Probabilistic Fuzzy Approach to Assess RDS Vulnerability and Plan Corrective Action Using Feeder Reconfiguration

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1 Energy nd Power Engineering, 2012, 4, Published Online September 2012 ( Probbilistic Fuzzy Approch to Assess RDS Vulnerbility nd Pln Corrective Action Using Feeder Reconfigurtion Mini S. Thoms 1, Rkesh Rnn 2, Rom Rin 3 1 Jmi Milli Islmi University, New Delhi, Indi 2 IITB, Sonept, Indi 3 Reserch Scholr, Deprtment of Electricl Engineering, Fculty of Engineering nd Technology, Jmi Milli Islmi, New Delhi, Indi Emil: romrin@yhoo.com Received July 28, 2012; revised August 30, 2012; ccepted September 13, 2012 ABSTRACT Two common problems for typicl Power distribution system re voltge collpse & instbility. Chllenge is to identify the vulnerble nodes nd pply the effective corrective ctions. This pper presents probbilistic fuzzy pproch to ssess the node sttus nd proposes feeder reconfigurtion s method to ddress the sme. Feeder reconfigurtion is ltering the topologicl structures of distribution feeders by chnging the open/closed sttes of the sectionlizing nd ties switches. The solution is converge using probbilistic fuzzy modeled solution, which defines the nodl vulnerbility index (VI) s function of node voltge nd node voltge stbility index nd predicts nodes criticl to voltge collpse. The informtion is further used to pln best combintion of feeders from ech loop in distribution system to be switched out such tht the resulting configurtion gives the optiml performnce i.e. best voltge profile nd miniml kw losses. The proposed method is tested on estblished rdil distribution system nd results re presented. Keywords: Brnch Voltge; Three Phse Lod Flow; Voltge Stbility Index (SI); Rdil Distribution System (RDS); Monte Crlo; Probbility Distributions; Fuzzy Set; de Vulnerbility Index (VI); Feeder Reconfigurtion 1. Introduction Power distribution systems, especilly in developing countries, re stedily pproching towrds its mximum operting limits nd voltge stbility is mor concern. Voltge instbility mkes the system unrelible nd results in system collpse nd blckout. Around 30% to 40% of totl investments in the electricl sector go to distribution systems, but sme hve not received the technologicl impct s genertion nd trnsmission systems. The voltge instbility cn be ddressed using the vrious techniques. One of the control options for mnging RDS is feeder reconfigurtion. Reconfigurtion is opening nd closing the sectionlizing nd tie-switches in RDS. It modifies the network structure nd thus reduces the rel power losses, nd improves voltge stbility. However reconfigurtion is effective only when tieswitches re plnned t optimum loction nd the best combintions re selected for the sme. Distribution systems hve combintions of lods like industril, commercil, domestic, lighting etc. nd ech of them pek t different times of the dy nd need to be effectively cptured, while plnning reconfigurtion or locting tie switches for n existing RDS expnsion system. There re methods proposed by vrious uthors on vrious methods for reconfigurtion. B. Venktesh nd Rkesh Rnn propose method tht uses fuzzy dpttion of Evolutionry Progrmming (FEP) s solution technique [1]. Tknobu proposed distribution network expnsion plnning method by network reconfigurtion nd genertion of construction plns [2]. Dong-Joon Shin represents n pproch for service restortion nd optiml reconfigurtion of distribution network using genetic nd Tbuserch method [3]. B. Venktesh, Rkesh Rnn, H. B. Gooi developed new method for optiml reconfigurtion of rdil distribution systems which mximizes fuzzy index developed using mximum lod bility index [4]. R. Rnn, B. Venktesh, D. Ds proposed novel method for selecting n optiml brnch conductor for rdil distribution networks bsed on fuzzy dption of evolutionry progrmming [5]. P. V. V. Rm Ro nd S. Sivngru proposes plnt growth simultion lgorithm to enhnce speed nd robustness nd does not require externl prmeters for loss minimiztion nd lod blncing [6]. This pper discusses the pln of optimizing the Rdil distribution system vi feeder reconfigurtion using probbilistic fuzzy modeled solution. The proposed solution clcultes node vulnerbility index nd use the sme for reconfigurtion. The solution is bsed on concept of prob-

2 M. S. THOMAS ET AL. 331 bilistic fuzzy rules nd is suitble for modeling rel world systems, where we hve both sttisticl nd non-sttisticl uncertinties. Probbilistic prt of the model uses Monte Crlo simultion (MCS) nd considers input prmeters s rndom vribles with predefined probbility distribution shpe. Further for clculting vulnerbility index, pper uses fuzzy bsed lgorithm, nd uses fuzzified node voltge nd node voltge stbility index s inputs. Bsed on vulnerbility index of nodes, scheme for plnning tie nd sectionlizing switches to chieve loss reduction is presented. While the scope of the feeder reconfigurtion problem discussed here is limited to the discussion of losses, the results developed provide significnt insight into useful chrcteristics ssocited with the modeling nd properties of relted feeder reconfigurtion problems. The bove technique cn be used for long term distribution network expnsion plnning purposes lso. The pper is orgnized s follows. In Section 2, the methodology & steps used re discussed. Section 3 defines formuls nd clcultion lgorithm used. Section 4 describes nodl vulnerbility index computtions, Section 5 elbortes the reconfigurtion plnning & clcultions showing reduction in losses nd Section 6 concludes the pper. 2. Methodology Pper presents RDS reconfigurtion plnning using following steps: Define the lod flow & stbility index formuls & clcultion lgorithm; Infuse rndomness in input vribles in line with rel time scenrio by modeling input dt s rndom vribles with predefined distribution to ddress combintion of lods; Use Monte Crlo simultion nd generte output distribution for nodl voltges & voltge stbility index nd clculte node vulnerbility index; Use de vulnerbility index s bsis for RDS reconfigurtion plnning; Reclculte the losses fter pplying proposed reconfigurtion. 3. Formuls & Clcultion Algorithm 3.1. Lod Flow & Stbility Index Clcultion Formul s & Algorithm For simultion purpose this pper uses lod flow lgorithm, bsed on concept described by R. Rin, M. Thoms, R. Rnn [7] nd modified to suite the probbilistic model (for Monte Crlo simultion). The lgorithm clcultes the totl rel nd rective system power loss, nodl voltges nd stbility index. The lod flow clcultion lgorithm uses the bsic systems nlysis method nd circuit theory nd requires only the recursive lgebric equtions to get the voltge mgnitudes, currents & power losses t ll the nodes. This lod flow methodology lso evlutes the totl rel nd rective power fed through ny node. Using concept of simple circuit theory, the reltion between the bus voltges nd the brnch currents in Figure 1 cn be expressed s: g g b c Vi V V Z Z Z bg bg b b bb bc Vi V V Z Z Z (1) cg cg c c cb cc Vi V V Z Z Z where; g Vi = Voltge of phse t node i with respect to ground; b Vi = Voltge drop between two phses nd b t node I; V = Voltge Drop between nodes i nd in phse ; I = Current through phse between nodes i nd ; Z = Selfimpednce between nodes i nd in phse ; b Z = Mutul impednce between phse nd b between nodes i nd ; Pi, Qi, Si = Rel, rective nd complex power lods t phse t i th bus; phse S = Complex power t phse (, b nd c) between nodes i nd ; phse PL = Rel power loss in the line between node i nd ; phse QL = Rective power loss in the line between node i nd ; phse SL = PL phse + QL phse. Rewriting (1) b c V V Z i Z Z I b b b bb bc b V Vi Z Z Z I c c c cb cc c V V i Z Z Z I Following equtions gives the brnch currents between the nodes i nd : I b I c I Z bb Z cc Z b Z bc Z c Z Figure 1. Three phse four wire line model.

3 332 M. S. THOMAS ET AL. I b b c c P Q P Q P Q, I, I b c b V V The rel nd rective power losses in the line between buses i nd re written s; SL PL QL V I i SL PL QL V I b b b b i SL PL QL V I c c c c i V V I i b b b V I i c c c V I i This lgorithm computes the rel & rective power nd uses the formul given in Eqution (2). Receiving end power t ny phse, sy phse A, of line between the nodes i nd is expressed s: QL k k mn mn (2) P Q P Q PL K = index of ll nodes fed through the line between nodes i &. mn = index of ll line connected between nodes m nd n through the line between nodes i nd. The simultion lso clcultes the voltge stbility index (SI) for ll the nodes of the rdil distribution system using the lod flow results. There re severl methods to estimte or predict the voltge stbility condition of power system. The simultion utilizes the voltge stbility index defined by N. C. Shoo, K. Prsd [8] to indicte the voltge stbility condition t ech bus of the system. Stbility index (SI) for the bus, for typicl brnch s shown in Figure 2 is defined s: 2 SI V 4 P R Q X (3) i The vlue of SI vries from 0 to 1. For stble opertion of the RDS, Stbility Index (SI) should be nering one. c For simultion purpose connected lod is ssumed to be vrying bsed on Tble 1 probbility distribution shpe. This simultion is run on typicl 19 bus distribution system from the D. Thukrm, H. M. W. Bnd, nd J. Jerome [9] for 500 trils nd distribution of output results re used s input for clculting node vulnerbility index nd input dt re given in Appendix of this pper Mote Crlo Simultion Results The simultion is run for 500 trils nd distribution of results is tbulted s frequency distribution. Tble 2 provides the Rel, Rective power loss vlues corresponding Figure 3. Sketch for Monte Crlo simultion method. Tble 1. Probbility distribution for connected lod. des Probbility Distribution Shpe Shpe Dt 3.2. Infusing Rndomness in Inputs & Monte Crlo Simultion to Address Combintion of Lods 2, 7, 13, 18, 19 = 20% b = 100% c = 130% Monte Crlo simultion principle is described in Figure 3. The principle is bsed on considering input prmeters s rndom vribles nd with predefined distribution shpe. Probbility distribution shpe describes the likelihood of sme future events. Uncertin input prmeter is considered s rndom vrible P nd numbers of reliztions P i of P re generted nd lod flow lgorithm is run for ech of them producing n output R i. Set of outputs R i represents the set of reliztions of the rndom vrible R. 4, 10, 16 5, 12, 15 c b c b = 90% b = 100% c = 140% = 15% b = 100% c = 105% c b V i α i R +X i V α 3, 6, 8, 9, 11, 14, 17 Men = 1.0 (100%) SD = 0.1 (10%) Figure 2. Electricl equivlent of one brnch. NORMAL DISTRIBUTION

4 M. S. THOMAS ET AL. 333 to 90% (0.9) cumultive probbility. The vlue of 90% (0.9) cumultive probbility signifies tht for simultion run of 500 trils, 90% time vlues were less thn kw/66.9 KVAr. Tble 3 shows the simultion distribution results for selected nodl voltges bsed on 500 trils including minimum nodl voltge corresponding to 90% cumultive probbility. Tble 4 shows the simultion distribution results for node stbility index bsed on 500 trils. Minimum stbility index corresponding to 90% cumultive probbility is lso clculted. The simultion results obtined bove re used s input for clculting vulnerbility index. 4. dl Vulnerbility Index Computtions As vulnerbility is not sttisticl uncertinty, this pper proposes fuzzy pproch nd uses voltge nd stbility index of ech node to clculte the vulnerbility index. The bus voltges nd the SI re selected s the crisp input prmeters nd expressed s fuzzy set nottion. The fuzzy If-Then rules re then used to evlute the vulnerbility index of ech node nd defuzzifiction provides the crisp vlue of the output. For clcultion purpose tringle membership functions is ssumed for bus voltge nd stbility index profile nd re represented in fuzzy set nottion. The bus voltge profiles re divided into five tringulr membership functions, s indicted in Figure 4. Fuzzy Interprettion of voltge (V); If V < 0.925, then Unstble (UN) ; If V < 0.925, then Unstble (UN) ; If V = , then Less Stble (LS) ; If V = , then Modertely Stble (MS) ; If V = , then, Stble (S) ; If V > 0.975, then, Over rnge (Over). Similrly the stbility index profiles re divided into five tringulr membership functions using fuzzy set nottions, s given in Figure 5. Tble 2. Distribution dt for rel & rective power. Dt Loss Std. Div. Minimum Mximum 90% Cum Probbility Vlue Rel Power Loss kw Rective Power Loss KVAr Tble 3. Distribution dt for voltge mgnitudes (smple nodes). de Phse A Phse B Phse C Men StDev 90% Prob Men StDev 90% Prob Men StDev 90% Prob Tble 4. Distribution dt for stbility index (smple nodes). de Phse A Phse B Phse C Men StDev 90% Prob Men StDev 90% Prob Men StDev 90% Prob

5 334 M. S. THOMAS ET AL. Fuzzy Interprettion of stbility index (SI); If SI < 0.85, then Unstble (UN) ; If SI = , then Less Stble (LS) ; If SI = , then Less Stble (LS) ; If SI = , then, Stble (S) ; If SI > 0.975, then, Over rnge (Over). Using fuzzy If-Then rules s shown in Tble 5, Vulnerbility index is clculted. Fuzzy If then rules, strengths of tringulr membership function, output rnge nd output clcultion formuls re shown in Appendix, Figure 4. Fuzzy number representtion of voltge. Figure 5. Fuzzy number representtion of stbility index. Tble S4, of this pper. The bove procedure is repeted for ll the nodes to clculte the output vulnerbility index for ll 500 trils results. Figure 6 shows the sctter plot of vulnerbility index men vlue of ll trils. A cut-off level of vulnerbility index vlue of 0.15 is proposed s unrelible node nd prone to voltge collpse. The results obtined re further plotted using box plot. In descriptive sttistics, boxplot grphiclly depict groups of numericl dt through their five-number summries. Figure 7 shows the boxplot of nodl vulnerbility index distribution for ll nodes t glnce. We cn note tht for node 10 to 19, some distribution of vulnerbility index flls below the cut-off vlue of This mens tht for simultion of 500 rndom trils, some combintion of input dt resulted vulnerbility index less thn To further study the node vulnerbility index, probbility of vulnerbility index vlues coming below 0.15 is clculted nd results re shown on Tble 6. The probblity is bsed on vulnerbility index distribution results for 500 trils. We cn sfely ssume tht if probbility is less thn 5%, node cn be considered sfe s they re bout the cutoff vlues 95% times. However nodes with probblity greter thn 5% need ddressing. 5. Reconfigurtion In rdil distribution system, network reconfigurtion is performed by closing/opening the tie-in nd sectionlistion switches. Conventionl lod flow techniques tke lrge number of itertion nd huge computtionl time to decide on optiml reconfigurtion. The proposed method nrrows down the reconfigurtion to only nodes which hve uncceptble vulnerbility index. The obective behind reconfigurtion is to mke uncceptble vulnerbility index vlue to cceptble level which intern will reduce the power loss nd will mke system more stble. Obective function of bove cn be expressed s below mthemticl model. Tble 5. Smple fuzzy if then rules. R1 If V < & SI < 0.85 Then UN Min Av & SI R3 If V = & SI < 0.85 Then UN Min Av & SI R9 If V = & SI = Then MS Min Cv & SIc R10 If V > & SI = Then S Min Dv & SId R11 If V < & SI = Then UN Min Av & SI R13 If V = & SI = Then MS Min Cv & SIc R14 If V = & SI = Then S Min Dv & SId R16 If V < & SI = Then UN Min Av & SI R21 If V < & SI > Then UN Min Av & SI R25 If V > & SI > Then O Min Ev & SIv

6 M. S. THOMAS ET AL. 335 Figure 6. Sctterplot of vulnerbility index men. P VI95% for ll nodes 95% 0.95 ; n1 i1 SL PL QL is minimum (i.e. Losses re minimum); where: P VI95% = Probbility of VI vlue greter thn 0.15; N = Number of nodes in RDS. The proposed method cn be used for n RDS hving existing tie-in & sectionlising switches. The method cn lso be used s plnning tool for identifying the best loction of instlling new tie-in switches in n existing RDS or for RDS expnsion. For plnning new tie/sectionlising switches, the proposed method considers nodes with low VI, its distnce to nerest helthy node on other lterl, instlltion limittion, cost of instlltion etc. s input. The flow chrt of lgorithm for proposed method is shown in Figures 8 nd 9. This simultion is run on typicl RDS from the D. Thukrm, H. M. W. Bnd, nd J. Jerome [9], which is without the tie-in switches. The result selects 5-10 s possible reconfigurtion. Refer Figure 10. Strt Identify the nodes with low Vulnerbility Index Figure 7. Boxplot of nodl vulnerbility index. Tble 6. Distribution dt for vulnerbility index (smple nodes). de Phse Men StDev Probbility of Vlue Minimum Less thn 0.15 A % 1 B % C % A % 12 B % C % A % 13 B % C % A % 14 B % C % A % 16 B % C % A % 17 B % C % A % 18 B % C % A % 19 B % C % Select upstrem node, if two or more nodes with low VI re on sme lterl Identify potentil node with-in 1 km rdius of Selected node on seperte lterl Check if instlltion limittion permits to instll t tie switch between bove two nodes Instlltion permits? Run the simultion nd identify VI & Totl Loss des bove VI cut-off? Solution Converge Increse the rdius from selected nodes nd identify potentil node on seprte lterl Additionl Tie-in switch would be needing Repete the step for new configurtion Figure 8. Flowchrt for plnning reconfigurtion tie-in switches.

7 336 M. S. THOMAS ET AL. Identify the nerest down strem node on sme lterl with tie-in switch Strt Identify the nodes with Lowest Vulnerbility Index Identify the nerest upstrem node on sme lterl with tie-in switch Upstrem tie-in vible? Close the tie switch Tble 7 shows Rel & Rective power with reconfiguring node The rel power loss hs been reduced by 28%, when compred to results before reconfigurtion s shown in Tble 2. Figure 11 shows the sctter plot of vulnerbility index men vlue of ll trils with reconfigurtion node The men VI hs incresed drsticlly nd is well bove 0.15 cut-off vlue, when compred to the results before reconfigurtion vlue s shown in Figure 6. Figure 12 shows the boxplot of nodl vulnerbility index distribution for ll nodes t glnce with reconfigurtion All nodes hve distribution of vulnerbility Tble 7. Distribution dt for rel & rective power with reconfiguring node Tie-in switch vible? To brek the loop, open the immedite upstrem sectionlizing switch from tie-in switch Clculte the system losses & Vulnerbility Index Dt Loss Std. Div. Minimum Mximum Rel Power Loss kw Rective Power Loss KVAr 90% Cum Probbility Vlue Identify the second tie-in switch on sme lterl Look for other methods for VI improvement Is VI with-in cceptble Limit? Solution Converge End Figure 9. Flowchrt for reconfigurtion with existing tie-in switches. Figure 11. Sctterplot of vulnerbility index men fter reconfigurtion Figure 10. Shows prcticl 19 bus distribution feeder used for the modeling nd simultion purpose with 5-10 reconfigurtion. Figure 12. Boxplot of nodl vulnerbility index.

8 M. S. THOMAS ET AL. 337 index well bove cut-off vlue of 0.15, when compred to the results before reconfigurtion s shown in Figure 7. This mens tht for simultion of 500 rndom trils no combintion of input dt resulted vulnerbility index less thn The method ws lso tried on the reconfigurtion of RDS with existing tie-in-switches in plce. 6. Conclusions This pper uses the ppliction of probbilistic fuzzy pproch to ssess the node sttus nd proposes reconfigurtion s method to ddress the sme. Solution is converge using probbilistic fuzzy modeled solution. The ccessing the node sttus, unique index nme Vulnerbility index is proposed which is function of node voltge nd node voltge stbility index. Reconfigurtion is proposed for the nodes which hve n cceptble VI vlue nd is chieved by selecting reconfigurtion which gives n cceptble vlue of VI, nd the optiml performnce i.e. best voltge profile nd miniml kw losses. The proposed method is tested on estblished RDS nd results re presented. Considering the fct tht input uses repeted rndom smpling, proposed methodology covers nd model ll possible scenrios nd comprison cn be drwn for wide vrition in lods. The method cn be used for design studies, initil stges plnning lso. REFERENCES [1] B. Venktesh nd R. Rnn, Optiml Rdil Distribution System Reconfigurtion Using Fuzzy Adpttion of Evolutionry Progrmming, Electricl Power nd Energy Systems, Vol. 25,. 10, 2003, pp [2] T. Askur, T. Geni, T. Yur, N. Hyshi nd Y. Fukuym, Long Term Distribution Network Expnsion Plnning by Network Reconfigurtion nd Genertion of Construction Plns, IEEE Trnsctions on Power Systems, Vol. 18,. 3, 2003, pp doi: /tpwrs [3] D. J. Shin,. O. Kim, T. K. Kim, J. B. Choo nd C. Singh, Optiml Service Restortion nd Reconfigurtion of Network Using Genetic-Tbu Algorithm, Electricl Power Systems Reserch, Vol. 71,. 2, 2004, pp doi: /.epsr [4] B. Venktesh, R. Rnn nd H. B. Gooi, Optiml Reconfigurtion of Rdil Distribution Systems to Mximize Lodbility, IEEE Trnsctions On Power Systems, Vol. 19,. 1, 2004, pp doi: /tpwrs [5] R. Rnn, B. Venkteshnd nd D. Ds, Optiml Conductor Selection of Rdil Distribution Networks Using Fuzzy Adpttion of Evolutionry Progrmming, Interntionl Journl of Power nd Energy systems, Vol. 26,. 3, 2006, pp doi: /journl [6] P. V. V. Rm Ro nd S. Sivngru, Rdil Distribution Network Reconfigurtion for Loss Reduction nd Lod Blncing Using Plnt Growth Simultion Algorithm, Interntionl Journl on Electricl Engineering nd Informtics, Vol. 2,. 4, 2010, pp [7] M. S. Thoms, R. Rnn nd R. Rin, Fuzzy Modeled Lod Flow Solution for Unblnced Rdilpower Distribution System, Proceedings of the IASTED Interntionl Conference on Power nd Energy Systems (EuroPES 2011), Crete, June 2011, pp [8] N. C. Shoo nd K. Prsd, A Fuzzy Genetic Approch for Network Reconfigurtion to Enhnce Voltge Stbility in Rdil Distribution Systems, Energy Conversion nd Mngement, Vol. 47, , 2006, pp doi: /.enconmn [9] D. Thukrm, H. M. W. Bnd nd J. Jerome, A Robust Three Phse Power Flow Algorithm for Rdil Distribution Systems, Journl of Electricl Power Systems Reserch, Vol. 50,. 3, 1999, pp doi: /s (98) Appendix A. Input Dt Input connected lod dt for the feeder re given in Tble S1, Conductor dt for the feeders re given in Tbles S2 nd S3. B. Fuzzy If-Then Rules For node; Voltge = V nd Stbility Index = SI. Then the corresponding membership vlues for ech zone of the five tringulr membership functions cn be defined s given in Tble S4. The strengths for five tringulr membership functions re shown in Eqution (5). Tble S5 shows the output rnges for vulnerbility index ssumed nd uses defuzzifiction clcultions given in Eqution (4) to find the crisp vlue of vulnerbility index. Over Over (4) UN LS MS Over r UNr UNs LSr LSs MSr MSs r s OUTPUT r r r

9 338 M. S. THOMAS ET AL. UN R1 R2 R3 R6 R11 R16 R21 s s s s LS R R R R b MS R R R R R c S R R R R R R R Over R25 e R24 d Tble S1. Input lod dt. Tble S4. Membership function representtion. de Phse Lod in kva A B C Membership Voltge Vlues SI UN Av SI LS Bv SIb MS Cv SIc Stble Dv SId Over Ev SIe Tble S5. Output rnge considered for vulnerbility index clcultion. Un r = 0 LS r = 0.5 MS r = 0.75 S r = 0.9 Over = 1 Tble S2. Conductor dt. Conductor type Resistnce Rectnce PU/km PU/km Tble S3. Conductor code & distnces. Sending End de(ir) Receiving End de(ir) Conductor Code Distnce in km (Tie Switch)