Electrical and Thermal Analysis of Single Conductor Power Cable Considering the Lead Sheath Effect Based on Finite Element Method

Transcription

1 Electrical and Thermal Analyi of Single Conductor Power Cable Conidering the Lead Sheath Effect Baed on Finite Element Method M. Raoulpoor*, M. Mirzaie* (C.A.) and S. M. Mirimani* Abtract: Thi paper invetigate the effect of metallic heath on loe and temperature of medium voltage power cable. Two grounding method of heath, including both end bonding and ingle point bonding that caue different ituation on cable ampacity, are conidered. Electrical loe of cable that are main ource of heat are calculated in both conductor and metallic heath of the cable. Sheathed and unheathed medium voltage ingle conductor cable in flat and trefoil formation with different ditance are conidered, while calculated loe are compared in different contruction. Calculation of reitive loe are performed baed on Finite Element Method (FEM) and IEC tandard formulation. The reult of two method are compared and analyzed. Moreover, the effect of eddy current and circulating current of heath on total reitive loe are evaluated. Finally, thermal analyi baed on FEM i executed to achieve maximum temperature of cable in different contruction. Simulation reult how the importance of metallic heath and grounding ytem effect in power cable ampacity analyi. Keyword: Medium Circulating Current Lo, Eddy Current Lo, Thermal Analyi, Voltage Cable. Introduction Power tranmiion cable are baically compoed of conductor and inulation. Some metallic layer uch a heath, armour and hield are ued in power cable. Metallic heath of power cable prevent penetration of moiture in cable. Moreover, metallic heath are protective layer againt mechanical damage, creation electromagnetic interface and are return path for fault and unbalanced current in three phae ytem []. Single point bonding, bonding at both end and cro bonding are the main method of grounding ytem in power cable []. Each of the grounding ytem method create current in metallic heath that affect the total reitive loe. Beide the metallic heath loe baed on grounding type, heath current can influence the conductor current by proximity effect. By thee notification it i obviou that conidering and analyi of metallic heath i an important factor in computation of heat loe and temperature in cable. Iranian Journal of Electrical & Electronic Engineering, 06. Paper received 5 November 05 and accepted 0 February 06. * The Author are with the Department of Electrical and Computer Engineering, Babol Univerity of Technology, Babol, Iran. m.raoulpoor@tu.nit.ac.ir, mirzaie@nit.ac.ir and mirimani@nit.ac.ir. Sheath loe in different cable arrangement, conductor reitivity, and heath reitance are computed in [3] by tandard formula. In [] a theoretical method i ued for the calculation of conductor and heath loe with heath bonding at both end. Loe calculation of high voltage cable in inuoidal current are performed in [5] for determination of volumetric heat ource in thermal analyi. Calculation of heath induced voltage i performed in [6] with conidering phae current variation, ditance and radiue of cable. Influence of cro bonding cable on loe with tranpoed and nontranpoed conductor are invetigated in [7]. In thi method baic matrix impedance and Kron reduction method are ued to determine of poitive equence impedance matrix and loe. Sheath lo tudy baed on improved coupled line model to calculation of admittance matrix i performed in [8]. The paper tudie on connecting impedance in cro bonding joint to reduce the heath lo. In the tudy of [9] an integral equation method i ued for heath loe calculation of three phae cable in triangular contruction. Analytical tudy i performed in [0] on the cable conductor loe without metallic heath in multi circuit ytem inide duct bank. Loe ditribution are conidered ymmetrical which i not valid for aymmetric Iranian Journal of Electrical & Electronic Engineering, Vol., No., March 06 73

2 configuration and cable cloe to each other. Standard and theoretical formulation are ued to loe computation in all of mentioned tudie. Standard formulation are traight forward for conductor and heath loe calculation in ome predefined contruction that are preented for engineer. But thee formula can not be ued for precie loe computation with conidering the kin and proximity effect in all complicated cable contruction. On the other hand FEM can be ued for electrical and thermal analyi of power cable in different formation and variou contruction [, ]. Although thi method i precie, deep computation i needed by computer. Alo imulation reult are enitive to accurate modeling of region, boundary condition and mehing of ytem. The lo attribute of HTS DC model cable uing FEM i preented in [3]. In the tudy the effect of HVDC converter on DC power cable i tudied. Author in [] invetigate electrical reitive loe of low voltage cable by FEM where there are no metallic layer in power cable. A thermal analyi i performed in [5, 6] for underground cable. Finite element imulation are performed in [7] for underground tranmiion line that are buried in multilayer oil. But none of the mentioned tudie are performed on the computation of heath loe and cable temperature by FEM. In thi tudy a new analyi i performed on determination of total reitive loe of power cable. A thorough invetigation i performed on the computation of cable conductor and lead heath loe eparately. Different contruction are conidered. Sheathed and unheathed cable in both flat and trefoil formation are invetigated. Alo calculation are performed in different ditance between cable. Calculation of conductor and heath loe are performed by IEC tandard equation and FEM for ingle point bonding and both end bonding grounding ytem. Reitive loe in each profile are calculated and reult are analyzed. For invetigation of the effect of each profile on cable temperature raiing a thermal analyi by FEM i performed. Electrical and thermal imulation reult how cable heath can increae or reduce the cable ampacity which ha not been tudied before. Alo analyi reult indicate the importance of conidering the heath, grounding method and cable formation in power cable loe and ampacity analyi. Determination of Reitive Loe. Conductor Loe Cable conductor loe are calculated by analytical method a tandard formulation and FEM a differential equation... Analytical Method Main ource of heat in power cable are central conductor reitive loe. Total reitive conductor loe in power cable can be calculated a [8]: w n.r.i c ac () where I i effective current of cable, R ac i ac reitance of conductor in operating temperature and n i the number of loaded conductor in power cable. Ac reitance of power cable i a function of DC reitance, proximity and kin effect of conductor. In IEC-6087, ac reitance of conductor i calculated a: R R (Y Y ) () ac dc p where R dc i DC reitance of conductor in operating temperature, Y and Y p are kin and proximity effect factor, receptively. Thee factor are dependent to conductor diameter, axial ditance of concoctor and frequency. Skin and proximity effect factor are defined a: x Y (3) x 8f 7 x.0.k () R dc xp dc Y p x p (5) dc x p x p 8f 7 x p.0.kp (6) R dc where d c i conductor diameter, i axial ditance of conductor, K, K p are contant factor that are preented in IEC table. Equation (-6) are ued to calculation of conductor loe in ome predefined formation and contruction of power cable. Thee relation give accurate reult for imple contruction and are unuable for complicated ytem or exact conidering of proximity effect between conductor. Computation baed on FEM are required in thee cae... Finite Element Method Finite element i a mathematical method for olving ordinary and partial differential equation. It i a numerical method with ability to olve complex problem that can be repreented in differential equation form. The method in electrical application i decribed by Maxwell' equation. In thi concept, electric and magnetic field are defined a force, that i inerted at a tet charge (q), if it were introduced at peed v and tated a: f q.(ev B) (7) where E and B are electric field and magnetic denity, repectively. Linear diffuion equation i: A ja (8) 7 Iranian Journal of Electrical & Electronic Engineering, Vol., No., March 06

3 where A,,, and are magnetic vector potential, magnetic flux, angular frequency, conductivity and magnetic permeability, repectively. FEM conider total current denity in a pecific conductor or region a below [9]: J Je J (9) where J e and J are related to the magnetic vector potential and electric potential, repectively. Current denitie are calculated in finite element equation a: J ja (0) e J () By olving for unknown value of A and J, current flowing in the conductor with cro ection of S can be determined a: I rm J.d () S In thi way, FEM can olve equation for determination of loe in ection of cable with different current denitie.. Sheath Loe Sheath loe are divided to circulating current and eddy current loe baed on grounding ytem type. Circulating loe are due to current flow in heath circuit of ingle conductor power cable that are bonding at both end and create a cloed path. Eddy current loe are due to induced current in heath which circulate radially a a reult of kin effect and azimuthally a a reult of proximity effect. Three type of grounding ytem are: I. Single point bonding, II. Both end bonding, III. Cro bonding. The advantage of ingle point grounding ytem i lower loe and it diadvantage i creating induced voltage at open end of cable. Although it hould be mentioned that in faulty power cable ytem, current hould pa all length of cable to ground which may caue additional loe []. There i not any induced voltage at the end of cable, in both end bonding ytem. In the fault ituation of uch ytem, current are divided in two portion where caue reduction of fault loe. But thee ytem have additional loe at teady- tate condition due to circulating current in metallic heath. Cro bonding method decreae circulating heath current and high induced voltage a well. In thi method, cable ytem i coniting of three ection with repeating all three phae heath in each part. In ideal cae, induced voltage in heath are equal in magnitude with 0 o phae difference. Thu total voltage in each part i equal to zero. Thi method can be ued only in cable ytem with long length. Alo it implementation i expenive and need killed worker to run. Therefore cro bonding method i not capable to perform in any ituation. Thu aement of loe in the other type of grounding i invetigated. It hould be mentioned that, eddy current of heath occur in both multi conductor and ingle conductor cable and alo in ingle point or two end bonding ytem. But in the cae of bonding heath at two end thee current are mall compared to circulating current. Thu eddy current loe can be ignored in cable analyi in both end grounding ytem... Analytical Method According to IEC-6087, heath or creen loe factor, conit of loe due to eddy or circulating current are defined a: (3) where, are circulating lo and eddy lo factor, repectively. Thee factor are computed baed on reitance and reactance computation of heath. Loe factor equation are preented in IEC-6087 for ome pecial cable contruction and bonding ytem. Eddy current and circulating current loe factor in ymmetrical configuration are obtained a: R. () R ac R Xm d 3 R.R ac.0 (5) where R, X m, d are heath reitance, mutual reactance between heath and conductor and mean diameter of heath, repectively. It hould be noted that uually eddy current loe are ignored in IEC calculation due to the low value... Finite Element Method FEM i another method for computation of heath loe that i ued for complicated ytem and precie calculation. In thi method, Sheath are mehed to the mall element (e), and current are calculated a wa decribed for conductor. Thu heath loe are calculated a: J(x,y).J(x,y) dxdy (6) * e e e P 3 Specification of Studied Cable In thi paper two categorie of underground power cable are tudied. One type i ingle core medium voltage cable without any metallic layer and other type i medium voltage cable with metallic lead heath according to IEC The material of inulation and outer covering are XLPE and PVC, repectively. All invetigated cable have copper conductor with 630 mm cro ection and the thickne of lead heath i mm. Outer diameter of cable are 5 mm and 9. mm, for heathed and unheathed cable that are very cloe to each other and thu are comparable fairly. Cable are conidered in both flat and triangular formation. Raoulpoor et al: Electrical and Thermal Analyi of Single Conductor Power Cable 75

4 Fig. 3 Conductor current denity in flat unheathed cable. Fig. Flat heathed cable. Table Adjacent unheathed cable loe. Lo(w/m) Trefoil Flat FEM IEC FEM IEC Pa Pb Pc Fig. Trefoil unheathed cable. Loe Computation by FEM and IEC Alo each contruction and formation i aeed for adjacent cable and paced cable with ditance equal to cable outer diameter. Fig. and how the diagram of heathed cable in flat formation and unheathed cable in trefoil formation, repectively. In thi ection conductor and heath loe are computed by IEC formulation and FEM. Finite element imulation i performed by Anoft Maxwell imulator in D-teady tate domain, for precie conideration of proximity and kin effect in conductor and heath layer. Three phae ytem ha balanced current a: Ia 00 3, Ib 00 0, Ic 00 3 (7) It hould be mentioned that 00 (A) i not rated current of thee cable and i elected only for loe computation of different ituation. Fig. 3 how the current denity in flat unheathed cable. Alo Table how the loe reult for unheathed cable in flat and trefoil formation of adjacent cable, where P i (i=a, b, c) denote to the power loe in three phae. It i een that IEC and FEM loe reult are in a good agreement for trefoil and flat formation. However the difference between two method i higher in flat formation than trefoil formation. IEC formula aume ymmetric poition for power cable. Thi aumption i reaonable for trefoil formation where give better agreement with the FEM reult in Table. However thi difference i very low, but more accurate reult are preented by FEM that conider exact ditance of conductor and thu proximity effect. Table Adjacent heathed cable loe. Lo(w/m) Trefoil Flat FEM IEC FEM IEC Pa Pb Pc Pa,e Pb,e Pc,e Pa,c Pb,c Pc,c It i een that loe in middle cable i higher than outer cable due to more proximity effect. Table how the conductor and lead heath loe for trefoil and flat formation of heathed cable in adjacent cable. In thi table P i,e and P i,c (i=a, b, c) denote the eddy current loe and circulating current loe of heath in each phae, repectively. Alo Fig. and 5 how the conductor and heath current denitie in ingle point bonding heathed cable. It i een from Table that FEM and IEC reult are more imilar in trefoil formation a decribed before. The difference of IEC and FEM i higher in flat formation. Epecially in heath loe computation, where IEC doe not conider the proximity effect of heath. Alo it i concluded from reult of Table that eddy current loe have little effect on cable total loe. Alo increaing the loe in ingle point bonding of heath are higher in flat formation due to the middle cable that i ubjected to the more magnetic field. Maximum total loe in heathed cable are 0.76% and.8% higher than unheathed cable in trefoil and flat formation, repectively. Increaing of heath loe i higher in the cae of olid bonding heath, epecially in flat formation. Increaing in maximum 76 Iranian Journal of Electrical & Electronic Engineering, Vol., No., March 06

5 total loe are about % and 6% in olid bonding heathed cable than unheathed cable in trefoil and flat formation, repectively. In the cae of circulating current, the minimum heath lo i occurred in middle cable and maximum lo i in outer cable with phae lag conductor current. In the next tep of power loe analyi, the ditance between cable are increaed. Table 3 how the loe of unheathed cable with ditance a much a cable outer diameter. However, paced cable are not very uual in directly burial cable in trefoil formation, but it i ued in prefabricated underground tunnel or duct. In the cae of paced unheathed cable, conductor loe in both formation are reduced due to the decreaing of proximity effect between conductor. Spaced cable loe for heathed cable are preented in Table. Reitive loe in both conductor and heath are very cloe to each other in FEM and IEC formula. In paced cable, proximity effect i lower than adjacent cable and conductor approximately act independent to each other. Fig. 5 Sheath current denity in trefoil heathed cable. Table 3 Spaced unheathed cable loe. Lo(w/m) Trefoil Flat FEM IEC FEM IEC Pa Pb Pc Fig. Conductor current denity in trefoil heathed cable Table Spaced heathed cable loe. Lo(w/m) Trefoil Flat FEM IEC FEM IEC Pa Pb Pc Pa,e Pb,e Pc,e Pa,c Pb,c Pc,c Fig. 6 Sheath current denity in trefoil heathed cable. Raoulpoor et al: Electrical and Thermal Analyi of Single Conductor Power Cable 77

6 Lo(P.U) T e (Trefoil-Eddy lo) T c (Trefoil-Circulating lo) F e (Flat-Eddy lo) F c (Flat-Circulating lo) T e T c F e Adjacent cable Fig. 7 Per unit total loe. F c Unheathed cable Sheathed cable T e T F c e Spaced cable Thu even in flat formation two method have imilar reult. In paced cable, conductor loe in both flat and trefoil formation of heathed cable are decreaed. Alo eddy current loe are reduced in heath of each cable, a a reult of lower influence of magnetic field in phae conductor. On the other hand, heath circulating loe have coniderable increae and are even comparable to conductor loe. Alo in ome formation and ditance, it can be more than conductor lo. In ingle point bonding of heath total reitive loe ha 0.38% and 0.6% increment in heathed cable than unheathed cable. It i een that increaing in lo i maller than adjacent cable. Fig. 6 how heath current denity in olid bonding cable in flat formation. In olid bonding of heath circulating current loe are 38.9 % and 73.5 % higher than unheathed cable in trefoil and flat formation, repectively. The increment i larger than adjacent cable. For better comparion of increaing loe in heathed and unheathed cable the graphical view of loe in different cae are hown in Fig. 7. In thi figure, maximum lo of unheathed cable in each cae i conidered a bae value in per unit converion. T e, F e and T c, F c denote the eddy current and circulating current loe in trefoil and flat formation. A it i een in Fig. 7 total reitive lo i increaed in heathed cable. Thi increment i mall in the cae of ingle point bonding ytem compared to both end bonding ytem. Alo cable loe are increaed ignificantly in paced cable in both end bonding ytem due to high circulating current in lead heath. 5 Thermal Analyi 5. Finite Element Method In thi ection, thermal analyi of different cae are performed by FEM to compare temperature increaing F c in different cae with repect to the calculated loe uing FEM. Thermal equation are preented for ome cable contruction and intallation in IEC tandard. But FEM can conider the accurate mutual heating effect of cable and give more precie reult than IEC. The generated heat from cable loe can be tranferred through conduction, convection and radiation. In the cae of underground cable the main heat tranmiion method i by conduction. By conidering the production of loe and diipation of heat, in each intant, energy balanced equation i expreed a []: W W Wo W (8) where W,W, Wand Wo are the entering energy to the cable from other cable or olar radiation, the energy due to the internal loe of cable, tored energy in cable and the rate of energy diipation from cable, repectively. In underground cable, becaue of longer length than it diameter, and by conidering homogeneou oil the heat diipation equation can be expreed a: q (9) x x y y where q, and are heat tranfer rate, temperature and thermal reitivity, repectively. Alo boundary condition are tated a: T T T(x,y),. q 0, n (0) T. h(tt inf ) n where T inf, and h are ambient temperature, region boundary and convection heat coefficient, repectively. Equation (9) can be applied for element that contitute linear matrix equation. Thee equation alo are dependent to the boundary condition. Two type of boundary condition are elected in imulation. Iothermal boundary at ambient temperature i conidered for upper ide of cable that repreent the ground urface. Other three boundarie are thermal inulation and the ize of boundary i elected large enough to enure the phyical infinite boundary. Fig. 8 how mehed configuration of heathed adjacent flat cable in finite element imulation. Fig. 8 Mehed configuration of adjacent flat heathed cable. 78 Iranian Journal of Electrical & Electronic Engineering, Vol., No., March 06

7 5. Simulation reult Thermal imulation are performed by FEM with oil and urface ambient temperature equal to 0 o C and 30 o C, repectively. The cable burial depth i 0.8 m and thermal reitivity of oil i.5 (K.m/w). Dielectric loe in under tudying cae are negligible and can be ignored in thermal imulation. Table 5 how the maximum temperature of cable in different contruction of adjacent cable. Fig. 9 how thermal imulation of ingle point bonding of trefoil heathed cable. Maximum conductor temperature in trefoil formation of unheathed cable i lightly higher than ingle point bonding heathed cable. While in the ection 3 total calculated loe in heathed cable are lightly higher than unheathed cable. Thi i due to the preence of lead heath in the cable contruction. In reality the thermal reitance of lead heath i much maller than inulation material in cable. Therefore, compoition of thermal reitance in heathed cable i maller than the only inulation reitance in unheathed cable. It may be expreed that the conductor loe have more effect on conductor temperature. Alo the conductor loe in unheathed cable are more than heathed cable. For repone to thi challenge, another thermal analyi i performed on heathed cable by conidering the conductor loe equal to unheathed cable and heath loe a ingle point bonding heathed cable Table 5 Temperature ( Unheathed Cable o C ) of adjacent cable. Sheathed Cable Single Point Bonding Sheathed Cable Solid Bonding Trefoil Flat Fig. 9 Adjacent trefoil heathed cable. Fig. 0 Spaced flat heathed cable. Table 6 Temperature ( Unheathed Cable o C ) of paced cable. Sheathed Cable Single Point Bonding Sheathed Cable Solid Bonding Trefoil 3. 9 Flat In thi cae maximum cable conductor temperature are 6.3 o C and 6. o C in trefoil and flat formation, repectively. In thee imulation, temperature are again lower than unheathed cable. It hould be noted that the difference between temperature of unheathed cable and ingle point bonding heathed cable are low and can be ignored; anyway temperature in heathed cable i not higher a it i expected. There i imilar analyi for flat formation of unheathed and ingle point bonding heathed cable. In olid bonding heath the conductor temperature i higher than unheathed cable due to the high circulating lo. The temperature increment i higher in flat formation than trefoil formation a the loe in flat i higher than trefoil formation. It hould be noted that in all cae the conductor temperature doe not reach to 90 o C becaue the current i not the value of rated current of thee type of cable. Thermal FEM reult for paced cable are preented in Table 6. FEM imulation for paced olid bonding heathed cable in flat formation i howed in Fig. 0. Maximum temperature of trefoil formation in unheathed cable i higher than ingle point bonding heathed cable. Similar behavior exit for flat formation in unheathed and ingle point bonding heathed cable. Maximum temperature in thee cae are maller than the imilar cae of adjacent cable. Thi i due to two reaon. Firt i that ditance between cable reult in maller conductor and heath loe and econd, mutual heating effect between cable are decreaed and thu each cable approximately ha independent thermal field. But in the cae of olid bonding of heath temperature are more than Raoulpoor et al: Electrical and Thermal Analyi of Single Conductor Power Cable 79

8 unheathed cable. In pite of the increaing the ditance between cable the temperature i higher than adjacent cable, due to the high heath circulating loe. 6 Concluion In thi paper a new analyi i performed on unheathed and lead heathed underground power cable. Single point bonding and olid bonding grounding ytem of heath are conidered. Conductor and heath loe are computed with IEC formulation and FEM. Thermal analyi are performed to invetigation of lead heath effect on maximum cable temperature. Summary of notification baed on imulation reult are tated a bellow: IEC get precie reult for conductor loe of trefoil formation. It ha accurate but not exact reult for flat formation, where cable formation i aymmetric. Difference of IEC and FEM become larger in heath loe of flat formation than trefoil formation. Epecially in circulating current loe where IEC doe not conidered the proximity effect of heath. Calculated loe of heath uing IEC and FEM, have more agreement with increaing of cable ditance, due to the decreaing of proximity effect which i neglected in IEC. Cable temperature i decreaed by increaing of cable ditance in unheathed and ingle point bonding heathed cable. Thi i due to the decreaing of conductor and heath loe, and alo mutual heating effect of cable. In both end bonding heathed cable, temperature i increaed by increaing of cable ditance. Becaue circulating current are larger in cable with higher ditance. Loe are increaed in ingle point bonding of heathed cable than unheathed cable. But owing to the lower thermal reitance of lead heath, temperature are decreaed. Moreover, in olid bonding heath, the circulating current caue more loe and temperature than unheathed cable and ingle point bonding heathed cable. Reference [] Naval Facilitie Engineering Command, Electric power ditribution ytem operation, 00 Stovall Street Alexandria, Virginia , 990. [] G. J. Ander, Rating of electric power cable in unfavorable thermal environment, ISBN , Intitute of Electrical and Electronic Engineer, 00. [3] O. E. Gouda and A. A. Farag, Factor affecting the heath loe in ingle-core underground power cable with two-point bonding method, International Journal of Electrical and Computer Engineering (IJECE), Vol., No., pp. 7-6, 0. [] I. Sarajcev, M. Majtrovic and I. Medic, Calculation of loe in electric power cable a the bae for cable temperature analyi, Journal of Advanced Computational Method in Heat Tranfer, Vol., pp , 003. [5] P. Oclon, P. Ciek, D. Taler, M. Pilarczyk and T. Szwarc, Optimizing of the underground power cable bedding uing momentum-type particle warm optimization method, Energy, Vol. 9, No., pp , 05. [6] M. Shaban, M. A. Salam, S. P. Ang and W. Voon, Calculation of heath voltage of underground cable uing variou configuration, 5th Brunei International Conference on Engineering and Technology (BICET), pp. -6, 0. [7] F. Leon, M. L. M. Aenio and G. A. Cordero, Effect of conductor counter-tranpoition on the poitive-equence impedance and loe of crobonded cable, IEEE Tranaction on Power Delivery, Vol. 6, No. 3, pp , 0. [8] Y. Lin and Z. Xu, Cable heath lo reduction trategy reearch baed on the coupled line model, IEEE Tranaction on Power Delivery, Vol. 30, No. 5, pp , 05. [9] E. Kuffel and J. Poltz, Loe in crobonded and bonded at bothend high voltage cable, IEEE Tranaction on Power Apparatu and Sytem, Vol. PAS-00, No., 98. [0] L. Zhang,, X. Tian, S. A. Bogg and E. J. Bartolucci, Determination of total reitive lo in a multiple circuit, three-phae cable ytem, IEEE Tranaction on Power Delivery, Vol. 6, No. 3, pp , 0. [] M. Rachek and S. N. Larbi, Magnetic Eddy- Current and Thermal Coupled Model for the Finite-Element Behavior Analyi of Underground Power Cable, IEEE Tranaction on Magnetic, Vol., No., pp , 008. [] S. Critina and M. Feliziani, A finite element technique for multi conductor cable parameter calculation, IEEE Tranaction on Magnetic, Vol. 5, No., pp , 989. [3] S. K. Kim, S. Kim, J. G. Kim, M. Park, I. K. Yu, Y. H. Choi and H. Lee, Harmonic current baed lo characteritic analyi of HTS DC model cable uing calorimetric method, IEEE Tranaction on Applied Superconductivity, Vol., No. 3, 0. [] C. Demoulia, D. P. Labridi, P. S. Dokopoulo and K. Gouramani, Ampacity of low-voltage power cable under noninuoidal current, IEEE Tranaction on Power Delivery, Vol., No., pp , Iranian Journal of Electrical & Electronic Engineering, Vol., No., March 06

9 [5] O. E. Gouda, A. Z. Dein and G. M. Amer, Improving the Under-Ground Cable Ampacity by uing Artificial Backfill Material, Proceeding of the th International Middle Eat Power Sytem Conference, Cairo Univerity, Egypt, 00. [6] Y. Wang, R. Chen, J. Li, S. Grzybowki and T. Jiang Analyi of Influential Factor on the Underground Cable Ampacity, 0 Electrical Inulation Conference, Annapoli, Maryland, pp , 0. [7] P. Oclon, P. Ciek, M. Pilarczyk and D. Taler, Numerical imulation of heat diipation procee in underground power cable ytem ituated in thermal backfill and buried in a multilayered oil, Energy Converion and Management, Vol. 95, pp , 05. [8] IEC publication Calculation of the continuou current rating of cable (00% load factor), 98. [9] D. Labridi and P. Dokopoulo, Finite element computation of field, loe and force in a threephae ga cable with non-ymmetrical conductor arrangement, IEEE Tranaction on Power Delivery, Vol. 3, No., pp , 988. Maoumeh Raoulpoor wa born in Ghaem-Shahr, Iran, in 986. She received her B.Sc. degree from Babol Univerity in 008 and her M.Sc. degree from Shahrood Univerity in 0, both in electrical Engineering. Currently, he i a Ph.D. tudent in high voltage engineering in Babol Univerity. Her intereted reearch area are high-voltage engineering, power ytem protection and power ytem dynamic. Mohammad Mirzaie wa born in Ghaem-Shahr, Iran in 975. Obtained B.Sc. and M.Sc. Degree in Electrical Engineering from Univerity of Shahid Chamran, Ahvaz, Iran and Iran Univerity of Science and Technology, Tehran, Iran in 997 and 000 repectively and Ph.D. Degree in Electrical Engineering from the Iran Univerity of Science and Technology in 007. He worked a an Aitant Profeor in the electrical and computer engineering department of Babol Univerity of technology from 007. Hi reearch interet include life management of high voltage equipment, high voltage engineering, intelligence network for internal fault aement in equipment and tudying of inulation ytem in tranformer, cable, generator, breaker, inulator, electrical motor. Seyyed Mehdi Mirimani wa born in Babol, Iran. He received the B.Sc. degree from the Univerity of Mazandaran, Babol, in 007 and the M.Sc. and Ph.D. degree on the ubject of electrical machine from Iran Univerity of Science and Technology, Tehran, Iran, in 03. He i currently an Aitant Profeor of electrical machine in Babol (Nohirvani) Univerity of Technology, Iran. Hi reearch interet include the deign, modeling, control, and finiteelement analyi of electrical machine and other electromagnetic device. Raoulpoor et al: Electrical and Thermal Analyi of Single Conductor Power Cable 8