Overvoltage propagation from transmission line into transformer winding

POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 13 |NUMBER: 5 |2015 |DECEMBER O e ol age P opaga ion om T ansmission Line in o T ans o me Winding Vacla KOTLAN, Zdenka BENESOVA Depa men o Theo y o Elec ical Enginee ing, Facul y o Elec ical Enginee ing, Uni e si y o Wes Bohemia in Pilsen, Uni e zi ni 26, 306 14 Pilsen, Czech Republic k[email p o ec ed], b[email p o ec ed] DOI: 10.15598/aeee. 13i5.1421 Abs ac . The pape deals wi h e y as ansien phe- nomena in a sys em consis ing o wo pa s: a cable line and a ans o me winding. In his case an ade- qua e model should be conside ed as a ci cui wi h dis- ibu ed pa ame e s. I s desc ip ion is gi en by a sys- em o pa ial di e en ial equa ions o hype bolic ype. Ou app oach is based on a nume ical solu ion in he ime domain and he me hod FDTD has been used. I allows ob aining esul s in a o m o ime-space ol age and cu en wa e dis ibu ion along he cable line and he ans o me winding. This dis ibu ion is depend- ing on many ac o s some o hem we e s udied in his pape . Keywo ds O e ol age on ansmission line, ansien s in ans o me winding. 1. In oduc ion I is a common p ac ice o connec a ans o me in a subs a ion o he incoming line h ough a cable. A su ge o e ol age wa e induced by swi ching-on and swi ching-o p ocesses a els no only along he ca- ble bu i p opaga es in o he ans o me winding. These p ocesses can cause ans o me ailu es and can be e y dange ous o i s isola ion sys em. Mo eo e , he shape o he a elling wa e is s ongly depending on pa ame e s o bo h pa s. Due o di e en su ge impedances o bo h, he cable and he ans o me winding, e lec ions appea a he ans o me wind- ing inpu . Because o hese e lec ions he ol age o cu en peak alue can each highe alues han i was conside ed in he design o he isola ion and p o ec ion sys ems. The o he ac o s which ha e a simila impac on he su ge wa e shape a e he manne o ans o me winding ou pu and he cable leng h. Many au ho s ha e been in e es ed in he analysis o e y as ansien s in a ans o me winding and hey used a ious me hods. Some o hem u ilized a simula- ion in EMTP o ATP so wa e [1], [2]. O he au ho s used ansmission line model sol ed in he equency domain [3], [4]. In [5] he nume ical analysis based on FDTD me hod in he ime domain was p esen ed. Ve y impo an ole in ansien s analysis play he pa- ame e s o winding, hose p oblems we e discussed in [4], [6], [7]. Simula ion o a ious swi ching condi ions has shown ha se e e in e nal o e ol age can a ise be ween adjacen coils o he high ol age windings, while he e minal ol age o he ans o me emains below he gua an eed basic insula ion le el [7]. In such cases su ge a es e canno p o ide a su icien p o ec- ion since high equency oscilla ions may cause pa ial winding esonance. All au ho s o hese pape s anal- ysed only ansien s in a ans o me winding. Acco ding o p ac ical expe iences he dis ibu ion o ol age and cu en wa e in a ans o me winding depends no only on ans o me pa ame e s bu also on he shape o a a elling su ge wa e which is p op- aga ing om he ansmission line connec ed o he ans o me . In his case is also necessa y o s udy an in luence o line pa ame e s. Fo such a complex analy- sis i is impo an o conside he whole sys em consis - ing o a ansmission line (cable-line) and a ans o me winding. In his pape an algo i hm o a complex analysis is p esen ed. Ou app oach published in [8] is based on modelling o he sys em consis ing o a ansmis- sion line and a ans o me winding as a ci cui wi h dis ibu ed pa ame e s. A gene al basic line elemen has been in oduced i allows o o mula e one com- mon ma hema ical model o bo h pa s. The ob ained equa ions can be e y simply modi ied o he line and c 2015 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 478 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 13 |NUMBER: 5 |2015 |DECEMBER he ans o me winding. This app oach allows a o - mula ion o a common algo i hm o nume ical compu- a ion. 1.1. Ma hema ical Model A gene al basic elemen espec ing a ansmission line elemen and a ans o me winding elemen is depic ed in he Fig. 1, all pa ame e s a e pe uni leng h. iL(x, ) R(x) xd R2(x) xdK(x)/ xd L(x) xd C(x) xdG(x) xd u(x, ) U(x, )+( ) xd∂u(x, )/ ∂ dx x Fig. 1: Basic elemen a dis ance x om he line beginning. In he p oposal ci cui elemen induc ance L(x)in- ol es sel -induc ance and in he case o a ans o me winding also mu ual induc ances u n o u n. Capaci ance K(x) espec s u n o u n capaci ances and i is in ol ed only in he ans o me winding pa . Capaci ance C(x) espec s a capaci ance o he ea h. Resis ance R(x)co esponds o Joule’s losses and esis- ance R2(x)in e up s a edundan capaci ance loop. The elemen on he Fig. 1 can be desc ibed wi h ollowing equa ions: −∂u ∂x =L(x)∂iL ∂ +R(x)iL,(1) −∂iL ∂x =C(x)∂u ∂ +K(x)∂2uK ∂x∂ +G(x)u, (2) −uK=∂u ∂x +R2(x)K(x)∂uK ∂ .(3) The Eq. (1), Eq. (2) and Eq. (3) o e come o he known ansmission line equa ions in he case ha R2→ ∞ and K=0. To ind he solu ion o hese pa ial di e en ial equa ions he knowledge o ini ial and bounda y condi ions is needed. The compu a ion s a s om he ze o ini ial condi ion, bounda y condi- ions desc ibe he ela ionship a he inpu o he line and he way o ans o me winding end. 1.2. Algo i hm o Nume ical Solu ion To de i e a sys em o di e ence equa ions o he pa - ial di e en ial equa ions Eq. (1), Eq. (2) and Eq. (3) he s able implici Wend o ’s o mula [9] was u ilized. The i s o de de i a i es ha e been eplaced by he ollowing di e ences: ∂ (x, ) ∂ k,l =1 2 l k− l−1 k ∆ + l k+1 − l−1 k+1 ∆ !,(4) ∂ (x, ) ∂ k,l =1 2 l k− l k+1 ∆ + l−1 k− l−1 k+1 ∆ !, k= 1,2, ..., N. (5) A di e ence scheme o he second o de de i a i e in Eq. (2) was e alua ed in he o m: ∂ 2(x, ) ∂x∂  l k ∼ = ∂ (x, ) ∂  l k+1 −∂ (x, ) ∂  l k ∆x= =1 ∆x l k+1 − l−1 k+1 ∆ − l k− l−1 k ∆ !. (6) Supposing ha he leng h o he cable line and he ans o me winding is di ided in o Nleng h ele- men s and applying hese di e ence app oxima ions o Eq. (1), Eq. (2) and Eq. (3) we ecei e a sys em o algeb aic equa ions o nodal alues o cu en s iLk in induc ance L, ol ages ukac oss capaci ance Cand ol ages uKk ac oss capaci ance Ka he ime l- h le el. These disc e e nodal alues a e a anged in he ec o (l)= [{iLk},{uk},{uKk}]. This sys em o al- geb aic equa ions is han supplemen ed by bounda y condi ions a he inpu and ou pu o he sys em ac- co ding o Fig. 2. I esul s in o 3N+ 3 equa ions in a ma ix o m: A· (l)=B· (l−1) +D.(7) Elemen s o ma ix Aand Bdepend on pa ame e s o he cable and he ans o me winding, elemen s o ma ix D espec a ol age sou ce. Ma ix Eq. (7) enables o e alua e unknown disc e e alues o ol ages and cu en s a l- h ime le el om he known alues a p e ious (l-1)- h le el, he compu a ions we e ca ied ou in MATLAB. 2. Illus a i e Examples The p oposal algo i hm has been used o he anal- ysis o e y as ansien phenomena in one phase 1 MVA ans o me connec ed o a 22 kV cable line. The unloaded HV ans o me winding was conside ed because i is he wo s case wi h ega d o an o e - ol age peak alue. The in luence o some impo an ac o s was s udied, he esul s ob ained o a ious ca- ble leng h and a ious ol age wa e shape a e discussed in he nex pa s. c 2015 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 479 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 13 |NUMBER: 5 |2015 |DECEMBER 2.1. O e ol age Induced by S ep Vol age Su ge Wa e A i s he ol age sou ce p oducing a s ep ol age o peak alue Un= 22 kV wi h a a ious slope was con- nec ed o he sys em on he Fig. 2. The e alua ion was ca ied ou o cable pa ame e s: R= 0.35 mΩ·m−1,L = 0.529 µH·m−1, C = 218 pF·m−1, he a ious cable leng h lC= 0, 100, 200, 300 and 400 m was supposed. ansmission line ans o me winding RLCG,,, RLCG,,,, K2 u 0() + lw lc Fig. 2: Sys em consis ing o line and ans o me winding sup- plied om ol age sou ce. The ime space dis ibu ion o ol age and cu en su ge wa e is depic ed on Fig. 3 and Fig. 4. The ca- ble line and he ans o me winding ha e di e en su ge impedances o his eason he e lec ions a he ans o me inpu cause he highe magni ude o ol - age wa e p opaga ing in o winding and opposi e he cu en wa e in he ans o me winding eaches lowe magni ude. The e y high alues o cu en wa e a he line inpu a e caused by a small impedance o he ol age sou ce (nea o sho -ci cui ed end). Fig. 3: Time-space ol age dis ibu ion, s ep ol age sou ce. On he Fig. 5 is shown he dependence o he ou - pu ol age in % uni on he slope o sou ce ol age ise and on he cable leng h. Vol age a winding inpu inc eases due o su ge wa e p opaga ion h ough cable o a g ea e a e o ise. I esul s in e y high peak alue a winding ou pu Uou > 3.2 Un. The ime ol age dis ibu ion a he inpu and ou pu ans o me winding (lC= 400 m, slope = 10 kV·µs−1) is depic ed on he Fig. 6. I is seen ha no only he high ol age peak alue bu also high equency oscilla ions depending on he slope alue ap- pea . Fo compa ison he ime ol age dis ibu ion a he ans o me inpu o a smalle pa ame e s (lC= Fig. 4: Time-space cu en dis ibu ion, s ep ol age sou ce. 1 2 3 4 5 6 7 8 9 10 200 220 240 260 280 300 320 340 360 380 Slope [kV/µs] Umax/Un [%] Maximal ol age on he winding ou pu s ep ol age lc=0m lc=100m lc=200m lc=300m lc=400m Fig. 5: Dependence o maximal ol age peak alue Uou on ca- ble leng h and s ep ol age slope. Fig. 6: Time ol age dis ibu ion o ans o me winding inpu and ou pu , s ep ol age sou ce: slope = 10 kV·µs−1, lC= 400 m. 100 m, slope = 1 kV·µs−1) is shown on he Fig. 7. The oscilla ions p opaga ing om he cable line a e much c 2015 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 480 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 13 |NUMBER: 5 |2015 |DECEMBER Fig. 7: Time ol age dis ibu ion a ans o me winding inpu o s ep ol age sou ce: slope = 1 kV·µs−1, cable leng h lC= 100 m. lowe and sho e , he peak alue is nea o Un= 22 kV. In his case he impac o wa e a elling along he ca- ble is insigni ican . F om ob ained esul s ollows ha he o e ol age in he ans o me winding can each dange ous peak alue o a high a e o ol age ise and a longe cable leng h. This in luence should be aken in o accoun in a p o ec ion sys em design. 2.2. O e ol age Induced by Vol age Su ge Wa e The p opaga ion o he su ge wa e 1.2/50 µs wi h peak alue Un= 22 kV along he cable in o he ans o me winding has been s udied in his pa . A i s he su ge ol age wa e was applied di ec ly a he ans- o me inpu . Secondly, he same su ge wa e p opaga - ing h ough he cable o he leng h 100 m and 400 m was in es iga ed. The pa ame e s a e he same as in he p e ious example. The ol age ime dis ibu ion a he ans o me winding inpu is depic ed on he Fig. 8. I is seen ha due o p opaga ion o ol age su ge wa e along he cable high equency oscilla ions occu and he peak alue is nea ly wice highe han Un. I is caused by e lec ions a he connec ion poin o bo h pa s. The ol age ime dis ibu ion a he ans o me winding ou pu is depic ed on he Fig. 9. Tab. 1: Vol ages on he inpu and ou pu o a ious cable leng hs. cable line Uin [kV] Uou [kV] 0 21.993 53.050 100 37.101 78.419 400 37.483 76.519 The e is seen how long needs he wa e o each wind- ing ou pu and oscilla ions caused by e lec ions a he winding inpu and ou pu . Compa ing he ime ol age dis ibu ion on he Fig. 8 and Fig. 9 we ind ha i is s ongly depend- ing on he cable leng h. No only he ol age peak 0 1 2 3 4 5 6 7 8 9 x 10−4 0 0.5 1 1.5 2 2.5x 104 [s] uin [V] lc = 0 m 0 1 2 3 4 5 6 7 8 9 x 10−4 −2 −1 0 1 2 3 4x 104 [s] uin [V] lc = 100 m 0 1 2 3 4 5 6 7 8 9 x 10−4 −3 −2 −1 0 1 2 3 4x 104 [s] uin [V] lc = 400 m Fig. 8: Time ol age dis ibu ion a ans o me winding inpu o su ge ol age wa e and cable leng h lC∈(0, 100, 400) m. alue bu also he equency o oscilla ions di e s o a ious cable leng hs. The e y high peak alues a e seen in he ollowing Tab. 1. c 2015 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 481 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 13 |NUMBER: 5 |2015 |DECEMBER 0 1 2 3 4 5 6 7 8 9 x 10−4 −6 −4 −2 0 2 4 6x 104 [s] uou [V] lc = 0 m 0 1 2 3 4 5 6 7 8 9 x 10−4 −8 −6 −4 −2 0 2 4 6 8 10x 104 [s] uou [V] lc = 100 m 0 1 2 3 4 5 6 7 8 9 x 10−4 −6 −4 −2 0 2 4 6 8x 104 [s] uou [V] lc = 400 m Fig. 9: Time ol age dis ibu ion a ans o me winding ou - pu o su ge ol age wa e 1.2/50 µs and leng h lC∈ (0, 100, 400) m. 3. Conclusion An e icien algo i hm o a nume ical analysis o e y as ansien s in he ans o me winding connec ed o he ansmission line was in oduced. I esul s in ime-space ol age and cu en su ge wa e dis ibu ion and allows assessing o dange ous swi ching condi ions in powe sys ems. The in luence o he shape su ge wa e, i s slope and he line leng h was s udied. I was ound ha besides he high o e ol age peak alue also oscilla ions wi h e y high equency can appea . These ac s a e e y dange ous o he isola ion sys em and can cause damage o he ans o me winding. The p oposed algo i hm p o ides a deepe iew in o e y as ansien phenomena and can be e y help ul o a co ec design o he p o ec ing and isola ion sys em o ans o me . Re e ences [1] POPOV, M. and E. ACHA. O e ol age due o swi ching o an unloaded ans o me wi h a akuum b eake . IEEE T ansac ions on Powe Deli e y. 1999, ol. 14, iss. 4, pp. 1317–1326. ISSN 0885-8977. DOI: 10.1109/61.796224. [2] MARTI, J. R. and L. R. LINARES. Real- ime EMTP-based ansien s simula ion. IEEE T ansac ions on Powe Sys ems. 1994, ol. 9, iss. 3, pp. 1309–1317. ISSN 0885-8950. DOI: 10.1109/59.336135. [3] POPOV, M., L. VAN DER SLUIS, R. P. P. SMEETS and J. L. ROLDAN. Analysis o Ve y Fas T ansien s in Laye -Type T ans o me Wind- ings. IEEE T ansac ions on Powe Deli e y. 2007, ol. 22, iss. 1, pp. 238–247. ISSN 0885-8977. DOI: 10.1109/TPWRD.2006.881605. [4] SHIBUYA, Y. and S. FUJITA. High equency model and ansien esponse o ans o me windings. In: T ansmission and Dis ibu ion Con e ence and Exhibi ion 2002. Yokohama: IEEE, 2002, pp. 1839–1844. ISBN 0-7803-7525-4. DOI: 10.1109/TDC.2002.1177736. [5] PREDOTA, A. and Z. BENESOVA. Modelling o T ansien s in T ans o me Winding. P zeglad Elek o echniczny. 2010, ol. 86, no. 1, pp. 14–16. ISSN 0033-2097. [6] HOSSEINI, S. M. H., M. VAKILIAN and G. B. GHAREHPETIAN. Compa ison o T ans o me De ailed Models o Fas and Ve y Fas T ansien S udies. IEEE T ansac ions on Powe Deli e y. 2008, ol. 23, iss. 2, pp. 733–741. ISSN 0885-8977. DOI: 10.1109/TPWRD.2008.915795. [7] SOYSAL, O. A. Vol age s esses in a dis ibu ion ans o me unde nonideal swi ching condi ions. In: Powe Enginee ing Socie y 1999 Win e Mee - ing. New Yo k: IEEE, 1999, pp. 1031–1035. ISBN 0-7803-4893-1. DOI: 10.1109/PESW.1999.747339. c 2015 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 482 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 13 |NUMBER: 5 |2015 |DECEMBER [8] BENESOVA, Z. and V. KOTLAN. New app oach o su ge phenomena analysis in ans o me wind- ing. In: IEEE In e na ional Powe Modula o and High Vol age Con e ence (IPMHVC). San a Fe: IEEE, 2014, pp. 263–266. ISBN 978-1-4673-7323- 4. DOI: 10.1109/IPMHVC.2014.7287259. [9] BENESOVA, Z. and V. KOTLAN. P opaga ion o Su ge Wa es on In e connec ed T ansmission Lines Induced by Ligh ning S oke. Ac a Technica CSAV. 2006, ol. 51, iss. 3, pp. 301–316. ISSN 0001-7043. Abou Au ho s Vacla KOTLAN (was bo n in Pilsen in he Czech Republic (1947). She g adua ed om Uni e si y o Wes Bohemia in Pilsen, Facul y o Elec ical Enginee ing in 1970; in 1985 she ecei ed he CSc. deg ee Ph.D. She has wo ked as an Associa e P o esso a Uni e si y o Wes Bohemia in Pilsen since 1994 and as a P o esso since 2002. He esea ch in e es conce ns on nume ical me hods o elec omagne ic ield analysis and on heo e ical p oblems o powe elec ical ene gy sys ems ( ansmission line pa am- e e s, nume ical me hods o analysis o ansien phenomena on ansmission lines, ans o me winding and EMC). She published mo e han 90 pape s and con ibu ions in a ious scien i ic and con e ence p oceedings. Zdenka BENESOVA (1979) g adua ed om he Facul y o Elec ical Enginee ing (Uni e si y o Wes Bohemia Pilsen, Czech Republic) in 2003. In 2008 he ecei ed his Ph.D. deg ee in he ield o Elec ical Powe Enginee ing. His esea ch in e es s a e aimed a heo e ical p oblems o elec ical powe sys ems ( ansmission line pa ame e s, nume ical me hods o analysis o ansien phenomena on ans- mission lines) and in he las yea s he also deal wi h nume ical solu ion o elec omagne ic and coupled ields. He published abou 80 pape s in scien i ic jou nals and con e ence p oceedings. c 2015 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 483