Research on the Method of Correlation Analysis Between Reliability Indices and Business Management Indices

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1 Cao Huazhe et al. Iteratoal Joural of Ecoomcs ad Maagemet Systems Research o the Method of Correlato Aalyss Betwee Relablty Idces ad Busess Maagemet Idces CAO HUAZHEN,, WU YAXIONG,, JIN YEXUAN 3, ZHANG JUNXIAO,, LIU YONG 3. Power Grd Plag Ceter of Guagdog Power Grd Compay,. Guagdog Power Grd Developmet Research Isttute Co. Ltd, 3. Shagha Provet Iformato Tech. Co. Ltd... Guagzhou 5080, 3. Shagha 0040 CHINA yexua777@63.com Abstract: - The busess maagemet dces ca preset the most of the fluece factors of relablty. I addto, busess maagemet dces are motored ad cotrolled by respectve departmets. It s possble to acheve the gve aual relablty dces by cotrollg busess maagemet dces mothly. I ths paper, the correlato betwee the relablty dces ad the busess maagemet dces s studed. A comprehesve relablty evaluato dex system based o busess maagemet dces s proposed, whch a mproved grey relatoal model s used to me the correlato betwee the relablty ad factors. The smulato results prove the effectveess of the method. Key-Words: - relablty dces, busess maagemet dces, grey relatoal degree, dyamc resoluto coeffcet, fuzzy weghtg Itroducto The basc task of the dstrbuto etwork s to provde users wth safe, stable, ad hgh-qualty power. The dstrbuto etwork has complex structures wth a large umber of devces ad applaces, so that power supply relablty s the most mportat problem dstrbuto etwork. Accordg to statstcs, about 80% of power outage s caused by the faults of dstrbuto etwork compoets []. Therefore, the research o the dstrbuto etwork relablty s oe of the core researches the feld of dstrbuto. Aalytcal method ad smulato method are two maor methods for relablty assessmet. The typcal smulato method s the Mote Carlo method, whch s tme cosumg, low precso, ad the scale of dstrbuto etwork has lttle effect o the computatoal complexty. The aalytcal method, represeted by the FMEA method, ca realze the accurate calculato of the relablty dces of the complex dstrbuto etwork. As both methods requre the complete topology ad equpmet parameters of the dstrbuto etwork, whch cause too much calculato work whe the dstrbuto etwork has a large sze, some rapd relablty assessmet method are proposed. Wth the cotuous developmet of tellget dstrbuto, the data acqured, trasmtted, ad appled varous dstrbuto maagemet systems cota abudat formato of operato, dspatch, mateace, ad marketg, whch ca provde the bass for dstrbuto etwork aalyss [-4]. Studes o relatoshp betwee the etwork structure ad relablty have bee carred out. Prcpal compoet aalyss ad parallel assocato rule mg techques are used to me assocato relatoshps, ad the future relablty dces are predcted based o artfcal eural etwork [5]. A method to use BP eural etwork to derve the aalytc relato expresso betwee relablty ad drvg factors s proposed [6]. The grey correlato degree s used to obta the correlato betwee relablty ad etwork structure factors [7]. A stepwse regresso model s establshed to obta the mathematcal expresso of the dcator assocato [8]. Ths sort of method belogs to the data-drve method. It has hgh speed ad extesve applcablty because t does ot rely o topology aalyss. The busess maagemet dces, such as le lk rate, cable rate, ad so o, ca preset the most of the fluece factors of relablty volves etwork structure, equpmet parameters, ad maagemet level. I addto, busess maagemet dces are motored ad cotrolled by respectve departmets. It s possble to acheve the gve aual relablty dces by cotrollg busess maagemet dces mothly. I ths paper, the relatoshp betwee the relablty dces ad the busess maagemet dces s studed, whch ca fd out the weakess the busess process. A comprehesve relablty ISSN: Volume 3, 08

2 Cao Huazhe et al. Iteratoal Joural of Ecoomcs ad Maagemet Systems evaluato dex system based o busess maagemet dces s proposed. A mproved grey relatoal model s used to me the correlato betwee the relablty of A+, A, B, C, D power supply area [9] ad factors the above relablty evaluato dex system. The smulato results prove the effectveess of the method. Establshmet of Comprehesve Relablty Evaluato Idex System Based o Busess Maagemet Idces The comprehesve relablty evaluato s teded to evaluate the level of techology ad maagemet of the power supply eterprses. The power supply compay s a techology tesve eterprse, whch volves plag, operato, mateace, schedulg, marketg ad other busess. Dfferet busesses have ther ow work processes. I addto to the level of power grd equpmet, the professoal skll of staff each busess process wll also have a mpact o the relablty of power supply. Through a comprehesve evaluato of the equpmet ad maagemet level of the dstrbuto etwork, the compay looks for the fluece factors affectg the relablty from all aspects of the busess, the defceces the relablty maagemet, ad mproves the staff s professoal skll order to mprove the relablty ad maagemet of the dstrbuto etwork [0]. Costructg a relablty evaluato dex system s the bass of relablty evaluato of dstrbuto etwork. By aalyzg the busess process the affects the relablty, the maagemet of each busess work s quatfed the form of dex to establsh the comprehesve evaluato dex system. Based o the statstcal data of maagemet formato system recet years, ths paper aalyzes the busess maagemet ad equpmet factors that affect the relablty four aspects lke etwork frame, operato ad mateace, producto schedulg, ad costructo operato. The varous busess processes ad equpmet factors that affect the relablty are aalyzed ad quatfed the form of dex to costtute a comprehesve relablty evaluato dex system. The comprehesve dex system s dvded to three levels, cludg evaluato dcators, busess stratfcato dcators, ad factor dcators. Amog them, the frst level s the evaluato dex whch represets power supply relablty. The secod level are made up of four dcators, etwork level, operato ad mateace, producto schedulg, ad costructo operato. The thrd level s eumerated accordg to the ursdcto scope of the secod layer. For example, the lve workg s related to the operato ad mateace, so the factor of lve workg rate s put to the operato ad mateace dex. The comprehesve dex system s show Fg.. Evaluato dex Busess stratfcato dex Factor dex Network level Cable rate Dstrbuto automato rate Le lk rate Average umber of segmets Average load rate Average le legth Operato & Mateace Elmatg defect rate Average fault arrval tme Lve workg rate Average repar tme Relablty level Producto Schedulg Outage plag rate Temporary outage rate Load trasfer rate Trasfer operato tme Costructo Operato Costructo outage rate Average costructo outage rate Fg. Comprehesve Relablty Evaluato Idex System 3 Correlato Aalyss of Relablty ad Busess Maagemet Idces Correlato aalyss, regresso aalyss, varace aalyss ad prcpal compoet aalyss ca be used mg assocato formato, but the applcato of these methods requres a large umber of samples, o correlato betwee the factors, ad a certa dstrbuto law. The grey relatoal aalyss, measurg the proxmty of each factor accordg to the proxmty of the shape of the sequece curve of each factor, s a quattatve aalyss method used to dstgush the complex relatoshp betwee varables ad multple factors []. The greater the degree of grey correlato s, the more the relatve chages the represetatve factors are the developmet process. Because the grey correlato aalyss s based o the aalyss of the developmet stuato, the method does ot have much requremet o the umber of samples, or does the sample obey the typcal dstrbuto. The results are good agreemet wth the qualtatve aalyss results. Therefore, the grey correlato aalyss s used to calculate the correlato betwee factor dex ad relablty dex.. Improved Grey Correlato Aalyss ISSN: Volume 3, 08

3 Cao Huazhe et al. Iteratoal Joural of Ecoomcs ad Maagemet Systems The tradtoal grey relatoal aalyss method determes the proxmty betwee elemets x of the comparso sequece X ( x, x,, x,, x ad the elemets x 0 of the referece sequece X x, x,, x,, x by calculatg the 0 ( grey correlato coeffcet ( x, 0 x ζ whch s calculated as follows. m m + ρ max max ζ ( x0, x + ρ max max ( Where, (,,, m s the umber of fluecg factors sequece, (,,, s the dmeso of each fluecg factor sequece, ρ [0,] s the resoluto coeffcet, x x. 0 The grey correlato coeffcet ( x, 0 x ζ ca be used to calculate the grey correlato betwee the comparso sequece X ad the referece sequece X 0. γ 0 ζ ( x0, x ( It ca be see from formula ( that the product of ρ ad max max has a greater fluece o the value of the etre formula. The value of the resoluto coeffcet ρ reflects the drect fluece of max max o the correlato. The default settg ρ of the tradtoal grey correlato aalyss s 0.5, whch wll result the smaller correlato degree dstrbuto, ad the reducto of the degree of the correlato betwee the factors. Therefore, the dyamc resoluto coeffcet should be troduced to the tradtoal grey correlato aalyss. I realty, the mportace of data vares from tme to tme. The closer the tme, the greater the correlato wth the curret data. However, the tradtoal grey relatoal aalyss, t ca be see form formula ( that the degree of grey correlato s obtaed by calculatg the mea value of the correlato coeffcet at each dfferet perod. The treatmet of averagg does ot reflect the cosstecy the degree of assocato. Therefore, the weghts are troduced the mproved grey correlato aalyss to reflect the mportace of dfferet hstorcal data to curret codtos []... Determato of segmetato dyamc resoluto The formula for calculatg the correlato degree coeffcet s obtaed as follows, m m + ρ max max ζ ( x0, x (3 + ρ max max Whe the sequece of fluecg factors s ot stable, max max >> ad max max >> m m wll appear. I ths case, f the resoluto coeffcet ρ s larger, ζ ( x, 0 x wll be domated by ρ, ad ts value wll be close to, whch makes t dffcult to reflect the effect of. Therefore, the rage of the grey correlato degree obtaed by the tradtoal grey correlato aalyss s arrow, ad the wrog cocluso that the referece sequece ad each comparso sequece are hghly correlated wll be obtaed. I the case, the resoluto factor ρ should be smaller, thereby reducg the domat effect of max max ζ x x. o (, 0 Whe the sequece of fluecg factors s ot abormal ad stable, max max ad are close to each other. If the resoluto coeffcet ρ s smaller, ζ ( x, 0 x wll be smaller. Therefore, the grey correlato degree of each fluecg factor wll be very smlar, ad the dstrbuto terval s small, whch make t dffcult to dstgush the correlato degree betwee the referece sequece ad each comparatve sequece. I ths case, the value of ρ should be creased as mush as possble to crease the domat effect of max max o ζ ( x, 0 x, so the tegrty of the correlato degree ca be fully reflected. Therefore, t s ecessary to establsh a dyamc resoluto coeffcet accordg to the smoothess of the sequece to obta the correlato degree betwee the sequeces more accurately. Defe λ as the sequece smooth coeffcet, whch s calculated by the flowg formula, ISSN: Volume 3, 08

4 Cao Huazhe et al. Iteratoal Joural of Ecoomcs ad Maagemet Systems λ max max (4 As ρ (0,], usg ρ 0.5 as the boudary value, the value of ρ ca be determed as follows [3], Whe λ < /3 (the data sequece s ot stable, ρ should take a smaller value less tha 0.5 to reduce the domace of max max o the degree of grey correlato. So ρ should be [ λ,.5 λ ], geerally takg ρ.5λ. Whe λ /3 (the data sequece s stable, order to crease the dstcto betwee sequeces, ρ should be [.5 λ, λ ], geerally takg ρ λ /6. By usg segmeted dyamc resoluto coeffcet stead of statc resoluto coeffcet, a ew correlato coeffcet formula based o dyamc resoluto coeffcet s obtaed as follows, m m + ρ max max ζ ( x0, x + ρ max max (5.. Tme weghtg based o fuzzy matrx The calculato formula for the horzotal th weghted correlato degree betwee the fluecg factor sequece ad the relablty level sequece γ 0 s ( x, x γ ωζ (6 0 0 Where, ω s horzotal weghtg factor. The horzotal weghtg coeffcet s calculated as follows [4]. Accordg to the prcple that the closer the tme of the data s, the greater the degree of correlato s ad the more mportat the data s, the fuzzy complemetary prorty F f relatoshp matrx ( hstorcal perods ad ca be formed. f dcates that the data of the hstorcal pot s more mportat tha the data of. Whe >, t meas that the data of the hstorcal pot s more mportat tha that of, so that f. O the cotrary, whe <, t meas that the data of the hstorcal pot s less mportat tha that of, so that f 0. Whe, the data of the hstorcal pot ad have the same degree of mportace to the curret stuato, so that f 0.5. Sum the les of the matrx F ( f get to s f,,,, (7 The fuzzy cosesus matrx S ( s s calculated, where s s s + 0.5,,,, (8 ( 3 Calculatg horzotal weght ω ω + s,,,, (9 k a a k Where, a.. Correlato degree algorthm of relablty ad busess maagemet dces I ths paper, a mproved grey correlato aalyss method s used to calculate the correlato betwee relablty ad busess maagemet dces, whch steps are as follows. Data tread processg. The grey correlato degree measures the cosstecy of the developmet tred of factors. Whe both factors are egatvely correlated, the tred of the curve s the opposte, whch wll lead to a small value of grey correlato. Therefore, ths paper, the comparso sequece of the data tred ad the referece sequece s compared. If ther tred are opposte, the data of comparso sequece should be reversed to adust the tred to the same as the referece sequece. Data stadardzato processg Stadardze fluecg factors sequece H h, h,, h, h ad relablty ( ISSN: Volume 3, 08

5 Cao Huazhe et al. Iteratoal Joural of Ecoomcs ad Maagemet Systems dcators sequece H0 ( h0, h0,, h0, h0 that have udergoe tred processg [5]. h m h x max h m h x 0 h0 m h0 max h m h Determato of the dyamc resoluto coeffcet x0 x ca be calculated by x ad x0. The sequece stablty coeffcet λ ca be obtaed accordg to equato (4, ad determe the value of the dyamc resoluto coeffcet ρ by the value of λ. 4 Grey correlato coeffcet calculato Usg the obtaed ad ρ, calculate the grey correlato coeffcet ζ ( x, 0 x accordg to formula (5. 5 Horzotal weghtg factor calculato Accordg to the tme-weghtg method based o fuzzy matrx, the fuzzy cosesus matrx S s ca be calculated accordg to ( formula (7 ad (8. The the horzotal weghtg factor ω ca be calculated accordg to formula (9. 6 Correlato coeffcet calculato Usg the grey correlato coeffcet ζ x x obtaed step 4 ad the horzotal (, 0 weght factor ω obtaed step 5, the horzotal weghted correlato degree γ 0 betwee the sequece of the frst fluecg factor ad relablty ca be calculated accordg to equato (6. 3 Case Study Ths paper takes a example from a coastal area as case aalyss. The rego provded a total of 8 factor dcators for the years of class A, B, C, ad D power supply areas, cludg cable rate X, dstrbuto automato rate X, le lk rate X 3, average umber of segmets X 4, average le load rate X 5, average dstrbuto trasformer load rate X 6, average repar tme X 7, lve workg rato X 8. The data s show Table. Table Factor data of each power supply area 03~06 X X 3 X A B C D Frstly, accordg to the determato method of the segmeted dyamc resoluto coeffcet, the resoluto coeffcet s determed by the degree of somoothess of the fluecg facotr sequece. The resoluto coeffcets are show Table.. Table Resoluto coeffcet of each fluecg factor sequece X X 3 A B C D The, accordg to the fuzzy matrx weghtg method, the weghts of the hstorcal perod are obtaed. Table 3 shows the weght coeffcets. Table 3 The weghts of hstorcal perod Year Weght Accordg to the mproved grey relatoal degree model, the grey relatoal degree betwee the fluecg factor dex ad the relablty dex s calculated. The results of the correlato degree are show Table 4. Table 4 Gray correlato degree betwee each fluecg factor ad SAIDI X A B C D ISSN: Volume 3, 08

6 Cao Huazhe et al. Iteratoal Joural of Ecoomcs ad Maagemet Systems X Table 4 shows the correlato betwee the fluecg factors of the dfferet power supply areas ad SAIDI (system average terrupto durato dex. I the A-class power supply area, the dstrbuto automato rate ad the average repar tme have a great fluece o SAIDI. Therefore, the eterprses charge of such area should gve prorty to stregtheg the costructo of dstrbuto automato, ad at the same tme, the ablty of the mateace team should be mproved to shorte the repar tme. I B- class power supply area, the average umber of segmets ad the average repar tme have a greater mpact o SAIDI. Therefore, the eterprses charge of such area should gve prorty to creasg the average umber of segmets ad shorteg the repar tme. I the C-class power supply area, the le lk rate, the average umber of segmets, ad the average repar tme have a greater mpact o SAIDI. Therefore, the eterprses charge of such area should gve prorty to upgradg the grd structure ad pay more atteto to the fault repar procedure optmzato. I the D- class power supply area, the le lk rate ad the average umber of segmets have a great fluece o SAIDI. Therefore, eterprses charge of such area should pay atteto to creasg the average umber of segmets ad le lk rate. From Table 4, t ca also be see that the correlato betwee power supply relablty ad le lk rate A-class rego s lower tha that C-class ad D-class regos. I addto, the correlato betwee the power supply relablty ad dstrbuto automato s hgher tha le lk rate A-class rego. Ths s because the le lk rate of the A-class rego durg s hgher tha that of the C-class ad D-class regos, ad a small crease the le lk rate wll have lttle mpact o the mprovemet of power supply relablty. However, 03-06, the dstrbuto automato rate the A-class rego s geerally ot hgh, ad there s a large space for mprovemet, whch has a great mpact o the relablty of power supply. The above aalyss verfes the ratoalty of the method from the sde. 4 Cocluso Ths paper proposes a relablty mg algorthm based o busess maagemet dcators. The ma coclusos are as follows. Through the aalyss of busess processes, a three-ter comprehesve relablty evaluato dex system s establshed. The system cludes four aspects, grd level, operato ad mateace, producto schedulg, ad costructo operato, whch fully reflects the techology ad equpmet level of power grd ad the maagemet level of power supply busess. A mproved grey relatoal degree model s adopted ths paper. Compared wth the tradtoal grey relatoal model, the dsadvatages of the set value of the resoluto coeffcet ad the mportace dfferece of the hstorcal data are take to cosderato, ad the dyamc segmetato resoluto coeffcet ad fuzzy weghtg are troduced to mprove t. The result of the mproved model s more realstc ad provdes more accurate gudace for the busess maagemet ad relablty mprovemet. 3 Compared wth the tradtoal relablty calculato method, ths method does ot deped o the topology of the power grd ad does ot requre a large umber of calculatos. It ca drectly aalyze the ma factors that affect the relablty of the power supply. Refereces: [] Ju Lu, Ja Su, Kag Ma, Ha Tao Lu, Tao We, Dstrbuto Network Relablty Calculato Based o Improved Mmal Path Method[J], Appled Mechacs ad Materals, Vol.5, 04, pp [] Kezuovc Mlade, Xe Le, Gralva Satago, The Role of Bg Data Improvg Power System Operato ad Protecto[C], Bulk Power System Dyamcs ad Cotrol-IX Optmzato, Securty ad Cotrol of the Emergg Power Grd(IREP, Rethymo, 03, pp. -9. [3] Beth-Ae Schuelke-Leech, Betsy Barry, Matteo Murator, B.J.Yukovch, Bg Data Issues ad Opportutes for Electrc Utltes[J], Reewable ad Sustaable Eery Revews, Vol.5, No., 05, pp [4] We Che, Kale Zhou, Shal Yag, Cheg Wu, Data Qualty of Electrcty Cosumpto Data a Smart Grd Evromet[J], Reewable ad Sustaable Eergy Revews, Vol.75, 07, pp [5] Yu Qg Feg, Ja Hua Yag, Le Huag, B J, Ja Su, Itellectualzato ad Relablty ISSN: Volume 3, 08

7 Cao Huazhe et al. Iteratoal Joural of Ecoomcs ad Maagemet Systems Evaluato of Dstrbuto Network Based o Prcpal Compoet Aalyss[J], Appled Mechacs ad Materals, Vol , 04, pp [6] Mohammoud M. Hadow, Ahmed N. Abd Allah, Sazal P. Abdul karm, Edgar Carreo, Relablty Evaluato of Dstrbuto Power Systems Based o Artfcal Neural Network Techques[J], Joural of Electrcal ad Computer Egeerg, Vol.0, No.3, 0, pp. -5 [7] L Wag, Zawe Lu, Xuebo J, Ya Sh, Relablty Estmato Based o the Degradato Amout Dstrbuto Usg Composte Tme Seres Aalyss ad Grey Theory[J], Cyberetcs ad Iformato Techologes, Vol.3, No.3, 03, pp [8] Ga Cell, Emlo Cha, Fabrzo Plo, Ga Guseppe Soma, Relablty Assessmet Smart Dstrbuto Networks[J], Electrc Power Systems Research, Vol.04, No.9, 03, pp [9] (DL/T The Gude for Plag ad Desg of Dstrbuto Network[S], Cha Electrc Power Press, 06. [0] Radomr Goo, Mchal Kratky, Staslav Rusek, Relablty of Dstrbuto Network Compoets Based o Falure Database[J], AASRI Proceda, Vol., 0, pp [] Hog Zhag, Zh Guo Le, Yue Cheg, Yu Mg Wag, Medum ad Log-Term Load Forecastg Usg Grey Theory Based o Rough Sets[J], Appled Mechacs ad Materals, Vol , 04, pp [] L Wag, Xao Ya L, Tog M Jag, Tg Tg Huag, Lfe Predcto of Costat-Stress Accelerated Degradato Testg Usg Tme Seres Method ad Grey Theory[J], Advaced Materals Research, Vol.8-0, 00, pp [3] L Wag, Zawe Lu, Xuebo J, Ya Sh, Relablty Estmato Based o the Degradato Amout Dstrbuto Usg Composte Tme Seres Aalyss ad Grey Theory[J], Cyberetcs ad Iformato Techologes, Vol.3, No.3, 03, pp [4] Jafag L, Xaohu Sog, Fe Gao, Yu Zhag, A Mult-Level Fuzzy Evaluato Method for Smart Dstrbuto Network Based o Etropy Weght[J], IOP Coferece Seres: Materals Scece ad Egeerg, Vol.99, 07, pp [5] K. Hsa, M. Che, M. Chag, Commets o Data Pre-Processg for Grey Relatoal Aalyss[J], Joural of Grey System, Vol.7, No., 004, pp ISSN: Volume 3, 08