Peak Load Shifting Distribution of Multi-zone Fuzzy Group Decision-Making

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1 Computer nd Informtion Science Februry, 8 Pe Lod Shifting Distribution of Multi-zone Fuzzy Group Decision-Ming Yng Li, Ji Liu, Liqun Go, Zhi Kong School of Informtion Science nd Technology, Northestern University - Wen Hu Rod, Shenyng, Chin E-mil: liyng@ise.neu.edu.cn Abstrct On the bsis of different expert nowledge structure, from the gretest fctors in power limiting distribution, using the method combining Anlyticl Hierrchy Process (AHP) nd fuzzy set theory, fuzzy comprehensive group decision model for multi-obects nd multi-zones power limiting distribution in pe lod shifting is built up. The problem of power limiting distribution between multi-zones is reserched. The result mnifests this model is resonble nd pplicble. Keywords: AHP, Fuzzy set, Group decision, Power limiting distribution. Current sitution of foreign funds in Chin insurnce industry With the quic development of economy, the power shortge circumstnce is ppered in most estern nd centrl regions in our country. To llevite the complexion of power shortge, ntionl nd regionl electric cpcities crry out lrge-scle invest item for extending generte electricity cpcity (including SnXi item). But the incresing speed of power consumption is more lrger thn the one of extension of power bsic equipments, the mount of power shortge in ech region is lrge, lthough some economy nd policy mens were crried out to control pe lod shifting, for the considertion of power grid sfety, so power limiting control for some regions in electro-pex is essentil. It is n urgent solving nd hving ctul mening problem tht how to scientificlly nd rtionlly distribute limited power limiting cpcity in ech region nd me the security of power grid of ech region highest nd loss lest, ccording to power limiting criterion nd sfety requirement of ech region, through the comprehensive nlysis of benefit on society, economy nd environment. Pe lod shifting distribution is n importnt ts nd it needs nowledge nd experiment of mny persons. At the sme time, it is little fuzzy. So the method of combining fuzzy sets theory with hierrchy nlysis is used to discuss the multi-obective group decision of multi-zone pe lod shifting, ccording to the systemic nlysis of society, economy, resource nd environment. Therefore, power limiting distribution belongs to nonliner multi-obective group decision ctegory.. Construct Pe Lod Shifting Distribution Decision System.Power limiting distribution guide line system nd hierrchy structure building The resonble time distribution of pe lod shifting in multi-zone is for the se of power cpcity stndrd nd lest loss bsed on the grid security. In this spect, there re mny fctors, which re relted to rnge nd time of power limiting, lso the conditions of socil economy, such s popultion, industry configurtion, prmeter of ntionl economy nd so on. Some of them cn be showed in economic quntity. Such s popultion in power limiting re, number of electricity enterprises in power limiting re nd gross product in power limiting re, etc. Furthermore, it is hrd to estimte some potentil indirect benefit lie effect on economy, dustment of economy structure, dmge for environment. The necessity of pe lod shifting control is usully pprised by economic benefit. And these lwys ffect the distribution of power limiting time. So it hs some deficiency. Thus, the guide line system nd hierrchy structure (Fig.) should be estblished ccording to the prmeters picing up from the fctors ffecting power supply limiting lie society, economy nd so on. This will be good to the resonble distribution of power limiting time nd lest loss. And the lw of cler conception, bundnt informtion, esy clcultion nd show ustice is necessry.. Building nd determining reltive membership degree functions of ech prmeter Decision-ming prmeters lwys hve four types in multi-obective decision problem. is excellent with lrge, b is excellent with smll, c is fixed vlue nd d is inter-zone. 8

2 Vol., No. Computer nd Informtion Science The type of fixed vlue prmeter is ind of prmeter tht the excellent vlue is constnt. Inter-zone mens tht the prmeter vlue in some fixed region is excellent. The purpose of decision prmeter clssifiction is for compre mong sme prmeters. According to the difference between decision prmeter types, prmeter set F cn be clssified. F = U F, Fi I F = Φ i i= (i, =,,,, i ). In this eqution, F ( i =,,,) is the ind of, b, c nd d respectively, nd Φ is null. i Becuse of the difference between multi-obective dimensions, it needs to stndrdize the decision mtrix M. And then, the eigenvlue of ech decision prmeter in reltive stte cn be got. The expression of stndrdiztion is s follows. mx = mx{ : i n, r} () min = min{ : i n, r} () ( r is reltive membership degree of prmeter in zone i, mx nd min is the symbol for ting mximum nd minimum respectively, α is the obective vlue of prmeter (r in ll) in zone i(n in ll) nd hve chrcter of fuzzy by effect of vlue nd sttisticl error.) For type, For type b, For type c, r r = mx = min mx mx min min ( i n, r, f F) () ( i n, r, f F ) () r., = =., mx{ } ( i n, r, f F ) () is the optiml constnt of prmeter For typed, f. b., < b mx{ b, b} r =., b b b., > b mx{ b, b} ( i n, r, f F ) (6) [, ] b b is the optiml region vlue of prmeter f. The decision eigenvlue mtrix cn be ten from the equtions bove. From Figure, the experts get tht the Power limiting region whose popultion re more, electro-enterprise re more, the totl vlue of produce re more, economic loss of Power limiting re more, proportion of using electricity pe re more, the verge temperture is more, the proportion of ice ir condition re less, the distributed proportion of Power Limiting distribution for Pe Lod Shifting re more. Thus, these fctors re ll b, except the scle of reconcilble pe enterprises nd ice ir condition re. 8

3 Computer nd Informtion Science Februry, 8 Figure. Decision system of Pe Lod Shifting Power Limiting Distribution fctor-the popultion of region fctor- The quntity of electro-enterprise fctor-the cpcity of using power fctor-the proportion of electro-enterprise tht cn be power-off fctor-the totl vlue of produce fctor6-the cpcity of power limiting fctor7-the economic loss of power liming fctor8-the totl popultion fctor9-the proportion of pe for using power fctor-the verge temperture fctor-the proportion of ice ir condition. Prmeter Reltive Weight Vlue Clcultion As multi-obective decision method for combintion of qulity nd quntity, hierrchy nlysis hs been pplied extensively. But there re few exmples bout how to solve the group decision problem with hierrchy nlysis method. In this pper, weighted geometry verge group vector sort method bsed on different expert nowledge structure, hs been used to del with the hobby of some experts in multi-zone pe lod shifting controlling time distribution nd the problem of group hobby from nowledge structure.. The choice of expert group The time of pe lod shifting is minly ffected by the fctors in Figure. Thus, the composition of expert group is lwys pe lod shifting control expert nd electric power progrmming expert, etc. Also including electric utility mnge expert, grid economy expert nd grid security expert, who re ccomplished in opertion, theory nd scientific reserch respectively. Obviously, the resonble decision weight of ech expert for ech fctor in Figure is different.. The weight vector clcultion of udging mtrix for ech expert In cse of the number of expert is s nd the number of resonble pe lod shifting control distribution fctor or prmeter is n, {,, } P P P P (7) = L n The importnt degree should be udged by every expert though ll effecting fctors. If V is the importnt degree udged mtrix for fctors building by expert i, 8

4 Vol., No. Computer nd Informtion Science v K v n V = M O M vs L vsn (8) V follows AHP method. And the weight vector of fctors udged by expert i cn be ten ccording to the udged mtrix. Normlized the udged mtrix V, V cn be ten. v K v n V = M O M vs L vsn (9). The synthesis of expert weight vector v = v n vi =, i=,, LL,s () During group decision, there re two methods of composing ech decision mer s weight vector: one method is to compose on the bse of udgment mtrix; nother method is to compose on the bse of weight vector. Weight vector composition minly dopts rithmetic weighted men composition, nd tht model thins over the reltive importnt degree between composition elements, nd permetes formul in the form of weight vlue, which rtionlizes evlution process. Becuse of experts difference in nowledge, experience, nd bility, their reltive importnce in decision my different. Supposing s experts reltive importnce is ll sme. Then the method of rithmetic weighted men composition is: ccording to the importnt degree s weight vector of n influencing fctors rrived t seprtely by s experts T V = ( v, v,, v ) i=,, LL,s () i i i in Afterwrd, ccording to nether formul clculte ll indictors reltive weight vector of weighted geometric men T group sorting vector = (,,,, n ) : λ = λ = = λ s = s (), s s θ = ( v λ ) () i i= = λ λ correspond weight coefficient of decision mer bility level. Finlly, clculte stndrd devition of < ( [ ]) = θ n θ, =,,,, n () σ s = ( ) s () = whenσ ε ε.,,we thin group udgment cceptble, nd feedbc the indictor bsolute weight vector of every decision mer to decision mers for their reference; if multiple decision mers ll ccept bove weight vector, then clcultion finishes. Otherwise, let decision mer offer mend udgment. Repet mny times in this mnner, nd up still ll decision mers obtin stisfying weight vector.. Optimized Distribution Decision Clcultion of Multi-obective Power Limiting Time Distribution For the hierrchy model structure in Figure, the fuzzy synthesized decision model of multi-obective power limiting time distribution in multi-zone is estblished s follows. r K r n Z = RoW = M O M o M r L r m mn n (6) In the eqution bove, R is the reltive membership degree mtrix, r mens the reltive membership degree of the 8

5 Computer nd Informtion Science Februry, 8 prmeter in zone i of m, W is the prmeter weight vector determined by group decision theory, is the weight of prmeter of n under group decision, Z is the scle vector of zone power limiting time distribution. o is the fuzzy rithmetic opertors. The scle of power limiting distribution of ech region cn be ten ccording to eqution (6).. Reserch of Exmples According to the dt from the chrge deprtment of Lioning province, pe lod shifting distribution in six regions is plnned to operte in summer of. The socil economy of six regions is shown in Tble I. The loss is in Tble II. If there re three decision-mer who prticipte in the decision of pe lod shifting controlling distribution, the result cn be got using the model bove. (The clcultion process is omit) Tble. The Prmeter of Socil Economy regions Popultion() Electricity consumption number Electricity cpcity(mw) Reconcilble pe scle (%) Product gross(rmb) Tble. The Economic Loss of Power Limiting region Power limiting cpcity(mw) Economic loss of power limiting(rmb) Popultion(myrid humn) Electricity consumption pe scle(%) Averge temperture Ice ir condition scle(%) ) Indictor bsolute weight vector of decision mer is = {.8,.69,.9,.,.978,.,.99,.9,.98,.6,.} ) Indictor bsolute weight vector of decision mer is = {.6,.6,.6,.7,.,.6,.9,.9,.7,.,.789} ) Indictor bsolute weight vector of decision mer is = {.9,.8,.86,.6,.,.6,.988,.86,.,.8,.} ) Indictor weight vector of group decision is 群 = i nd normlized i= = {.7,.677,.7,.98,.6,.7,.,.9,.98,.9,.} 8

6 Vol., No. Computer nd Informtion Science ) Every region s Power Limiting Distribution for Pe Lod Shifting control proportions re: Z =7.8%, Z =9.7%, Z =.87%, Z =.%, Z =.98%, Z 6 =.% 限电分配比例 (%) 6 8 Figure. corresponding curve schemtic digrm of socil economic indictor nd Power Limiting Distribution in every region Popultion- The quntity of electro-enterprise- The cpcity of using electricity- The proportion of moving-pe enterprise- The totl vlue of produce- 限电分配比例 (%) 6 - Figure. corresponding curve schemtic digrm of the economic loss indictor of Power limiting nd Power limiting Distribution proportion Limited cpcity- The economic loss of Power limiting- Popultion- Proportion of using electricity pe- Averge temperture- The proportion of ice ir condition-6 6. Conclusion It cn be seen from the corresponding curve schemtic digrm of vrious decision indictors nd Power Limiting Distribution proportion in bove region (Figure ; Figure ): With the chnge of socil economic indictors nd the economic loss of power limiting in vrious regions, the finl Power Limiting Distribution proportion lso chnges: the Power limiting region whose popultion re more, electro-enterprise re more, the totl vlue of produce re lrger, economic loss of Power limiting is lrger, proportion of using electricity pe is bigger, the verge temperture is higher, the proportion of ice ir condition is smller, is distributed smller proportion of Power Limiting distribution for Pe. In word, power limiting distribution is complex multi-obect group decision problem, the decision of power limiting 86

7 Computer nd Informtion Science Februry, 8 time distribution is not only relted to technology, economy nd power limiting criterion but lso to the supplying sfety of power grid nd the stbility of society, so the reserch of decision of power limiting time distribution is more complex. Anlyzing from min fctors effecting to region power limiting time distribution, criterion system of region power limiting distribution is built up in this pper, nd the model nd method of lrge-scle systemticl multi-obect group decision combining hierrchy nlysis nd fuzzy comprehensive evlution is proposed lso, nd stisfied reserch results of ctul exmple is obtined. But in the future it should be more strengthened on the society evlution of power limiting distribution of pe lod shifting control, economicl evlution, environmentl evlution, decision method of power limiting uncertin distribution nd its relibility reserch. References Chicln F, Herrer F & Herrer Viedm E (998). Integrting three representtion models in fuzzy multipurpose decision ming bsed on fuzzy preference reltions. Fuzzy Sets nd Systems, 9, -8 Delgdo M, Herrer F Herrer Viedm E (998).Combining numericl nd linguistic informtion in group decision ming. Informtion Sciences,, 77-9 H.C.Hung, R.C.Wng & J.G. Hsieh (). A new rtificil intelligent pe power lod forecster bsed on non-fixed neurl networs. Electr.Power Energy Syst,, - Herrer F & Herrer Viedm E (). Linguistic decision nlysis: steps for solving decision problems under linguistic informtion. Fuzzy Sets nd Systems,, 67-8 Herrer F & Herrer Viedm E (). Choice functions nd mechnisms for Linguistic preference reltion. Europen Journl of Opertionl Reserch,, -9 J. M, Z.P. Fn & L.H. Hung (999). A subective nd obective integrted pproch to determine ttributes weights. Europen Journl of Opertionl Reserch,, 97- Mrmol AM, Puerto J & Fernnndez FR (998). The use of prtil informtion on weights in multi-ttribute decision problem. Journl of Multi-ttribute Decision Anlysis, 7, -9 M. Krunic, K.I. Slvis & N. Rovic (). An improved neurl networ ppliction for short term lod forecsting in power systems. Electr. Mch. Power Syst, 8, 7-7 M.R.G. Al-Shrchi & M.M. Ghulim (). Short term lod forecsting for Bghdd electricity region. Electr. Mch. Power Syst, 8, 7 Noel Bryson & Ayodele Mobolurin (999). An ction lerning evlution procedure for multiple criteri decision ming problems. Europen Journl of Opertionl Reserch, 6, 79-86, Shmsuddin Ahmed (). Sesonl models of pe electric lod demnd. Technologicl Forecsting nd Socil Chnge, 7,