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Energy and Power Engineering, 2009, 65-71 doi:10.4236/epe.2009.12010 Published Online November 2009 (http://www.scirp.org/journal/epe) Copyright © 2009 SciRes EPE Computational Aspects of Electromagnetic Fields near H.V. Transmission Lines Ossama E. GOUDA1, Ghada M. AMER2, Waleed A. SALEM2 1the Engineering College, Cairo University, Cairo, Egypt 2the High Institute of Technology, Benha University, Benha, Egypt Email: prof_ossama11@yahoo.com, {dr_ghada, eng_waleed269}@benha-univ.edu.eg Abstract: Biological effects of electromagnetic fields on the human body, animals and plants have been a subject of scientific interest and public concern for their risk on the living organisms such as blood leukemia and others. The high voltage transmission and distribution lines, which pass beside some houses, factories and schools are source of electromagnetic fields. This paper presents the field calculations around and near of high voltage transmission lines 220 kV and 500kV. To calculate the induced current, the power density, the electric field and the magnetic field of grounded and ungrounded human body cylindrical model are used. MATLAB program package is used for mathematical calculation of the distribution of the EMF in human body under high voltage power transmission lines. Keywords: computational aspects, EMF, H. V., transmission lines 1. Introduction Electric and magnetic fields produced by electric power systems have recently been added to the list of environ- mental agents that are a potential threat to public health [1, 2]. The increasing use of distribution and transmission of electrical energy between randomly occurring causes concerns regarding the risks of human exposure to near- field radiation from the transmission lines and electric substations. The studies into the health effects of long- term exposure have been progressing on several fronts [1]. At ground level, beneath high-voltage transmission lines, the electric fields created have the same frequencies as those carried by the power lines. The characteristics of these fields depend on the line voltage, and on the geo- metrical dimensions and positions of the conductors of the transmission line. [1] Inside buildings near HV transmis- sion lines, the field strengths are typically lower than the unperturbed field by a factor of about 10-100, depending on the structure of the building and the type of materials [1]. The magnetic field beneath high-voltage overhead transmission lines is directed mainly transversely to the line axis. In this paper calculations are carried out for the electromagnetic fields near the overhead transmission lines and also the induced current produces in human body due to these fields. 2. Computational Model for EMF under H.V. Transmission Line Calculation In this paper the electric field E, induced in the human body when exposed to a transmission power line electric field Einc, is determined in analytical form using the sur- face integral equation method. Account is taken of the presence of the earth below the three-phase Power line [3]. Model of long-distance power line consists of three- phase power lines which are arranged in several different configurations that are used in this study. The central conductor number l is in the plane y = 0, while conduc- tors number 2 and number 3 are respectively in the planes y = L and y = -L. Three conductors in the plane z=d in the air (Region 0) above the surface z = 0 of the earth (Region 1) are shown in Figure 1. The electromag- netic fields near 220 kV and 500 kV high voltage tower are calculated in three dimensions by using (1) to (6). The analytical formulas for the field calculations of the three phase's power system are derived in [4] Final Stage 2 22 2 03 00 22222 1 () ()()2 (0,, )()[( )][( )()] i x il zd yzdyL Eyz kde kzdy zdyL 22 222 2 3 2 ])()[( 2)()( Lydz Lydz e i (1) O. E. GOUDA ET AL. 66 2 2 0 0 2 2 2 01 1 3 022222 22 2 0 22 11 11 (0,, )[]()[] 2() ()()()()() i y kk il kk EyzyeyL kzd y zd yzdyLzdyL ] )()( 2 1 )()( 1 )[(22 2 1 2 0 22 3 2 Lydz k k Lydz Lye i (2) 2 03 022222 22 2 0 (0,, )2()()()( )()( ) i z lzd zdzdzd Eyz e kzd y zd yzdyLzdyL 23 22 22 ()()()() izd zd ezd yL zd yL (3) 22 00 33 02222 2222 1 2() ()()()() (0,, )[()][()() ][()() ] ii x ilk yz dyLz dy Lz d Byze e kzdyzdyLzdyL 22 (4) 22 2 00 0 3 02 2222222222 222 1 1 4()( )4()( ) 2[( )] (0,, )1 2[( )]( )( )()[( )()] i y lz dkdz dkd zd yzdzd Byz e kzd yzd yzd y zd ykzdyL 22 20 3 2222 2222 1 4()( ) 2[()() ] 1()() ()()()()[()()] izdkd zd yLzdzde zd yLzdyLzdyLkzd yL 22 222222 22 )()()()()()( ])()[(2 1Lydz dz Lydz dz Lydz Lydz (5) 22 2 yL 22 2 00 10 3 02222 2222222 1 (12/)4()2[( )]() (0,, )1 2()()[() ]()()() i z lykkykd yzdy Byz e z d yzd ykzdyzd yzdyL 22 22 2 01 03 222222 222 1 ()(12/) 4()()2[()() ]() 1 ()() [()()]()()()() i yLkkyLkdzdyLyL e2 z d yLkzd yLzdyLzd yL 22 22 2222 1 0 22 2 1 2 0 )()( ])()[(2 1 ])()[( ))((4 )()( )/21)(( Lydz Lydz Lydzk dkLy Lydz kkLy (6) Figure 1. Tower of power line simulation, conductors at height “d” over earth (flat configuration) Copyright © 2009 SciRes EPE O. E. GOUDA ET AL. Copyright © 2009 SciRes EPE 67 where E0x(0,y,z), E0y(0,y,z), and E0z(0,y,z) are electric field components of the three phases in x, y and z planes respectively. B0x(0,y,z), B0y(0,y,z), and B0z(0,y,z) are magnetic field components of the three phases in x, y and z planes respectively. L is the distance between power line phases. d is the vertical distance from the earth to the power lines. I is the line current in ampere. k0 is the wave number of the air and k1 is the wave number of the earth and μ0 is the permeability of free space. The parameters for the transmission lines 220 kV and 500 kV are given in Table 1. The electromagnetic field for 220 kV and 500 kV are shown in Figures 2 to 10 at distances 0, 2, 4, 6, 8, 10, 12, and 20 meters starting from the transmission lines conductors. Figure 4. E0z (0, y, z) near a 220kV three-wire power line over vertical distance from 0 to 20 m, current =300 Amp Table 1. the parameters for the transmission lines 220 kV and 500 kV parameters 220 kV 500 kV L 3m 12m D 15m 19.1m I 300A 1200A F( frequency) 50 Hz 50 Hz Z From 0 to 15 m From 0 to 18 m Figure 5. B0x (0, y, z) near a 220kV three-wire power line over vertical distance from 0 to 20 m, current =300 Amp Figure 2. E0x (0, y, z) near a 220kV three-wire power line over vertical distance from 0 to 20 m, current =300 Amp Figure 6. B0y (0, y, z) near a 220kV three-wire power line over vertical distance from 0 to 20 m, current =300 Amp 3. Computational Model for Induced Current in Human Body The human body is a complex structure with parts like skin, fat, bone, marrow, muscle, blood, nerve fibers, etc., each of which is characterized on the macroscopic level Figure 3. E0y (0, y, z) near a 220kV three-wire power line over vertical distance from 0 to 20 m, current =300 Amp O. E. GOUDA ET AL. 68 and within definite boundaries by a conductivity σ and a relative permittivity εr, that may be frequency dependent and anisotropic. The average conductivity σ for most tis- sue types 0.5 S/m is taken in calculation of electric field inside human body [5]. To study the induced current, the power density, the electric field and the magnetic field of grounded and ungrounded human body cylindrical model is represented by a cylinder as shown in Figure 11. Figure 7. B0z (0, y, z) near a 220kV power line over vertical distance from 0 to 18 m, current =300 Amp Figure 8. E0x (0, y, z) near a 500kV power line over vertical distance from 0 to 20 m, current =1200 Amp Figure 9. E0y (0, y, z) near a 500kV three-wire power line over vertical distance from 0 to 18 m, current =1200 Amp Figure 10. E0z (0, y, z) near a 500kV three-wire power line over vertical distance from 0 to 18 m, current =1200 Amp Figure 11. Coordinates x′ , y′, z with origin O on axis at center of cylinder and x′, y′, z′ with origin O ′on axis at base (surface of earth); z′= z+ h, h′=2h (a) (b) Figure 12. Induced current in a cylindrical conducting body (a) governed by an integral equation (b) governed by am- pere’s law Copyright © 2009 SciRes EPE O. E. GOUDA ET AL. 69 The integral equation for the current induced in a cy- lindrical conducting body as shown in Figure 12 is read- ily evaluated when the body is electrically short, a) E2z inc(0) and B2y inc(0) induce an axial current I1z(z') by using an integral equation, and b) E2z inc(0) and B2y inc(0) induce a circulating current governed by ampere’s law. The circulating current of electric field induced in the cylindrical body by B2y inc component is smaller than that induced by E2z inc and it can be ignored. When a person is under or near a power line not too close to the earth, such as lying in a bed in an upstairs bedroom near a power line, or a lineman in an elevated basket works under one of the wires, the body acts as an isolated electrically very short parasitic antenna excited by the component of the electric field parallel to its length. Since the body is a good conductor at f= 50 Hz and is long compared with its cross sectional dimensions, the well-known integral equation for the total axial cur- rent induced in a conducting cylinder by the field Es inc can be applied. Here Es inc is the part of the axial field that is constant in amplitude over any transverse cross section of the body. With a body length 2h = 1.75 m and a mean radius al = 0.14 m, the electrical half-length at f= 50 Hz is ko = 9.l6 X lo-7 << 1, where ko is the wave number of the air. The current induced in a parasitic antenna parallel to an s-directed electric field is [6–10]. 00 00 0 4coscos () cos( ) inc s s dU U jEks kh Is kkh h (7) where: s = 0 is the center of the body. s = ± h are its two ends of the body. ko is the wave number of the air, ko = ω/ c =2πf/c and c is the velocity of the light. ζ0 = (μ0/ εo) 1/2, μ0 is permeability of free space and εo is permittivity of free space. When koh<<1, (7) can be reduced to 0 0 2 () 1 Zinc Z s sZ dU jkhE s Is h (8) Note that the current at the center, s=0, is 0 0 2 (0) Z inc s s dU jkhE I (9) where 1 2 2ln() 3 dU ha , 1 0hk 1 ss s Z J sIs Es a (10) The heat generated in the body by J(s) is given by power density 2 Ps Es (11) the magnetic field in the body due to the axial current 2 ,, I sJs is given by: 1 0 2, s pB sIs, or 0 ,0.5s Bs Js The magnetic field equation can be written as 2 7 2 ,1 inc s s BsjE h 10 (12) is the radius of the cylinder. A man in good contact with the earth as shown in Fig- ure 11 can be represented by a cylinder of radius a1 has a collinear image in the earth. He may have insulated soles with a capacitive impedance ZL = - j/ ωC between them and their image, or he may be barefooted with ZL=0. The current in the body in the general case is given by [6] 2 0 2 00 211 zinc ZL Z L jkhEZ ZZ IZ ZZ hh 0zh h2 (13) where z' = z + h is measured upward from the surface of the earth and h'= 2h is the length of the body (half-length of the body and its image). 0 0 0 2 ,21n 2 m mm jh Zkh a 3 (14) where h'm is the distance from the top of the head at z'= h' to the point of maximum current at z' = z'm. Z0 is the im- pedance of the body referred to the maximum of current at the distance h'm from the top of the head. z' is the maximum height of human body. z'm is the point at the maximum current and am is the equivalent radius am= (A/π)0.5 where A is the area of the cross section at z'm. The location of the maximum current is [3] 0 2 L m L Z h Z Z Z (15) So that L L mZZ Z hh 0 2 1 1 (16) When (13) is expressed in terms of z and h, it becomes 00 00 22 11 ZincZ Z ZZ L jkhE Z zz IZ Z Zhh (17) where z is measured upward from the center of the body and h is its half-length. In (17) 0 0 0 2 -,2ln 2 m mm j Zkh a 3 h (18) where hm is the distance from the top of the head at z = h to the point of maximum current at z= zm. Where 00 m 00 -,1 m LL Zh Z Zhh Z ZZ Z (19) Copyright © 2009 SciRes EPE O. E. GOUDA ET AL. 70 Three cases of special interest are: 1) ZL= ∞ this means that the person is far from the sur- face of the earth. 2) ZL= -j/ωC this means that the person is standing on a paved road or sidewalk or directly on the earth with insulating soles, and 3) ZL=0 this means that the person is barefooted in good contact with the earth. The first case is given by (8) with s = z. the other two cases are considered as the following: The capacitance C between the soles of the feet and their image is approxi- mately given by (20) and the impedance between the soles of the feet is given by (21). Where A= 0.06 m2 is the area of the soles, εr = 2 is the relative permittivity of the insulating layer of asphalt, cement or rubber and its image, εo = 8.85×10-12 and d is the thickness of the layer and its image [3]. C=Aεrε0/d (20) ZL =-j/ωC (21) The electric field, magnetic field, axial current in the human body model, power density, electric and magnetic field due to axial current are calculated for the three cases as: 1) The human is grounded then ZL=0 this means that the person is barefooted in good contact with the earth. With ZL=0, h'=1.75 m, k0h'=2.2×l0-6, h'm = h, am =0.138, ψ=3.47, and Z0= -j0.79×108. From (13) takes the form: 8 2.22 101,0 Z inc Zz Z z I zj Ezh h (22) 2) The human is standing on a paved road or sidewalk or directly on the earth with insulating soles:-consider the first layer is consisting of 13cm of asphalt and 1.5cm of rubber, i.e. the thickness of the layer and its image of two layers is d=29cm, From (20) C = 3.66 ×10-12 F, ZL = -j8.69×108 Ω is calculated using (21) where f equals 50 Hz. At am= (A/π)0.5= (0.06/ π)0.5 = 0.138, for maximum current at zm = 0.117 m then hm=0.992m. From (14) it is found that Z0 = -j9.34×107Ω is calculated. The axial cur- rent from (17) is calculated by the following equation: 9 8.261010.194 1 Z inc Zz Z zz Iz jEhh hzh (23) 3) For a human stand directly on moist earth with rub- ber soles of 1cm thick, d = 2cm, C = 53.1×10-12 F, ZL = -j0.6×108 Ω, z'm = 0.165h' = 0.289m, h'm = 0.835h' = 1.461m, ψ = 3.11 and Z0 = -j0.847×108 Ω. The axial cur- rent is calculated as: 8 2.471010.415 1 Z inc ZZ Z z Iz jEhh 0zh (24) The electric and magnetic fields, the total current, and power densities in the interior of a human body when the body is exposed to l04 V/m in the three cases are deter- mined and graphed as shown in Figures 13 to 16. 4. Conclusions 1) The electromagnetic field near a high voltage trans- mission line is determined in analytical form. Cylindrical model is used in calculating the electric and magnetic fields, the total axial current, and power densities in the interior of a human body are determined when the human is standing on the ground under or near the line . 2) Analytical method is used for calculating the inte- rior currents and power densities of human body when the human body is grounded, isolated by soles and iso- lated in moist soil. Figure 13. Total axial current in grounded and ungrounded human model; σ=0.5 S/m, Ez inc = l04 V/m and f =50 Hz z Figure 14. Total power density in grounded and unground- ed human model; σ=0.5 S/m, Ez inc = l04 V/m and f =50 Hz Copyright © 2009 SciRes EPE O. E. GOUDA ET AL. Copyright © 2009 SciRes EPE 71 REFERENCES [1] A. H. E. Manders and N. S. Van Nielen, “The magnetic field surrounding high tension lines in the Netherlands and their influence on humans and animals,” Elektrotech- niek, Vol. 59, No. 7, 1981. [2] R. Hauf, “Non-ionizing radiation protection,” Copenha- gen, World Health Organization Regional Office for Europe, WHO Regional Publications, European Series No. 10, 1982. [3] R. W. P. Kinga and T. T. Wu, “The complete electro- magnetic field of a three-phase transmission line over the earth and its interaction with the human body,” Journal of Applied Physics, Vol. 78, No. 2, 1995. [4] D. Margetis, “Electromagnetic fields in air of travel- ing-wave currents above the earth,” Journal of mathe- matical physics, Vol. 39, No. 11, pp. 5870–5893, 1998. Figure 15. Total axial electric field in grounded and ungrou- nded human model; σ=0.5 S/m, Ez inc = l04 V/m and f =50 Hz [5] F. Barnes and B. Greenebaum, “Book of bioengineering and biophysical aspects of electromagnetic fields,” 2006. [6] J. Jin, “The finite element method in electromagnetics,” Wiley, New York, 1993. [7] D. M. Sullivan, D. T. Borup, and O. P. Gandhi, “Use of the finite-difference time-domain method in calculating EM absorption in human tissues,” IEEE Transactions on Bioengineering, Vol. BME-34, pp. 148–157, February 1987. [8] R. W. P. King, “Fields and currents in the organs of the human body when exposed to power lines and VLF transmitters,” IEEE Transactions on Biomedical Engi- neering, Vol. 45, No. 4, pp. 520–530, April 1998. [9] D. G. Wu, “Numerical analysis of interactions between fields and human bodies,” Ph.D. Thesis, University of Houston, May 2006 [10] A. Barchanski, M. Clemenc, H. De Gersem, and T. Weiland, “Efficient calculation of current densities in the human body induced by arbitrarily shaped, low frequency magnetic field sources,” Journal of Computational Phys- ics, Vol. 214, pp. 81–95, 2006. Figure 16. The magnetic field in the body due to axial cur- rent in grounded and ungrounded human model; ρ = 0.14m, σ=0.5 S/m, Ez inc = l04 V/m |