Computation of Electric Field and Human Body Induced Current under Overhead Transmission Lines

Transcription

1 Computation of Electric Field and Human Body nduced Current under Overhead Transmission Lines Adel Z El Deinl Mohamed A A Wahab2 Mohamed M Hamadd and Tamer H Emmar/ l Electrical Engineering Department High nstitute of Energy-As wan South Valley University 2 Electric Engineering Department Faculty of Engineering Minia University Minia Egypt ABSTRACT n this paper the Charge Simulation Method (CSM) is implemented to compute the electric field distribution around Egyptian three phase 500kY transmission line with the presence and absence of the human model The human body is simulated as a conducting cylinder object with a hemisphere for his head Three positions of human body model are considered to compute the induced current in it These positions are defined as under maximum minimum and average conductor heights A method to estimate the human body model induced current from the electric field computed without the presence of the human body model is proposed and its results are in good agreement with those computed with the presence of human body model under the transmission line ndex Tenns-Charge Simulation Method (CSM) Electric Field Human Body Model nduced Current 1 NTRODUCTON Power frequency (50/60Hz) electric field exposure still draws the attention of many researchers worldwide to investigate its harmful effects on living bodies especially on human beings n light of this attention as the population increases the overlap between the overhead transmission lines (OHTL) and the settlement areas causes a problem [1-4] AC electric and magnetic fields induce surface charges on human bodies and weak current flows in these bodies This is one reason why there is a potential for electric and magnetic fields (EMFs) to cause biological effects The amount of this current even if a human is directly beneath a transmission line is extremely small The maximum body current induced by electric field from a transmission line is much greater than the body current or the body current density induced by the magnetic field So induced currents from electric fields are more imortant than the current induced by the magnetic field [5-7] n this paper the charge simulation technique (CSM) is used to calculate the internal electric field and the induced current densities in human body at different positions under 500kY transmission lines (TL) these positions are identified to be under maximum minimum clearance above ground and the average height of the TL The human body is approximately simulated as a conducting cylindrical object with a hemisphere for his head An estimation method to calculate the induced current in the human body from an unperturbed electric field (without human model) is introduced the results from this estimation method and those from the charge simulation method at different positions for a human body are compared 2 STUDY MODEL OF THE SYSTEM UNDER STUDY 21 Description of the System The model of the system under study consists of a grounded human body model standing under overhead transmission lines The large conductivity and the large relative equivalent dielectric constant of the human body (about 01 S/m and ) cause the external power frequency electric field near the human body to be perpendicular to the body surface [6] This is why the human body is treated as a conducting body Using this assumption electric field at the surface of a grounded human body standing under an overhead transmission lines is computed Also because the human body is electrically very short at extremely low frequency (ELF) and very low frequency (YLF) the axial current depends primarily on the length of the human body and it is virtually independent of the cross-sectional shape [8] The simulation of a human body by cylinder with the same length and mean cross sectional area of the human body is a good approximation where the axial current induced in the cylinder is a good approximation of the current induced in an actual human body with the same length and mean cross sectional area [8-9] /10/$ O EEE

2 22 Charge Simulation Method By using CSM to model the system under study surface charges on the overhead transmission lines are simulated by infinite line charges located at each line axis and the human body is modeled by a hemisphere for the head and a cylinder of mean cross sectional area for the whole body The surface charge on the human body model is simulated by a set of ring charges arranged along the vertical axis of the human body Fig 1 shows the simulation of the system under study over a ground surface which is simulated as a perfect electric surface by using the mage Method (1M) with the CSM Values of simulation charges are determined by satisfying the following boundary conditions at a number of contour points which are selected on the surface of the overhead transmission lines and on the human body surface [5-7] 1) The potential calculated at the contour points chosen on surface of the overhead transmission lines is equal to the applied own voltage 2) The potential calculated at the contour points chosen on the human body surface is equal to zero voltage where the human body is grounded H D Ground Level a M Figure The model of the human body standing under OHTL n three-phase overhead transmission line systems the applied voltages on the three-phase overhead transmission lines are sinusoidal and can be put in a phasor form as: = VrmsLO V2 = VrmsL -120 V3 = VrmsL -240 The potential of the grounded human body model is considered to be zero voltage mposing these potentials as boundary conditions at a set of contour points on the surfaces of the overhead transmission lines and grounded L D (1) (2) (3) human body model leads to a linear system of equations in the unknown complex charges These equations have the form: n PijQj = V; (4) j=1 i = i2 n and j =i2 n where n is the number of contour points or simulating charges Pij are the potential coefficients [6] and Qj are the unknown simulating charges Equation (4) can be put in a matrix form as: [p][q] = [V] (5) The charges simulating the conductors and the human model of the system under study are given by: [Q]= [M][V] (6) where [p] [Q] [v] is a square matrix containing the potential coefficients is a complex vector of the unknown simulating charges is the vector of boundary conditions' voltages and is the inverse matrix of the matrix [p] To check the accuracy of the simulation method points at positions other than those used in the simulation technique are verified using the static form of the simulating charges given in (6) 23 Calculation of Human Body Surface Charges and nduced Currents Once the simulation charges are calculated and checked the electric fields at the surface of the human body are computed [7] The induced surface charge current density and induced current at the surface of the human body are determined as follows [10-1 1]: The charge density a at a boundary point on the human body surface at a given height = is expressed as: where En is the normal component of the electric field calculated at the boundary point on the human body and Co is the permittivity of the free space At the boundary point the induced current density J is normal to the surface and just inside the boundary is expressed as: (7)

3 Where OJ is the angular frequency of the appl ied voltage to the overhead transmission lines The induced current k just inside the boundary of a part of the body say klh is obtained by integrating J over the surface area Sk of this part as: =fmcrds S k (8) (9) 3 ESTMATON OF HUMAN BODY SURFACE CHARGES AND NDUCED CURRENTS As was explained above in (7) the charge density a at any boundary point on the human body surface is related directly to the normal component of the electric field En calculated at this boundary point on the human body surface where the human is treated as a conducting body in which the internal electric field is zero and hence the tangential component of the surface electric field is also zero This means that the surface electric field is perpendicular to the surface of the human body hence En is taken as the total surface electric field at the boundary point on the human body Then the charge density aand hence the induced current density J and the induced current k are related to the total surface electric field at this boundary point on the human body surface which in tum depends on the unperturbed electric field the shape of the human body model and its location relative to ground (grounded or isolated) Therefore by referring all calculated values (the charge densityo; the induced current density J and the induced current) to the unperturbed electric field it is possible to estimate all these values for the same human body model standing under other overhead transmission lines' configurations and hence other unperturbed electric field values 4 RESULTS AND DSCUSSON The human body model is standing under 500kY overhead transmission lines at three different positions namely; under maximum minimum and average overhead transmission lines' heights The induced current density J and the f(h section part induced current k are calculated for the same human body model standing under 500kY overhead transmission lines at those three different positions by using a different ring charges' arrangement to obtain minimum error in each case where the data in Appendix (A) are used and the phase bundles are treated in term of their equivalent radius [8] Then the induced current density J and the f(h section part induced current k are estimated for the human body model standing under minimum and maximum 500kY overhead transmission lines' heights from those values which are calculated by using CSM for the same human body model standing under average 500kY overhead transmission lines' height Fig 2 shows the calculated errors (actual potential voltage) on the check points which are located on the surface of the human body model (other than the contour points) that when standing under OHTL of maximum average and minimum heights over ground level it is noticed that the maximum errors are; and respectively Fig 3 shows the calculated annular induced current (ijnm) entering the human body model standing under various OHTL heights at various portions of its surface Fig 4 shows the calculated induced currents (ija) which are the cumulative values of the annular induced currents on the human body model standing under various OHTL heights t is seen that the maximum values occur at section part of zero height '--_--;'--' : T : :: ' t 1 - Q L = : ::1 :: :: ::: o- : :1 - S : -!i 0 ' :: =' Jt- _;f l_ ::11 :'11 rn T t T : - - : Check points on the human surface ::U t :' 1_ 1 _ C Figure 2 The calculated errors on the human body model surface standing under various OHTL heights and model points 18 r;;;; ;;;;r; :-;-;-:==:: 0' ---_-: --- ::::::::::::::::: -OU': f /'-;:: =X 16 g 14 : Hmin : : :v 12 - i) 1: : [ 1 : :5 : u 08 : : i - c 06 : : J 04 : 1: : The annular induced current (Alm) Figure 3 The calculated annular induced currents on the human body model standing under various OHTL heights

4 f14 2! 12! '0 :E 04 1: 02 :::: ' ' L ; ' The induced current (A) Figure 4 The calculated induced currents on the human body model standing under various OHTL heights Fig S shows the induced current density (ma/m 2 ) at any horizontal section in the human body standing under various OHTL heights which is the total induced current crossing this section per unit area Fig 6 and Fig 7 show the contour distribution of electric field under average height of OHTL without and with the presence of the human body model t is seen that the presence of the human body model perturbs the electric field to which it is exposed where the human body is an electrical conductor Also it is noticed that with the presence of the human body the electric field around the OHTL have no changes this means that the presence of the human body (with its approximately height of 17Sm) can't disturb the original charge distribution on the OHTL however only the local electric field around the human body is perturbed Therefore the annular induced current induced current and the induced current density depend on the OHTL heights and hence on the unperturbed electric field intensity Fig 8 shows the ratio between the perturbed and unperturbed electric field (with and without the human body model respectively) t is seen that these ratios are nearly the same under SOOkV OHTL of various heights this means that the perturbed electric field by a given human body model under OHTL depends on the unperturbed electric field This conclusion can be used to estimate the charge densityo; the induced current density J and the induced current directly from unperturbed electric field under various overhead transmission lines' configurations for the same human body model as will be explained in the following results Table 1 presents the unperturbed electric field (without the human model) perturbed electric field (with the human model) and the ratio between them at some points located on the surface of the human body standing under OHTL of average height This ratio can be used to estimate perturbed electric field from the given unperturbed electric field at its related point on the surface of the same human model Then the induced current density J and the induced current at this point are estimated by using the estimated perturbed electric field - --Hmax f 14 2! '0 c 04 1: Hae Hmin o ' :' ': 2 ---' 0 ' '' 0 -: :0-'-:: 5 07 The induced current density (mnm2) Figure 5 The induced current density distribution along the height of the human body model standing under various OHTL heights Distance from the center phase (m) Figure 6 The contour distribution of electric field under average height of OHTL without the presence of the human body u c 10 c w Distance from the center phase (m) Figure 7 The contour distribution of electric field under average height of OHTL with the presence of the human body

5 Tables 2 and 3 present the comparison between the calculated and estimated values of perturbed electric field annular induced current and induced current for the same human body model standing under OHTL of maximum and minimum heights respectively Where the estimated values are estimated by using the ratios of table 1 and the calculated unperturbed electric field in each case and the calculated values are calculated by the CSM by using a different ring charges' arrangement to obtain minimum error (Fig 2) in each case t is seen that both the estimated and calculated results are in excellent agreement C ' 3 o '- [ _ Hmin J --- Have --Hmax ol - L- L- L- L- L- o The ratio between total Electric field with and without human body Figure 8 The ratio between the electric field with and without the human body model standing under various OHTL heights Table 1 the ratio between unperturbed and perturbed electric field on some points on the human model surface standing U n d er OHTL fa H 0 verage elgl h t Height of Under OHTL of Average Height calculated Unperturbed Perturbed Ratio points on the Ew(kV/m) E2w (kv/m) E2vo / E w Human model o (m) (m) OA (m) (m) (m) OA97 (m) (m) A (m) (m) A (m) Table 2 the comparison between calculated and estimated values of perturbed electric field annular induced current and induced current for the human model standing under OHTL of mnmum h elgl h t Height of Perturbed Annular nduced Current calculated Electric Field nduced (la) points on (kv/m) Current (la/m) the Human Calc Estim Calc Estim Calc Estim model O(m) (m) A188 OA (m) (m) A (m) (m) (m) A (m) 9A (m) (m) Table 3 the comparison between calculated and estimated values of perturbed electric field annular induced current and induced current for the human model standing under OHTL of maximum height Height of Perturbed Annular nduced nduced Current calculated Electric Field Current (la/m) (la) points on (kv/m) the Human Calc Estim Calc Estim Calc Estim model O(m) A (m) OA (m) OA627 OA A05 5A (m) (m) D (m) A (m) A (m) (m) (m) A CONCLUSON A method for estimation of the perturbed electric field from the unperturbed electric field and hence estimation of the charge density a the induced current density J and the induced current from this estimated perturbed electric field for a given human body model is proposed and its results are in excellent agreement with those which are calculated by the rigorous CSM Also it is concluded that with the presence of the human body (with small height compared with OHTL height) under the OHTL the electric field around the OHTL has no changes and only the local electric field around the human body is perturbed ApPENDX (A) To calculate the charge density a the induced current density J and the induced current on the human body model under 500 kv OHTL single circuit the following data are used Tower span (d) Height of phases (H) Number of subconductor per phase (N) Diameter of a subconductor (2r) Spacing between subconductors (B) Minimum clearance to ground (h) Distance between adjacent two phases (D) The average length of the human body (L) Mean radius of the human body (a) 6 REFERENCES 400 m 191 m mm 47c m 9m 12 m 175 m 0135 m [] R W P King A Review of Analytically Determined Electric Fields and Currents nduced in the Human Body When Exposed to Hz Electromagnetic Fields

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