371-其他资源-学生作品11-the ionized fields and the ion current on a human model

1、指导教师评语：李学宝同学（学号：1071181312）在本科学习期间积极主动参加科学研究活动，进步明显，本篇论文就是该生本科生期间撰写的一篇科研论文。李学宝同学利用电磁场理论研究了特高压直流输电系统离子流场合离子流密度；建立人体模型，研究了教师：崔翔2013年8月10日该论文于2012年10月在IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 27, NO. 4, OCTOBER 2012上发表。The Ionized Fields and the Ion Current on A Human Model under 800kV HVDC Transmissi

2、onLinesXuebao Li, Xiang Cui, Yongzan Zhen, Tiebing Lu, Zhaonan Luo, Chao Fang, Xiangxian Zhounumerical methods up to now. It will be important and veryvaluable to research the ionized fields, especially the ion current through human body under the UHVDC transmission lines in order to satisfy the per

3、mitted current limit through the human body. In the past, the ionized fields and the ion current through human body under HVDC transmission lines in the vicinity of human were mostly obtained through experiments. There are few literatures about how the ionized fields and the ion current through huma

4、n body are calculated by the analytical or numerical methods. However, the experimental approach mostly depends on parameters of the transmission lines and the weather. At the same time, the known measurement technology of the ionized fields still cannot be used to consider the human body. So in the

5、 design phases, the experimental approach has great limitation and is very difficult to be used widely in the evaluation of environment effects of the UHVDC projects. It is necessary to develop numerical methods to analyze the ionized fields and the ion current through human body when there is a hum

6、an body standing under transmission lines in order to design a safer and more reliable UHVDC transmission system.Many numerical methods 1-5 have been presented for calculating the ionized fields under DC transmission lines without the human body or any buildings. These methods have been validated by

7、 the model test or engineering measurement, and they have been used successfully to calculate two-dimensional ionized fields without any objects under HVDC or UHVDC transmission lines in the design. The reference 6 applied the two-dimensional finite elementAbstractUltra High Voltage Direct Current (

8、UHVDC) system has many advantages in long distance power transmission. This paper is aimed at analyzing the distributions of the ionized fields and the ion current on the human model under 800kV UHVDC transmission lines. A numerical method which combines with three-dimensional charge simulation meth

9、od and Deutschs assumption is used for this purpose in this paper. And the validity of the presented method is demonstrated through a test in the laboratory. For 800kV UHVDC transmission lines, the ionized fields and the ion current on the human model are calculated and numerical results show that t

10、he ionized fields and the ion current density on the top of the human model increase evidently when the human model stands under 800kV UHVDC transmission lines. And the total ion current flowing on the human model is far lower than the permitted limit.IndexTermsionizedfields,ioncurrent,UHVDCtransmis

11、sion lines, human model, 3D numerical methodsI. INTRODUCTIONUhasmanyadvantagesinlongdistancepowerLTRA High Voltage Direct Current (UHVDC) systemtransmission. Now two 800kV UHVDC transmission projects, i.e. Yunnan to Guangdong and Xiangjiaba to Shanghai, have been built and have been operating in Chi

12、na since 2009 respectively. And other some 800kV UHVDC transmission projects have also been planned and designed in China. These 800kV UHVDC transmission projects are playing or will play important roles in power transmission from the west to the east in China.In China, the UHVDC transmission lines

13、usually pass through farmland or area with people activity. Therefore, the ionized fields due to the corona effects of 800kV UHVDC transmission lines and the ion current through a human body that stands on the ground under the transmission lines are always attended by the government and the people w

14、ho live area near the transmission lines. With the presence of a human body under the transmission lines, the ionized fields are highly perturbed with an enhancement. Although the ionized fields and the ion current through human body under the UHVDC transmission lines are concern by designers, they

15、have not been analyzed sufficiently due to the limit ofmethod method ionizedand 7 used two-dimensional boundary element to analyze the influence of the human body on fields when there is a human body near the DCtransmission lines. But due to the influence of a human bodyunder the transmission lines,

16、 the ionized fields where the human body stands will increase a lot and the ionized fields far away from the human body are free from the impact of the human body. Therefore, the ionized fields should be a three- dimensional problem and the traditional two-dimensional method cannot correctly reflect

17、 the distribution of the ionized fields 8.A three-dimensional numerical method which combines with three-dimensional charge simulation method and Deutschs assumption to calculate the ionized fields and the ion current on the human model under HVDC transmission lines is developed in this paper. Consi

18、dering the humanAuthors are with the State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing, China (email: ; ; ).学生作品9-The Ionized Fields and the Ion Current on A

19、Human Model under 800kV HVDC Transmission Linesmodel under the HVDC transmission, the number of simulation charges is larger than that of two-dimensional charge simulation method and the types of simulation charges are also more than those of two-dimensional charge simulation method. In addition, it

20、 is complex to calculate the flux line of a three-dimensional field. So the three- dimensional problem of ionized fields is much more complex than two-dimensional problem in all.This paper consists of the following three sections. Firstly, a three-dimensional numerical method presented in this paper

21、 is described. Then, a test in the laboratory is set up and the comparison between the measured and calculated results shows the validity of the presented method. Finally, the ionized fields and the ion current on the human model under800kV UHVDC transmission lines are analyzed in detail, and some d

22、iscussions are given. J- = Rr+ r- / ewhere, j is potential in the ionized fields, and are(7)+-e0 ispositive and negative ion densities respectively,permittivity in air, J+ and J- are positive and negative ioncurrentdensitiesrespectivelyK, + and Ka-repositiveandnegative ion mobility within the corona

23、 area respectively, Ris ion recombination coefficient in air, and e is charge value of the electron.To solve (2)-(7) the following boundary conditions are required:1) The potential on positive or negative conductors is applied by known voltage.2) The potential on the ground is zero.3) The human mode

24、l is treated as a conducting body with zero potential.Based on above assumptions, the scalar function A can becalculated along the flux lines according equations 4, 9.Ar = Ae retothefollowingII. METHOD OF ANALYSISA. Assumptions and Governing EquationsIn order to calculate the ionized fields and the

25、ion current on the human model under 800kV UHVDC transmission lines, a three-dimensional numerical method which combines with three-dimensional charge simulation method and(8)2 + 2 Ae redjU2A2= A(9)ee02Ej1U dj112=+(10)Deutschsassumptionisdeveloped.Thefollowingrree 0 AereE22j1assumptions are used in

26、the calculation 4, 9.1) The space ions (i.e., space charges) onlywhere, Ae and re are values of A andion density on theaffect thesurface of the conductor respectively, j1 and U are potentials of the start point of the flux line in the integration and applied known voltage on the conductor respective

27、ly. After getting A, Es may be obtained from (1) and J+ , J- may be derived from(4) and (5).B. Calculation of Space-Charge-Free FieldThe space-charge-free electrostatic field and potential are foundations for calculating the ionized fields and ion current on the human model. For the case existing hu

28、man model, the space-charge-free electrostatic field may be calculatedmagnitude of the ionized fields without changing thedirection of the ionized fields, which assumption, i.e.Es = A EiscalledDeutschs(1)where Es is the ionized field intensity, E is the space-charge- free electrostatic field intensi

29、ty generated only by charges on the transmission lines when the space ions are not taken intoconsideration, and A is a scalar function dependent position in the space.on2) Kaptzovs assumption is applied, i.e., the surfaceelectric field intensity on the conductor remains constant at the onset value a

30、fter the corona having been stable.throughmanypresentedthree-dimensionalnumericalmethods, for example, the finite element method, the simulation charge method etc. In this paper, an improved three-dimensional charge simulation method is adopted and3) The positive and negative ion mobility is constan

31、t which is independent to the ionized field intensity.4) The thickness of the ionized layer around the conductors is small enough to be neglected.its basic idea is to put some simulation charges inside electrodes by the traditional approach and to select some contour points on the electrodes. But th

32、e number of contour points is larger or far larger than the number of simulation charges in order to ensure the contour points can fit shapes of the electrodes better. So it can save computational cost and reduce heavy works including change or adjustment of positions and types of the simulation cha

33、rges. The simulation charges may be solved by the following equationsj1 = P11Q1 + P12Q2 +K+ P1nQn5) The diffusion of the positive neglected.6) There are only positive ionsand negative ions isbeneath the positivetransmission lines and only negative transmission lines.7) The movement of the neglected

34、as well.negative ions beneath thespace ions due to wind isThe governing equations in the ionized fields are given by2j= -(r+ - r- ) / e0Es = - j(2)(3)(4)(5)(6)j2 = P21Q1+ P22Q2 +K+P2nQn jm(11)K= Pm1Q1+ Pm2Q2 +K+J = K r E+ + sJ- = K- r- Es J+ = -Rr+ r- / ePmnQnwhere Pij is the potential coefficient o

35、f the charge Qj at the学生作品9-The Ionized Fields and the Ion Current on A Human Model under 800kV HVDC Transmission Linescontour point i determined by the type of simulation charges 10, 11 and ji is the known potential at the contour point i.Obviously, the number of row is not equal to the number of c

36、olumn in (11). So the approach of generalized inverse matrix12 is used to solve simulation charges in (11).After the simulation charges in (11) are solved, the threem nm nIn general,orintheimprovedchargesimulation method is required.field intensity Exi , Eyi ,components of the space-charge-freeThe d

37、imension of the human model is much smaller thanthe height of UHVDC transmission lines when calculatingand Ezi at point (xi , yi , zi ) may be calculated 10 byN1 + N2the space-charge-free field. The UHVDC transmission lines= j =1N1 + N2are simulated by a setofN1infiniteline charges withoutExifxij Qj

38、(20)unknown charge line density and the human model is simulated by another set of N2 unknown point charges that are= j =1Eyif yij Qj(21)set inside the human model but close to the skin of human model. Images of all simulation charges with respect to the ground plane are considered in the calculatio

39、n.The potential coefficients Pij and field coefficients fi,j at a point (xi , yi , zi ) above the ground, i.e., z=0, for infinite line charge that parallels to the y-axis with unit line densityN1+2 NE =f Q(22)zizijjj =1C. Calculation of the Ion Current on the Human ModelThe ion current density on th

40、e skin of the humanmodellocated at a point follows:(xj , 0, z j )and its image are expressed asmay be solved based on (4) or (5), which is regarded as theinjected ion current. Then the total injected ion current equivalent to the total ion current through the human model can be calculated.The follow

41、ing two steps are performed to calculate the ion current on the human model. Firstly, the surface of the human model is divided into n surface pieces, and the ion current density on each piece is calculated. Secondly, the injected ion currents on all surface pieces are summed as the total current fl

42、owing through the human model.The total ion current I flowing on the human model isn(x - x )2 + (z + z)212pe0ijijP =ln(12)ij(xi - xj )2 + (zi - z j )2xi - x j1f=xi j2pe(x - x )2 + (z - z)20ijij(13)x - xij-(xi - x j )2 + (zi + z j )2= 0f yi j(14)= 1 zi - zjI = J kSf(23)zi j2pe(x - x )2 + (z - z)2k0ij

43、ij(15)k =1z + z ij-where J is the injected ion current density on surface piece kk(x - x )2 + (z + z)2and Sk is the area of surface piece k.ijijAnd the potential coefficientsand field coefficientsPijfijcalculated at a point(xi , yi , zi )above the ground, i.e., z=0,III. VALIDITYA test arrangement sh

44、own in Fig. 1 is built infor a unit point charge located at a point image are expressed as follows:(xj , y j , z j )and itsthelaboratory to testify the validity of the numerical method presented in this paper. The height and length of two wires14pe01P =ij(xi - x j )2 + ( yi - y j )2 + (zi - z j )2ar

45、e 1m and 8m respectively. The wires have same radius 0.9mm, and their spacing is 1.26m. As shown in Fig. 1, a metal cubic box with dimensions 0.2m0.2m0.2m which is insulated to the ground by an insulator is under the wires. The total ion current of the box is measured through measuring the voltage o

46、ver the sampling resistor with 1M.(16)- 1(xi- x )j2 + ( y -i y )2 + (z +i zj )2jxi - xj1f=xij4pe(x - x )2 + ( y - y )2 + (z - z)2 3/2i0ijjij(17)x - x j-i(xi - x j )2 + ( yi - y j )2 + (zi + z j )2 3/2yi - y j1f=yij4pe(x - x )2 + ( y - y )2 + (z - z)2 3/ 2i0ijjij(18)y - y-ij(xi - xj )2 + ( yi - y j )

47、2 + (zi + z j )2 3/2zi - z j1f=zij4pe(x - x )2 + ( y - y )2 + (z - z)2 3/2i0ijjij(19)z + z j-iFig. 1 The test arrangement(xi - x j )2 + ( yi - y j )2 + (zi + z j )2 3/2The schematic diagram of the box under negative polar学生作品9-The Ionized Fields and the Ion Current on A Human Model under 800kV HVDC

48、Transmission Linesline is shown in Fig. 2. In the calculation, the number of the infinite line charges N1 in the wires is 8, the number of thepoint chargesbox is 368, and the averageNin2distancebetween the simulation charges in the box and the contour points on the box is 6mm. Numbers of the contour

49、 points onthe wires and on the box are 264 and 1760 respectively. The average distance between any two neighboring contour points on the box is 9mm.The ion currents flowing on the box under applied different voltages on the positive and negative polar wires are calculated and measured respectively.

50、The height of insulator is 0.1cm, 4cm and 8cm respectively. All of the results are shown in Fig. 3. We can see that the calculated results have a good agreement with the measured results. The validity of the presented numerical method is testified by the test.(c) The height of insulator is 8cmFig. 3

51、 The calculated and measured results in the testIV. APPLICATIONA. Numerical CalculationThe three-dimensional numerical method presented in Section II was used to calculate the ionized fields and the ion current flowing on the human model under 800kV UHVDC transmission lines. The position of the huma

52、n model standing under 800kV UHVDC transmission lines is shown in Fig. 4.Fig. 2 Two wires and a metal cubic box in the testFig. 4 The position and sizes of the human model under the positive polar lineA 800kV UHVDC transmission lines with 18m height and 50m length is considered in the calculation. T

53、he bipolar lines have two 61.538cm bundled conductors with bundle spacing of 0.45m and the distance between positive andnegative polar lines is 22m.The dimension of the human model shown in Fig. 5 is obtained from the standard of human dimensions of Chinese adults for males 13. The height of the hum

54、an model is 1.7m. The head is modeled by a sphere with radius 0.1m; the upper part is modeled by a cuboid with 0.6m height, 0.45m width and 0.23m thickness. The lower part is modeled also by a cuboid with 0.9m height, 0.3m width and 0.23m thickness.(a) The height of insulator is 0.1cmFig. 5 The huma

55、n model(b) The height of insulator is 4cmIn the calculation, 754 simulation charges are used, among学生作品9-The Ionized Fields and the Ion Current on A Human Model under 800kV HVDC Transmission Lineswhich the number of infinite line charges located in eachcenter of the sub-conductors of 800kVUHVDCtrans

56、mission lines is 12 and the number of point charges inside the human model is 742. The number of the contour points on all sub-conductors of 800kV UHVDC transmission lines is 1584 and the number of the contour points on the human model is 4765. A path along the ground and the human model is given in Fig. 6 in order to show the distributions of the ionized fields and the ion current density on the human model.To show the distorted effect caused by the human model,kEkJthe enhancement factorsandare defined as follow