Power Distribution System Planning Evaluation by a Fuzzy Multi-Criteria Group Decision Support System

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1 Internatonal Journal of Computatonal Intellgence Systems, Vol.3, No. 4 (October, 2010), Power Dstrbuton System Plannng Evaluaton by a Fuzzy Mult-Crtera Group Decson Support System Tefeng ZHANG School of Electrc&Electronc Engneerng, North Chna Electrc Power Unversty Yonghua North Road, 619, Baodng, Hebe, , P.R Chna E-mal: ncepuztf@126.com Guangquan ZHANG, Jun MA, Je LU Faculty of Engneerng and Informaton Technology, Unversty of Technology Sydney PO BOX 123, Broadway, NSW 2007, Australa E-mal: {zhangg, junm, jelu}@t.uts.edu.au Abstract The evaluaton of solutons s an mportant phase n power dstrbuton system plannng (PDSP) whch allows ssues such as qualty of supply, cost, socal servce and envronmental mplcatons to be consdered and usually nvolves the judgments of a group of experts. The plannng problem s thus sutable for the mult-crtera group decson-makng (MCGDM) method. The evaluaton process and evaluaton crtera often nvolve uncertantes ncorporated n quanttatve analyss wth crsp values and qualtatve judgments wth lngustc terms; therefore, fuzzy sets technques are appled n ths study. Ths paper proposes a fuzzy mult-crtera group decson-makng (FMCGDM) method for PDSP evaluaton and apples a fuzzy mult-crtera group decson support system (FMCGDSS) to support the evaluaton task. We ntroduce a PDSP evaluaton model, whch has evaluaton crtera wthn three levels, based on the characterstcs of a power dstrbuton system. A case-based example s performed on a test dstrbuton network and demonstrates how all the problems n a PDSP evaluaton are addressed usng FMCGDSS. The results are acceptable to expert evaluators. Keywords: Power dstrbuton system plannng, decson support systems, mult-crtera decson makng, group decson-makng, fuzzy sets. 1. Introducton The evaluaton of solutons s an mportant phase n power dstrbuton system plannng (PDSP), 1 whch conssts of two stages. The frst stage s to dentfy what characterstcs must be ncorporated by the power dstrbuton system, what benefts the power dstrbuton system wll provde, and how consumers, the utlty, and the government wll be satsfed wth the power dstrbuton system. In the second stage, the decson maker(s) makes a decson on whch plannng soluton wll be determned and put nto practce. Rankng plannng solutons s the man task of the evaluaton. Tradtonally, the soluton that provdes the optmum cost (.e. provdes the mnmum economc and fnancal mpact) would be selected for mplementaton after the correspondng power dstrbuton system s assessed by performng network analyss when the power flows n a crcut or substaton exceed desgnated capactes. 2-4 In today s demandng envronment, more and more ssues such as qualty of supply, cost, socal 474

2 T. Zhang, G. Zhang, J. Ma, and J. Lu servce and envronmental mplcatons must be consdered n PDSP actvtes. 1, 5-7 At the same tme, the planners are strongly nvolved n cost reducton projects to fnd the best compromse between performance and cost. Before mplementaton, the solutons should be evaluated by mult-crtera analyss of mult-aspects (techncal, economc, envronmental and socal) by expert trade-off to determne the most sutable. There are fve ssues whch need to be consdered to conduct PDSP evaluaton. (1) The determnaton of evaluaton crtera and ther degrees of mportance to the requrements of the PDSP. In prncple, PDSP evaluaton s often very complex, because multple evaluaton crtera are herarchcal n structure, and these crtera have dfferent roles n developng a soluton. For PDSP, we need to consder crtera from techncal, economc, envronmental and socal aspects. 6 Mult-crtera decson makng (MCDM) refers to makng decsons for alternatves n the presence of multple conflctng crtera. A man contrbuton area of MCDM s makng a preference decson (e.g., evaluaton, prortzaton, selecton) over the avalable alternatves, such as a set of alternatves that are characterzed by multple, usually conflctng, attrbutes. 8 As PDSP nvolves multple aspects and each aspect has a set of crtera and even sub-crtera, the PDSP evaluaton needs a mult-level MCDM method to handle ts herarchcal crtera system. In addton, some crtera may be more mportant than others, so crtera on all levels of an evaluaton model need to be gven ndvdual weghts. (2) The PDSP evaluaton requres the multple perspectves of dfferent people because one evaluator may not have enough knowledge to ndvdually expertly assess an alternatve. Therefore, evaluatons of PDSP solutons are often made n groups, for example, by experts from dfferent sectons of electrcty dstrbuton companes and nvted peer experts n ths feld, and requre the gatherng, processng and assessng of nformaton from dverse functonal groups wthn an organzaton. Group decson-makng (GDM) s the process of arrvng at a judgment or a soluton for a decson problem based on the nput and feedback of multple ndvduals. However, the process may nvolve a set of uncertan factors, whch ncludes an ndvdual s role (weght) n the ranked plannng solutons and an ndvdual s preference and understandng of the plannng solutons evaluated, and the crtera. 9 (3) In PDSP evaluaton, group members may have a dfferent understandng of the same nformaton, dfferent experences n the area of PDSP, and dfferent preferences for dfferent solutons. These dfferent preferences among group members may mpact drectly on the soluton evaluaton results; therefore, the fnal rankng of solutons wll be obtaned by the sutable fuson and ntegraton of these ndvduals vewponts. Because of the complexty, the fuson process has to be supported by a software tool. (4) Both quanttatve and qualtatve crtera are ncluded n PDSP evaluaton, whch requre dfferent technques to handle them. Quanttatve crtera are often ndrect and are consdered objectve; thus, we call them ndrect crtera. Qualtatve crtera are often drect and beng consdered subjectve, are called drect crtera. An ndrect crteron s obtaned by quanttatve analyss (such as calculated by a physcal or economcal equaton) wth crsp values. A drect crteron s evaluated subjectvely accordng to knowledge, obtaned by qualtatve judgments wth lngustc terms. For lngustc terms, there s a requrement for lngustc nformaton processng. For example, to express the weght of a crteron, the terms mportant and very mportant can be used; for an evaluator s weght, normal, mportant and more mportant can be used; and for a soluton s score, lngustc term such as low and hgh could be used. The concept of lngustc varables s useful n dealng wth stuatons that are too complex or ll-defned to be reasonably descrbed n conventonal quanttatve expressons. 10, 11 Precse mathematcal approaches are not suffcent to tackle such uncertan varables and derve a satsfactory soluton. (5) How to handle data uncertanty. In PDSP evaluaton, cost coeffcents, forecastng demand, electrcty prce, technology development and equpment falures are fraught wth uncertanty, whch wll affect the data of ndrect crtera. Even these lngustc terms reflect the uncertanty, naccuracy and fuzzness of humans, and these uncertantes wll affect the optmzaton process. Neglectng uncertantes n an optmzaton process may result n mssed nformaton and thus lead to non-robust decson support. To deal wth the above ssues, many prevous studes have formulated PDSP as an MCDM problem and proposed varous methods. The smple mult-attrbute ratng technque (SMART) and analytcal herarchy process (AHP) 12 were used to determne the weghted decson scores for each of the alternatves; a unform 475

3 possblty dstrbuton was used to represent uncertan data entres. 7 In Ref. 13, an nterval AHP-based method was proposed and appled to a practcal plannng case, n whch the uncertan nformaton was handled by ntervals. A fuzzy AHP-based method was proposed and appled n urban power system plannng, 14 n whch fuzzy number was used to deal wth data uncertanty. 15, 16 Outrankng relaton based technques have been used for PDSP evaluaton, and the uncertanty of data was ncorporated by thresholds reflectng the decson maker s rsk atttudes. Other MCDM methods used for PDSP evaluaton nclude data envelopment analyss, 17 grey correlaton degree and TOPSIS 18 and lnear programmng. 16, 19 Generally speakng, AHP s a most popular method used n PDSP evaluaton, and to deal wth the uncertanty of data, nterval technology, 13, 19 fuzzy numbers 14, 20, probablty dstrbuton 7 15, 16 and outrankng relaton were employed n dfferent stuatons. Each has ts ndvdual advantages and lmtatons. At present, no methods have been used to deal wth all fve ssues n PDSP evaluaton, especally for the GDM aspect. Therefore, ths paper proposes a fuzzy mult-crtera group decson-makng (FMCGDM) method and apples a fuzzy mult-crtera group decson support system (FMCGDSS) to support the evaluaton task. Ths paper s organzed as follows. Followng the ntroducton, Secton 2 presents a PDSP evaluaton model. Secton 3 descrbes a FMCGDM method. A FMCGDSS and ts applcaton n PDSP evaluaton are llustrated by a PDSP case study n Secton 4. Conclusons are outlned n Secton A PDSP Evaluaton Model In ths secton, we analyze how the varous factors and crtera nteract and nfluence PDSP evaluaton, and then present an evaluaton model and ts establshment process. The plannng of a power dstrbuton system comprses development, operaton and mantenance of the nfrastructure as well as the ntegraton of dstrbuted generatons and multple end-uses. Objectves and tasks n the plannng process may be summarzed as: to cover supply dutes wth acceptable qualty of supply and to contrbute to effectve power markets to specfy nfrastructure and power lnes and substatons at mnmum cost, acceptable envronmental mpact, and good socal servces The overall objectve of PDSP evaluaton can be formulated as Maxmzng socety s welfare, and can be broken down naturally nto four man major objectves, as n the evaluaton model shown n Fg.1. The evaluaton model has three levels. The crtera on the frst level are called aspects; the crtera on the Fg. 1. A PDSP evaluaton model second are called crtera; and on the thrd level are called sub-crtera. These aspects and crtera (subcrtera) are determned by a group of experts n PDSP desgn by consderng power dstrbuton system characterstcs and may be obtaned n a varety of dfferent ways,.e. by economc analyss, judgmental assessment and techncal analyss. These drect crtera can not be measured and easly quantfed. Ths evaluaton model consders four aspects: Economy, Technology, Envronment and Socety. Each aspect has a set of crtera. For example, Technology s assessed by two crtera, Relablty and Capacty constrants. Each crteron may be assessed by a set of sub-crtera; thus, the crteron Relablty has two sub-crtera: System securty and Supply avalablty. Evaluators need to gve ther evaluaton (scores) on all these ndrect crtera Economy The Economy aspect s probably the most mportant for the majorty of decson makers. To assess ths crteron, there are several objectves that can be consdered separately, dependng on who the decson maker s and the nature of hs/her decson envronment. In ths model, the Economy aspect conssts of Captal cost and Annual energy losses. 1 Captal 476

4 T. Zhang, G. Zhang, J. Ma, and J. Lu cost s an mportant factor when assessng plannng solutons, as t s a summaton of the costs nvolved n mplementng each of the optons selected for each dentfed problem, plus any ongong costs related to mplementaton or other operatonal aspects assocated wth the dstrbuton network. The cost of each opton (and soluton) should be expressed ether as the current cost of mplementaton, or as the future-worth equvalent at the end of the plannng perod (horzon year), converted usng a present-worth calculaton. The am of the Annual energy losses crteron s to provde an accurate assessment of the power losses assocated wth each plannng soluton. Here only real power losses assocated wth each soluton wll be calculated Technology In ths model, the Technology aspect conssts of the crtera Relablty, and Capacty constrants. 1 The crtera Relablty conssts of two sub-crtera: System securty and Supply avalablty. Dstrbuton network relablty s an ssue of partcular mportance to large ndustral connected customers, as even short supply nterruptons may result n sgnfcant downtme and assocated cost penaltes n some countres. System securty s calculated as: number of customers nterrupted per 100 connected customers = the sum of the number of customers nterrupted for all ncdents*100 / the number of connected customers. Supply avalablty s calculated as: average customer mnutes lost (CML) per connected customer = the sum of the customer mnutes lost for all restoraton stages for all ncdents / the number of connected customers. The crteron Capacty constrants assesses each plannng soluton to dentfy where the system capacty remans below the forecasted scenaro load, and t can be determned by performng a power flow calculaton for each feasble soluton for the load scenaro Envronment Envronmental mpact s an mportant ssue that must be consdered by all dstrbuton companes before the mplementaton of a PDSP project. Envronmental mpact ncludes land occupaton, nose, aesthetc mpact, and so on. Ideally, all mpacts on nature,.e. the whole lfecycle mpact (constructon, operaton and dsposal) of the varous alternatves, should be ncluded n the analyss. Dfferent solutons of a PDSP project have a dfferent mpact on the envronment. The decson maker must decde whch envronmental aspects to take nto consderaton, accordng to the nformaton about possble techncal alternatves. Some types of envronmental mpact may be quantfable whle others wll have to be consdered n qualtatve terms. In ths model, the Envronment aspect conssts of two sub-crtera: Crcut length and Vson. Crcut length 1 s adopted to express the land occupaton and to consder the total crcut length of new or modfed network crcuts, so t s quantfable. Vson 6 s used to assess vsual obstructon and manly refers to the coordnaton of surroundng buldng or envronment; t wll be consdered n lngustc terms. Ther degree of mportance depends on the plannng area. In an urban area or park, more attenton wll be pad to envronmental mpact than n a rural area Socety The man reason for buldng energy facltes and nfrastructure s to provde socety wth energy servces. Increasng numbers of stakeholders wth dfferent objectves and crtera are nvolved n the plannng process, such as electrcty dstrbuton companes, large-scale customers, regulators/local authortes, and local resdents. Some are drectly nvolved as decson makers, whle others are manly affected by the fnal outcome wthout havng taken an actve part n the decson process. Therefore, t s useful to understand the socal mpact of varous changes (local employment opportuntes, local ndustral development and potental publc protests, etc.) n the power dstrbuton system s nfrastructure by takng nto consderaton socal values and publc atttudes n the plannng process. In ths model, the Socety aspect ncludes Publc atttude and Socal value. 6 Publc atttude s to mnmze publc protest and Socal value s to maxmze servce. It s not easy to measure publc atttudes and socal values, however, they are both drect crtera, and can be expressed by lngustc terms. In ths study, to allow each possble plannng soluton to be assessed, a PDSP evaluaton model s establshed and several crtera have been selected. Nevertheless, ths does not restrct the ncluson of addtonal crtera, f requred, for partcular plannng studes. 477

5 3. A Fuzzy Mult-level Mult-Crtera Group Decson-Makng Method for PDSP evaluaton In ths secton, a fuzzy (mult-level) mult-crtera group decson-makng (FMCGDM) method for PDSP evaluaton s descrbed. The FMCGDM method s based Zadeh s fuzzy set theory nto conventonal decsonmakng models 21 and the concept of lngustc varables proposed by Zadeh 22 to handle lngustc terms n a decson-makng problem. In ths method, AHP and TOP- SIS 23 technques are used and some of the GDM technques 24-29, 31 are also ncorporated. For brevty, we ntroduce only the prncple and steps of the proposed FMCGDM method below; some basc notons n FMCGDM method have been descrbed n Ref. 30, and all fuzzy numbers are symmetrc trangular numbers. 21 Stage one: Determne solutons, assessment-crtera, and ndvdual weghts, generate data for quantfable crtera Step 1: A set of solutons S = {S 1, S 2,, S m } s determned as alternatves and a set of decson makers (evaluators) P = {P 1, P 2,, P n } set up an evaluaton group, generally mn, 2. Also, three levels of assessment-crtera model wthn a tree herarchy: C = {C 1, C 2,, C t }, C = {C 1, C 2,, C j }, = 1, 2,, t, and ther sub-crtera Cj C j1, Cj2, Cjk j 1,2, j j for assessng these solutons are determned n the group, as shown n Fg.1. For those quantfable crtera, data must be generated descrbng the performance of each soluton n each crteron; those performance data are thought to be objectve and wll not be nfluenced by evaluators. Step 2: Each evaluator s assgned a weght that s descrbed by a lngustc term v k, k 1, 2, n. These terms are determned through dscussons n the evaluator group or assgned by a hgher management level before, or at the begnnng of, the decson process. Possble lngustc terms used here are Normal, Important, More mportant, and Most mportant, as shown n Table 1. Step 3: Set up weghts for all crtera wthn three levels. Let WC WC1, WC2,, WCt, = 1, 2,, t be the weghts of crtera on level 1, where WC s descrbed by a lngustc term. Possble lngustc terms used are as shown n Table 2. For a crteron C, let WC { WC1, WC2, WCj }, = 1, 2,, t be the weghts for the set of crtera on level 2, and for a subcrtera Cj, let WCj { WCj1, WCj2, WCjk }, j j 1,2, j, be the weghts for the set of crtera on level 3, where WC j wll be assgned a value from the same lngustc table as WC above. Table 1. Lngustc terms for descrbng weghts of decson makers (evaluators) Lngustc terms Fuzzy numbers Normal (2,3,4) Important (3,4,5) More mportant (4,5,6) Most mportant (5,6,6) Table 2. Lngustc terms and related fuzzy numbers for descrbng the weghts of aspects and crtera The mportance degrees Fuzzy numbers Absolutely unmportant (0,0,1) Unmportant (0,1,2) Less mportant (1,2,3) Important (2,3,4) More mportant (3,4,5) Strongly mportant (4,5,6) Absolutely mportant (5,6,6) j { j1 j2 jkj Stage two: Indvdual preference generaton Step 4: Set up the relevance degree of each alternatve on each crteron for each evaluator P y yk yk yk yk Let SC SC, SC, SC } be the relevance degree of alternatve S k on crteron C, 1,2, t, j 1,2, j, k 1,2, m, where j yk jkj SC s descrbed by one of lngustc terms as shown n Table 3. Table 3. Lngustc terms for preference of alternatves Lngustc terms Fuzzy numbers Lowest (0,0,1) Very low (0,1,2) Low (1,2,3) Medum (2,3,4) Hgh (3,4,5) Very Hgh (4,5,6) Hghest (5,6,6) In ths step, once the quantfable crtera are maxmzed, the crtera data are mapped to a closed nterval [0, 6]. For each crteron, Let MAX be the maxmum value of alternatves, MIN s the mnmum value of alternatves, MAX MIN, the alternatve values are mapped to correspondng values n [0, 6] by a lnear functon descrbed by 478

6 T. Zhang, G. Zhang, J. Ma, and J. Lu 6*( x MIN) f( x) (1) MAX MIN The mapped values are then transformed to fuzzy numbers accordng to the symmetrc trangular membershp functon as shown n Fg.2. For each crteron, MAX s transformed to hghest wth the grade of 1 and MIN s transformed to lowest wth the grade of 1, and each alternatve value s transformed to the correspondng fuzzy number f the membershp grade s the bggest. Here, f the bggest membershp grade nvolves more than one fuzzy number, we adopt the rght-hand one. As the crtera data s objectve, all evaluators take the same transformed values as ther ndvdual preferences. Fg.2. Symmetrc trangular membershp functon Step 5: Calculate the relevance degrees yk The relevance degree CS of the aspect C on the solutons S k, 1,2, t, k 1,2, m, are calculated by yk yk j yk CS WC SC WC SC (2) k j j 1 j yk SCjz where yk SCj WC z 1 jz, 1,2, t, k 1,2, m. Step 6: Calculate the aspect relevance degrees For the evaluator P y, the relevance degree S y of the k crtera C on the alternatves S k, k 1,2, m s calculated by usng y yk t yk Sk CS WC CS WC 1 y k 1,2, m. Here, S s stll a fuzzy number. k Step 7: Normalse the relevance degrees y The relevance degrees S k k 1,2, m y y Sk Sk, for k 1,2,, m. (3) m yr S 1 k 0 yr where the S s the rght end of 0-outset. 9 k 0 Stage three: Group Aggregaton Step 8: Evaluator P y has already been assgned a weght that s descrbed by a lngustc term v y, y 1, 2, n as shown n Table 1. A weght vector s obtaned: V = { v y, y 1, 2, n }. The normalzed weght of an evaluator P y (y = 1, 2,..., n) s denoted as j v v, for y 1,2,, n. (4) * y y n R v 1 0 R where the v 0 s the rght end of 0-outset. Step 9: Consderng the normalzed weghts of all group members, we can construct a weghted normalzed fuzzy decson vector S1 S2 Sm 2 2 2,,, *, *,, * S1 S2 Sm r1 r2 rm v1 v2 vn (5) n n n S1 S2 Sm where n * k r j v. k 1 k S j Step 10: In the weghted normalzed fuzzy decson vector the elements r j, j 1,2,, m, are normalzed as postve fuzzy numbers and ther ranges belong to the closed nterval [0, 1]. 9 We can then defne a fuzzy postve-deal value r* and a fuzzy negatve-deal value r - as: * r 1 and r 0. The dstances between each r j and r*, rj and r - can be calculated as: * * d j d( rj, r ) and d j d( rj, r ), j 1, 2, m, (6) where d (.,.) s the dstance measurement between two fuzzy numbers. 9 * Step 11: After the d j and d j of each S j (j = 1, 2,..., m) are obtaned, a closeness coeffcent s defned to determne the rankng order of all solutons. The closeness coeffcent of each alternatve s calculated by 9 : d (1 d ), j 1, 2, m. 1 j * j CC j (7) 2 The plannng soluton S j that corresponds to Max (CC j, j=1, 2,, m) s the most sutable plannng soluton for the PDSP project. Ths proposed FMCGDM method has been mplemented n a FMCGDSS called Decder A Case Study usng FMCGDSS for PDSP Evaluaton The applcaton of the proposed plannng methodology to a test network based on an exstng dstrbuton network n an electrcty dstrbuton company s shown n Fg

7 ts weght s Absolutely mportant; the crteron Capacty constrants can well represent the aspect Technology, and can thus have a weght of Strongly mportant. Table 5 shows the weghts of these aspects and crtera correspondng to the model shown n Fg.1. Table 4. The generated data of fve solutons under the ndrect crtera Soluton1Soluton2Soluton3Soluton4Soluton5 Fg.3. A test dstrbuton network The test network ncludes seven load centers, representng the accumulated load of the 11 kv dstrbuton network at each connecton pont, as well as 17 exstng transformers and a number of exstng underground cables and overhead lnes. Owng to network load growth predcted for the plannng perod, load scenaros of 2.7% are consdered. Wth the ntal network data known, some relevant plannng problems relatng to the dstrbuton network durng the plannng perod are dentfed as follows: some transformers and crcuts are overloaded at peak demand n the load scenaro, some need replacement due to poor condton, and the 11 kv load s currently experencng poor relablty. In our study, there are fve dfferent plannng solutons to be evaluated by fve evaluators based on the PDSP evaluaton model shown n Fg.1. The evaluators are fve experts: a chef engneer as the leader of the group, a planner, a regulator, an expert representng large-scale customers and an nvted peer expert. They are denoted as experts 1 to 5 respectvely. The data of ndrect crtera have been obtaned by network analyss and are shown n Table 4; they are mnmzed, so they wll be processed to be maxmzed n calculaton. The three remanng crtera are drect and wll be determned by a group of experts/evaluators wth lngustc terms; they are consdered to be maxmzed n a postve drecton. Each of these aspects and crtera (sub-crtera) s assgned a weght, also determned by the group of experts. These weghts reflect the mportance degrees, nfluence degrees, and/or closeness of each crteron to ts parent crteron. These weghts are descrbed n lngustc terms. For example, the crteron Relablty can be very mportant to the aspect of Technology, so Energy losses MWh System securty Supply avalablty Capacty constrants MWh Crcut length km Captal cost We also need to ndcate that these weghts can be changed when a PDSP project emphaszes a partcular characterstc. Each evaluator s assgned a weght that s determned by the group of experts through dscusson and descrbed by a lngustc term as shown n Table 6. For three drect crtera, evaluators are asked to provde scores such as Low, Hgh, Very hgh and so on, for each soluton. To obtan ths data, a questonnare, whch has all the questons related to the three crtera descrbed above, was desgned to gve to evaluators. In the questonnare, almost all questons are desgned n the form of statements, and the scores of the level of achevement of each plannng soluton was descrbed n lngustc terms, as shown n Table 7. For example, f an evaluator agrees wth the statement the plannng soluton looks very good for vson, he/she can gve Very hgh (strongly agree) to the queston (statement). Ths evaluaton data wll be entered nto the FMCGDSS. Table 5. The weghts of aspects and crtera Aspects Crtera Sub-crtera Absolutely mportant Absolutely mportant More mportant Absolutely mportant Absolutely mportant Absolutely mportant Absolutely mportant Strongly mportant More mportant Absolutely mportant Strongly mportant Important More mportant More mportant 480

8 T. Zhang, G. Zhang, J. Ma, and J. Lu Table 6. The weghts of evaluators Weght Expert 1 Most mportant Expert 2 Normal Expert 3 More mportant Expert 4 Important Expert 5 More mportant The workng process of the FMCGDSS s summarzed n seven steps as follows: Step 1: Create a new fle for the evaluaton ssue (Fg.4, Fg.5). Table 7. The relevance degrees of solutons under drect crtera Vson Publc atttude Socal value Expert 1 Soluton 1 Medum Hgh Medum Soluton 2 Medum Low Medum Soluton 3 Very low Very low Medum Soluton 4 Very hgh Hghest Very hgh Soluton 5 Very hgh Hgh Very hgh Expert 2 Soluton 1 Medum Medum Medum Soluton 2 Medum Medum Medum Soluton 3 Low Low Low Soluton 4 Hghest Hghest Hgh Soluton 5 Hgh Very hgh Very hgh Expert 3 Soluton 1 Medum Low Medum Soluton 2 Medum Medum Medum Soluton 3 Very low Low Low Soluton 4 Hghest Hghest Hgh Soluton 5 Very hgh Hgh Very hgh Expert 4 Soluton 1 Low Medum Medum Soluton 2 Low Low Low Soluton 3 Lowest Lowest Medum Soluton 4 Hghest Hghest Hgh Soluton 5 Hgh Very hgh Hgh Expert 5 Soluton 1 Medum Hgh Medum Soluton 2 Low Low Low Soluton 3 Very low Very low Medum Soluton 4 Hghest Hghest Very hgh Soluton 5 Very hgh Hgh Hghest The obtaned objectve value s then transformed nto an ntegral numerc evaluaton value between (1, 7) accordng to a pre-defned membershp functon. 30 After obtanng weghts (mportance degrees) for these aspects and ther crtera, and all scores for the fve plannng solutons, the group can use the newly developed FMCGDSS to conduct the performance evaluaton results and rankng among the plannng solutons evaluated. Fg.4. Creatng a new project for evaluaton Fg.5. Settng up a PDSP evaluaton problem Step 2: Input the PDSP evaluaton model wth ts levels of crtera, crtera weghts, and related descrptons. Fg.6 shows the PDSP model and a crteron s weght and descrpton. Fg.7 shows the data nput process of a crteron. 481

9 Fg.6. The evaluaton model wth three levels of crtera Fg.8. All members of the evaluaton group are entered Fg.7. Data entry process of a crteron Step 3: Input evaluators and ther weghts n lngustc terms. Fg.8 shows the fve evaluators, an evaluator s nformaton and weghts are shown n Fg.9. Fg.9. An evaluator s nformaton and weghts Step 4: Input plannng solutons to be evaluated. Fg.10 shows these solutons names. 482

10 T. Zhang, G. Zhang, J. Ma, and J. Lu Fg.10. All plannng alternatves to be evaluated Fg.12. Fnal rankng result for possble plannng solutons Step 5: Enter all the evaluator scores. Based on the crtera, for each plannng soluton, every evaluator has a score to be entered (Fg.11). Fg.13. Rankng result for solutons under the crteron Vson Fg.11. Assessment nput for all alternatves under all crtera Step 6: Generate the fnal rankng result of the problem. When all data s entered n ths software, we run the developed FMCGDM method. We can see that plannng Soluton 3 receves the hghest closeness coeffcent value and therefore s the most sutable soluton for ths PDSP project. Fg.12 shows the group s evaluaton result for these plannng solutons. We can also conduct further analyss on the evaluaton result n each aspect or each subgroup. Fg.13 shows evaluaton results on the crteron Vson of the fve solutons where Soluton 4 has the hghest score. The case study for PDSP evaluaton shows that the proposed method can deal wth all ssues mentoned n ths paper n a comprehensve way and expert evaluators are satsfed wth the results and evaluaton process. 5. Conclusons The comprehensve evaluaton of plannng solutons s an mportant phase n the PDSP process to ensure the development of a robust plannng soluton. Ths evaluaton process s a preference based decson but nvolves a complex stuaton n whch both quanttatve and qualtatve crtera are wthn a herarchy and multple members are nvolved wth dfferent opnons. In partcular, experts opnons are often n vague, usng crsp numbers to express s not suffcent. Therefore, a 483

11 FMCGDM method s presented n ths paper and appled to evaluate PDSP solutons. The man advantage of our work from prevous studes s that we not only formulate PDSP evaluaton as an MCDM problem, but also take nto account GDM for all evaluators preferences. In partcular, lngustc varables are used to express human judgment and fuzzy sets are appled to present and calculate lngustc varables. In practcal projects of PDSP evaluaton, the quanttatve values of crtera are often dffcult to determne and the stuaton s far more complex than that dscussed n ths paper. Usng lngustc varables n evaluatons s very common, and the evaluaton process often nvolves an expert team, so the proposed FMCGDM method and the FMCGDSS are expected to have more real cases. Snce experts have dfferent professonal knowledge backgrounds and practcal experences, the assgned weght for each expert should vary from crteron to crteron, rather than beng the same for all crtera, as n ths study, whch wll be mproved n future work. Acknowledgements The work presented n ths paper was partly supported by the Australan Research Councl (ARC) under dscovery project DP References 1. P. Espe, G.W. Ault, G.M. Burt and J.R. McDonald, Multple crtera decson makng technques appled to electrcty dstrbuton system plannng, IEE Proceedngs- Generaton, Transmsson and Dstrbuton, 150(5) (2003) T. Gonen and I.J. Ramrez-Rosado, Optmal mult-stage plannng of power dstrbuton systems, IEEE Trans. on Power Delvery, 2(2) (1987) Y. Tang, Power dstrbuton system plannng wth relablty modelng and optmzaton, IEEE Trans. on Power Systems, 11(1) (1996) A. Chowdhury, T.C. Melnk, L.E. Lawton, M.J. Sullvan and A. Katz, Relablty worth assessment n electrc power delvery systems, Proceedng of the 2004 IEEE Power Engneerng Socety General Meetng (Denver, CO, Unted States, Jun 2004), Vol.1, pp S. Wong, K. Bhattacharya and J.D. Fuller, Electrc power dstrbuton system desgn and plannng n a deregulated envronment, IET- Generaton, Transmsson & Dstrbuton, 3(12) (2009) E. Jordanger, B.H. Bakken, A.T. Holen, A. Helseth and A. Botterud, Energy dstrbuton system plannngmethodologes and tools for mult-crtera decson analyss, Proceedng of the 18th Internatonal Conference and Exhbton on Electrcty Dstrbuton(Turn, Italy, 2005), pp P. Espe, G.W. Ault and J.R. McDonald, Multple crtera decson makng n dstrbuton utlty nvestment plannng, Proceedng of the 2000 Internatonal Conference on Electrc Utlty Deregulaton and Restructurng and Power Technologes (London, UK, 2000), pp K. Yoon and C. Hwang, Multple attrbute decson makng An ntroducton (SAGE Publcatons, Thousand Oaks, 1995). 9. J. Lu, G. Zhang, D. Ruan and F. Wu, Mult-objectve group decson makng: methods, software and applcatons wth fuzzy set technology (Imperal College Press, London, 2007). 10. N. Karacaplds and C. Papps, Computer-supported collaboratve argumentaton and fuzzy smlarty measures n multple crtera decson-makng, Computers and Operatons Research, 27(7) (2000) M. Maran, I. Hatono and H. Tamura, Lngustc labels for expressng fuzzy preference relatons n fuzzy group decson makng, IEEE Trans. on Systems, Man, and Cybernetcs, 28(2)(1998) T. L. Saaty, The analytc herarchy process (McGraw- Hll, New York, 1980). 13. J. Xao, C.S. Wang and M. Zhou, IAHP-based MADM method n urban power system plannng, Proceedngs of the Chnese Socety of Electrcal Engneerng, 24(4) (2004) D.Y. Chen, J. Xao and C.S. Wang, A FAHP-based MADM method n urban power system plannng, Proceedngs of Electrc Power System and Automaton, 15(4) (2003) T.F. Zhang and J.S. Yuan, Decson-ad for power dstrbuton system plannng problems usng ELECTRE III, Proceedng of the 7th Power Engneerng Internatonal Conference, (Sngapore, Dec. 2005). 16. J.S. Yuan, T.F. Zhang, J.X. Lu and Y.H. Kong, An MADM method based on outrankng relaton and lnear programmng n power dstrbuton system plannng, Proceedngs of the Chnese Socety of Electrcal Engneerng, 26(12) (2006) G. We, W.L. Wu, J. Lu and X. Zhang, Comprehensve judgment for power system plannng alternatves based on SE-DEA model, Power System Technology, 31(24) (2007) L.G. Fan and Y.H. L, A new MCDM method n transmsson network plannng based on gray correlaton degree and TOPSIS, Proceedng of the 27th Chnese Control Conference(Kunmng, Chna, 2008), pp J. Pan, Y. Teklu and A. de Castro, An nterval-based MADM approach to the dentfcaton of canddate alternatves n strategc resource plannng, IEEE Trans. on Power Systems, 15(4) (2000) D.P. Bernardon, V.J. Garca, A.S.Q. Ferrera, L.N. Canha and A.R. Abade, New fuzzy multcrtera decson makng algorthm to dstrbuton network reconfguraton, Proceedng of the 44th Unverstes Power Engneerng 484

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