analysis of electromagnetic fields generated by lightning in different configurations of protection...

8/14/2019 Analysis of Electromagnetic Fields Generated by Lightning in Different Configurations of Protection Structures

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Analysis of Electromagnetic Fields Generated by Lightningin Different Configurations of Protection Structures

Caixeta, G. P.UNICAMP - FEEC/DSCE13081-970, Campinas, S.P., BrazilE-mail: [email protected]

Abstract : This paper presents results of the electro-magnetic field generated by different configurations of pro-tection structures, when lightning strikes such structures.The transitory of current in the structure, and the returncurrent is taken into account in the calculation of the field.This paper also presents an elegant expression for calculat-ing the resultant electromagnetic field produced by a tran-sient on cable currents or transmission lines. By takinginto consideration a line disposed arbitrarily in the Carte-sian coordinate system, using the Maxwell equations andapplying the magnetic potential vector, we come to thegeneralized expressions for the electric and magnetic fieldsas a function of current and position in the time domain.This expression is a generalization of the expression pro-posed by Christopoulos in [l]. The method has been shownto be very useful in applications where lines are disposedin arbitrary manners and especially in systems in whichvarious lines are interconnected, such as lightning protec-tion systems (LPS) or a grounding system. The resultsobtained with such expressions are compared to other nu-merical methods. The results are obtained applying TLM(Transmission Line Modeling) method to obtain the cur-rent transient.

I. INTRODUCTIONThis article presen ts a method fo r calculating eletromag-netic fields due to the current transient in cables or trans-mission lines in time domain. Some papers have shownresults only to a line disposed in parallel with one of thethree coordinating axes. These results are not applicable tothe majority of practical systems in which various lines areinterconnected, as, for instance, lightning protection sys-tems, grounding systems, lightning channels, transmissionlines such as parallel tracks in printed circuit boards, etc

[l] [2] [3] [4]. The technique presented in this paper solvesthis kind of problem by applying directly the proposed ex-pression, as shown in Fig. 1.In the simulation process, each component line of thesystem is discretizated on dipole elements c&r, dy or dzshort enough so that current can be considered constantalong the length of each dipole [5].Using the Maxwell equations and the magnetic potentialvector, the electric and magnetic fields are derived fromthe current of the dipole elements [5] [6]. Summing vecto-rially the contributions of each dipole element of the wholesystem, the Cartesian coordinate components (Ez, Ey, E,,HZ, HY and Hz) for the electric and magnetic fields are

Pissolato Filho, J.UNICAMP - FEEC/DSCE13081-970, Campinas, S.P., BrazilE-mail: [email protected]

Az,:,.I

.:Fig. 1. Transmission line at 3D space.

obtained from (1) and (5).

Ex=&-[($--&+($-$)$$+($-;lj)l&dr+Fiy+$$!$+3XY t--s i,dr +

3x2 zx ai,T5 0 --i,+--T4C r3c2 at +-J 1x.z ti drr5 o (2)($--$)Jdti.dr+zii+ZY ai, + 3YZ t.-- -r3c2 at T5 o d-I 1 (3)

xz ai,--+r3c2 at

1710-7803-5057-X/99/$10.00 1999 IEEE


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3zx t-I

3ZYr5 0 iadr + -i, +r4cZY di 3ZY t.-A+-r3c2 dt I

(~m2-j~z:[~

5) $+ ($-$)[&d7-] (4)

where:i, f i2(2, t-r/c), i, E i,(y, t-r/c), i, E i,(z, t-r/c),X E (z - z), Y y (y - y), 2 E (z - z), r is the distanceof the infinitesimal element (dz, dy or dz) from the pointwhere the field will be calculated P(z, y, z), c is the velocityof light in free space, t - r/c is the retarded time.In expressions (2)-(4), the three components of the elec-tric field are presented: the electrostatic component (nearfield) that is a function of charge, the radiated component(far field) that is a function of derivative current, and theinduced component that is a function of current.Fig. 3 shows the results of the electric and magneticfields obtained applying TLM (HTLM and ETLM ) andapplying the expressions above (Hcalc. and Ecalc.) at pointP( 10; 30; 5). The source considered here is a bi-exponentialwave-form given by [7] and presented on Figure 2, appliedat point P(0; 0; 20) of the lightning protection system of abuilding (Fig. 7.These expressions were applied in other simulation cases.The results obtained with the proposed expressions werecompared to the particular results obtained with the ex-pressions suggested by [l] using a simple structure consist-ing of two lines parallel to z axis. The results obtainedwith both approaches were the same.

II. RESULTSThe expressions 1 and 5 were applied in the calculationof the intensity of electric and magnetic field, respectively,for those cases shown in Figure 5 (case l), Figure 6 (cases2 and 3), and Figure 7 (case 4). For all of those cases,the lightning return stroke and the transient of current inthe structure were taken into account. Figure 2 shows the

current stroked at point P(0; 0; 20) of the LPS.

I(A)/16001200800400

0 I 1 I I I0 0.5 1.0 1.5 2.0 t (us)a) Source connected at point A(0;0;20) in LPS.

Fig. 2. Source connected at point A(0; 0; 20) of the LPS.

0 5e-07 le-06 1.5e-06a) Magneticield

~800zw 600

400200

Of 3 I I I0 0.5 1.0 1.5 2.0 t (us)b) Electric field.

Fig. 3. Electric and magnetic fields simulated by expressionsaboveand TLM model.

g30- 60 -

40 -20 -

0 I I I I , I0 5.0 10.0 15.0 20.0 25.0 30.0 t(ps)

Fig. 4. Current stroke at point P(0; 0; 20) of the LPS.

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Fig. 5. Lightning Protection System for the case 1.

. . ,, / ..,_.I,:,,.(,.,:l (20, a -3)a) LPS, case 2

Ib) LPS, case 3

Fig. 6. Lightning Protection System for the cases 2 and 3.

Fig. 7. Lightning Protection System for the case 4.

Figures 8 and 9 shows the intensity of electric and mag-netic field, respectively, obtained at the point P(5; 5; 5)for the four different cases. It shows that the intensity ofelectric field for the case 1 (Figure 5) it is a little greatherthan (pick value for about 60 kV/m) that obtained for thecase 2 (Figure 6a), and the transitory went practically thesame for these cases. For the case 3 (Figure 6b), the inten-sity of electric field is smaller than the one of the cases 1and 2, but it is greather than the one of the case 4 (Figure7). The intensity of magnetic field (Figure 9 at point P(5;5; 5) it is almost the same for all the cases, and the p ickvalue is of the order of 6,0 kA/m. From the Figure 9, wecan see that Hfieldcase 4 < Hfieldcase 2 < Hfi&caSe 1


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cases the intensity it is almost the same.

Fig. 10. Electric Fields at point P2(15 ; 20 ; 0) for four cases.Fig. 12. Electric Fields at point P3(5; 5; 15) for four cases.

Fig. 13. Magnetic Fields at point P3(5; 5; 15) for four cases.

Fig. 11. Magnetic Fields at point P2(15; 20; 0) for four cases.Figures 12 and 13 shows the intensity of electric andmagnetic field, respectively, obtained at the point P(5; 5;15) for the four cases. It shows that the intensity of electricfield for the case 4 (value of pick of 40 kV/m, aproximately)it is smaller than those obtained for the other cases. Thecase 1 presents the worst case (value of pick o f 150 kV/m,aproximately), followed by the case 2 (value of pick of 140kV/m) and for the case 3 (value of pick of the order of 130kV/m). Figure 13 shows that the intensity of magneticfield at point P(5; 5; 15) is almost the same ones for thecases 1, 2 and 3 (with value o f pick of the order of 9,5kA/m), but it is smaller for the case 4 (with the value ofpick of 5,9 kA/ m, aproximately).Figures 14 and 15 shows the intensity of electric and mag-netic field, respectively, obtained at the point P(10; 20; 15)for the four cases. It shows that the intensity of electric fieldfor the case 2 (value of pick of 90 kV/m, aproximately) it isgreather than those obtained for the other cases, followedfor the case 3 (with value of pick of 70 kV/m) and the case1 (value of pick o f 35 kV/m). The case 4 presents the bet-ter case, with value of pick of 30 kV/m. The intensity ofthe magnetic field (Figure 15) at point P(10; 20; 15) it isgreather for the case 4, followed by the case 2 and the case

value of pick of aproximately 3,7 kA/m.With the purpose of obtaining an appropriate protection,we can verify that the inclusion or exclusion of protectioncables belonging to a structure, it will depend on the anal-ysed point. For the results shown above, we can verify thatthe inclusion of cables in local close to the desirable point itshould not be done, therefore the field intensity increases.III. CONCLUSIONS

The vectorial treatment for the field components andfor distances, and the simplicity required for computa-tional applications, justifies the utilization of the proposedexpressions in problems associated with the Electromag-netic Compatibility (EMC) or Electromagnetic Interfer-ence (EMI) fields, where analytical solutions are manytimes more difficult to obtain.For more detailed analysis, to find the point with lessinfluence of the field through the study of equipotentiallines, or to find the better advantage of cables present atthe protection structure, it is easier when these expressionsare used. To find the best advantage of cables present a tthe structure it is very important to have in mind low ex-penses for the installation and the protection desired. Theelectric field due to transient current at the ground systemis not considered in this work . Nevertheless, the inclusion3. The results for the case 1 were better at this point, with of this effect is in progress as is also that of concrete walls

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Fig. 14. Electric Fields at point P4(10; 20; 15) for four cases.5000 I

Fig. 15. Magnetic Fields at point P4(10; 20; 15) for four cases.

belonging to the building, and the construction of a modelin scale reduced for field measurements.

REFERENCES[l] D. Thomas, C. Christopoulos, and E. Pereira, Calculation of ra-diated electromagnetic fields from cables usina time-domain sim-ulation, IEEE ?r-ansaction on Electromagnetic Compatibility,vol. 36, August 1994.[2] M. Rubinstein and M. A. Uman, Methods for calculating theelectromagnetic fields from a know source distribution: Aplica-tion to lightning, IEEE Transaction on Electromagnetic Com-patibility, vol. 31, May 1989.[3] C. R. Paul and D. R. Bush, Radiated fields of interconnected ca-bles, IEEE International Conference on Electromagnetic Com-patibility, pp. 259-264, September 1984.141 G. P. Caixeta and J. Pissolato Filho, Electromagnetic fields gen-erated by lighting on protection structures of telecommunicationcenters, in IEEE International Symposium on ElectromagneticCompatibility, August 1997.[5] J. R. W. S. Ramo and T. V. Duzer, eds., Fields and W aves inCommunication Electronics. John Wiley & Sons, 1984.[6] G. P. Caixeta and J. Pissolato Filho, Calculation of electro-magnetic fields from arbitrary conductors configurations in time-domain simulations, in International Symposium on Electromag-netic Compatibility, EMCRomaS8, September 1998.[7] C. Christopoulos, Propagation of surges above the corona thresh-old on a line with a lossy earth return, COMPEL, vol. 4, no. 2,pp. 91-102, 1985.

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