Discussion on the Deutsch Assumption in the ... - IEEE Xplore

IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 25, NO. 4, OCTOBER 2010

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Discussion on the Deutsch Assumption in the Calculation of Ion-Flow Field Under HVDC Bipolar Transmission Lines Wei Li, Bo Zhang, Rong Zeng, Senior Member, IEEE, and Jinliang He, Fellow, IEEE

Abstract—Deutsch assumption greatly simplified the calculation of the ion-flow field under HVDC transmission lines. However, its applicability remains to be proved for the 800-kV HVDC projects in contemplation in China. The ground-level electric field and ion current density are calculated with an upwind differential-based 2-D method and a Deutsch assumption based on the 1-D method to analyze the errors of the ion-flow field caused by Deutsch assumption. A dc bipolar line laboratory model is established to verify the methods. The parameters indicating the corona discharge intensity and the field distortion degree are introduced to evaluate the errors caused by Deutsch assumption. Then, the applicability of the Deutsch assumption is discussed on the 800-kV HVDC test line established in China. The relationship of the corona discharge intensity, the field distortion degree, and the errors caused by Deutsch assumption are analyzed. Using the corona discharge intensity to evaluate the errors caused by Deutsch assumption seems to be reasonable. Index Terms—Corona, electric fields, simulation, space charge, transmission lines.

I. INTRODUCTION

T

HE ION-FLOW field produced by corona discharge on HVDC transmission lines is an important problem of the electromagnetic environment. Townsend [1] first made efforts on the research of corona discharge. After that, Deutsch expanded the method proposed by Townsend, and applied it to the line-to-plane structure in two dimensions [2]. Several assumptions are introduced in Deutsch’s works. The most important ones are as follows: 1) The space charges affect only the magnitude but not the direction of the electric field. 2) The charge density remains constant along any field line. 3) The electric field at the passive electrode remains at its Laplacian value. Assumptions 2) and 3) prove not to be acceptable when the applied voltage is significantly higher than the corona onset value, whereas the assumption,. generally referred to as the Manuscript received March 30, 2009; revised June 15, 2009. Date of publication September 02, 2010; date of current version September 22, 2010. This work was supported in part by the China 11th Five-year National Key Technologies R&D Program under Grant 2006BAA02A20. Paper no. TPWRD-00260-2009. The authors are with the Department of Electrical Engineering, Tsinghua University, Beijing 100084, China (e-mail: [email protected]; [email protected]; [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPWRD.2010.2050153

“Deutsch assumption,” is popularly employed in the simulation of the ion-flow field because the two-dimensional (2-D) problems are reduced to one-dimensional (1-D) ones with this assumption, and the calculation process is greatly simplified [3]–[10]. However, some researchers think that the Deutsch assumption should be discarded because of the unbearable errors introduced. So, more accurate but inefficient 2-D algorithms have been proposed [11]–[16]. Experimental and theoretical studies were carried out to analyze the applicability of the Deutsch assumption. However, controversial conclusions were obtained. The analytical calculation objected to the application of the Deutsch assumption on the pin-to-plate structure in [17]. Measurements of positive corona from twin-wire systems proved that the interaction of the spacecharge electric field can cause significant trajectory distortion for corona from more than one source in [17]. In [19], the corona discharge effects of a single wire in noncoaxial cylinders were tested and simulated. It was suggested that Deutsch assumption is acceptable when the corona discharge is very weak (little space charges are produced) or very strong (the space charge approaches saturation). In [20], it was concluded that the electric-field lines are forced to concentrate in the regions with highfield strength in a single-line-to-plate coronating model basing on semiempirical analysis. The ion-flow field of the single line to plane was analyzed in [21]. The results suggested that the distortion of the ion trajectories would be suppressed in the saturation case. In general, research has been conducted on the applicability of the Deutsch assumption on simplified models as noncoaxial cylindrical geometry, pin-to-plate, and single line to plate. And the applied analytical or semianalytical methods may be inadequate to solve an actual bipolar bundle-conductor transmissionline structure. Especially in China, 800-kV HVDC projects are going to be constructed. The corona effects may be more serious and more errors may be introduced by Deutsch assumption. In this paper, the calculation results of the upwind differential-based 2-D method and the Deutsch assumption based 1-D method are compared on a laboratory bipolar dc transmission line model and an actual size HVDC test line. The experimental results of the ground-level electric field and ion current density are posed to evaluate the methods. Then, the excess of the maximum Laplacian (space-charge-free) field on conductor surfaces and the angle differences between the than the onset field directions of total field and Laplacian field along Laplacian field are calculated for all cases. With these two paramelines ters, the influences of corona discharge intensity and space field

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distortion on the errors caused by Deutsch assumption are analyzed. Finally, for practical purposes, the ion-flow field of the actual size HVDC transmission line with different conductor radius and bundle number is simulated. The relationship of the conductor type and the errors of the ion-flow field caused by the Deutsch assumption are analyzed.

II. ION-FLOW FIELD CALCULATION OF DC TRANSMISSION LINES The equations that constitute the mathematical description of the bipolar ionized field in air are Poisson’s equation (1) The positive and negative current density vectors (2) (3) The current continuity condition (4) (5) The total current density vector (6) where total electric field (in volts per meter); absolute values of positive- and negative-space charge density (C/m );

and and and

positive, negative, and total ion current density vector (A/m ); positive and negative ion motilities (m /V s); wind velocity vector (in meters per second); permittivity of air electron charge

F/m;

Part 2) Calculate the charge density distribution in space with the upwind differential method. Part 3) Calculate the total electric field in space with the finiteelement method (FEM). And then recalculate the charge density on conductor surfaces according to Kaptzov’s assumption. Parts 2) and 3) are executed iteratively until the accuracy requirements are met. Then, the electric field and charge density distribution can be obtained. The most important part of the calculation is the upwind differential method for the calculation of the space charge density. The main idea of the upwind differential method is to give more weights on the elements laying on the direction of flow in the discretization. This method maintains the computational stability of the convection-dominated diffusion-convection-reaction equations. The application of the upwind differential method on the problem of the ion-flow field has become mature and has been proved. Further details of the method can be found in previous works [11], [12], [16]. And in our previous work, improvements have been made on boundary conditions for the consideration of calculating accuracy and speed [22]. In the Deutsch assumption-based method, the space charge only affects the magnitude of the electric field without changing the direction of the electric field. Therefore, we have

(7) is the Laplacian field generated by the transmission where lines, and is a scalar function dependent on the position in the and . space which means the relation between or Then, an integral equation can be derived for along a flux line with boundary conditions of field on the two ends of the flux line. And the calculation of the ion-flow field can be divided into two steps: 1) calculating of flux lines and 2) solving an integral equation on each flux line. Details of this method can be found in [3], [4], [10]. The implemented method in this work is based on [10] and has been proved with the posed results. In the following paragraphs, the upwind difference based 2-D method is called “method A,” while the Deutsch assumption based on the 1-D method is called “method B.” Both method A and B accept Kaptzov’s assumption as the boundary condition on conductor surfaces. That is, the surface field of the coronating conductors remains constant at the onset values and irrespective of the corona intensity. The onset field is calculated with Peek’s law [23]

C;

coefficient of recombination (cm /s). For the upwind differential based method, these differential and the space charge denequations are solved for the field and , as functions of the space coordinates. sity The process of calculation is mainly constituted by the following three parts: Part 1) Calculate the Laplacian field in space with the charge simulating method (CSM). And then estimate the initial value of charge density on conductor surfaces.

(8) where is the surface irregularity factor; and are empir33.7 and 0.24 for positive polarity and ical constants 31.0 and 0.308 for negative polarity; is the relative air density factor; and is the conductor radius. The calculation accuracy of both methods 1) and 2) are controlled by the errors between the surface field and the onset field.

LI et al.: DISCUSSION ON THE DEUTSCH ASSUMPTION

Fig. 1. Ground-level electric field under the laboratory model.

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Fig. 2. Ground-level ion current density under the laboratory model.

An average error of 0.2% on all surface points has been set as the convergence criterion for both methods. III. ERROR ANALYSIS OF DEUTSCH ASSUMPTION ON LABORATORY MODEL First, a laboratory bipolar dc transmission line model is established to evaluate the calculation methods. Two wires with a 1.2-mm radius and 0.6-m spacing are placed 0.6 m above a metal plate. Voltages of same absolute value and different polarity are applied on the two wires separately. The ground-level electric field and ion current density are measured under the transmission-line model. Calculations are executed with both methods A and B with same calculating parameters. For the calculation of onset field, is set as 0.8 and is set as 1 in (8). The results are illustrated in Figs. 1 and 2. The different colors of blue, olive, and red indicate different applied voltages of 35 kV, 40 kV, and 45 kV. The scalar points are experimental results. The solid lines are calculated results with method A, while the dash lines are calculated results with method B. Figs. 1 and 2 show that the results of method A agree with the experiment well. The results of method B agree with the experiment at relatively low voltage and the errors increase with the applied voltage. The reason may that be the field distortion is more serious with a higher applied voltage. The ratios of the maximum calculated field between method B and A are 94.2%, 90.9%, and 87.2% with an applied voltage of 35 kV, 40 kV, and 45 kV while the ratios of the ion current density between method B and A are 90.4%, 86.4%, and and 85.3%. These indicate the errors of ground-level field caused by the Deutsch assumption. ion current density Fig. 3 illustrated the Laplacian and total field lines near the positive polar conductor for different applied voltages. This figure shows the field distortion clearly and directly. As the Laplacian field changes linearly with the voltage, the Laplacian field lines stay the same for different voltages. The total field lines are gradually pressed toward the interelectrode region with the voltage increasing. This is because the field on the conductor surfaces is extremely nonuniform in the bipolar case. The corona discharge occurs more easily on the points facing the interelectrode region on conductor surfaces. So more space

Fig. 3. Laplacian and total field lines for different applied voltages of the laboratory model.

charges are distributed in the interelectrode region. And this affects the direction of field lines significantly. The errors of the ion-flow field caused by Deutsch assumption correlate closely with the field distortion. And the field distortion is in close relation to the corona discharge intensity. The corona discharge intensity is indicated here with the excess of the maximum Laplacian field on conductor surfaces than the onset field (9) is the maximum Laplacian field strength on conwhere ductor surfaces. is the corona onset field calculated with (8). is 9.4%, 25.0%, and 40.6% For this laboratory model, with applied voltages of 35 kV, 40 kV, and 45 kV. On the other hand, a parameter quantitatively indicates that the distortion degree of the field is helpful to understand the calculation errors caused by Deutsch assumption. Here, the angle difference between the directions of the total electric field and Laplacian electric field along a Laplacian electric field line is employed

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TABLE I CALCULATED RESULTS OF THE LABORATORY MODEL

To summarize, Table I lists the parameters indicating the corona discharge intensity, the field distortion degree, and the errors of the ground-level electric field and ion current density. and increase with the applied Table I shows that and decrease so that the Deutsch asvoltage, while sumption becomes more unreliable with the corona discharge intensity and the field distortion degree increases. Furthermore, the increasing field distortion degree tends toward saturation with applied voltage while this saturation cannot be observed in , or . As a result, the correlation curve may be more uniform to describe the errors caused by the Deutsch assumption with the corona discharge intensity rather than the field distortion degree.

Fig. 4. Azimuth angle of the start point of the field line.

IV. APPLICATION ON ACTUAL SIZE HVDC TEST LINE

Fig. 5.

d on different field lines of the laboratory model.

(10) where is the azimuth angle of Laplacian field and is the azimuth angle of the total field. Then, is considered to be zero if the Deutsch assumption is supported. Here, the total field is calculated with method A. The ion-flow field of the laboratory model with 45 kV is analyzed with . Different field lines are identified with the azimuth angle of start points, as Fig. 4 illustrated. Calculations of on different field lines are presented in Fig. 5. The electric potential along field lines is marked on the coordinate. In general, the extreme value of can be found is relatively small at in the potential region of 5–20 kV. And the start and the end of the field lines. This is because at the start of field lines near conductors, the Laplacian field dominates the total field, and the space charges cannot affect the direction of total field lines significantly while at the end of field lines near ground, the direction of total field lines is forced to be vertical, regardless of whether the effects of space charges are counted is relatively large on the field lines and . The in. is 22.5 , which is obtained on the maximum value of field line . So the degree of field distortion of the laboratory model with on the field different applied voltage can be evaluated with . on the field line with an applied voltage of line 35 kV, 40 kV, and 45 kV is 17.7 , 21.2 , and 22.5 .

A test line with a length of 800 m has been built for the research of the electromagnetic environment of HVDC transmission lines in Yunnan Province in China recently. The research methods of the Deutsch assumption proposed in the preceding paragraphs are employed to analyze this actual size test line. The test line is built for 800-kV bipolar configuration. The line height is 18 m. The wire spacing is 22 m. The conductor bundle is constituted with six conductors with a section of 630 mm . The bundle spacing is 45 cm. The ground-level electric field and ion current density under the positive polar line were measured with an automatic measuring system for several fair weather days. The average values are demonstrated here. For the calculation of onset field, is set as 0.5 for stranded conductors and is set as 0.82 for an altitude of 2000 m where the test line is constructed. The ion-flow field is simulated with methods 1) and 2). The results are illustrated in Figs. 6 and 7. The colors of blue, olive, and red indicate different applied voltage of 600 kV, 700 kV, and 800 kV. The scalar points are experimental results. The solid lines are calculated results with method 1, while the dash lines are calculated results with method 2. As the influence of the environmental factors, the dispersion of the test results on the test line is more serious than on the laboratory model. Nevertheless, the results of method 1 generally agree with the experiment. The results of method 2 agree with the experiment on low voltage (600 kV), and the errors increase with the applied voltage. As the maximum values of method 1 agree with the fitting curves of test results, method 1) is again employed to evaluate the errors of method 2). The ratios of the maximum calculated field between methods 2and 1 are 99.6%, 85.0%, and 78.9% with an applied voltage of 600 kV, 700 kV, and 800 kV while the ratios of the maximum ion current density are 86.1%, 80.3%, and 76.1%.


Fig. 6. Ground-level electric field under the test line.

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Fig. 9. d on different field lines of the test line.

TABLE II CALCULATED RESULTS OF THE TEST LINE

Fig. 7. Ground level ion current density under the test line.

Fig. 8. Laplacian and total field lines for different applied voltages of the test line.

Fig. 8 illustrates the Laplacian and total field lines for different applied voltages. The characteristics of this pattern are similar to Fig. 3 of the laboratory model. The field distortion is more serious with higher applied voltage. And saturation of this distortion can be observed.

The excesses of the maximum Laplacian field on conductor surfaces than the onset field are also calculated for the test line. is 0.8%, 17.6%, and 34.4% with an applied voltage of 600 kV, 700 kV, and 800 kV. on different field lines with an applied Calculations of voltage of 800 kV are presented in Fig. 9. An extreme value can be found in the potential region of 50–300 kV. And of is relatively small at the start and the end of the field lines. is 13.1 , which is obtained on the The maximum value of field line 0. So the degree of field distortion of the test line with on a different applied voltage is evaluated on this field line. the field line 0 with applied voltages of 600 kV, 700 kV, and 800 , and . kV are The parameters indicating the corona discharge intensity, the field distortion degree, and the errors of the ground-level electric field and ion current density are listed in Table II. Similar to the conclusions of the laboratory model, the Deutsch assumption becomes more unreliable with the corona discharge intensity and the field distortion degree increases. And the errors of the ion-flow field caused by the Deutsch assumption on the test line get even more serious than on the laboratory model. Again, the increasing field distortion degree tends toward saturation with applied voltage. V. DEUTSCH ASSUMPTION DISCUSSION WITH DIFFERENT BUNDLE CONDUCTOR TYPES The surface Laplacian field is related to the bundle conductor types (such as the subconductor radius and bundle number). So the corona discharge intensity is different; the influences of space charges on the field are different and the errors caused

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TABLE III CALCULATED RESULTS WITH DIFFERENT CONDUCTOR RADIUS

Fig. 10. Ground-level electric field with a different conductor radius.

Fig. 12. Ground-level electric field with a different bundle number.

Fig. 11. Ground-level ion current density with a different conductor radius.

by the Deutsch assumption may be different with different conductor types. In this section, the Deutsch assumption is discussed for a different conductor radius (6 400 mm , 6 560 mm , 6 630 mm ) and a different bundle number (4 630 mm , 5 630 mm , 6 630 mm ). The other calculating parameters are set the same as the test line analyzed in previous paragraphs. Calculated results of the different conductor radius with both methods 1) and 2) are illustrated in Figs. 10 and 11. The ratios of the maximum calculated field between method 2) and 1) are 67.2%, 74.0%, and 78.9% with a conductor radius of 400, 560, and 630 mm while the ratios of the maximum ion current density are 55.7%, 68.6%, and 76.1%. and are also calculated. Table III listed the corona discharge intensity, the field distortion degree, and the errors of the ground-level electric field and ion current density. The Deutsch assumption becomes more unreliable with a smaller radius as the corona discharge intensity and the field distortion degree become higher. Calculated results of the different bundle number with both methods 1) and 2) are illustrated in Figs. 12 and 13. The ratios of the maximum calculated field between methods 2) and 1) are 56.1%, 67.0%, and 78.9% with a bundle number of 4, 5, and 6

Fig. 13. Ground-level ion current density with a different bundle number.

while the ratios of the maximum ion current density are 52.0%, 65%, and 76.1%. and are also calculated. Table IV lists the corona discharge intensity, the field distortion degree, and the errors of the ground-level electric field and ion current density. The Deutsch assumption becomes more unreliable with a lower bundle number as the corona discharge intensity and the field distortion degree become higher. VI. RELATIONSHIP OF THE ERRORS CAUSED BY THE DEUTSCH ASSUMPTION AND AND The direct result of changing the applied voltage or changing the bundle conductor type is the change of the surface field. Consequently, the corona discharge intensity is affected. Then, the space charge distribution is changed. At last, the total


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TABLE IV CALCULATED RESULTS WITH A DIFFERENT BUNDLE NUMBER

Fig. 15. Errors caused by the Deutsch assumption with different corona discharge intensity.

Fig. 14. Field distortion degree with different corona discharge intensity.

electric field is influenced, and the field distortion degree is affected. This field distortion is the root of the errors caused by the Deutsch assumption. So the relationship of the corona discharge intensity, the field distortion degree, and the errors caused by the Deutsch assumption should be analyzed. All of the results of the test line analyzed before are concentrated on here for this purpose. Fig. 14 illustrated the field distortion degree with different corona discharge intensity. It shows that the field distortion is not very serious and tends to saturation for the actual size test line. Fig. 15 illustrated the cause of errors by the Deutsch assumption with different corona discharge intensity. The approximate is calculated linear relationship can be observed. In (9), with the maximum value of the conductor surface field. This neglected the ununiformity of surface field distribution. The errors introduced by this neglect are different for different conductor types. So unflatness is observed in Fig. 15. However, using to evaluate the errors caused by the Deutsch assumption is still reasonable. Fig. 16 illustrated the errors caused by the Deutsch assumption with different field distortion degrees. The curves decline sharply above 12 . This may be caused by the saturation observed in Fig. 8. The errors caused by the Deutsch assumption increase consistently with the field distortion degree. However, to evaluate the errors caused by the Deutsch assumpusing tion is not so appropriate. VII. CONCLUSION The applicability of the Deutsch assumption is discussed with the calculation of the ion-flow field of bipolar HVDC transmission lines. The ground-level electric field and ion current density are calculated with an upwind differential-based 2-D method

Fig. 16. Errors caused by the Deutsch assumption with a different field distortion degree.

and a Deutsch assumption based 1-D method. The results are compared to experiments on a laboratory dc bipolar line model. The errors caused by the Deutsch assumption are found to increase with the corona discharge intensity and the field distortion degree. The Deutsch assumption is acceptable when the corona discharge intensity is relatively low. However, for the ion-flow field simulation of the 800-kV HVDC test line established in China, the errors introduced by the Deutsch assumption can be more than 20%. And these errors increase with the applied voltage increasing, the conductor radius decreasing, or the bundle number decreasing. The relationship of the corona discharge intensity, the field distortion degree, and the errors caused by the Deutsch assumption are analyzed. The field distortion degree increases with the corona discharge intensity and tends to saturation. The errors caused by the Deutsch assumption increase with the corona discharge intensity and the field distortion degree. But the relationship is approximately linear only with the corona discharge intensity. So using the corona discharge intensity to evaluate the errors caused by the Deutsch assumption is reasonable.

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ACKNOWLEDGMENT This work is supported by China 11th Five-year National Key Technologies R&D Program under Grant 2006BAA02A20. REFERENCES [1] J. S. Townsend, Electricity in Gases. Oxford, U.K.: Clarendon, 1915. [2] Ann. Phys. vol. 5, no. 16, pp. 588–612, 1933, Deutsch. Über die Dichteverteilung unipolarer Ionenströme. [3] M. P. Sarma and W. Janischewskyj, “Analysis of corona losses on DC transmission lines, part i-unipolar lines,” IEEE Trans. Power App. Syst., vol. PAS-88, no. 5, pp. 718–731, May 1969. [4] M. P. Sarma and W. Janischewskyj, “Analysis of corona losses on DC transmission lines, part ii-bipolar lines,” IEEE Trans. Power App. Syst., vol. 88, no. 10, pp. 1476–1489, Oct. 1969. [5] S. Fortin, H. Zhao, J. Ma, and F. P. Dawalibi, “A new approach to calculate the ionized field of HVDC transmission lines in the space and on the earth surface,” presented at the Int. Conf. Power System Technology, Chonqing, China, Oct. 2006. [6] T. Lu et al., “Analysis of ionized field under 800 kV HVDC transmission lines,” presented at the 17th Int. Zurich Symp. Electromagnetic Compatibility, Singapore, Feb. 2006. [7] M. Aboelsaad, L. Shafai, and M. Rashwan, “Improved analytical method for computing unipolar DC corona losses,” in Proc. Inst. Elect. Eng., 1989, vol. 136, no. A1, pp. 22–40. [8] Y. Wang, C. Q. Sun, T. Tang, X. J. Lang, and D. L. Luo, “Distribution of ground electric field strength and ionic current density under different operating modes of UHVDC transmission lines,” Power Syst. Technol., vol. 32, no. 2, pp. 29–33, 2008. [9] J. Liu and J. S. Yuan, “Calculation of total electric field and ionic current density of double-circuit HVDC transmission lines,” Power Syst. Technol., vol. 32, no. 2, pp. 61–70, 2008. [10] Y. Yang, J. Y. Lu, and Y. Z. Lei, “A calculation method for the electric field under double-circuit HVDC transmission lines,” IEEE Trans. Power Del., vol. 23, no. 4, pp. 1736–1742, Oct. 2008. [11] T. Takuma, T. Ikeda, and T. Kawamoto, “Calculation of ion flow fields of HVDC transmission lines by the finite element method,” IEEE Trans. Power App. Syst., vol. PAS-100, no. 12, pp. 4802–4808, Dec. 1981. [12] T. Takuma and T. Kawamoto, “A very stable calculation method for ion flow field of HVDC transmission lines,” IEEE Trans. Power Del., vol. 2, no. 1, pp. 189–197, Jan. 1987. [13] B. L. Qin, J. N. Sheng, Z. Yan, and G. Gela, “Accurate calculation of ion flow field under HVDC bipolar transmission lines,” IEEE Trans. Power Del., vol. 3, no. 1, pp. 368–376, Jan. 1988. [14] B. Zhang, J. He, R. Zeng, S. Gu, and L. Cao, “Calculation of ion flow field under HVdc bipolar transmission lines by integral equation method,” IEEE Trans. Magn., vol. 43, no. 4, pp. 1237–1240, Apr. 2007. [15] Y. Zhang, Y. H. Wei, and J. J. Ruan, “Finite element iterative computation of high voltage direct current unipolar ionized field,” in Proc. CSEE, 2006, vol. 26, no. 23, pp. 158–162. [16] T. B. Lu, H. Feng, and X. Cui, “Analysis of the electric field and ion current density under ultra high-voltage direct-current transmission lines based on finite element method,” IEEE Trans. Magn., vol. 43, no. 4, pp. 1221–1224, Apr. 2007. [17] J. E. Jones and M. Davies, “A critique of the Deutsch assumption,” J. Phys. D: Appl. Phys., vol. 25, pp. 1749–1759, 1992. [18] A. Bouziane, C. Taplamacioglu, K. Hidaka, and R. T. Waters, “NonLaplacian ion trajectories in mutually interacting corona discharges,” J. Phys. D: Appl. Phys., vol. 30, pp. 1913–1921, 1997. [19] A. Bouziane, K. Hidaka, J. E. Jones, A. R. Rowlands, M. C. Tapiamacioglu, and R. T. Waters, “Paraxial corona discharge. II. Simulation and analysis,” Proc. Inst. Elect. Eng., Sci., Meas. Technol., vol. 141, no. 3, pp. 205–214, 1994. [20] M. M. Aboelsaad and M. M. Morcos, “Computation of ground current density profiles of unipolar DC corona,” in Proc. 21st Annu. North American Power Symp., 1989, pp. 222–230. [21] V. Amoruso and F. Lattarulo, “Investigation on the Deutsch assumption: Experiment and theory,” Proc. Inst. Elect. Eng., Sci., Meas. Technol., vol. 143, no. 5, pp. 334–339, 1996. [22] W. Li, B. Zhang, and J. L. He, “Research on calculation method of ion flow field under multi-circuit HVDC transmission lines,” in Proc. 20th Int. Zurich Symp. Electromagnetic Compatibility, 2009, pp. 133–136. [23] M. P. Sarma, Corona Performance of High-Voltage Transmission Lines. New York: Research Studies Press, 2000, pp. 82–83.

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Wei Li was born in Tianjin, China, in 1983. He received the B.Sc. degree in electrical engineering from Tsinghua University, Beijing, China, in 2005, where he currently pursuing the Ph.D. degree. His main research interests are electromagnetic compatibility and electromagnetic environment of power systems and corona effects on power lines.

Bo Zhang was born in Shanxi Province, China, in 1976. He received the B.Sc. and Ph.D. degrees in electrical engineering from the University of Hebei, Hebei, China, in 1998 and 2004, respectively. He became a Lecturer in the Department of Electrical Engineering, Tsinghua University, Beijing in 2005, and then Associate Professor in the same department in 2008. His interests are grounding technology, electromagnetic compatibility, and electromagnetic environment of power systems.

Rong Zeng (M’02–SM’06) was born in Xunyang City, Shaanxi, China, in 1971. He received the B.Sc., M.Eng., and Ph.D. degrees in electrical engineering from Tsinghua University, Beijing, China, in 1995, 1997, and 1999, respectively. Currently, he is the Vice Dean of the Department of Electrical Engineering at Tsinghua University. He became a Lecturer in the Department of Electrical Engineering, Tsinghua University, in 1999, and Professor in the same department in 2007. His research interests include high-voltage technology, grounding technology, power electronics, and distribution system automation.

Jinliang He (M’02–SM’02–F’08) was born in Changsha, China, in 1966. He received the B.Sc. degree in electrical engineering from Wuhan University of Hydraulic and Electrical Engineering, Wuhan, China, in 1988, the M.Sc. degree in electrical engineering from Chongqing University, Chongqing, China, in 1991, and the Ph.D. degree in electrical engineering from Tsinghua University, Beijing, China, in 1994. He became a Lecturer in 1994 and an Associate Professor in 1996 in the Department of Electrical Engineering, Tsinghua University. From 1994 to 1997, he was the Chair of the High Voltage Laboratory at Tsinghua University. From 1997 to 1998, he was a Visiting Scientist at the Korea Electrotechnology Research Institute, Changwon, Korea, involved in research on metal–oxide varistors and high-voltage polymeric metal–oxide surge arresters. In 2001, he was promoted to Professor at Tsinghua University. Currently, he is the Chair of the High Voltage Research Institute at Tsinghua University. His research interests include overvoltages and electromagnetic compatibility in power systems and electronic systems, lightning protection, grounding technology, power apparatus, and dielectric material. He is the author of five books and 200 technical papers. Dr. He is a senior member of China Electrotechnology Society, Chinese Society for Electrical Engineering, and Chinese Institute of Electronics. He is the Vice Chief of the China Lightning Protection Standardization Technology Committee, a member of the Electromagnetic Interference Protection Committee and Transmission Line Committee of the Chinese Society for Electrical Engineering, member of the China Surge Arrester Standardization Technology Committee, member of the Overvoltage and Insulation Coordination Standardization Technology Committee and Surge Arrester Standardization Technology Committee in Electric Power Industry, Vice Chief of the Overvoltage and Insulation Coordination Subcommittee in High Voltage Technology Committee of the Chinese Society for Electrical Engineering, Vice Chief of the Substation Electromagnetic Environment Committee in the Electromagnetic Interference Protection Committee and Transmission Line Committee of the Chinese Society for


Electrical Engineering. He is the China representative of IEC TC 81; secretary of the Standard Education and Training Committee of the IEEE EMC Society; member of CIGRE Working Group C4.501; member of IEC TC81 MT3, MT8, and MT9; and a member of the International Compumag Society. Dr. He is the Chief Editor of the Journal of Lightning Protection and Standardization (in Chinese) and Associate Editor of the Journal of Lightning Research.

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