Investigation and Analysis of Inception Voltage and Field Distibution in Powe Cables with Intenal Cavities in Dielectic A. A. Hossam-Eldin Electical Eng. Depatment Faculty of Engineeing Alexandia Univesity, Alexandia, Egypt E-mail hossamudn@yahoo.com S. S. Dessouky, S. M. El-Mekkawy and R. A. Abd El-Aal Electical Eng. Depatment Faculty of Engineeing Suez Canal Univesity, Pot Said, Egypt E-mail makkawy_6@hotmail.com ABSTRACT Patial dischage (P.D. in mico cavities in the insulation of H.V. powe cables dastically affect the pefomance, the field distibution and hence the ating of these cables. It is well known that, P.D. deteioates powe cables and lead to its complete failue. This has advese effects on the eliability and maintainability of powe supply, which affects diectly the poduction of industial factoies. In this wok a study and investigation of the effect of patial dischages in cavities in the solid insulation of H.V. powe cables is caied out. The field distibution along that pat of the conducto which lies within the tiangle fomed by joining the conducto centes will give the closest epesentation of the cable, and hence the ating of these cables wee detemined by modeling and simulation of these P.D. Cables thee coe powe wee tested and investigated at diffeent voltages at low voltage, medium voltage and high voltage unde altenating voltage at oom tempeatue. The cavity shapes, spheical and cylindical, with diffeent sizes wee tied. The insulation thickness was vaied. The location of the mico cavity in the insulation was changed at diffeent angles. The position of maximum electic stess in cables was detemined. A developed simulation pogam using bounday element method was applied. The inception voltage was calculated and the applied voltage was changed as a function of the inception voltage. The dischage inception voltage was minimum at the conducto/insulation inteface due to the high stess at this egion. The esult showed that cylindical cavities ae moe sevee than spheical ones. The simulation esults ae in good ageement with the expeimental findings and the pactical expeience. This shows the effectiveness of this study as a non-destuctive method of cables evaluation. -INTRODUCTION Insulating systems contain some mico cavities o voids within the insulation o at boundaies between the dielectic and the conductos. In case of cables, cavities ae fomed by the diffeential expansion and contaction of the cable mateial unde cyclic loading conditions. The cavities being effectively pockets of low pessue electically weak and will ionize at quite low electic stesses. The ionization and occuence of patial dischages within the cavities would cause eosion and local deteioation of the insulation eventually leading to a complete failue of the cable. Thus knowledge of the inception voltage is impotant fo the pope design []. Methods of calculating the dischage inception voltage in voids fo single coe and fo thee-coe belted type cables have been poposed [2-4]. Fo the optimization of the insulation design fo thee-coe powe cables, it is fundamental to know the location and the magnitude of the maximum field stess as a function of the cable dimensions. The pesent pape descibes the application of the bounday element method [5] to accuately detemine the stess in theecoe cables. The electic field is detemined as a function of the location in the thee-coe cables. The maximum field in the cable which is used to calculate the voltage ating of the cable fo a dischage inception at voids ceated duing the manufactues of and/o opeation of the cable is calculated. The phase voltage in a thee-coe belted cable which is capable to initiate patial dischages anywhee in the cable is detemined. The voltage is calculated fo diffeent locations of the void and as a function of the void thickness and shape. 2- THREE-CORE BELTED CABLE Fig. ( shows the coss section of the thee-coe belted cable having the following paametes: d the diamete of each coe conducto, T the conducto electical insulation thickness, t the belt insulation thickness, S = (2T+d/ 3 the distance between the conducto and the cable cente, and R= S+d/2+T+t the inne adius of the metallic sheath. The insulation consists of thee main pats; conducto insulation, belt insulation and the filling mateial in the intestices between the coes. 3- SIMULATION TECHNIQUE In ode to calculate an electic field distibution, one has to solve Laplace s patial diffeential equation with bounday conditions pescibed ove the bounday. When complicated geometies ae encounteed, as in the case of HV engineeing applications, numeical techniques ae geneally the only viable appoach [5]. In this wok Bounday element method is used to calculate the electic field distibution and the maximum field stess within a cavity embedded in a dielectic mateial in the theecoe belted cable. The electic field distibutions within the dielectic ae studied as a function of applied voltage, cavity shape, (spheical and cylindical, with diffeent sizes, insulation thickness and location of the mico cavity in the insulation. The position of the maximum electic stess in
Metallic sheath cable was detemined. Thus, the method can be diectly elated to supeposition of chage contibutions to yield potential distibutions. Fig ( Thee coe cable A moe complex and fuitful genealization involves the use of stip chages, divide the cable coes and dielectic boundaies into individual stips ove each the chage density is appoximated as constant. Values of the stip chages e detemined by satisfying the bounday conditions at a selected numbe of contou points. Once the values of simulation chage ae known, the potential and field distibution anywhee in the egion can be computed easily. 4- BOUNDARY ELEMENT METHOD. The bounday element method does not ely upon fictitious chages; instead it seeks to calculate chages distibuted ove boundaies. Then, appoximating the eal chage distibution athe than assigning values to nonphysical ones. The electic potential due to a suface chage density is witten as in [6] * φ( = ρ ( (, Γ( s φ d ( 2παε Γ Whee ( : epesents potential at location : is a constant and equal to o 2 fo two o thee dimensional poblems espectively. ( ρ : is the suface chage density at location Γ : denotes the bounday between diffeent egions : denotes a field point and denotes a souce point * (, : is the fundamental solution of the potential poblem. Equation ( is the basic equation of the souce fomulation of the bounday element method. A system of bounday conditions is equied fo detemining the unknown chage density. Afte successive simplification [6], a set of linea equations to satisfy Diichlet bounday conditions on enegized conductos and flux continuity though dielectic boundaies ae obtained and expessed by: [ A].[ ρ ] = [ φ] (2 s 8 Belt Insulation. (t s A 3 2 33 5 24 2 B Whee: [A] is a known vecto potential-coefficient matix. ] is the unknown suface chage density vecto matix. 27 9 C Coe Insulation. ( T 6 3 Filling mateial ] is the potential vecto matix By solving this system of equations we can find the unknown values of chage density. Consequently, using this chage distibution, potential and electic field values can be calculated. 5- DISCHARGE INCEPTION VOLTAGE. Conside a gas filled cavity of spheical shape having a diamete within the solid insulation pesent at a location in degee anywhee within the tee-coe cable. The oigin is the cente of the cable. The conducto voltage V i which causes a dischage inside the cavity is to be detemined. Knowledge of this voltage is impotant fo a satisfactoy design, manufactue and a pope opeation of electic powe cables. The electic field E in solid dielectic just outside the gaseous cavity at a location is calculated by using the bounday element method. It has been shown that the electic field inside a spheical cavity within dielectic is given by [3] (E c = 3ε /( + 2ε ( E And fo a cylindical cavity ( E c = ε ( E Whee (E C is the electic field (in p.u inside the cavity at a location and (E is the electical field in (p.u in the dielectic at location. is the elative pemittivity of the solid dielectic used to insulate the cable. The deivation of Eqns. (3 and (4 is based on the assumption that the electic field stength of an ai cavity within a solid insulation mateial is appoximately the same as that between a pai of matel electodes of the same gap length and the linea dimension of the cavity [5]. The inception voltage fo a dischage in the cavity can be calculated as follows: [( V i ] = [(E g ]/(E c (5 Whee [(V i ] is the magnitude of the nomalized inception voltage, i.e., the voltage of the conducto whose insulation contains a cavity of thickness, and this voltage shall be sufficient to cause a dischage inside the cavity and [(E g ] is the magnitude of the electic stength of the entained gas inside the cavity having a thickness at pessue p. The inception voltage Vi is calculated fom Equ. (5 fo a given cavity of thickness and gas pessue p. The value of [(Eg ] p ae obtained fom Table I[7]. Fo completeness (E C is computed using Equ.(3 fo a spheical cavity and Equ.(4 fo a cylindical cavity. (E is calculated using Bounday element method. Table I: the maximum electical field E g of a cavity inside a solid insulato fo diffeent ai pessues and cavity thickness. ba. ba. ba (mm E g (mm E g (mm E g (kv/cm (kv/cm (kv/cm.5 7.2 3.9 5. 375.25 2. 35.2 23.36.2 2.5 4.5 65.4.. 35.7 5.2 75.2 23.2 3.5 55.5 4.23 2 45 3.5 2 4 2 7.5 2 2.2 6- RESULTS AND DISCUSSION Fo the pupose of calculations, the following paametes (3 (4 2
ae consideed: The voltages on the thee coes of the cable ae absolutely symmetical and sinusoidal. Fig. (2 Shows the vaiation of esultant stess E aound all thee conductos and the sheath coesponding to (wt= 9 and 5 espectively as a function of stess location. It is clea that, the maximum stess in dielectic is aound the conducto of highest potential, the field vaiation at the sufaces of othe conductos is about the same while the stess at the sheath is lowe. The nomal component of the electic field at the sheath suface pulsates accoding to the vaiation of the applied voltage at the conducto with time. Cond.(A,B,C and sheath at wt=9, T/d=.5.5.4 Cond. A Cond. B Cond. C Sheath.3.2..9.8.7.6.5.4.3.2. 3 6 9 2 5 8 2 24 27 3 33 36 Fig. (2-a Electic field aound conductos of coes A, B and C and sheath Fig. (2-a the instantaneous values of the phase voltages at wt = 9 on the thee conductos ae V A =, VB = -.5 and V C =-.5 p.u. Fo each conducto is measued fom its cente in counteclockwise diection. It is clea that, the field stess aound the conducto A which has a peak potential is of highe value than conductos C and B. when the stess location is nea conducto A, thee is a maximum stess fo conducto B and C at the points of touch with conducto A (i.e. = 2 fo conducto B and = 5 fo conducto C. The stess values at location = and = 36 fo conductos B and C ae of the same values. The sheath stess is pulsating and its maximum value occus at = 8 which is between the two maximum point of B and C. Fig. (2-b The instantaneous values of the phase voltages at wt = 5 on thee conductos ae V B =-, V A =.5 and V C =.5 p.u. It is clea that fo conducto A the maximum stess occus at = 3 and fo conducto C at = 9. It will be obseved that the field values at the sufaces of the conductos A and C ae about the same while at B is high. Geneally, the field stess aound the conducto which has a peak potential is highe than othe two conductos. The maximum stess fo the othe two conductos is at the points of touch with the peak potential conducto. As expected the stess distibution becomes moe and moe non unifom as the conductos ae bought neae each othe. Fig. (3 Shows the vaiation of middle insulation stess fo all thee conductos coesponding to wt= 9 and 5 espectively, as a function of stess location. The middle insulation stess fo a conducto which has a peak potential is lowe than the conducto suface stess and is highe than the sheath stess. The middle insulation stess fo othe conductos is nealy the same, and is maximum at the points of touch with the conducto having the peak potential. Fig. (3-a It is clea that, the insulation stess on conducto A which has peak potential is lowe than the conducto stess and highe than the sheath stess. The maximum insulation stess which occus at =2 fo conducto B and =5 fo conducto C ae the same with the insulation stess of conducto A..2.8.6.4.2 Mid.Ins. at wt =9 3 6 9 2 5 8 2 24 27 3 33 36.2 Mid.Ins. at wt=5.6.4 Cond.(A,B,C. and sheath at wt=5 T/d=.5 Sheath.8.6.4.2.8.6.4.2 3 6 9 2 5 8 2 24 27 3 33 36 Fig. (2-b Electic field aound conductos of coes A, B and C and sheath.2 3 6 9 2 5 8 2 24 27 3 33 36 Fig. (3-a, b Electic field at middle insulation of A, B and C The same esults can be obtained fom Fig. (3-b whee wt=5. Figs. (4 a, b illustate the vaiation of sheath stess with stess location at diffeent values of wt. namely, wt= 9, 5,. 3
It is obseved that the field distibution is moe non unifom and this is due to intefeence between fields fo thee sheath sufaces. Fo the points at which the conducto insulations touch each othe thee is a maximum field stess at sheath suface. These values ae highe than the field in sheath suface fo a conducto which has a peak potential..5 and VC=-.5. Fig. (5-c at wt =6, (V A =.866, V B = and V C =-.866. Because the potential on conductos A and C ae equal thee is a distotion and intefeence between the stess on the two Cond.(A,C at wt= (Va=, Vc=-.866 Oute Ins. at wt=9 Aound Cond.A Mid.Ins.A Oute Ins.A Aound.Cond.C Mid.Ins.C Oute Ins.C.4.2.9.8.7.6.5.4.3.2. 3 6 9 2 5 8 2 24 27 3 33 36 E lectic field ( V/cm/V.8.6.4.2 3 6 9 2 5 8 2 24 27 3 33 36 Fig. (5-a Electic flied (V/cm/V.9.8.7.6.5.4.3.2 Oute Ins. at wt=5 Cond.(A,C at wt=3 (Va=.5, Vc=- Aound Cond.A Mid.Ins.A Oute Ins.A Aound Cond.C Mid.Ins.C Oute Ins.C.4.2.8.6.4.2. 3 6 9 2 5 8 2 24 27 3 33 36 Fig. (4-a,b Electic field at oute insulation of A,B and C Fig. (5-a shows the vaiation of stess aound conducto, inside insulation and on the sheath fo conductos A and C at wt=. Thus the instantaneous values of the phase voltages at wt= (V A =, V B =.866 and V C = -.866. It is shown that fo conducto C the electical field is maximum value aound conducto and deceased inside the insulation and its minimum value is at the sheath. Fo conducto A, in the zone between = 2 and 24 thee is nealy minimum potential so, thee is a minimum field stess on it. The field stess in this zone is almost the same fo conducto A, inside insulation and at sheath. Fo the zone between = (-2 and = (24-36 whee the conducto A stess is nealy same as the two conductos B and C. The field stess is inceased in the diffeent cases. It is clea that, in conducto A the stess in the fist and end zones is opposite in conducto C while the field in sheath is lage than in the insulation aound the conductos. The same esults can be obtained when wt=2, (V A =.866, V B =-.866 and VC= Fig. (5-b at wt=3, (V A =.5, V B =.5 and V C =- It is illustated that the stess aound conducto C is of high value and deceases towad the insulation. Fo conducto A the stess aound conducto is highe than inside insulation and the sheath but this field is smalle than the stess fo conducto C. The same esults can be obtained when wt=9, (V A =, V B =- Electic field(v/cm/v 3 6 9 2 5 8 2 24 27 3 33 36 Fig. (5-b Cond.(A,C at wt=6 (Va=.866,Vc=-.866 Aound Cond.A Mid.Ins.A Oute Ins.A Aound Cond.C Mid.Ins.C Oute Ins.C.6.4.2.8.6.4.2 3 6 9 2 5 8 2 24 27 3 33 36 Fig. (5-c Fig.(5 vaiation of stess aound conducto inside insulation and at the sheath fo conductos A and C. conductos A and C. The stess aound conducto is of maximum value and deceases inside insulation and on the sheath. The same esults can be obtained when wt=5 (V A =.5, V B =- and VC=.5. 4
INCEPTION VOLTAGE Fig. (6-a, b, c Shows the elation between the electical field distibution aound conductos A, B and C at wt = 3, 9,5 espectively. With diffeent cavities namely, spheical and cylindical (vetical and hoizontal which ae located at =33,2 and 9 espectively as a function of field location. It is clea fom the figues that, the maximum value of stess occus at cavity in all cases. It is also clea that in the case of hoizontal cavity the stess has the highest value and in case of insulation without cavity it is of the lowest value.the field distibution in the est of the insulation is almost constant and equal to the designed value..8.6.4.2.8.6.4 Cond. A at wt=3 (Vc=-, with cavity at (=33 Without cavity Spheical cavity Cylind. Cavity (hoizontal Cylind. Cavity (vetical Fig.(7 show the influence of the shape, size and location of the cavity as well as the gas pessue inside the cavity, on the inception voltage of a belted powe cable. It is clea that fo Inception voltage (P.U 7 6 5 4 3 2 AoundCond. A and sheath, at wt=9 and =33, ba Cond.(spheical cavity Cond.(cylindical cavity.5..2.5..2.5 2 t (mm sheath (spheical cavity sheath (cylindical cavity Fig (7 Inception voltage fo a conducto A and sheath at diffeent shape cavity.2 3 6 9 2 5 8 2 24 27 3 33 36 Stess location(degees 8 7 Aound Cond. A at wt=9,with Cylind. cavity at =33 p= ba p=.ba p=.ba Cond.B at wt=9(va=, with cavity at (=2 without cavity spheical cavity Cylind. Cavity (hoizontal Cylind. Cavity (vetical 2.5 2.5.5 Inception voltage (PU 6 5 4 3 2..2.5..2.5 2 t (mm Fig.(8 Inception voltage fo a conducto A at diffeent gas pessue inside the cavity 3 6 9 2 5 8 2 24 27 3 33 36 2.5.5.5 Cond.C at wt=5,(vb=- with cavity at(=9 without cavity spheical cavity Cylind. Cavity (hoizontal Cylind. Cavity (vetical 2 3 6 9 2 5 8 2 24 27 3 33 36 Fig. (6-a, b, c Electic field distibution aound Cond. A, B, C with and without cavity a constant pessue at ba, V i deceases as t is inceased. Due to the emnant chage on the walls of the cavity. Moeove, spheical cavities have highe inception voltage when compaed to the cylindical ones. Fo given cable and cavity paametes, V i is lowest when the cavity is located at the conducto suface whee E max has the highest value. Howeve, the cavities at the sheath ae significantly lage than those in the conducto insulation. Fig.(8 Shows the elation between inception voltage and thickness of cavity fo conducto A at t = 9 at diffeent gas pessue inside the cavity. It is clea that, with inceasing the thickness of cavity the inception voltage deceases and patial dischage inceased. Theefoe voltage ating of belted cables is decided by dischage inception in cavities pesent in the fille mateial o at the sheath inteio. 7- CONCULSIONS Fo an accuate stess analysis of thee-coe belted type cables bounday element method can be used. The field stess aound the conducto which has a peak potential is highe than the othe two conductos. The maximum stess in the middle of insulation fo the othe conductos occus at the touch with the conducto that has the peak potential and equal to that at the middle of insulation fo a conducto which has the peak potential. 5
Compaed to spheical voids, cylindical shaped voids ae much moe vunable to patial dischages. The inception voltage is a function of the location of the void in the insulation of the cable. Inceasing the thickness of the cylindical cavity the inception voltage deceases and patial dischages incease. 8- REFERENCES : []-A.A Hossam Eladin " Behavio of solid dielectics at low tempeatue" Int. Conf. on H.V Insulation, Bighton, G.B, 974,PP.5-8 [2]- D. Pommwenke, R. Jobava and R. Heinich "Numeical simulation of P.D. popagation in cable joints using the finite diffeence time domain method" IEEE Electical Insul. Magazine Vol. 8, No.6, PP 6-, 22. [3]- Steven Boggs and John Densley "Fundamentals of P.D. in the context of field cable testing" IEEE Electical Insul. Magazine Vol. 6, No.5, PP 3-8, 2. [4]- G.C. Montanai, A. Cavallini and F. Puletti "A new appoach to P.D. testing of HV cable system" IEEE Electical Insul. Magazine Vol. 22, No., PP 4-23, 26. [5]- A.A. Hossam-Eldin, S.S. Dossouky, S.M. El-Mekkawy and R.A.Abd El-Aal "Analysis and simulation of field distibution in mico cavities in solid insulating mateials" CEIDP 27, Oct, Vancouve, Canada, pp. 792-796 [6]- Miko Sposojevic and Pete L.Levin: On adaptive efinement fo bounday intenal methods in electostatics", IEEE Tans. EI, Vol., No.6, pp.963-973, 994. [7]-- A.A. Hossam-Eldin, S.S. Dossouky, S.M. El-Mekkawy and R.A.Abd El-Aal "Study and Analysis of Field Enhancement and H.V Rating of Powe Cables Containing Mico Cavities" CEIDP 27, Oct, Vancouve, Canada, pp. 797-8 6