AHIVES OF ELETIAL ENGINEEING VOL. 66(), pp. 7-28 (207) DOI 0.55/a-207-0002 A n cas-rsin ransformr hrmal modl basd on rcurrn nural nors DAVOOD AZIZIAN, MEHDI BIGDELI 2 Dparmn of Elcrical Enginring, Abhar Branch, Islamic Azad Univrsiy, Abhar, Iran -mail: d.azizian@abhariau.ac.ir l.: +98 92248353 2 Dparmn of Elcrical Enginring, Zanjan Branch, Islamic Azad Univrsiy, Zanjan, Iran -mail: mhdi.bigdli@iauz.ac.ir (civd: 06.03.206, rvisd: 9.07.206) Absrac: Thrmal modling in h ransin condiion is vry imporan for cas-rsin dry-yp ransformrs. In h prsn rsarch, o novl dynamic hrmal modls hav bn inroducd for h cas-rsin dry-yp ransformr. Ths modls ar basd on o arificial nural nors: h Elman rcurrn nors (ELN) and h nonlinar auorgrssiv modl procss ih xognous inpu (NAX). Using h xprimnal daa, h inroducd nural nor hrmal modls hav bn raind. By slcing a ypical ransformr, h raind hrmal modls ar validad using addiional xprimnal rsuls and h radiional hrmal modls. I is shon ha h inroducd nural nor basd hrmal modls hav a good prformanc in mpraur prdicion of h inding and h cooling air in h cas-rsin dry-yp ransformr. Th inroducd hrmal modls ar mor accura for h mpraur analysis of his ransformr and hy ill b raind asily. Finally, h raind and validad hrmal modls ar mployd o valua h lif-im and h rliabiliy of a ypical cas-rsin dry-yp ransformr. Ky ords: cas-rsin ransformr, dynamics, rcurrn nural nors, hrmal modling. Inroducion In many criical applicaions such as miliary and rsidnial aras, ransformrs mus b procd agains xplosion. Thus, nonflammabl insulaions (such as Asarl and Epoxy sins) hav bn offrd o b usd in ransformrs. As h usag of Asarl has bn phasd ou, poxy rsins hav provn hmslvs and ar idly usd in ransformrs. Thrfor, a cas-rsin dry-yp ransformr, 2] has bn dvlopd as a nonflammabl ransformr. Whil a dry-yp ransformr lacs any cooling fluid and h lif-im of insulaing sysm dpnds on mpraur, h hrmal bhaviour analysis of h dry-yp ransformr is crucially imporan. Unauhnicad Donload Da 4/2/8 8:06 AM
8 D. Azizian, M. Bigdli Arch. Elc. Eng. Prviously, h sady-sa hrmal modling for diffrn gomris of h dry-yp ransformr as inroducd in 2-8]. Addiionally, i is ssnial o sudy h ransin hrmal bhaviour and h lif-im of h dry-yp ransformrs; hus, i is hlpful o inroduc som applicabl dynamic modls for his purpos. Diffrn lif-im and ransin hrmal modls hav bn prsnd for oil-immrsd ransformrs 9-3]. Thr ar f rsarchs on dynamic hrmal modling of h dry-yp ransformrs 4-7]. frncs 4, 5] inroduc simplifid modls for h dynamic hrmal modling of h dry-yp ransformrs. Diffrn hurisic algorihms hav bn mployd o sima h paramrs of hs hrmal modls. As i has bn shon in 5], h simplifid modls ar accura nough for h hrmal modling of h dry-yp ransformr. Addiionally, som daild hrmal modls hav bn prsnd in 6, 7] for h hrmal modling of h cas-rsin dry-yp ransformr. Th modls ha ar basd on h physical srucur of h ransformr ar accura nough o analys h dynamic hrmal bhaviour of h dry-yp ransformrs. Bu h accura hrmal modling of h ransformr, spcially hn h currn variaion is high, canno b achivd. Thus, i is ndd o inroduc som compaibl mhods o modl h dynamic hrmal bhaviour of h dry-yp ransformr. Noadays arificial nural nors (ANN) ar idly usd for mpraur prdicion in diffrn problms and phnomna 8-24]. Svral ANN basd dynamic hrmal modls hav bn prsnd for oil-immrsd ransformrs 2-24]. onsqunly, novl dynamic hrmal modls basd on h Elman rcurrn nors (ELN) and h nonlinar auorgrssiv modl procss ih xognous inpu (NAX) for h hrmal modling and mpraur prdicion of h cas-rsin dry-yp ransformrs ar inroducd in his papr. Employing h masurd mpraurs, h ANN modls hav bn raind and h prdicd mpraurs ar validad agains xprimnal rsuls, h hrmal modls 5-7] and h classic IE mhod 25]. Afrards, using h raind ANN modls, h lif-im and rliabiliy of h cas-rsin ransformr ar sudid. I is shon ha, h inroducd ANN modls hav br fficincy in h mpraur prdicion of h casrsin dry-yp ransformr rahr han ohr radiional mhods. Main conribuions and novlis of his papr can b lisd as folloing: - N and simpl ANN basd hrmal modls ar inroducd for h dynamic hrmal modling of h cas-rsin dry-yp ransformr. - Th rsuls of h inroducd modls ar compard o xprimnal rsuls, h basd modls, IE quaions and o ach ohr. - Using h prdicd and validad ANN modls, h lif-im and rliabiliy of h cas-rsin ransformr hav bn sudid. 2. as-rsin dry-yp ransformr hrmal modls 2.. IE hrmal quaions Pracically, hr ar f convnional modls ha ar mployd for mpraur prdicion of dry-yp ransformrs 25, 26]. In hs radiional modls, if h rquird xprimnal Unauhnicad Donload Da 4/2/8 8:06 AM
Vol. 66 (207) A n cas-rsin ransformr hrmal modl basd on rcurrn nural nors 9 paramrs ar no accssibl hn h modls canno b mployd. Hr, h radiional hrmal quaions ha hav bn prsnd by h IE sandard 25] ar discussd. I is non ha h dynamic bhaviour of mpraur is similar o a simpl xponnial quaion. Thus, by drminaion of h iniial and h final valus of his xponnial quaion, h inding s mpraur ris ( ) can b govrnd a ach im () as givn in (). τ ( ) 0 = +, () hr: τ is h hrmal im-consan of a inding, 0 is h iniial ( = 0) inding mpraur ris a h bginning of h im priod, and is h final (sady-sa) inding mpraur ris ha can b xprssd as n = K, (2) hr: n is h nominal sady-sa inding mpraur ris, K is h load facor (load currn/nominal currn) and n is an xprimnal corrcion cofficin. IE sandard proposs τ = 0.5-2 hours and n =.6 for dry-yp ransformrs 25]. n 2.2. hrmal modl A schmaic vi of a cas-rsin ransformr is shon in Fig. a. Thrmal bhaviour of h indings can b xprssd as (3) 6]. r r r r + 2 q + = 2 z α, (3) hr: qo is h spcific loss dnsiy, is h mpraur, is h hrmal conduciviy and α is h hrmal diffusion. No, assum h solid pars o b dividd ino a numbr of cylindrical unis ha ar rlad o ach ohr by hrmal rsisancs (Fig. b). a) b) Edg Band or Lg Δr, n + HV Dis asd sin Δz m-, n - m,n n- m + LV Layr m, n- Fig.. as-rsin dry-yp ransformr: a) schmaic vi; b) a parial par Unauhnicad Donload Da 4/2/8 8:06 AM
D. Azizian, M. Bigdli Arch. Elc. Eng. 20 In h ransin condiion, h ransfrrd hrmal nrgy o ach uni appars as an incras in h oal nrgy and h uni bhavs as an ingrad capacior 6]. If only on uni is slcd in h indings and if h ha ransfr from horizonal surfacs is nglcd (ha ransfr is assumd o occur in h radial dircion) 2], h hrmal bhaviour of h inding and h cooling air (on op of h nclosur 27]) can b xplaind as folloing 5]: P d d =, (4), hr, d d P P = = (5) hr: / ar h avrag mpraur riss, P /P ar h hrmal flo sourcs, / ar h hrmal rsisancs, and / ar h hrmal capaciancs of h inding/cooling air. onsqunly, (4) and (5) rprsn a scond ordr circui as givn in 5]. No ha, and P ar mpraur dpndn 7]. And P also dpnds on h load facor and h nominal inding losss (P n ) as shon in (6).. n n K P P = (6) ombining (4)-(6), h marix form of h hrmal modl can b xplaind as (7). n K P + = 0 d d d d 0. (7) Applying h forard Eulr discrizaion rul ( ( ) Δ = / ] ] & ), a discr im form of (7) can b xracd as: ]) ],, ( ] ] 0 Δ Δ Δ Δ ] ] 0 = + + + + = K f K P n. (8) 2.3. Novl hrmal modls basd on rcurrn nural nors An arificial nural nor (ANN) is a s of inrconncd nurons ha mploys a mahmaical modl o simula a biological nural nor. ANN is formd by conncing h arificial nurons o ach ohr among adjusabl ighs. Nural nors can b mployd o modl complicad inracion bn a s of inpus and oupus. ANN can b raind o rach a arg oupu for a spcific s of inpus. In his rsarch, i is assumd ha only o nods in h inding and h cooling air can modl h hrmal bhaviour of h cas-rsin dry-yp ransformr ih sufficin accuracy. This mans ha only h inding s avrag (or hos spo) mpraur and h cooling air Unauhnicad Donload Da 4/2/8 8:06 AM
Vol. 66 (207) A n cas-rsin ransformr hrmal modl basd on rcurrn nural nors 2 mpraur on op of h inding ar imporan and masurabl. Obviously, if h masurd cooling air mpraur is no accssibl, on can nglc h rlad nod and hus h ordr (numbr of h oupus) of h hrmal modl ill b rducd. As i can b sn from (8), hrmal modl nds on inpu for h load facor (K) and o oupus for h inding mpraur ( ) and h cooling air mpraur ( ). For mor simplificaion in h hrmal modl, and ar assumd o b mpraur riss (absolu mpraur - ambin mpraur) insad of h absolu mpraurs; his hlps o rmov h ambin mpraur from h inpus and o simplify h modl. No ha mpraurs ar prsnd in boh sids of (8); so h hrmal modls mus hav dynamic bhaviours. Addiionally, h hrmal paramrs in his quaion ar mpraur dpndn and consqunly, h hrmal modl mus b abl o modl h nonlinar bhaviour of his sysm. In ordr o achiv hs goals, o modls basd on rcurrn nural nors ar inroducd hr. 2.3.. Elman rcurrn nors (ELN) ELN is a parial rcurrn arificial nural nor and is a idly usd modl for dynamic sysms modling. Prviously, his nor has bn mployd for mpraur prdicion in many diffrn problms 8-24]. Th ELN is composd of inpu, hiddn, conx, and oupu layrs (Fig. 2). Fig. 2. Srucur of h ELN Th rcurrn lins in h conx layr causs h ELN o b snsiiv o h oupu s hisory; dynamic bhaviour of h ELN is providd only by hs inrnal conncions. In his rsarch, diffrn raining procsss r carrid ou and h opimal numbr of nurons in h hiddn layr (5), yp of ransfr funcions ( logsig for h hiddn layr and purlin for h oupu layr), h numbr of pochs, and c. hav bn drmind using a rial and rror procss. Th nor has bn raind using h Lvnbrg-Marquard mhod. 2.3.2. Nonlinar auorgrssiv modl procss ih xognous inpu (NAX) NAX is a porful dynamic nural nor for modling nonlinar and im varian sysms. Du o br gradin dscn, h NAX larning procss is mor ffciv and convrgs fasr han in ohr arificial nural nors 28]. In modling long im dpndncs, Unauhnicad Donload Da 4/2/8 8:06 AM
22 D. Azizian, M. Bigdli Arch. Elc. Eng. h NAX modl is br han ohr rcurrn nors. Th NAX nors can b implmnd in diffrn ays. A simpl ay is o us a fd-forard nor ih dlayd inpus in addiion o a dlayd oupu lin o inpu (Fig. 3). A dynamic bac-propagaion mhod is rquird for larning purpos; raining may b rappd in local opima. On can us h masurd oupus insad of h simad ons o rain h NAX modl; hus h fdbac lins ar dcoupld. Th rsulan nural nor is a non fd-forard nor ha could b raind using h classical saic bac-propagaion algorihm. Bu unforunaly, i as sn ha his causd unsuiabl rsuls. In his rsarch, h opimal numbr of nurons in h hiddn layr (5), yp of h ransfr funcions ( logsig for hiddn layr and purlin for oupu layr), h numbr of iraions, and c. hav bn drmind using a rial and rror procss. Th nor has bn raind using h Lvnbrg-Marquard mhod. In his problm, i has bn sn ha hr as no nd for inpu dlays and ach oupu as dlayd ic. Fig. 3. Srucur of h NAX 3. liabiliy quaions for dry-yp ransformr Insulaion s Lif-im in a ransformr dpnds on h inding s mpraur. To compu h lif-im of a cas-rsin dry-yp ransformr, IE 9] and IEEE 0] sandards proposd som quaions. In his rsarch, h xpcd lif-im (L) and h failur ra (λ) of h casrsin dry-yp ransformr hav bn calculad using h folloing quaions 5, 27]: Unauhnicad Donload Da 4/2/8 8:06 AM
Vol. 66 (207) A n cas-rsin ransformr hrmal modl basd on rcurrn nural nors 23 20475 80000.25( + amb ) + 273 = 8 L, (9) 875 0 λ 6 20475 0.25( + amb ) + 273 = = L 0.96. (0) Th failur ra in (0) dpnds upon h inding mpraur ris and h ambin mpraur. Th inding mpraur is also rlad o h ransformr load. 4. Tmpraur and lif-im valuaion in a ypical ransformr In ordr o rain h inroducd nural nor modls, h load cycl of Figur 4 is applid o a ypical 400 VA, 20 KV/400 V ransformr 5] and h mpraurs of h inding and h cooling air on op of h nclosur 29] ar gahrd. Fig. 4. A Typical load cycl mployd for raining h nural nor modls Using h gahrd xprimnal daa, h ELN and h NAX modls hav bn raind. Figur 5 shos h raining procss of h ELN and h NAX nural nor modls. From his figur, i can b sn ha h NAX modl is raind fasr and has som br prformanc comparing ih h ELN modl. Fig. 5. Training procss for nural nor hrmal modls Unauhnicad Donload Da 4/2/8 8:06 AM
24 D. Azizian, M. Bigdli Arch. Elc. Eng. In h folloing figurs (Figs. 6-8), h prdicd mpraurs of h inroducd nural nor modls ar compard o h rsuls xracd from radiional IE and hrmal modls. Th inroducd nural nor modls ar accura in h hrmal modling of h cas-rsin ransformr. No ha hs modls nd lss informaion abou h srucur and h hrmal bhaviour of h cas-rsin dry-yp ransformr. Unforunaly, h inroducd modls nd gahring mor xprimnal daa for raining rahr han h radiional hrmal modls. Th IE simpl hrmal modl is implmnd asily, bu i is no so accura. Th hrmal modl is accura nough; bu hil h load variaion is oo high, h rsuls may no b accpabl. I is sn ha h inroducd nural nor basd hrmal modls ar rahr mor accura hrmal modls han h radiional ons. Thy nd no informaion abou h sysm opology and is physical bhaviour. Bu hs hrmal modls nd mor gahrd xprimnal daa for raining purpos. Finally, using h inroducd hrmal modl, h rliabiliy of h cas-rsin ransformr can b valuad according o h load and h ambin mpraur variaions. onsidr a ypical opraing condiion as shon in Fig. 9. By applying h mniond load and ambin mpraur o h inroducd hrmal modl, inding mpraur has bn prdicd as shon in Fig. 0a. Using h prdicd inding mpraur, h rliabiliy indics can b calculad from (9) and (0) as shon in Fig. 0b. Winding Tmpraur ( ) Fig. 6. Prdicd inding mpraur Fig. 7. Prdicd cooling air mpraur on op of h nclosur Unauhnicad Donload Da 4/2/8 8:06 AM
Vol. 66 (207) A n cas-rsin ransformr hrmal modl basd on rcurrn nural nors 25 (a) (b) Fig. 8. Error of h prdicd mpraurs: a) ELN; b) NAX (a) (b) Fig. 9. A ypical opraing condiion: a) load facor; b) ambin mpraur variaions On can s ha h lif-im and h rliabiliy indics of h cas-rsin ransformr ar mor snsiiv o h load facor and h ambin mpraurs hil i is compard o h oilimmrsd yps 9]. Unauhnicad Donload Da 4/2/8 8:06 AM
26 D. Azizian, M. Bigdli Arch. Elc. Eng. (a) (b) Fig. 0. a) inding mpraur; b) failur ra du o variaions in load and ambin mpraur I may b so inrsing o analys h ffcs of load and ambin mpraur on h rliabiliy of ransformr sparaly. Fig. a shos h ffc of load variaion and Fig. b shos h ffc of ambin mpraur on h failur ra of h cas-rsin dry-yp ransformr. (a) (b) Fig.. Transformr failur ra du a variaion in: a) load; b) ambin mpraur Unauhnicad Donload Da 4/2/8 8:06 AM
Vol. 66 (207) A n cas-rsin ransformr hrmal modl basd on rcurrn nural nors 27 5. onclusions Th analysis of h dynamic bhaviour of h inding and cooling air mpraurs is vry imporan in h cas-rsin dry-yp ransformrs. Thus in his papr, n dynamic modls basd on ELN and NAX nural nors r inroducd for h cas-rsin ransformr hrmal modling. Using h gahrd xprimnal daa, h nors hav bn raind and ih h hlp of addiional masurmns h accuracy of h hrmal modls ar vrifid. As i has bn prsnd in his papr, h inroducd hrmal modls sho a good prformanc in h dynamic hrmal modling of h cas-rsin ransformr. Th IE quaion nds lss informaion abou h dsign paramrs of ransformr; bu i is vry simpl and i is no an accura hrmal modl. Th hrmal modl ha dpnds on h physical and acual srucur of h ransformr is accura nough. Alhough h proposd ELN and NAX modls nd mor daa gahring, bu hir accuracy is highr han h radiional IE and hrmal modls and nd lss informaion abou sysm characrisics. Th NAX modl has som br raining spd hn i is raining by xprimnal daa. Finally, by mploying h raind and validad hrmal modls, h rliabiliy indics ar analysd. Variaion in inding mpraur affcs h lif-im and rliabiliy of h cas-rsin dry-yp ransformr. Som facors ha hav mor ffcs on h mpraur and rliabiliy of h ransformr ar ambin mpraur and load currn. In comparison ih h oil-immrsd yps, h lif-im of h cas-rsin dry-yp ransformr is mor snsiiv o h load facor and h ambin mpraurs. I as shon ha h mos srious ffc is du o h load currn bu h ambin mpraur also has considrabl ffcs on h lif-im of h cas-rsin dry-yp ransformrs. frncs ] Azizian D., Bigdli M., Faiz J., Dsign opimizaion of cas-rsin ransformr using naur inspird algorihms, Arabian Journal for Scinc and Enginring, vol. 4, no. 9, pp. 349-3500 (206). 2] ahimpor E., Azizian D., Analysis of mpraur disribuion in cas-rsin dry-yp ransformrs, Elcrical Enginring, vol. 89, no. 4, pp. 30-309 (2007). 3] Pirc L.W., An invsigaion of h mpraur disribuion in cas-rsin ransformr indings, IEEE Transacion on Por Dlivry, vol. 7, no. 2, pp. 920-926 (992). 4] L M., Abdullah H.A., Jofri J.., Pal D., Fahrioglu M., Air mpraur ffc on hrmal modls for vnilad dry-yp ransformrs, Journal of Elcrical Por Sysm sarch, vol. 8, no. 3, pp. 783-789 (20). 5] Eslamian M., Vahidi B., Eslamian A., Thrmal analysis of cas-rsin dry-yp ransformrs, Journal of Enrgy onvrsion and Managmn, vol. 52, no. 7, pp. 2479-2488 (20). 6] Dianchun Z., Jiaxiang Y., Zhnghua W., Thrmal fild and hos spo of h vnilad dry-yp ransformr, IEEE 6h Inrnaional onfrnc on Propris and Applicaions of Dilcric Marials, Xi an, hina (2000). 7] ho H.G., L U.Y., Kim S.S., Par Y.D., Th mpraur disribuion and hrmal srss analysis of pol cas rsin ransformr for por disribuion, IEEE onfrnc Inrnaional Symposium on Elcrical Insulaion, Boson, USA (2002). 8] Azizian D., Windings mpraur prdicion in spli-inding racion ransformr, Turish Journal of Elcrical Enginring and ompur Scinc, vol. 24, no. 4, pp. 30-3022 (206). Unauhnicad Donload Da 4/2/8 8:06 AM
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