294 IEEE Transactions on Power Delivery, Vol. 14, No. 1, January 1999

ulticonductor Lines Above a Lossy

F. Rachidi, Member IEEE University of Toronto

Dep. of Electrical Engineering

C.A. ~ u c c i , Member IEEE University of Bologna

Dep. of Electrical Engineering

M. Ianoz, Fellow IEEE Swiss Federal Inst. of Technology

Power Systems Laboratory Toronto, Ontario M5S 3G4 40136 Bologna CH-1015 Lausanne

Canada Italy Switzerland

Abstract: ]In this paper, we first extend the Sunde logarithmic approximation for the single-wire line ground impedance to the case of a multiconductor line. The new approximate forms are compared to the general expressions which involve integrals over an infinitely long interval and an excellent agreement is found. The inverse Fourier transform of the ground impedance presents singularities which complicate the numerical solution of the transmission line equations. The order of the singularity is reduced by 1, and a careful numerical treatment is then employed to derive an equivalent and numerically more appropriate form of coupling equations in which there is no longer a singular term. Finally, finite-difference time-domain (FDTD) solutions of the coupling equations are presented and the theory is applied to calculate lightning-induced voltages on a multiconductor line. The lightning- induced voltages are calculated for the case of lossless/lossy, single-conductor/multiconductor lines and the effect of ground Posses and the presence of other conductors on the magnitude and shape of induced voltages are illustrated.

Keywords: Transient analysis, multiconductor lines, ground impedance,

I. INTRODUCTION

Telegrapher's equations for a multiconductor line above a lossy ground involve the so-called ground impedance matrix term [l]. The general expression for the elements of the ground impedance matrix are not suitable for a numerical evaluation. Accurate approximations for the diagonal terms of the ground impedance matrix (corresponding to single-wire lines) have already been presented in the literature (e.g. [2- 41). Among these approximations, the one proposed by Sunde [2] has been shown to be particularly accurate [1,5,6] within the limits of transmission line theory and, furthermore, is expressed in a very simple way.

PE-509-PWRD-0-03-1997 A paper recommended and approved by the IEEE Transmission and Distribution Committee of the IEEE Power Engineering Society for publication in the IEEE Transactions on Power Delivery Manuscript submitted August 11, 1997, made available for printing March 9, 1998

In the first part of this paper, we will extend the Sunde approximation also to the off-diagonal terms of the ground impedance matrix associated with a multiconductor line. The new approximate form will be compared to the general expressions which involve integrals over an infinitely long interval.

The second part of the paper deals with the time-domain representation of transmission line equations which is inherently more complex than in the frequency domain because of the presence of convolution integrals. Additionally, the general expression for the ground impedance in frequency-domain does not have an analytical inverse Fourier transform. Under the low frequency approximation, however, it is possible to obtain analytical inverse Fourier transform for the ground impedance matrix elements [7,8]. These time-domain analytical approximate forms can be used for instance in the transmission line coupling equations used to calculate lightning-induced effects on overhead lines (e.g. [6]) .

The inverse Fourier transform of the ground impedance presents singularities which complicate the numerical solution of the Telegrapher's equations. We will present a careful numerical treatment of the singularity and we will derive an equivalent and numerically more appropriate form of coupling equations in which there is no longer a singular term. Finally, we will apply the presented theory to calculate lightning-induced voltages on a three-phase distribution line.

II. GENERALIZED TELEGRAPHER'S EQUATIONS IN THE FREQUENCY DOMAIN

Transients occurring on overhead power lines are in general evaluated using the transmission line (TL) approximation. These transients are due to various sources such as switching operations, faults, direct lightning strikes to the lines, but also to the action of external electromagnetic fields (e.g. nearby lightning strokes). Making reference to the geometry of Fig. 1, the generalized telegrapher's equations for the case of a multi-wire system along the x-axis above an imperfectly conducting ground and in presence of an external electromagnetic excitation are given by [ 1)

%.

in which - (x)] and [Ii (x)] are vectors of voltage and current

along the line, in the frequency domain;

0885-8977/99/$10.00 0 1998 IEEE

- [L'ij], [ G i j ] , and [ Ci j ] are the matrices of per-unit- length line inductance, transverse conductance, and capacitance respectively; [ZSq] is the matrix of ground impedance which will be

discussed later in this section; - [Spi(x)] and [Sgi(x)] are the vectors of distributed source

terms representing the effect of an external exciting electromagnetic field. These terms are equal to zero in absence of an external electromagnetic field. Different equivalent expressions of these source terms can be found in [9] and are discussed in [ 101. Note that in (1) and (2), we have neglected the terms

corresponding to wire impedance and the so-called ground admittance. Indeed, it has been shown that for typical overhead lines and for typical frequency range of interest (below I O MHz), these parameters can be disregarded with reasonable approximation [6 ] .

The boundary conditions for the two line terminations, represented by their ThCvenin equivalent circuit, are given by

( 3 )

-

(4)

in which [ZA], [ Z B ] , and vAi v are respectively the [ 1 9 1 Bil equivalent ThCvenin impedances and sources at the two line terminations.

-L

111. FREQUENCY -DOMAIN GROUND IMPEDANCE MATRIX APPROXIMATE EXPRESSIONS

The expression for the mutual ground impedance between two conductors i and j (see Fig. 1) have been derived by Sunde [2, sect. 4.51 and is given by'

(5)

Note that several other expressions for the ground impedance have been proposed in the literature (e.g. [25-281). Expression ( 5 ) has been found to be accurate within the limits of transmission line approximation [I ] .

295

where Y g = djWCLo ( o g + jOEoErg ) (6) in which ox and E , . ~ are respectively the ground conductivity and relative permittivity.

In particular, the diagonal terms of the ground impedance matrix are given by

(7)

Expressions (5) and (7) are not suitable for a numerical evaluation since they involve integrals over an infinitely long interval. Several approximate expressions for 2 .. have been presented in the literature (e.g. [l-41). One of the most simple forms was proposed by Sunde himself [2] and is given by the following logarithmic function

It has been shown [5,6] that (8) is an excellent approximation of the general expression (7). In what follows, we will extend this logarithmic approximation also to off- diagonal terms. To do this, let us use the Euler's relation

j q p + e - j y

2 cos(@ = e (9) Inserting (9) in ( 5 ) , and after straightforward

mathematical manipulations, we get c

(10) in which i g is a complex quantity given by

A *

and hc is its complex conjugate.

between expressions (7) and (8), we can write Now, using the earlier-mentioned approximate identity

and

Introducing (12) and (13) into (lo), the following of the approximation can be derived for the general term Z

ground inmedance matrix gij

296

Figures 2 and 3 present a comparison between the proposed simplified expression (14) and the integral expression (5). In these figures, we have considered a two- conductor line with /q=lOm, h2=12m, separated by a horizontal distance q2=lm. The ground parameters are o g = O . O l S/m, crg=10 in Fig. 2, and og=O.OO1 S/m, crg=lO, in Fig. 3. The shaded areas in these figures indicate frequencies for which the use of transmission line approximation becomes questionable, that is when h < lOh1 (light-shaded area) and h < hl (dark-shaded area).

It can be seen that (14) represents an excellent approximation of ( 5 ) for all the considered frequency range.

Figure 4 illustrates the dependence of the mutual ground impedance, calculated using both the integral expression (5) and the proposed formula (14), as a function of horizontal distance.

1 5

A c!

& P

1

0 5

0 I E

b) 7-TTm 03 1

Frequency (Hz)

Frequency (Hz)

Fig. 2. Comparison between the expression (5 ) and the simplified form (14) for a two-wire line. The ground conductivity and relative

permittivity are 0.01 S/m and 10 respectively.

In this figure, the two conductors are at the same height above ground 151 = h2 =10m and the magnitude and the phase of the mutual ground impedance are represented as a function of horizontal distance 9 2 for a fixed frequency of B MHz (the ground parameters are og=O.Ol S/m, crg=lO).

Figure 5 presents the variation of the mutual ground impedance as a function of the vertical separation between the two conductors, for the same frequency and the same ground parameters. In this case, the horizontal distance q 2 has been set to zero, hl =lOm, and h2 has been varied from 1 m to 20 m above ground.

The comparison between figures 4 and 5 shows that while z' .. is not very sensitive to the horizontal distance, its value is markedly affected by the vertical distance between the conductors.

84

1.5 A $1

& F

1

0 5

0 1I

Frequency (Hz)

b) I I 1 1 1 1 1 1 1 I I 1 1 1 1 1 1 1 I I I I ~

)3 1E+04 E+05 1

Fiequency (Hz)

Fig. 3. Comparison between the expression ( 5 ) and the simplified form (14) for a two-wire line. The ground conductivity

and relative permittivity are 0.001 S/m and 10 respectively.

297

* 0 4 E . 5 - 2 A

0 38

0.36

0 34

0 32 0 2 4 6 8

Horizontal Distance (m)

0.87 n N,

@4

4 0.86

0.85

0.84

0.83 I I I I 2 4 6 8

Horizontal Distance (m)

Fig. 4. Dependence of mutual ground impedance of two 10 m high wires as a function of their horizontal distance.

IV. GENERALIZED TELEGRAPHER'S EQUATIONS IN THE TIME-DOMAIN

The transmission line equations (1) and (2) can be converted into time-domain to give [ 11

"[Vi a t ax

Vertical Separation (m)

Vertical Separation (m)

Fig. 5. Dependence of mutual ground impedance of two wires as a function of their vertical distance.

where €3 denotes convolution product. The matrix [Cgi j ] is

called the transient ground resistance matrix and its elements E,,? are defined as [ 111 ,

The inverse Fourier transforms of the boundary conditions for resistive loads [RA ] and [ Rg ] read

[Vi ( 0 4 = - [ R A ] [ i i ( O , t ) ] + [ v A i ( t ) ] (18)

('9)

298

V. TIME-DOMAIN TRANSIENT GROUND RESISTANCE APPROXIMATE EXPRESSIONS

The general expression for the ground impedance matrix terms in frequency-domain does not have an analytical inverse Fourier transform. Therefore, the elements of the transient ground resistance matrix in time-domain are to be, in general, determined using a numerical inverse Fourier transform algorithm.

however, it is possible to find an analytical inverse Fourier transform for the ground impedance. Adopting such an approximation, the general expression (5) becomes

In the low-frequency approximation ( og >>

And in particular, the &agonal terms are given by

for og (21)

Figures 6 and 7 present a comparison between the general expression (7) and its low-frequency approximation (21) for a 10-m high conductor above a ground with a conductivity of 0.01 S/m (Fig. 6), and of 0.001 S/m (Fig. 7). It can be seen that the validity of the low frequency approximation extends to frequencies of some MHz. This approximation could therefore be applied to the case of lightning, for which the frequency spectrum does not exceed a few MHz. For faster electromagnetic sources (such as NEMP), or poorer ground conductivity, the general expression (5) should be used to obtain more accurate results.

Timotin [7] has derived the following analytical formula for the transient ground resistance of a single-wire line under the low-frequency approximation

in which ~ ~ i i = h f p o o g and erfc is the complementary error function defined as

in which an = 1 ' 3 " ' (2n + 1)

The Timotin formula has been recently extended to the case of a multiconductor line [8]. The expression for the general term of the ground transient resistance matrix reads [81

5 ?-. E G . v - x4

3

2

1

0 1EtO3 1E+04 1E+05 1E+06 1E+07 1Et08

Requency (Hz)

Frequency (Hz)

Fig. 6. Comparison between the expression (7) and its low- frequency approximation (21). The ground conductivity and relative

permittivity are 0.01 S/m and 10 respectively.

cos(0ij) cos(- B i j ) - -

2n+1 1 - 2n-1 - can(+) 2& n=O 2 4

in which ql and e,, are defined as follows

15

E c

- %

h . v

- M

10

5

0 1I 03 1E+04 1E+05 1E+06 1E+07 1E+08

Frequency (Hz)

1 5

n

& s 1

0.5

0 1E+03 1Ec04 1E+05 1E+06 1E+07 lE+OX

Frequency (Hz)

Fig. 7. Comparison between the expression (7) and its low- frequency approximation (21). The ground conductivity and relative

permittivity are 0.001 Slm and 10 respectively.

Note that by imposing hi = hj and qj = 0 in (24) and (25),

(24) reduces to the expression (22) for 5' - ( t ) . gzl

VI. SINGULARITY TREATMENT

The ground transient resistance matrix elements 5' ..(t)

present a singularity at t = O which complicates the numerical solution of the transmission line equations. In this section, we will present a careful numerical treatment of the singularity and we will derive an equivalent and numerically more appropriate form of transmission line equations in which there is no longer a singular term.

Let us consider the first transmission line equation (15),

89

299

126) \ - - I

In order to analytically account for the singularity at t = z [12], the convolution integral in (26) can be decomposed as

where At is enough small so that a i j ( x , z ) / a z can be considered as constant in the time interval t - At I z I t ; in that case, the second integral in (27) becomes

The integral in the second member of (28) can be evaluated analytically using the small-argument approximation of the transient ground resistance given by

(29)

where qj and 0~ are defined in (25).

The result is given by

cos(0G / 2) for At << qj (30)

Specifically, for the diagonal terms we have

Taking into account (27), (28), and (30) the first transmission line equation in the time-domain (26) can be written in the following form, more appropriate for a numerical solution

where - '*

L.. =Le+- -cos Bij/2) 9 :J,""n ( written for the conductor number i 1 -.,

(33)

300

in which At is a small time step (that must satisfy the condition At << qj 1, 5' q is the transient ground resistance defined in (24), and qj and €lq are defined in (25). Note that in (32) there is no longer a singular term.

The FDTD solutions of coupling equations (32) and (16) are presented in the Appendix.

VIH. APPLICATION TO LIGHTNING-INDUCED VOLTAGES ON A MULTICONDUCTOR LINE

In our analysis, we chose two line configurations illustrated in Fig. 8. In the first, the line is composed by a single conductor located at a height h = 10 m above the ground plane. The second configuration is a three-phase line where the conductors are located at the same height above ground hl = h2 = h3 =10 m.

Fig. 8. Two considered line configuration for the calculation of lightning-induced voltages.

Each conductor is terminated on a resistance equal to its characteristic impedance determined in absence of the other conductors. The line length for the two considered configurations is I km. The electromagnetic field radiated by lightning return stroke channel is evaluated using the Modified Transmission Line (MTL) model [13,14]. The vertical component of the electric field is calculated assuming the ground as a perfect conductor. The horizontal component of the electric field radiated by lightning is computed using the Cooray-Rubinstein formula proposed by Cooray [ 151 and by Rubinstein [16].

The cliannel-base return stroke current has a peak value of 12 kA and a maximum time-derivative of 40 kA/ps, typical of subsequent return strokes [17]. The return stroke velocity is assumed to be 1.3.108 m/s [18]. Induced voltages are calculated at the line ends for a stroke location 50 m from the line center and equidistant to the Pine terminations considering (a) a perfectly conducting ground, and, (b) a ground plane charactcrized by og=O.OOB S/m and ~ ~ ~ - 1 0 .

Fig. 9 shows the induced voltages calculated at wire #I extremity. It can be seen that - the ground conductivity affects markedly the induced

voltage shape and magnitude (a detailed discussion of such an effect for the case of a single-wire line is given in

there is a shielding effect of about 20% on the induced voltage peak amplitude, due to the presence of the other conductors, as discussed in [22];

[6,19-21]). -

VIIH. SUMMARY AND CONCLUSIONS

The general expression for the elements of the ground impedance matrix in the multiconductor transmission line equations are in terms of infinite integrals. Accurate approximations for the diagonal terms of the ground impedance matrix have already been presented in the literature. Among these approximations, the one proposed by Sunde is particularly accurate within the limits of transmission line theory and furthermore is expressed in a very simple way. Hn this paper, we have extended the Sunde logarithmic approximation to the o€f-diagonal terms of the ground impedance matrix. The new approximate form is compared to the general expressions which involve integrals over an infinitely long interval and an excellent agreement has been found.

The inverse Fourier transform of the ground impedance presents singularities which complicate the numerical solution of the coupling equations. The order of the singularity is reduced by 1, and a careful numerical treatment has been employed to derive an equivalent and numerically more appropriate form of coupling equations in which there is no longer a singular term.

Finally, an FDTD representation of the coupling equations has been given and the theory is applied to calculate lightning-induced voltages on a multiconductor line. The lightning-induced voltages are calculated for the case of losslessfiossy, single-conductor/multiconductor lines and the effect of ground losses and the presence of other conductors on the magnitude and shape of induced voltages has been illustrated.

3-Phaqe. Peifect Giodnd

Single, Lorsy Giound

-40 -/ I I I I I I I 0 1 2 3 4 5 6 7 8

i Time (ps)

Fig. 9. Lightning-induced voltages.

YX. ACKNOWLEDGMENTS

Financial supports from the Swiss National Science Foundation and the Italian Ministry of Education and Research are acknowledged. Special thanks are due to F.M. Tesche for his valuable comments and suggestions.

301

(vf); = v / ( ( k - l ) h , n A t )

( i i ) ; = i i ( ( k - l )Ax ,nA t )

( s i ) ; = E g ( ( k - l ) A ~ , n A t , ~ = h i )

n , (vgi)k = v g i ( ( k - l ) h , n A t )

X. APPENDIX: for k = 1,. . . , kmax - 1

[ V B ~ ] , the boundary conditions at the line ends read [24]

-1 -1 - i);A'"

(A-4) [ ( v f ) y + l ] = [ [ g ] + [ z ] ] {[ ( ]+

[ [ ~ ] + [ ~ l - l ] [ ( v / ) ~ ] + ~ vAi)Y+1'2 ]I (A-11) hRAii

-~ FINITE-DIFFERENCE SOLUTIONS OF ' * -1 I+

[ ~ ] [ ( i i ) ; ] - [ ( v ( g i ) ~ + l / ~ ~ } ( A 4

MULTICONDUCTOR TRANSMISSION LINE EQUATIONS (vi" );+I - (vi" ); [ ( i i ) i I ! ; i l = [ 21 { [ ( s l i ) i+1 /2] - [ h

The two transmission line equations in the time domain ' * read (see Sects. IV and VI)

d [ vi (x, t ) ] + [ 4 $ [ ii (x, I)] + (A- 1) ax

for k = 2 , ..., km, - 1

L J

Note that the source term in (A-6) is computed on temporal voltage nodes and on spatial current nodes, and the source term in (A.7) is evaluated on spatial voltage nodes and temporal current nodes. Therefore, no semi-implicit approximation is used as in [23,24].

The iterative solutions of (A .6 ) and (A.7) in terms of the line-induced current and scattered voltage read

F.M. Tesche, M. Ianoz, T. Karlsson, EMC Analysis Methods and Computational Models, J . Wiley&Sons, New York, 1996. E. D. Sunde, Earth conduction effects in transmission systems, Dover publications, New York, 1968. E. F. Vance, Coupling to shielded cables, Wiley Interscience,

B , Nr 314, pp. 5-20,1976. K. C. Chen, K. M. Damrau, "Accuracy of approximate transmission line formulas for overhead wires", IEEE Truns. on EMC, vol. 31, no 4, pp . 396-397, 1989. F. Rachidi, C. A. Nucci, M. Ianoz, C. Mazzetti, "Influence of a lossy ground on lightning-induced voltages on Overhead

Lines", IEEE Trans. on EMC, Vol. 38, No 3, pp. 250-264, August 1996. A. Timotin, "Longitudinal transient parameters of a unifilar line with ground return", Rev. Roum. Sc. Techn., Electrofechn. et Energie, Vol. 12, Nr. 4, pp. 523-535, Bucarest, 1967. D. Orzan, "Time-domain low frequency approximation for off-diagonal terms of the ground impedance matrix", IEEE Trans. on EMC, vol. 39, No. 1, Feb. 1997, p. 64. F. Rachidi, "Formulation of the field-to-transmission line coupling equations in terms of magnetic excitation field", IEEE Trans. on EMC, vol. 35, no 3, August 1993. C A . Nucci, F. Rachidi, "On the contribution of the electromagnetic field components in field-to-transmission line interaction",", IEEE Trans. on. EMC, vol. 37, no 4, pp. 505- 508, Nov. 1995. F.M. Tesche, "On the inclusion of loss in time-domain solutions of electromagnetic interaction problems", IEEE Trans. on EMC, vol. 32, no 1, pp. 1-4, February 1990. T.K. Liu, F.M. Tesche, "Analysis of antennas and scatterers with nonlinear loads", IEEE Trans. on Antennas and Propagation, vol. 24, no 2, pp, 131-139, March 1976. C. A. Nucci, C. Mazzetti, F. Rachidi, M. Ianoz, "On lightning return stroke models for LEMP calculations", 19th Int. Conference on Lightning Proteciion, Graz, April 1988. C. A. Nucci, F. Rachidi, "Experimental validation of a modification to the Transmission Line model for LEMP calculation", 8th Symposium and Technical Exhibition on Electromagnetic Compatibility, Zurich, March 1989. V. Cooray, "Lightning-induced overvoltages in power lines. Validity of various approximations made in overvoltage calculations", 22nd International Conference on Lightning Protection, Budapest, Hungary, Sept. 19-23, 1994. M. Rubinstein, "An approximate formula for the calculation of the horizontal electric field from lightning at close, intermediate and long ranges", IEEE TTans. on EMC, Vol. 38, Nr. 3, pp. 531-535, August 1996. K. Berger, R.B. Anderson, H. Kroninger, "Parameters of lightning flashes", Electra, No. 41, 1975, pp. 23-37. C. A. Nucci, G. Diendorfer, M. A. Uman, F. Rachidi, M. Ianoz, @. Mazzetti, "Lightning return stroke current models with specified channel-base current: a review and comparison", Journal of Geophysical Research, Vol. 95, pp.

F. Rachidi, C. A. Nucci, M. Ianoz, C. Mazzetti, "Importance of losses in the determination of lightning-induced voltages on overhead lines", International Symposium on EMC, EMC ROMA'96, Rome, September 1996. S. Guerrieri, M. Ianoz, C. Mezzetti, C A . Nucci, F. Rachidi, "Lightning-induced voltages on an overhead line above a lossy ground a sensitivity analysis", 23rd Int. Conference on Lightning Protection, Florence, September 1996. S. Guerrieri, C.A. Nucci, F. Rachidi, "Influence of the ground resistivity on the polarity and intensity of lightning induced voltages", loth Int. Symp. on High Voltage Engineering, Montreal, August 1997. F. Rachidi, C. A. Nucci, M. JTanoz, c. hfazzetti, "Response of multiconductor power lines to nearby lightning return stroke electromagnetic fields", IEEE PES Transmission and Distribution Conference, Los Angeles, September 1996, to be published in IEEE Trans. on Power Delivery, 1997. A. K. Agrawal, H. J. Price, S. H. Gurbaxani, "Transient response of multiconductor transmission lines excited by a nonuniform electromagnetic field', B E E Trans. on EMC, vol. EMC-22, no 2, pp. 119-129,1980. C.R. Paul, Analysis of multiconductor transmission lines, Wiley Interscience, New York, 1994.

20395-20408, NOV. 1990.

[25] 9.R. Wait, "Theory of wave propagation along a thin wire parallel to an interface", Radio Science, Vol. 7 , No. 6, pp. 675-679, June 1972.

[26] A. Semlyen, "Ground return parameters of transmission lines. An asymptotic analysis for very high frequencies", IEEE Trans. on PAS, Vol. 100, No. 3, pp. 1031-1038, March 1981.

[27] R.G. Olsen, T.A. Pankaskie, "On the exact, Carson, and image theories for wires at or above the earth's interface", IEEE Trans. on PAS, Vol. 102, No. 4, pp. 769-778, April 1983.

[28] M. D'Amore, M.S. Sarto, "Simulation models of a dissipative transmission line above a lossy ground for a wide frequency range. Parts 1 and II", IEEE Trans. on EMC, Vol. 38, NO. 2, pp. 127-149, May 1996.

XI. BIOGRAPHIES

Farhad Rachidi (M'93) was born in Geneva in 1962. He received the M.S. degree in electrical engineering and the Ph.D. degree from the Swiss Federal Institute of Technology, Lausanne, in 1986 and 1991. He worked at the Power Systems Laboratory of the same institute from 1992 to 1996. He is currently with the electrical engineering department of the University of Toronto. His research interests concern lightning and EMP interactions with transmission lines. He is a member of the Task Force 33.01.01 "Eightning- induced overvoltages" of the CIGRE Working Group 33.01 "Lightning", and of the joint Task Force CIREDKIGRE "Protection of distribution networks against lightning". He i s author or co-author of more than 50 scientific pagers published on reviewed journals and presented at international conferences.

Carlo Albert0 Nucci (M'91) was born in Bologna, Italy, in 1956. Received his degree in electrical engineering in 1981 from the University of Bologna, joined the same university in 1982 as researcher in the Power Electrical Engineering Institute, where he is now Associate Professor of Power Systems. His research interests concern lightning and NEMP impact on power lines, power system simulation, and the study of powei components including medium voltage capacitors and traction batteries. He is the responsible member of the Task Force 33.01.01 "Lightning-induced overvoltages" of the CIGRE Working Group 33.01 "Lightning", and member of the joint Task Force CIREDKIGRE "Protection of distribution networks against lightning". He is author or co-author of more than 70 scientific papers published on reviewed journals and presented at international conferences.

Michel Ianoz (SM'85, F'96) was born in 1936. He received the B.S. degree in electrical engineering in 1958 from the Bucharest Polytechnic Institute, Rumania and the Ph.D. degree in 1968 from the Moscow University. He worked on magnetic field calculations for particle accelerators and focusing devices in different Nuclear Research Centers among which the European Center for Nuclear Research (CERN) in Geneva. Since 1975 he joined the Power Systems Laboratory of the Swiss Federal Institute of Technology in Lausanne where he is presently teaching EMC as a Professor of the electrical engineering department and engaged in research activities concerning electromagnetic field computation, transient phenomena, lightning and EMP effects on power and telecommunication networks. He is co-author of two books (on high voltage and EMC), editor of a book on EMC and author or co- author of more than 100 scientific papers. Prof. Hanoz is the President of the Swiss Committee of the URSP, member of the study committee 36 "EMC" of CIGRE and of the WG1 of the TC77 (EMC) of the International Electrotechnical Commission (IEC). He is also an associate editor of the IEEE Trans. on EMC.