt one copy of any publcaton from the publc portal for the purpose of prvate study or research.? You may not further dstrbute the materal or use t for any proft-makng actvty or commercal gan? You may freely dstrbute the URL dentfyng the publcaton n the publc portal? Take down polcy If you beleve that ths document breaches copyrght please contact us at vbn@aub.aau.dk provdng detals, and we wll remove access to the work mmedately and nvestgate your clam. Downloaded from vbn.aau.dk on: januar 01, 2019

2 Hybrd Mxed-Integer Non-Lnear Programmng Approach for Drectonal Over-Current Relay Coordnaton Mohammad Sadegh Javad 1, Al Esmaeel Nezhad 2, Amjad Anvar-Moghadam 3, Josep M. Guerrero 3 1 Department of Electrcal Engneerngm, Shraz Branch, Islamc Azad Unversty, Shraz, Iran 2 Department of Electrcal, Electronc, and Informaton Engneerng, Unversty of Bologna, Italy 3 Department of Energy Technology, Aalborg Unversty, 9220 Aalborg East, Denmark Correspondng Author: Javad@aushraz.ac.r Keywords: Coordnaton, Drectonal Over-Current Relay, Integer Genetc Algorthm, Mxed-Integer Non-Lnear Problem. Abstract Ths paper proposes the optmal coordnaton problem of protectve relays wthn a hybrd optmzaton framework whch s presented based on nteger coded genetc algorthm (ICGA) and non-lnear programmng (NLP). The optmal coordnaton problem of drectonal overcurrent relays (DOCRs) s mplemented whle amed at fndng the optmal plug settng multpler (PSM) and tme dal settng (TDS). In ths respect, PSM s a functon of the current transformer (CT) sze and the tap of the relay whch s dscrete n nature. TDS s a functon of the operatng tme of the relay for dfferent short-crcut currents at dfferent locatons of the system. In ths paper, the varables of the problem are decomposed nto contnuous and dscrete varables. The frst stage of the problem uses the ICGA to determne the sze of CTs consderng the permtted tap of relays whle the second stage utlzes the NLP method to evaluate the feasblty and optmalty. The presented framework s then smulated on a 8- bus test system. The obtaned results verfy the effectveness and the applcablty of the optmzaton technque to fnd the optmal settngs of DOCRs. 1 Introducton Usng overcurrent relays are of the most prmary methods to detect and solate the faulty areas n power systems. In nterconnected power systems, doubly-fed power systems, and the power systems wth parallel lnes, drectonal overcurrent relays (DOCRs) must be used to precsely determne the fault locaton and solate the faulty areas. Such relays use the current and voltage sgnals, smultaneously to specfy the magntude and the drecton of short-crcut currents. However, optmal coordnaton of DOCRs regardng the clearance tme of the prmary and backup relays s a challengng ssue n power systems. In general, the optmal coordnaton of DOCRs s done to fnd the optmal settngs of relays ncludng the tme dal settng (TDS) and plug settng multpler (PSM). It s noteworthy that a coordnaton tme nterval (CTI) should be consdered to omt the overlap between the operaton of the prmary and backup relays for a gven fault. Many researches have nvestgated the optmal coordnaton problem of DOCRs and varous optmzaton technques have been presented to fnd the optmal settngs. PSM s obtaned expermentally wth respect to the load current and the fault current n lnear programmng technques. In such methods, TDS s the only varable whch ts optmal value s derved wth respect to the coordnaton constrants of the prmary and backup relays,.e. CTI [1-6]. Determnng the two varables, smultaneously, turns the optmzaton model nto a mxed-nteger non-lnear programmng (MINLP) model whch s dffcult to solve. In ths regard, authors n[7] have employed an enhanced partcle swarm optmzaton (PSO) algorthm whle the repar method and non-random approach for ntalzaton have been presented to modfy the orgnal algorthm. An evolutonary PSO (EPSO) has been employed n [8] to solve smlar optmzaton problem. Researchers n [9] have proposed an optmzaton framework usng leachng-learnng based optmzaton (TLBO) n whch LINKNET confguraton (utlzng merely far vector) s employed to dagnose the backup pars for every prmary protectve relay. Besdes, Ref. [10] presented a modfed adaptve TLBO (MATLBO) and frefly algorthm (FA) has been proposed n Ref. [11]. The effect of fault current lmter (FCL) on the coordnaton of DOCRs has been dscussed n [12]. Authors of [13, 14] also utlzed a chaotc FA (CFA) and a modfed swarm FA (MSFA), respectvely. Addtonally, Ref. [15] presented the artfcal bee colony (ABC) method whle Ref. [16] solved the mentoned problem usng mproved group search optmzaton algorthm (IGSOA). Informatve dfferental evoluton (IDE) [17], and seeker algorthm [18] are used to fnd the optmum relay settngs. The applcaton of modfed dfferental evoluton algorthms [19], opposton based chaotc dfferental evoluton algorthm [20], PSO [21] and modfed PSO (MPSO) [22] algorthms are also presented by the researchers to fnd the optmal settngs for TMS and PSM. The capablty of dual settng relays s evaluated n [23] for the optmum coordnaton of DOCRs. Besdes, an adaptve protecton scheme s presented n [24] to mtgate mpact of dstrbuted generaton. Meanwhle, some research works have utlzed hybrd technques to solve the coordnaton problem 1

3 of DOCRs. For nstance, Ref. [25] has utlzed Genetc Algorthm (GA) together wth lnear programmng (LP) known as GA-LP and Ref. [26] has adopted GA along wth non-lnear programmng known as GA-NLP to solve the coordnaton problem of DOCRs. An optmzaton framework has been developed n [27] usng bogeography based optmzaton (BBO) together wth a novel hybrd BBO combned wth LP known as BBO-LP to solve the coordnaton problem of DOCRs. However, t should be noted that none of the obtaned solutons are global optmum. Each research work has consdered dfferent assumptons to obtan the optmal settngs of DOCRs. In ths regard, the nput data ncludng the short-crcut currents and the fault locaton (for near-end, far-end or at the md-pont of the feeder) should be verfed and the problem assumptons are the same. The research work n [28] proposes a comprehensve revew on the assumptons made n dfferent research works for the optmal coordnaton of DOCRs. Ths paper proposes the optmal coordnaton problem of DOCRs for the 8-bus test system takng nto account dfferent assumptons made so far n research works. The hybrd ICGA-NLP optmzaton technque s used to solve the problem. The remander of the paper s categorzed as follows. Secton 2 provdes the mathematcal modellng of the optmal coordnaton problem of DOCRs. The hybrd optmzaton approach s presented n secton 3. Secton 4 ncludes the smulaton results whle accurately nvestgates the short-crcut currents and the protecton settngs. Fnally, secton 5 draws some relevant conclusons. 2 DOCRs Coordnaton Problem The coordnaton problem of DOCRs has been presented n the MINLP framework whle the objectve functon s defned as the mnmzaton of fault clearng tme of prmary relays, TP. Mn N = 1 TP where 0.14 TDS TP =, = 1,2,..., N M 1 ( ) 0.02 Subject to: 0.14 TDS j TBj, =, j = 1,2,..., N ( M j ) F F I I M =, M j = PSM CTR PSM CTR j j PSM PSM PSM (5) Mn Max TDS TDS TDS (6) Mn Max j, (7) TB TP CTI where, TP and TB show the clearng tme of prmary and backup relays, respectvely. In ths respect, Eq. (2) and Eq. (3) are used to obtan TP and TB, respectvely. The characterstc curve used for the DOCRs s the IEC standard (1) (2) (3) (4) nverse characterstc. Besdes, TB s derved takng nto account the current seen by the prmary relay. Ths parameter s used to specfy the tme needed so that the backup relay operates and sends the trppng command. In (2)-(3), M and M j denote the effectve currents for prmary and backup DOCRs, respectvely. The PSM and TDS should be selected from the permssble values for the -th DOCR. The PSM can be ether contnuous or dscrete and should be selected from the acceptable range of relays as stated n (5). It should be noted that the relay s clearng tme should be n the allowed range. Furthermore, as nequalty (6) states, TDS should be also n the allowed range. However, as stated n (7), the conflctng condtons regardng the operaton of the prmary and the backup relay must be omtted. To ths end, a CTI s consdered. It s noteworthy that the ICGA determnes the nteger values related to PSM and TDS s obtaned accordng to the PSMs of each relay. 3 Hybrd ICGA-NLP Algorthm Decomposton of the problem and the varables nto two parts s a common technque n solvng MINLP problems. In ths respect, one part s devoted to solvng the mxed-nteger programmng (MIP) problem and the other one s devoted to solvng the NLP problem. Usng the suggested technque, the nteger varables of the problem are obtaned as the remanng NLP problem s solved faster whch overall mproves the soluton tme compared to MINLP. In ths respect, the ICGA s employed to determne the current settng (PSM) of the relay whch s an optmzaton problem wth dscrete varables. The NLP method s also utlzed to obtan the TDS of the relay. The detaled descrptons of the ICGA method and the decomposton technque are descrbed n the followng. 3.1 Integer Coded Genetc Algorthm There are several sgnfcant factors that should be accurately consdered n the GA. These factors are the crossover, mutaton as well as other operators defned for each problem and they should be determned n a way mposng the mnmum computatonal burden. To ths end, an effectve representaton of the GA has been utlzed n the paper whle ts soluton confguraton s an ordered structure of nteger numbers wth dmenson, N, showng the total number of DOCRs. The nteger varables are presented to descrbe the controllers, as assgned to the vector elements ndcated by the DOCRs through mplementng a mappng procedure. In the proposed mappng strategy, the dscrete settng multples of DOCRs wll be determned as shown n Fg.1. Number of DOCRs N-1 N Integer Selecton PSM of DOCRs Fg. 1: Representaton of an Indvdual s Chromosome and Mappng Procedure 2

4 So far, varous technques have been suggested to tackle the constrants of the problem n GA, whle the most wdely used one s to assgn penalty functons to the problem. [29], [30]. In ths respect, ths method s mplemented usng a penalty to avod the nfeasble solutons by decreasng the related ftness values proportonally to the extent of the volaton. Ths technque would hghly depend upon the value consdered for the penalty parameter. In ths paper, the proposed GA ncorporates an NLP sub-problem to evaluate the feasblty and optmalty of the suggested settngs from GA. The procedure of the proposed GA s as follows: 1- Intalze by producng the populaton of K varous solutons bult at random whle the sze of the ntal populaton s ndcated by K. In ths respect, every ntal soluton s produced by randomly allocatng a PSM for correspondng DOCRs. 2- Decodng the structure of the soluton to derve the value of the ftness computed based on a ftness functon. Generally, the obtaned objectve functon from the NLP sub-problem must be consdered. However, the method suggested n [31] s used n ths paper to replace the method based on assgnng the penalty functon to the problem. 3- Usng the bnary tournament to select each parent by randomly selectng two players and afterwards, selectng the most desred ndvdual among that sets as a parent (smaller ftness value) [32]. The chld s also selected usng two bnary tournaments to generate a parent. 4- Matng random pars. By takng the crossover operators presented n the lterature [33], [34], a unform one on the bass of a random mask s utlzed n ths paper. In ths respect, a crossover between two parents would have a sngle chld whle the gene of the chld soluton s generated by duplcatng the equvalent gene from one of the other parent, selected based on a random bnary number generator. Ref. [35] provdes the comprehensve nformaton. 5- The next step after the crossover s the mutaton process generated by selectng a gene p {1,..., N} at random. After that, the value would be replaced by a randomly generated nteger number, PSM, chosen unformly from {1,..., S} so that the compatblty constrants are satsfed. 6- Substtutng an ndvdual n the populaton wth the chld soluton,.e., mutated chld. Once the mutated chld s feasble wth a lower value of ftness, the ndvdual wth the hghest ftness would be replaced provded that the populaton ncludes the entre solutons whch are feasble, otherwse, no replacement. By usng ths technque, the nfeasble solutons of the populaton would be rejected. Moreover, a coped chld whch s descrbed as a soluton wth the smlar structure to other soluton structures avalable n the populaton would not be permtted to get nto the populaton. Ths s due to that fact that n case of occurrence of such a thng, the populaton wll probably nclude all dentcal solutons whch hghly restrcts the capablty of the algorthm for producng new solutons. Ths phenomenon s n lne wth the prncple that we desre to obtan the best solutons from the feasble space. 7- Redong the steps 3 to 6 for pre-defned teratons excludng any replacement n the exstng populaton. It s worth-mentonng that numerous solutons can be produced snce t s desred to produce dfferent settngs to attan the best results Coordnaton of DOCRs usng hybrd ICGA-NLP The decson varables of the optmal coordnaton of DOCRs are TDS and PMS of relays. Accordngly, the presented optmzaton problem has two degrees of freedom. The PSM and TDS are determned usng ICGA and NLP, respectvely. It should be noted that TDS s a postve varable. The problem wth one degree of freedom would be solved to fnd the TDS for the values of PSM obtaned from the ICGA method. Besdes, the operatng tme of the relay s calculated wth respect to the characterstc curve chosen for the relay. Ths characterstc curve s selected proportonally to the short-crcut current seen by the current transformer (CT) and the relay. It s worth-mentonng that approprately choosng the characterstc curve of relays mpacts the optmal coordnaton of prmary and backup relays. Thus, the coordnaton constrant may not be satsfed n the NLP subproblem. To ths end, the NLP objectve functon and the CTI must be reconsdered. Accordngly, the objectve functon would be as (8) and the prmary and backup protecton coordnaton tme constrant would be as nequalty (9). N Mn TP + Penalty SL N = 1 = 1 TBj, TP + SL CTI (9) SL 0 (10) where SL s a slack postve varable used to avod not meetng constrant (9). However, a penalty s appled to the objectve functon to consder ths constrant wth a penalty factor. Therefore, the problem of optmal coordnaton of DOCRs would be tractable. 4 Smulaton Results A standard test system.e. the 8-bus test system has been consdered to evaluate the proposed protecton coordnaton framework. The test system has been used n the lterature to valdate the models and optmzaton methods. However, the results for the short-crcut currents and the assumptons on the load and network modelng as well as selectng protecton settngs are dfferent. Ths paper has studed the mentoned problem takng nto consderaton dfferent condtons consdered n the lterature. The proposed framework s mplemented on the standard 8- bus test system usng data of protectve relays, current CTs, generatng unts, the external grd as well as the load demand data reported n [22]. (8) 3

5 1 B.7 B.1 B.3 B B.2 B.6 B.5 B.8 Fg. 2 Sngle lne dagram of 8-bus test system [18] External Grd Fg. 2 demonstrates the sngle-lne dagram of the test system. Dfferent short-crcut currents have been reported n the lterature whle n some cases, the external grd has not been modeled and the mpact of the pre-fault load currents have not been taken nto consderaton. Hence, the protecton settngs have been dfferently reported. Besdes, dfferent values have been proposed for smlar short-crcut currents. For nstance, Table 1 represents the short-crcut currents whle the prefault currents have been neglected and by consderng the mpact of the external grd wth the short-crcut level equal to 400 MVA as well as excluson of the external grd. These results are smlar to those reported n [18] and [36] for these scenaros, respectvely. Includng Ext. Grd Excludng Ext. Grd (P:B) Prmary Back up Prmary Back up (1:6) (2:1) (2:7) (3:2) (4:3) (5:4) (6:5) (6:14) (7:5) (7:13) (8:7) (8:9) (9:10) (10:11) (11:12) (12:13) (12:14) (13:8) (14:1) (14:9) Table 1. Short-crcut currents for dfferent network topology 4 4 Includng Ext. Grd Excludng Ext. Grd Relay TDS PSM TDS PSM Obj. (Sec.) Table 2. Optmal settngs of DOCRs for dfferent network topology Includng Ext. Grd Excludng Ext. Grd Ref. [25] N/A Ref. [25] N/A Ref. [27] N/A Ref. [27] N/A Ref. [37] N/A Ref. [18] N/A Ref. [36] N/A ICGA-NLP Table 3. Comparson of results for dfferent network topology CTI TDS mn Includng Ext. Grd Excludng Ext. Grd Table 4. Optmal settngs of DOCRs for dfferent network topology TDS s assumed to be n [ ] n ths paper for base case. However, seven dscrete settng multples are taken nto consderaton to draw a comparson as (0.5, 0.6, 0.8, 1.0, 1.5, 2.0, and 2.5) Besde the current transform ratos of the DOCRs (1, 2, 4, 5, 6, 8, 10, 11, 12, 13) and (3, 7, 9, 14) are (1200:5) and (800:5), respectvely [18]. Table 2 represents the results obtaned for the optmal settngs of the relays nstalled n the 8-bus test system both by ncludng and excludng the external grd connected to bus 4. It should be noted that the smulaton has been done for CTI=0.3 seconds and TDS mn =0.1 seconds. In ths respect, the results obtaned by consderng the external grd are exactly the same as the ones reported n Ref. [18]. Table 3 llustrates the comparson made between the obtaned results and those 4

6 reported by other methods. Moreover, Table 4 ncludes the smulaton results derved for dfferent CTIs and dfferent values of TDS mn. The smulaton results show that the operatng tme of the relay ncreases wth the ncrease n the short-crcut current whch s due to ncludng the external grd. By decreasng the CTI and TDS mn, the operatng tme has reduced whch s true for both network topologes. DIgSILENT Powerfactory has been used to calculate the short-crcut currents and the ICGA algorthm has been mplemented n MATLAB software. Also, the NLP sub-problem has been solved usng CONOPT n GAMS. The number of teratons s 200 and the populaton sze s 100. Furthermore, the number of varables, N, s 14, the varaton range of nteger varable, S, s equvalent to seven dfferent PSMs and the penalty factor equvalent to the slack varable has been consdered Concluson Ths paper nvestgated the optmal coordnaton problem of drectonal overcurrent relays (DOCRs) usng a hybrd optmzaton technque. In ths respect, the hybrd optmzaton method ncluded the nteger coded genetc algorthm (ICGA) and non-lnear programmng (NLP) technque. Frst, the short-crcut currents were obtaned usng DIgSILENT PowerFactory for dfferent network topologes,.e. by both ncludng and excludng the external grd wth short-crcut current level 400 MVA at bus 4. Afterwards, these results were fed nto the optmzaton problem of optmal coordnaton of DOCRs as the nputs. Snce dfferent assumptons were made for the values of coordnaton tme nterval (CTI) and the mnmum Tme dal settng (TDS mn ), dfferent cases were smulated for the sake of comparson. The smulaton results verfed that the proposed optmzaton technque s capable of fndng acceptable solutons wth respect to the mentoned assumptons. It should be also noted that as the short-crcut currents reported n some references for these two scenaros are dfferent or the number of states of plug settng multpler (PSM) are dfferent, t was not possble to compare the results. 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