Thermal Studies on Low Voltage Power Cable

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1 Theml Studies on Low Voltge Powe Cble DOINA ELENA GAVRILA, COSTEL PAUN 1 Physics Deptment, Univesity "Politehnic" of Buchest Polytechnic Univesity of Buchest 313 Spliul Independentei, Buchest, Romni ROMANIA emil: gvil@physics.pub.o Abstct:- Relibility nd pefomnce depend on chcteistics wiing insultion. Lifetime cble is pcticlly equl to tht of thei insultion Action of het (due to Joule effect) led to chemicl degdtion ections, such ievesible tnsfomtions occu leding to chnging popeties of ognic mteils (especilly polymes) which e fomed insultion. As mnufctues nd uses of electicl instlltions must know exctly the chcteistics nd behvio ove time, in diffeent opeting modes, the electicl cble insultion nd long tem functioning of thei. To study the insulting popeties of mteils cn be themlly degded novembe degdtion in shot time using inductive heting. Phenomenon of electomgnetic induction heting is bsed on the enty field in conductos, eddy cuents induced electomotive voltge detemined, leding to its heting by Joule-Lenz [6] This ppe exmines the possibility of stight equivlence heting insultion of n electicl cuent to nothe conducto heted by induction.with the esults obtined by numeicl simultion e equivlent theml effect poduced by pssing n electic cuent conducto with theml effect due to induction. It cn mke coeltion with the theml insultion on the conductos, poduced by electic cuent (lod o fult) tht psses though the conducto nd its insultion degdes [6]Using ou numeicl simultion esults cn equte inductive heting effect which is smll-scle test with het insultion effect in noml o defective in diffeent settings nd opeting modes [6] Key-wods induction heting; insultion of cicul cylindicl conductos; finite element method. 1. Intoduction Induction heting is non-contct heting pocess tht uses electomgnetic induction pinciple to poduce het. Induction heting uses high fequency powe supply to poduce high intensity AC though coil. The cuent though the coil genetes mgnetic field pidly vible inside the coil. Wokpiece to be heted is plced within this intense ltenting mgnetic field, the eddy cuents e geneted in the wokpiece nd the electicl esistnce of the metl leds to Joule effect heting it. At the beginning of the lst centuy inductive heting pinciples hve been used s mens to melt steel. Now this opetion is most commonly used in steel lloys nd to hdening the steel sufce. Mny mechnicl pts of devices e subjected to sufce tetment befoe delivey, in ode to impove thei behvio. Method is used to obtin induction funce, fo welding, bzing, seling, to fit, bonding, nneling, foging, melding, stightening, etc. But induction heting is used too extensively not only in mchine, hevy industy, utomotive pplictions etc. but lso in cble mnufctuing, textile nd ppe industy, chemicl, wood nd food industy. This method is often used in the industil pplictions of plstic pocess with injection nd extusion mchines becuse impoves enegy efficiency fo injection nd extusion. Diffeent cbles nd wies must be heted befoe the isoltion-extuding pocess ccoding to the tempetue of used mteil. Fo this ppliction the induction heting is vey common s ceful nd pollution fee solution. Becuse the wmth is geneted without contcting, the cble sufce emins pefectly clen nd without sctches. Impotnt fo the qulity of the cble-poduction pocess is lso pefect dheence to the equied tempetue. ISBN:

2 2.The study found monowie heting conducto in mgnetic field vible. 2.1 The poblem of electomgnetic field Appent powe flow S complex unit heted sufce =, is expessed: 2 λh I1( λ ) S = E( ) H ( ) =. [5] (7) σi ( λ ) Fig.1 Cylinde vible mgnetic field Penettion depth of the mgnetic field in the wie studied is given by: 2 δ = [5] (1) ωµσ [5] (6) be,bei the functions of Kelvin. 2.2 Theml field poblem Theml conduction tkes plce continuously in phs. Theml diffusion is descibed by the eqution: T div λ gdt + c = p [6] (8) t c= volumetic het cpcity. λ = theml conductivity. p= volume density of powe tht is conveted into het in the fom of electomgnetic. Boundy condition is: T λ = α( T Te ) [6] (9) n ω = 2 π f is the ngul fequency AC; µ = mgnetic pemebility of conducto mteil; α = sufce het tnsfe coefficient. σ = electicl conductivity of the mteil T e = tempetue outside the nge. If α = obtin homogeneous Neumnn conditions. Mgnetic field inside the cble is: If λ = Diichlet boundy condition esults. H ( ) = AI ( λ ) + BK ( λ ). [5] (2) I nd K e modified Bessel functions of the fist 2.3 The coupled cse nd the second cse zeo ode. + j λ = 1 Due to the tempetue dependence of mteil popeties coupled model clcultes the outputs. (3) δ sequentilly. Theml het souce in question is the Induced cuent density is detemined by the Joule losses due to eddy cuents. [6] At the sme time expession: theml poblem is nonline due to the tempetue d H dependence of theml conductivity. [6] J = = λ [ AI 1( λ ) + BK1( λ )]. [5] (4) In ode to solve the coupled set of equtions in phse d develops numeicl model using the finite element Boundy conditions: method. [6] Used finite element discetiztion in spce J ( ) = şi H ( ) = H,[5] (5) which led (5) to diffeentil equtions of ode 1. [6] leding to the solution: I 3.Considetions on numeicl modeling ( λ) be ( / δ ) + jbei ( / δ ) H ( ) = H = H of heting wie I ( λ) be ( / δ ) + jbei ( / δ ) The object modeling study designed to undestnd specific physicl mesuements nd mthemticl models chcteistic. [6] Knowledge in ny field device llows ccess to the compute ovell pefomnce in ny opeting mode, pemnent o tnsitoy. [6] ISBN:

[6] simultion ws done with Flux 2D softwe pckge. 3.1.

3 The finite element method involves detemining globl function tht is studied phenomenon t ny point in the nge clcultion. [6] As the computing field is divided into multiple djcent subdomins clled finite elements globl function is n ssembly of functions ssocited with ech of these elements. [6] simultion ws done with Flux 2D softwe pckge. 3.1.The physicl model Fig.2 Physicl model fo conductive lod. 1 conducto.2-insultion. Fig.3 Physicl model fo wie-induce ensemble Anlyzed conducto (Cu) 3 density d = 8933Kg / m specific het c p=38j/kgk theml conductivity λ = 38W / mk 8 electicl esistivity ρ = 2 1 Ω m eltive mgnetic pemebility µ = 1 coefficient of theml convection α = 2W / m 2 K theml dition coefficient β = Insultion (PVC) 3 density d = 13Kg / m specific het c p=18j/kgk theml conductivity λ =,15W / mk coefficient of theml convection α = 2W / m 2 K eltive mgnetic pemebility µ = 1 theml dition coefficient β =.3. 4.Numeicl simultion esults in the heting of conducto in the chge monowie Studied cble is the sme s it is heted inductively. At the end is the potentil diffeence U =.15 V. Meshing ws done by softwe simultion in time t = 1s. Neumn boundy conditions e povided t the intefce conducto insultion nd insultion convection-bode envionment The initil tempetue of the envionment ws set to T = 2 C. 1-induce. 2-insultion. 3-conducto. conducto dimete d 1 = 42mm conducto insultion thickness g = 3mm; cble length l = 126mm induce dimete d 2 = 65mm Inducto coil is teted s solid conducto hving cuent density J = 5A/mm2. Fequency f = 1Hz cuent in the inducto initil tempetue T =2 C Fig.4 Inducto conducto ssembly Fig.5. Mesh viewing e in lod conducto. ISBN:

4 Colo Shde Results Quntity : Cuent density A/(mm ce) Time (s.) : 1 Scle / Colo 47,6962 / 47, ,7891 / 47,882 47,882 / 47,975 47,975 / 47, ,1679 / 47, ,1169 / 47, ,12538 / 47, ,13467 / 47, ,14396 / 47, ,15326 / 47, ,16255 / 47, ,17184 / 47, ,18114 / 47, ,1943 / 47, ,19972 / 47,291 47,291 / 47,21831 Fig.6 View cuent density in lod conducto t t = 1s Colo Shde Results Quntity : Tempetue Deg. Celsius Time (s.) : 1 Scle / Colo 294,34238 / 294, ,44678 / 294, ,55118 / 294, ,65555 / 294, ,75995 / 294, ,86435 / 294, ,96875 / 295, ,7315 / 295, ,17755 / 295, ,28195 / 295, ,38635 / 295, ,4975 / 295, ,59512 / 295, ,69952 / 295, ,8392 / 295, ,9833 / 296,1273 Fig.7 View theml field in lod conducto t t = 1s ISBN:

d e g e e s C 35 3 25 2 15 1 5 2 4 6 8 1 12 S Fig.8. Vition of theml field in the conducto in chge of coodinting the point A (1, 35). 5.The esults of numeicl simultion of induction heting cble The initil tempetue of the envionment ws set t To = 2 C.

5 d e g e e s C S Fig.8. Vition of theml field in the conducto in chge of coodinting the point A (1, 35). 5.The esults of numeicl simultion of induction heting cble The initil tempetue of the envionment ws set t To = 2 C. Meshing ws done by softwe simultion in time t = 5s.. Neumn boundy conditions e povided t the intefce conducto insultion nd insultion convection boundy-domin nlysis mediu.l edge (wll) Diichlet condition is imposed Fig.9. Mesh viewing e in inducto conducto ssembly ISBN:

6 Isovlues Results Mthemticl Models in Engineeing nd Compute Science Colo Shde Results Quntity : Flux density Tesl Time (s.) : 5 Phse (Deg): Scle / Colo 36,195E-6 / 17,9621E-3 17,9621E-3 / 35,8882E-3 35,8882E-3 / 53,81428E-3 53,81428E-3 / 71,7438E-3 71,7438E-3 / 89,66648E-3 89,66648E-3 / 17,59257E-3 17,59257E-3 / 125,51866E-3 125,51866E-3 / 143,44476E-3 143,44476E-3 / 161,3786E-3 161,3786E-3 / 179,29696E-3 179,29696E-3 / 197,2235E-3 197,2235E-3 / 215,14913E-3 215,14913E-3 / 233,7523E-3 233,7523E-3 / 251,133E-3 251,133E-3 / 268,92743E-3 268,92743E-3 / 286,85352E-3 Quntity : Equi flux W ebe Time (s.) : 5 Phse (Deg): Line / Vlue 1 / -2,84849E-6 2 / 44,36739E-6 3 / 91,58326E-6 4 / 138,79912E-6 5 / 186,1499E-6 6 / 233,2386E-6 7 / 28,44675E-6 8 / 327,66262E-6 9 / 374,87849E-6 1 / 422,9437E-6 11 / 469,3124E-6 Fig 1 View the mgnetic field in inducto conducto ssembly t t = 5s Colo Shde Results Quntity : Tempetue Deg. Celsius Time (s.) : 1 Phse (Deg): Scle / Colo 19,41626 / 19, ,92394 / 2, ,43161 / 2, ,93929 / 21, ,44697 / 21, ,95465 / 22, ,46232 / 22, ,9691 / 23, ,47768 / 23, ,98535 / 24, ,4933 / 25,71 25,71 / 25, ,5838 / 26,166 26,166 / 26, ,52374 / 27, ,3142 / 27,5399 Fig.11 View theml field in inducto conducto ssembly t t = 1s ISBN:

7 Colo Shde Results Quntity : Tempetue Deg. Celsius Time (s.) : 31 Phse (Deg): Scle / Colo -44,3762E-3 / 11, ,9116 / 24, ,26243 / 36, ,6138 / 48, ,96516 / 61, ,31653 / 73, ,66791 / 86, ,1927 / 98, ,3764 / 11, ,7211 / 123, ,7338 / 135, ,42474 / 147, ,77611 / 16, ,12749 / 172, ,47885 / 184, ,8322 / 197,18158 Fig.12 View theml field in inducto conducto ssembly t t = 31s 4 degees C S Fig.13 Vition field induction het conducto coodinte point A (1, 35). degees C mm b Fig 14. Vition in lye insultion theml field point coodintes C (21, 57). (24.57) in the 2 cses eview. - conducto lod; b-inducto conducto ssembly. ISBN:

8 degees C mm b Fig 15. Vition in theml field insultion lye between the coodinte points C (21, 5) nd D (24, 5). - conducto lod; b-inducto conducto ssembly. degees C mm b Fig 16. Theml field vition between points of coodintes G (, 32) nd H (24, 32) cble to chge b-inducing cble ssembly. - conducto lod; b-inducto conducto ssembly. Mesuements wee mde with simultion softwe Flux ISBN:

9 6.Conclusions nd contibutions of this thesis The pupose of this ppe is to initite functionl test ptten, scle, to obtin infomtion bout the behvio of electicl cble insultion. With inductive heting insultion degdtion eching electicl conductos without diect contct with the tck heting inducto in shot time with low enegy consumption, the size of the conducto unde test is negligible. Using numeicl simultion esults e equivlent inductive heting effect of het insultion effect in diffeent opeting modes. The model pesented cn be extended to othe types of insulted conductos nd othe electicl pplinces s hving the composition of metl pts geneting het which cn wosen the popeties of insultion mteils. [6] The esults of simultion show tht you cn mke pecise equivlence between the two systems nlyzed numeiclly. [6] Numeicl solution is wy to get ccute esults nd study unde lbotoy conditions mny opeting modes. Numeicl simultion development educe the numbe of tests which is solution to educe design time with miniml effot[6]. REFERENCES [1] Gvilă Doin, Physics, volume 2, E.D.P. Buchest, [2] Co. Flueşu nd C. Flueşu, Cus de Electotemie, Univ. "Politehnic" Bucuesti, Romni, [3] M.L. Bown, "Clcultion of 3 dimmensionl eddy cuents t powe fequencies", Physicl Sci., Mesuement nd Instumenttion, Mngement nd Eduction-Rev., IEE Poc. A, vol.129, Iss.1, pp , [4] E.C. Mldin, M. Stn, Elemente vnste de conducńie temică şi difuzie msică, Editu Mtix Romni, Bucuesti, 26. [5] T. Leuc, Şt. Nghy, T. Mghi, Pocese mteilelo în câmp mgnetic. AplicŃii utilizând tehnici infomtice, Editu UnivesităŃii Ode, Romni, 22. pp [6] C. Păun, Aspects egding numeicl modeling of inductive heting pocess fo low voltge cbles, UPB Sc. Bull., Seies C, vol. 72, Iss. 3, pp , 21 ISBN:

School of Electrical and Computer Engineering, Cornell University. ECE 303: Electromagnetic Fields and Waves. Fall 2007

School of Electrical and Computer Engineering, Cornell University. ECE 303: Electromagnetic Fields and Waves. Fall 2007 School of Electicl nd Compute Engineeing, Conell Univesity ECE 303: Electomgnetic Fields nd Wves Fll 007 Homewok 3 Due on Sep. 14, 007 by 5:00 PM Reding Assignments: i) Review the lectue notes. ii) Relevnt