Electri c Machines and Control Vol. 21 No. 9 Sep :,, RC, ElecNet ± 400 kv 78%, 36 :

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1 Electri c Machines and Control Vol. 1 No. 9 Sep :,, RC, ElecNet ± 400 kv 78%, 36 : ; ; ; ; DOI: /j. emc TM 401 A X Analysis of linear and nonlinear electric field of HVDC convert transformer oil-board insulation LIU Wen-li 1 BAI Shi-guang LI Yi-chun 3 LI Jia-xin 4 1. School of Electrical and Electronic Engineering Harbin University of Science and Technology Harbin China. Datang Northeast Electric Power Test & Research Institute Changchun China 3. China State Grid Eastern Inner Mongolia Electric Power Company Limited Material Branch Company 4. China State Grid Eastern Inner Mongolia Electric Power Company Limited Tongliao Power Supply Company Abstract Converter transformer oil-board insulating material's conductivity changes nonlinearly with electric field intensity and temperature. This nonlinear change rule is data-fitted in order to study the influences of material's nonlinearity to the distribution of converter transformer polarity reversal electric field. Calculation and analysis were carried out using RC equivalent circuit. The upper part of line and valve side windings electric field of one ± 400 kv converter transformer were simulated by using the finite element software ElecNet. The results show that while the polarity reversal finishes the maximum field strength of nonlinear material is of 78% compared with linear material. While at steady state the field strength in the nonlinear oil is 36 times of linear oil. The conductivity change caused by electric field would homogenize the the electric field gradient caused by the temperature gradient. Finally a few im : ( ) : ( 1956 ),,,, ; ( 1991 ),,, ; ( 1990 ),,, ; ( 1990 ),,, :

2 9 81 provement measures are offered according to calculation and simulation results. Keywords converter transformer electric field distribution polarity reversal oil-board insulation nonlinear material RC 1 1 RC Takashi E Rongsheng L 6-7 LI Jinbiao ANSYS Takashi E Fig. 1 Oil-board insulation structure and its equivalent circuit 50% C - N RC Matlab 4 Runge-Kutta Fig. Polarity reversal voltage circuit t = t ElecNet N - R 0 t 0 "! RC C U 1 t 0 = - U C C m t = 0

3 8 1 U 1 0 = R 1 R 1 + R - U m R ( 1 R 1 + R ) U 1 t = - U mr 1 C - U R 1 + R m - C 1 + C τ = R 1R C 1 + C R 1 + R e -t-t 0 τ 0 < t < ΔT KI50X C 1 du 1 t + U 1 t R 1 du t = C + U t 1 U 1 t + U t = U t U t = U m ΔT t - U m 1 C 1 + C du 1 t + R 1 + R U R 1 R 1 t = C du t + U t R 1 U 1 t = U mr 1 t R 1 + R ΔT R Table 1 C - τ ( ) + ΔT K 1 exp - t τ + K R U 1 0 = - U mr 1 + R R 1 K 1 = - U mr 1 R C - τ exp K R 1 + R ΔT K 1 - τ { T U 1 t = - U mr 1 + U mr 1 t R 1 + R R 1 + R ΔT + R C Δ [ 1 - exp - t ] } τ t > ΔT U 1 t = ( ) R 1U m + R 1 + R U 1 ΔT - R 1U m + R R 1 e -t-δt τ 3 U 1 t γ d 1 / γ d 1 #γ 1 d γ 1 > > γ γ 1 d U 1 t U 1 t t = ΔT U 1 ΔT = U mr 1 R 1 + R 1 + R C - τ { ΔT [ ] } 1 - exp - ΔT τ ΔT τ τ kv /. 5 mm 5 ppm % KI50X kv /mm Two materials' conductivity under different temperature at 6 kv /mm / K150X / S /m / S /m Table 65 KI50X Oil conductivity under different electric strength at 65 / kv /mm /10-17 S /m KI50X R C - τ = R R C - R 1 C 1 R 1 + R 50 kv /mm R C > > R 1 C 1 U 1 t 1 KI50X 1 γ = e 0. 07T 0. 8E +1 e S /m γ = e T S /m T E R 1 R R 1 R

9 83 mm 1 Matlab 4 Runge-Kutta E 1 t 4 5 b 6 b 0 < t < 60 s 5 1 U 1 t U 1 t 75 0 kv /. 5 mm 75 3 7 3 Fig.

4 9 83 mm 1 Matlab 4 Runge-Kutta E 1 t 4 5 b 6 b 0 < t < 60 s 5 1 U 1 t U 1 t 75 0 kv /. 5 mm Fig. 3 Curved surfaces of oil conductivity changing with electric field intensity and temperature circuit 1.. $ $ 1 ( ) ε 0 ε 1 + ε 0ε d 1 d ( 1 du 1 t + γ + γ d d ) U 1 t = ε 0 ε du t + γ U t 3 d d d 1 /d d 1 /d 1 d 1 /d = 1 3 ε 0 ε 1 + ε 0 ε du 1 t + γ + γ U 1 t = ε 0 ε du t + γ U t 1 ε 0 = F /m ε 1 =. ε = 4. 4 d 1 = d = m U m = 10 5 V ΔT = 60 s Matlab 0 ~ 105 E 1 t 0 < t < ~ 6 4 E 1 0 E E Fig. 4 5 Fig. 5 E 1 0 E ~ kv /mm 65 Fig. 6 5 a 6 a 0 < t < 60 s E 1 t 0. 3 kv / 4 0 /60 /6 000 s Curve of electric field intensity changing with temperature in oil at 0 /60 /6 000 s 0 Curve of electric field intensity and voltage changing with time in nonlinear oil at Curve of electric field intensity and voltage changing with time in nonlinear oil at 105

5 Table 3 Comparing of electric field strength between linear and nonlinear oil at 75 % E / kv /mm E 1 0 E 1 60 E % = E! ε 0 ε J 10 = E 10 γ 10 7 Fig Curve of electric field intensity and voltage changing with time in linear oil at 75 τ ' = σ J 10 = E!ε 0 ε E 10 γ 10 = R 10 R! C 1 + C R 1! + R! R! U d 1 ε 0 ε R 1! + R! = C U d γ 10 C 1 + C τ ' = R 1 R C 1 + C / R 1 + R = τ 7 a 0 < t < 60 s R! > > R 1! τ ' R 10 E 1 t 0. kv /mm s 7 b C 1 #C τ ' γ 1 1 /τ ' U 1 t E 1 t 3 E E % t = s 18. 3% s 1. 3 "! < t < Q = U 1 t - U t [ -! R 1 ] = R C - R 1 C 1 ± 400 kv - U R R 1 + R m ElecNet R C > > R 1 C 1 GB /T U pr = 1. 5 N U dm #0. 35U vm = kv

6 9 85 U vm = kv 5 10 c U dm = 04 kv s 1 6 N = 5 10 d s 7 8 A B 5 C D E 10 e s 8 ab 5 10 f s Table 4 Temperature parameters of convert transformer model / / 8 / / Fig. 8 Model of upper part of Line-valve side winding of convert transformer 1 75 /75 0 /0 60 /75 0 /3 A B ab C D /75 3 / /75 5 / /70 3 / /80 3 /3 7 0 /0 0 /0 8 0 /0 0 / /75 0 / /75 3 /3 Fig. 9 9 Applied voltage on model 0 mm τ 5% s s s Newton-Raphson 0 kv /mm kv /mm 0. 1% s a 0 s ~ 4. 1 kv /mm ~ kv /mm 10 b s kv /mm 76% kv /mm Matlab s 0. 0 kv /mm

86 1 Table 5 5 5 400 /5 460 s Maximum electric field strength at 5 400 /5 460 s 5 400 s 5 460 s / kv /mm / kv /mm 1 17. 17 1. 03 15. 55 11. 74 3 15. 7 11. 47 4 14. 08 11. 1 5 14. 94 11. 63 6 15.

7 86 1 Table /5 460 s Maximum electric field strength at /5 460 s s s / kv /mm / kv /mm Fig Distribution of electric field 40 kv /mm 8 LI Jinbiao 10 kv /mm in HVDC transmission systems C 13 kv /mm WAC 008. World s s s s s s % M ELLIOTT FE LAVIER BE KUEHN WP et al. FEM-study on converter transformer failures in the Celilo HVDC converter station J. PESW HP Moser. Transformerboard II M. Germany Zürich J LI Xiaoli CHEN Zusheng. Summary of ultrahigh voltage direct current transmission technology J. Guangxi Electric Power ± 800 kv J LI Wenping CHEN Zhiwei SONG Xiusheng et al. Analysis on main insulation structure of converter transformer for ± 800 kv HVDC transmission J. Electrical Equipment TAKAHASHIE SHIRASAKA Y OKUYAMA K. Analysis of an anisotropic nonlinear electric field with a discussion of dielectric tests for converter transformers and smoothing reactors J. IEEE Transactions on Power Delivery RONGSHENGL WAHLSTROM G. Measurements of the DC electric field in liquid impregnated pressboard using the pressure wave propagation technique C. Australia Brisbane XIE Dexin WANG Xiaoyan. Adaptive FE analysis of nonlinear and anisotropic DC electric field of converter transformer. Automation Congress J ZHANG Shiling PENG Zongren FENG Hua. Iterative finite element method applied to nonlinear electric field of composite insulation. power system technology J. Power System Technology J

8 9 87 LIU Gang LI Lin LI Wenping et al. Analysis of nonlinear electric field of converter transformer under polarity reversal voltage J. High Voltage Engineering D WENKC ZHOU YB FU J et al. A calculation method and some features of transient field under polarity reversal voltage in HVDC insualtion J. IEEE Transactions on Power Delivery Insulation J WANG Bing WANG Qingpu SUN Youliang. Calculation and a- nalysis of polarity reverse transient electric field in valve winding end of converter transformer J. Transformer WANG Yonghong WEI Xinlao ZHU Baosen et al. Breakdown characteristics of transformer oil at DC polarity reversal voltage J. Electric Machines and Control J. Austria Graz IEEE WANG Yonghong WEI Xinlao. Characteristics of oi-pressboard insulation under polarity reversal voltage J. Proceedings of the CSEE J ZHOU Yuanxiang TIAN Jihuan WANG Yunshan et al. Analysis of electrical field on oil-paper insulation system under polarity re- 17. versal voltage J. High Voltage Engineering J WEI Xinlao NIE Hongyan CHEN Qingguo et al. Analysis of e- lectrical field on oil-paper insulation system under polarity reversal voltage J. Electric Machines and Control and Technology J DING Zhongni LI Guangfan. Electric field characteristic calculation on typical oil-paper combination insulation under polarity reversal J. Power System Technology J L Xiaode CHEN Dunli. The study on electric field characteristics of converter transformer under polarity reversal J. High Voltage Engineering temperature on dielectric parameters of oil & pressboardand the e- D lectric field distribution of oil-paper insulation under compound 1. KI150X KI150GX voltage J. Journal of Harbin University of Science and Technology 015 J YU Huimin ZHANG Qi GUO Chunmei et al. Application study on KI150X and KI150GX Transformer Oils J. Lubricating Oil UHV J YUHuimin ZHENG Pengyu ZHANG Peiheng et al. Condu-ctivi- 11. ty comparative study of transformer oils for uhv converter transformer in HVDC electric field J. Insulating Materials KATOK OKUBO H ENDO F et al. Investigation of charge behavior in low viscosity silicone liquid by Kerr electro-optic field measurement J. IEEE Transactions on Dielectrics and Electrical 4 OKUBOH SHIMIZU R SAWADA A et al. Keer electro-optic field measurememt and charge dynamics in transformer oil / solid composite insulation systems J. IEEE Transactions on Dielectrics and Electrical Insulation CHEN George. Research on the feature extraction of DC space J charge behavior of oil-paper insulation J. Science China Technological Sciences CIOBANU R SCHREINER C PFEIFFER W et al. Space charge evolution in oil-paper insulation for DC cables application C. 8. J ZHANG Mingze ZHAO Dongxu HUANG Ling et al. Dielectric response measuring method on moisture content of oil-paper insulation in transformer J. Journal of Harbin University of Science 9. J WANG Zhengwei ZHAO Dawei YANG Jiaxiang et al. Numerical analysis of liquid dielectric breakdown process applied in step 19. voltage J. Journal of Harbin University of Science and Technology J ZHANG Qiuye ZHU Xuecheng GAO Ziwei et al. Influence of ( : )

34 22 f t = f 0 w t + f r t f w θ t = F cos p - ω 0 t - φ 1 2 f r θ t = F cos p - ω 0 t - φ 2 3 p ω 0 F F φ 1 φ 2 t A B s Fig. 1

34 22 f t = f 0 w t + f r t f w θ t = F cos p - ω 0 t - φ 1 2 f r θ t = F cos p - ω 0 t - φ 2 3 p ω 0 F F φ 1 φ 2 t A B s Fig. 1 22 2 2018 2 Electri c Machines and Control Vol. 22 No. 2 Feb. 2018 1 2 3 3 1. 214082 2. 214082 3. 150001 DOI 10. 15938 /j. emc. 2018. 02. 005 TM 301. 4 A 1007-449X 2018 02-0033- 08 Research of permanent