Modeling of an EMP conducted environment

400 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 38, NO. 3, AUGUST 1996

of an E Conducte V t Michel Ianoz, Fellow, IEEE, Bogdan I. C. Nicoara, and William A. Radasky, Senior Member, IEEE

Abstract- The International Electrotechnical Commission (IEC) decided in 1988 to produce a civil standard on the electromagnetic effects of a High Altitude EMP (HEMP). Different documents pertaining to the radiated environment and to specifications and test methods have been elaborated and are circulated. A standard conducted environment dependent on many parameters is, however, more difficult to define. The aim of this work is to present a probabilistic approach which has been adopted to define a typical current shape for the conducted environment. The distribution functions of the peak current value for horizontal and vertical polarizations based on 1710 calculated cases reflecting a variation of the elevation and azimuthal angles from 0 to 90” are presented and discussed.

Index Terms- EMP, conducted environment, peak current probability, IEC standard.

I. INTRODUCTION

N December 1988 [I] the Advisory Committee on Elec- tromagnetic Compatibility (ACEC) decided to set up a

working group in order to prepare a civil standard on the electromagnetic effects of a high altitude nuclear burst. The electromagnetic field produced is known as a high-altitude electromagnetic pulse (HEMP). This working group was placed under the authority of the Technical Committee 77 of the International Electrotechnical Commission (IEC). In March 1992, recognizing the specificity of this problem, the member countries agreed to create a Subcommittee 77C to deal with this subject [2].

The first tasks assigned to the working group were to define the radiated and conducted environments, and the specifications and tests methods for these two kinds of environments.

The radiated environment is defined as an environment in which the electromagnetic field propagates through air, soil, or any kind of dielectric material surrounding a conductor, component, or system susceptible to electromagnetic effects.

The conducted environment is a consequence of the radiated environment and cannot exist without it. The conducted environment is represented by currents or voltages induced in conductors by the electromagnetic wave due to the burst and propagating to loads representing sensitive components or installations. Because of the complexity of simulating the

Manuscript received April 20, 1995; revised April 1, 1996. This work was supported in part by the Swiss National Science Foundation which has permitted the collaboration between the Ecole Polytechnique Fkdkrale de Lausanne and the University “Politehnica” of Bucharest.

M. Ianoz is with the Ecole Polytechnique, FBdkrale de Lausanne, CH-1015 Lausanne, Switzerland.

B. I. C. Nicoara is with the Facultatea de Energetica, Universitatea “Politehnica,” Bucharest, Romania.

W. A. Radasky is with the Metatech, Goleta, CA 93117 USA. Publisher Item Identifier S 0018-9375(96)06142-X.

HEMP environment, the conducted environment is usually calculated.

In order to calculate a conducted environment, it is necessary to:

* define the HEMP radiated environment. have at your disposal a reliable field-to-transmission line coupling model to calculate the currents and voltages induced on aerial lines by the radiated environment. choose a certain number of parameters depending on the victim line geometry and its position with respect to the burst point.

As the variety of these last parameters is too great and their number large, it is impossible to define a typical conducted environment without using a probabilistic method in which a certain acceptable risk is included.

The aim of this paper is to describe the probabilistic method chosen for estimating the typical conducted environment.

11. THE RADIATED ENVIRONMENT The radiated environment due to a high altitude nuclear

burst is defined in terms of three parts: the early-time (0 5 t 5 lps), the intermediate-time (1ps 5 t 5 1 s), and the late-time (t > 1 s) HEMP [3]. In this paper we are going to consider only the early-time HEMP radiated environment which propagates as a spherical wave with a radius generally greater than 100 km; given the large radius, the HEMP environment can be considered to be a plane wave for coupling problems of interest. This high frequency field propagates along a straight path and its coverage of the earth’s surface depends on the height of burst (Fig. 1).

The electromagnetic field intensity on the ground surface is not uniform but often displays a pattern known as the “smile diagram” for burst positions located at magnetic latitudes greater than 45” (Fig. 2). Although the peak fields may vary as indicated, it has been found that variations in the HEMP field polarization, angle of incidence, and the line orientation are more important coupling factors than the pkak field value. For this reason this paper uses a single HEMP radiated environment waveform, but considers all other pertinent parameters.

This early-time field has a double-exponential shape given for the electric field by the relation

E( t ) = IC . Eol(eWat - e--bt) (1)

where the values of k , Eel, a, and b will be given later. For many years, the civil EMP assessments were based on

an electric field shape representing an envelope of the field shapes at various positions under the burst (Fig. 2) calculated under a maximizing hypothesis. This shape was known as the

0018-9375/96$05.00 0 1996 IEEE

IANOZ et al.: MODELING OF AN EMP CONDUCTED ENVIRONMENT 40 I

n, - , i o GiGiIGJ

500 3 I I 0 100 200 300 4 00 500

Hcighl of burst HOO (km)

Fig. 1. EMP illumination range on the earth’s surface as a function of the burst height.

“Bell Laboratories” wave-shape [4]. The main characteristics of this HEMP environment waveform included a peak field of 50 kV/m, a rise time of less than 5 ns, and a pulse with at half maximum of less than 200 ns. A conducted environment based on this wave-shape has been calculated by Tesche and Barnes in 1988 (51. More recent calculations performed by Longmire [6] have been analyzed and curve fit by Radasky (see Figs. 1 and 2 in Baum (31). This new curve fit represents a less severe environment than the Bell Laboratories waveform. In particular, the rise time is slightly shorter and the pulse width is narrower. Table I presents the parameters needed to represent each curve using (1) and the characteristics of each waveform. The new early-time HEMP waveform is considered to be more reasonable for a civil standard than the worst-case waveform of the Bell Laboratories, and it has been adopted by Subcommittee 77C of the IEC as the early-time portion of the IEC HEMP radiated environment.

111. ELECTROMAGNETIC WAVE-POLARIZATION

Depending on the burst location and the angle of elevation, the HEMP electromagnetic field can have different polarizations. An electromagnetic wave is vertically polarized if the electric field component is contained in the incidence plane and the magnetic field component is parallel to the ground surface. This type of polarization is also called parallel or transverse magnetic TM. An electromagnetic wave is horizontally polarized if the magnetic field component is in the incidence plane and the electric field component is parallel to the ground surface. This type of polarization is also called perpendicular or transverse electric TE.

The electromagnetic field due to a high altitude nuclear burst is partially horizontal and partially vertical polarized except over the magnetic poles. The polarization angle y is defined

as the angle between the electric field and the incident plane of the wave (Fig. 3).

This angle depends on (Fig. 4): the line of sight angle 6’ between the line of sight vector u from the burst and the vertical from the burst and ground zero. the dip angle 6’b between the earth’s magnetic field vector and the horizontal plane at the observation point. the orientation angle S between the projection of the line of sight vector on the horizontal plane at the observation point and the south magnetic pole direction in the same plane.

Table I1 gives a few values of the dip angle for different parts of the world.

The horizontally and vertically polarized incident electric field components for an arbitrary position on the earth can be determined as a function of these different parameters. In a coordinate system with Ox the vertical axis, let Ox be directed to the south magnetic pole, and Oy to East. The burst point B is situated on the Ox axis and the observation point where the field is calculated is A (Fig. 4).

The horizontally and vertically polarized incident electric fields can be calculated using the Marable approximation [4] which is generally accepted, where the incident electric field intensity E; is parallel to the polarization Ei 1 ) p, where the polarization p reads

where u is the unit vector from the burst to the observation point (Fig. 4).

Taking into account that

u = i sin 6’ cos S + j sin 6’ sin S + k cos 6’ (3) (4) Be = -iB, cos o b - kB, sin o b

the polarization reads

p = i sin 6’ sin 6 sin 6’b + j(sin 6 cos S sin 6’b

- cos 6’ cos 6’6) - k sin 6’ sin S cos 6’b

= ipZ +jp, + kp, ( 5 )

where i, j, and k are the unit vectors of the Cartesian coordinate system.

In the plane perpendicular to u, looking from the observer to the burst (Fig. 3), we define the unit vectors e6 (perpendicular to the plane of incidence) and e g (in the incidence plane and perpendicular to u). Then

(6) (7)

The components of the polarization p in the two planes

e6 = i sin S - j cos S eg = -i cos 6’ cos S - j cos 6’ sin S + k sin 6’.

defined previously read

p s = p . e6

= sin 6’ sin 6’b - cos 6 cos 6 cos d b (8) p9 = P ’ e9

= -sin S cos d b . (9)

402

Atr(10-90%) (ns) Atpw (50-50%) (ns) t , k (ns) W (J/m2)

IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 38, NO. 3, AUGUST 1996

4.1 2.5 184 23 10.1 4.8 0.983 0.193

Magnetic North

Fig. 2. Peak electric field intensity variation on earth's surface between 30° and 60° northern magnetic latitude.

TABLE I COMPARISON OF BELL LABORATORIES AND IEC EARLY-TIME HEMP WAVEFORMS

I Bell Laboratories I IEC lEoi ( V M * I 5 x 104 I 5 x 104 I

I 4 x 106 I 4 107 I

Using these two expressions, the unit components of the horizontal and vertical polarization read H; I

I

S

(10) Fig. 3. Definition of the polarization angle, y. P6 a h = - IPI Pe a, = - IPI The two components of the electric field corresponding to

the horizontal and to the vertical polarization are where IpI is the absolute value of the polarization defined by (5). Eih = ah IEi 1 % (12)

IANOZ et al.: MODELING OF AN EMP CONDUCTED ENVIRONMENT 403

t up

U

\ \ \ \ \ \ \ \ k \

Be o i I * Y I I b - - I - c

- 4 A'

south

Fig. 4. burst and observation point location.

Coordinate system and definition of various angles pertaining to the

TABLE I1 DIP ANGLE IN DIFFERENT PARTS OF THE WORLD (IN DEGREES)

Europe I USA I North Canada I Tokyo I North Brasil 55-75 1 60-75 I 90 1 50 1 0

At any particular place of a victim on the earth, the incident field which illuminates the line consists in a combination of these two components, the weight of which is determined by the calculation of y given as

sin 0 sin o b - cos 8 cos 6 cos o b

- sin S cos o b = tan-'

Iv. THE "DOMINANT" HORIZONTAL POLARIZATION

A field is completely horizontal polarized if E;, = 0, (Le., for av = 0 and y = 90") and completely vertical polarized if Eih = 0, (Le., for ah = 0 and y = 0"). From (8)-(11) it can be seen that a, = 0 if pe = 0 i.e., if 6 = 0 or K . This means that in order to have a completely horizontal polarized field the ground zero and the observation point must be situated on the same meridian line connecting the north to the south magnetic pole. From the same equations it follows that a h = 0 if p6 = 0, i.e., if the dip angle = 0 and 6 = 7r/2 or 3 ~ 1 2 . This means that a completely vertical polarized field can be obtained if the ground zero and the observation point are on the magnetic equator. The magnetic equator is defined as a circle whose circumference is perpendicular on the magnetic meridians, situated at equal distance from the two magnetic poles.

Instead of the angle 0 as described in Fig. 4 which defines the relative position of the victim with respect to the burst, the elevation angle q (Fig. 5) is easier to use.

Together with Q, an independent parameter, the azimuthal angle q5 is also defined in Fig. 5.

The relation between the angles q!~ and @ can be found from the triangle E,AB (Fig. 6) where E, is the center of the earth, B the burst point, and A the position of the line. The line AT is the tangent to the earth surface at point A and is assimilated to the ground plane, i.e., to point A' from Fig. 4.

From the triangle E,AB

where Re is the earth radius (Fig. 1). The two components of the exciting electric field the hor-

izontal Eih and the vertical Ei, given by (12) and (13) can now be calculated and used in the coupling model.

Apart from these particular cases, it is possible to find large portions of the earth where the polarization can be considered as dominant horizontal. This can be seen from the Marable curves defined as in [4 (Fig. 7)] where the coefficients ah

[Fig. 7(a)] and a, [Fig. 7(b)] are plotted as a function of the angle S with 9 as parameter (see Fig. 5), for a dip angle @b = 67" and for a burst height Hb = 100 km. It can be seen that for elevation angles 9 5 50°, ah is very near to 1 for all 6 values. For a dip angle @b = 45", the same remark applies for 9 5 30°, and for @b = 75", up to 9 5 70". Large 9 angles mean that the observation point is close to the ground zero, i.e., circles with a small curvature radius, resulting in relatively small exposed surface areas. The conclusion is that if the dip angle o b 2 45", for a majority of observation points the horizontal polarization can be regarded as dominant.

The vertically polarized field which is adopted in most HEMP coupling calculations is mainly important for burst locations near the magnetic equator and for observer locations near surface zero. On the other hand, vertical polarization does produce the worst case currents that may be important for special, high reliability systems.

V. COUPLING MODEL One of the coupling models mostly used in EMP and

lightning calculations has been introduced by Agrawal, Price, and Gurbaxani in 1980 [7], in terms of the scattered voltage and with only one source term due to the tangential net (incident and earth reflected) electric field

where 2' and Y' are the series line impedance and the parallel line admittance per unit length, defined as

404 E E E TRANSACnONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 38, NO. 3, AUGUST 1996

HORIZONTAL POLARIZATION -. inn I I C ~ T I ~ A ~

Fig. 5. Definition of the elevation angle @ and of the azimuthal angle 4.

O T B

A

Fig. 6. Relation between the burst angle 0 and the elevation angle Q.

with Rl, GI, L', and Cl the per unit length values of the resistance, conductance, inductance, and capacitance of the line.

The total voltage induced on the line V ( Z ) can be expressed in terms of the scattered voltage V" (2) and the exciting voltage V " ( 4

V ( z ) = V ( Z ) + Ve(2) h

= V " ( Z ) - 1 E: (z, z ) dz. (20)

The lumped circuit described by (16) and (17) is shown in Fig. 8.

When a finite-length line is considered, care must be taken about the terminal conditions which involve the total voltages and currents. In terms of the scattered voltage and the total current, as used in (16) and (17), the boundary conditions are expressed by

Vs(0) = -ZA . I (0) + E ~ ( x , Z ) dx (21)

Vs(0) = Zg . I ( L ) + (22)

This means that two lumped voltage sources at each end of the line, which are due to the interaction of the excitation

vertical electric field with the vertical ends of the line, are to be taken into account.

The Agrawal form of the coupling equations can be solved analytically in the frequency-domain, as shown for instance in [8], or numerically in the time-domain using the finite difference point centered method as indicated by Agrawal et al. [7].

This formulation has been used in many calculations in the frequency-domain for EMP [9]-[ 1 11 and in the time-domain for lightning-induced voltages [12], [13]. A validation of the Agrawal coupling model using a time-domain approach has been performed by using an EMP simulator [14].

VI. INDUCED PULSE PARAMETERS

The parameters of the current pulse which is induced as a result of the field-to-transmission line coupling and which are needed to define protection measures are the following (Fig. 9):

the peak value Ipeak; * the rise time T, = t 3 - tl;

the time to peak Tp = t 4 ;

the half-amplitude width T h = t 6 - t 2 ; the decay or tail time Tf = t 7 - t 5 ;

the total charge q = s,"-.. i ( 7 ) d ~ . Identical parameters are used for the induced voltage. The

probabilistic method described in what follows will be used to calculate these parameters.

VII. DERIVATION OF THE PROBABILITY FUNCTIONS

A. Horizontal or Vertical Polarization

instance the peak of the current pulse presented in Fig. 9). Let C be a characteristic value of the HEMP parameter (for

The probability function of this value is given by

Fc(z) = Prob (C 5 z) (23)

405 IANOZ et al.: MODELING OF AN EMP CONDUCTED ENVIRONMENT

0 .5

0 .o

-0.5

-1 .o

0 90 180 270 360

Marable approx. for nagn. dip 67 deg 6 (deg)

(a)

1 .o av 0.5

0 .o

-0.5

-1 .o

0 90 180 270 360

Marable approx. for nagn. dip 67 deg 6 (deg)

(b) Fig. 7. and a burst height Hb = 100 km.

(a) Unit polarization components Lyh and (b) cyu as a function of the angles of orientation 6 and elevation q, for a dip angle Ob = 67'

or by its complement

- F c ( 2 ) = 1 - Fc(x)

=Prob(C > x).

For a given polarization and for each elevation and azimuthal angles a certain value of C will result from the coupling calculation. It can be assumed that C is constant over the interval 9 - A 9 / 2 to 9 + A 9 / 2 and #J - A4/2 to #J + A#J/2, which is an acceptable assumption for small values


Fig. 8. to exciting field E:.

Differential equivalent lumped circuit of a lossy wire-ground transmission line section excited by an electromagnetic field with source due

I

1.

0

0

0

C

Fig. 9. Pulse parameters.

d tl

of A s and Aq5. (A@ = I" and Ad = 5"). The ends of the intervals are treated in a symmetric way. The probability of a particular value of C is given by the product of the derivatives of the probability functions assigned to each angle

Equation (24) is based on the assumptions that a burst is located within line of sight of a system of interest (a ground range up to 2000 km), and the random variables elevation angle and azimuthal angle are independent in probability from each other.

This assumes that the precise burst location relative to an observer is unknown, which is reasonable given current and future concerns about terrorist threats and regional conflicts. This paper is not intended to provide conducted environments appropriate for strategic conflicts where high priority facility locations may be directly targeted.

The expression of the function FQ(z) is given in the Appendix and

?r 0, Y < O

F@(Y) =

1, "52.

IANOZ et al.: MODELING OF AN EMP CONDUCTED ENVIRONMENT

lpeok ( A ) - Hor.Pol .

Rise l i m e ( s ) - Hor.Pol.

Pulse wid lh ( s ) - Hor.Pol

Pulse wid th (5) - Verl.Pol.

(b) ( 4

Fig. 10. Current peak value, rise time, and pulse width as a function of the elevation and of the azimuthal angles for (a) horizontal and (b) vertical polarization.

Let us note in what follows C ( q k , &) = c k . In this way, pairs of c k and probability values p k are determined, with k = 1, 2, . . . , n, where n is the volume of the statistical population at disposal. The pairs ( C k , p k ) are introduced in a table in the order in which they are calculated.

After the table is filled, it is arranged and renumbered in the increasing order of the C values i.e., C 1 5 Cz 5 5 C,.

The cumulative probabilities are then calculated using the relations


Fig. 11. Probability function of the peak current value for a horizontal polarization.

B. Combined Horizontal and Vertical Polarizations In a real situation, the electromagnetic field due to a HEMP

is neither completely horizontally nor vertically polarized but has an arbitrary polarization. The horizontal and vertical polarization components of the wave must be determined, and the effects of both polarizations must be superposed, which is acceptable for these linear calculations. It is also necessary to take into account that the angle 6 (see Fig. 4), takes arbitrary values between zero and 27r, with a probability function Fs(z):

2 5 0 F~(x) = { z, 0 < X 5 2 7 r

1, 2 > 2n.

The burst height is also an arbitrary parameter which can be considered as uniformly distributed between 0 and 400 km, which gives the following probability function, with w in meters:

w < o 0 < w 5 4 . lo5 F H ( w ) = 0.25 + w . i :: > 4 . io5.

The probability for C ( Q k , 4&, Sk, Hk) = C k is then

[ED ( q k >nq1 [F’4(4k) A41 ( S I , as1 [F:,(Hk)AHI = Pk. (27)

The cumulative probabilities are built up as in Section VII-A.

VIII. NUMERICAL RESULTS

A. Line Parameters The two values which are needed for defining a protection

the open circuit voltage Vo(& = 00, see Fig. 6), which when correlated with the voltage-time characteristic of

against the conducted environment due to a HEMP are:

the protection element permits one to determine the breakdown level. the short-circuit current Isc(Z2 = 0), which permits to determine the residual voltage and to define the thermic capacity of the protection element.

As the open-circuit voltage and the short-circuit current are connected through Vo = ZcIsc, where 2, is the characteristic impedance of the line, only the short-circuit current was calculated, using the combined horizontal and vertical polarization approach and the possibility of occurrence of the q, 4, 6, and H values described under Section VII-B.

The other line parameters were fixed as follows: line length: L = 1000 m; line height: h = 10 m;

0 conductor radius: rc = 0.01 m; characteristic impedance 2, = 456Q; soil permittivity: E, = 10; soil conductivity: os = S/m;

* load at the other end of the line 2 1 = 0. It should be noted that while a particular set of physical

parameters was selected for this study, the results are applica- ble over a broad range. In particular, calculations indicate that for lines above 5 m in height, the impact of conductor radius is small as it contributes primarily through the characteristic line impedance which has a logarithmic dependence on h/rc. In addition, for line heights above 5 m, ground conductivity variations between and 1O-I S/m produce peak current variations of less than &lo%. Clearly, shorter line Iengths reduce the maximum peak currents coupled at grazing angles, but the selection of 1 km length lines and the fact that the conclusions remain valid for heights over 5 m permits us to cover a reasonable variety of power distribution and telecommunication lines. It is true that for cables near or on the surface of the ground, variations in line height, conductor radius, and ground conductivity impact the coupled cursent strongly, but those cases do not enter into the aim of the


h = 100 km

409

h = 400 km

1.01

./.-.-. .. ....... ............ .............. ........................ ............... --I

0.2 f- .......................................................................................................... I

---I 1 I i THOUSANDS !

0.0 I I -.- 0 1 2 3 4 5 I [AI

Fig. 12. Probability function of the peak current value for a vertical polarization.

present paper, but are being examined separately in ongoing work at the IEC.

The incidence under a certain angle \I, is not equally probable [Fig. (Al)], but as the line can be completely arbitrarily oriented with respect to the burst location, the probability function of the azimuthal angle 4 is equally distributed.

A number of 1710 cases resulting from 90 values of the elevation angle (from 1 to 90" with a step of 1") and 19 values of the azimuthal angle (from 0 to 90" with a step of 5") have been calculated for both the horizontal and vertical polarizations. The results obtained from these 1710 cases were used to calculate the 6 parameters of the induced pulse defined in Section VI, as a function of the two angles \I, and 4 in three dimensional (3-D) graphs. In Fig. 10 the graphs for the peak current value, rise time, and pulse width are shown for both horizontal and vertical polarizations.

It can be seen that all the three functions are much more uniform for the horizontal polarization than for the vertical, although in both cases the peak currents are largest for values of 9 less than 20" (the most probable XD angles). It should be noted that the large rise times and pulse widths observed in Fig. 10 for the vertical polarization for 9 < 5" and 4 M 20" are due to the presence of two separate current pulses with similar amplitudes. The coupling to the vertical risers occurs first in time and is followed by the coupling to the long line itself. These two pulses complicated the algorithm used to evaluate the rise time and pulse width parameters.

B. Peak Current Probabilities for Horizontal and Vertical Polarizations

Using the procedure described under Section VII-A and the 1710 calculated values, the probability functions of the peak current P k ( l k ) for the horizontal and vertical polarizations have been determined and plotted in Figs. 11 and 12, respectively. Both have been calculated for a burst height of 100 km.

TABLE I11 PROBABILITY TO EXCEED DIFFERENT VALUES OF THE PEAK CURRENT (IN AMPS)

Table I11 presents the probability to exceed different peak current values for both horizontal and vertical polarizations and for two burst heights. For a 100 km burst height, these values are based on the curves presented in Figs. 11 and 12.

As expected and as seen also in Figs. 11 and 12, the peak current values for the case of the vertical polarization are larger than the values obtained for the horizontal polarization. For an equal probability to exceed a current value, the differences are more important for the high currents (small probabilities).

C. Peak Current Probabilities for Combined Horizontal and Vertical Polarization

By combining the calculation results for the horizontal and vertical polarization, four burst heights (100,200,300, and 400 km) and 36 values of the angle 6 between 0" and 360" which gives a number of 246240 cases, the method introduced in Section VII-B has permitted us to calculate the probabilities of peak current values at different geomagnetic dip angles. The result of this process for a dip angle of 67" is plotted in Fig. 13, and in Fig. 14 the peak current value probabilities for several dip angles, 0, 45, 67, 75, and 90" have been plotted. Note that with respect to Figs. 11 and 12 in this figure the definition of the probability is reversed.

From Tables I and I1 and Figs. 13 and 14 it can be seen that: the curves corresponding to dip angles greater than 45" are well grouped. The 0" results while larger are not


Fig. 13. Probability function of the peak current value for a combined horizontal and vertical polarization.

1 o4 n

f

E s - i o 3

V 3 t%

1 o-2 10" Probability > Ipeak

Fig. 14. Probability to exceed peak coupled current values for vanous local geomagnetic dip angles.

realistic due to the assumption here that the HEMP electric field peak does not decrease with o b .

the peak current values obtained for o b = 90" (vertical geomagnetic field) are the same as those presented in Table I1 for y = 90" (horizontal polarization).

* the peak current values obtained for O b = 0" (horizontal geomagnetic field) are similar (but not the same) to those presented in Table I1 for y = 0" (vertical polarization).

Given the general agreement of the horizontal and vertical polarization peak current results with those of real geomagnetic field cases, it is reasonable to apply the time waveform data computed with a single polarization to real cases. In particular, Fig. 15 illustrates the probabilities of rise time and pulse width at half maximum computed separately for horizontal and vertical polarizations. It is interesting to note that the vertical polarization produces a wider coupled current, but the horizontal polarization produces a faster rise time.

Ix . STANDARD CURRENT FOR THE CONDUCTED ENVIRONMENT

It is possible to use the information presented in this paper to develop standard current waveforms for the conducted

lo" 10.' Probability

Fig. 15. Probability to exceed rise time and effective pulse width values of coupled current for horizontal and vertical polarizations.

HEMP environment. In addition to the rise time and pulse width characteristics previously shown in Fig. 15, the rectified impulse (pulse area for a monopolar waveform) was also tabulated in this study. This parameter is more useful than the pulse width data as it supplies infomation concerning both the pulse widths and the amplitudes of the current waveforms. Table IV below presents the current rectified impulses and peak values from Fig. 14, for 6$ = 4 5 O , as a function of probability; in addition, the effective pulse width (rectified impulse divided by peak) is computed.

For this evaluation, the maximum effective pulse width of 127 ns is selected and translated into a pulse width at half maximum of 88 ns (the effective pulse width is the pulse width of a decaying exponential at a value of e-', which is wider than the pulse width at half maximum). This half width will be approximated as 100 ns.


Probability 50% 10%

1%

411

R.I. (As)> Peak I ( A ) > At,,eff.(ns) 3.7 x 10-5 500 14 1.9 x 10-4 1500 127 3.0 x 10-4 4000 75

TABLE IV RECTIFIED IMPULSE AND COMPUTED EFFECTIVE PULSE

WIDTHS FOR VERTICAL POLARIZATION OF THE EARLY-TIME HEMP FOR AN ELEVATED CONDUCTOR (h = 10 m)

The evaluation of the rise time characteristics was more difficult for this coupling study. The 10-90% rise time was shown in Fig. 15 for both horizontal and vertical HEMP polarization. The results indicated minimum rise times of 2.3 and 5.1 ns for horizontal and vertical field polarization. After careful examination it was found that these rise times did not occur when the peak currents were the largest. Since the derivative itself was not tabulated, additional calculations were required.

For complete vertical polarization of the IEC radiated electric field pulse, a maximum current derivative of 2.7 x 10l1 AIS was calculated at an elevation angle of y5 = 5" and 4 = 0". This maximum value was found from a series of calculations, and the peak value of the coupled current was maximized at the same angle. For the 1% probability case, the computed 10-90% rise time is therefore

4000 A 2.7 x 10l1 AIS

At, = (0.8)

= 1.2 x s. (28)

For the purposes of a standard, a worst case rise time of 10 ns was selected. Although it appeared likely that slower rise times would be appropriate for the more probable cases, detailed calculations showed that the 50% case indicated a rise of only 14.4 ns. Therefore, given the relatively small difference, the same pulse rise time is recommended for all cases presented in Table 111.

Given the characteristics of the current pulse derived above (t, = 10 ns, At,, = 100 ns), it is possible to construct an analytic pulse waveform that matches these characteristics

where

I p 71 = 11.5 ns TZ = 116.4 ns IC = 1.2938

is the peak value in amperes

Fig. 16 plots the suggested current waveform for the 1% probability case (I, = 4000 A). Other current pulses may be evaluated using the peak values indicated in Table 111.

X. CONCLUSION A probabilistic method to determine a HEMP conducted

environment has been developed. The method was applied to

Time (m)

Fig. 16. Suggested current waveform for the 1% probability case (Ip = 4000 A).

A

Fig. 17. Geometry used to describe elevation angles.

a typical aerial line of 1 km length and 10 m height short- circuited at both ends. First, induced peak current values for a combined horizontal and vertical polarized incident electromagnetic wave have been calculated using the probabilistic method. The result of this calculation shows that there are no large differences in the peak current values for dip angles larger than 45".

This means that it is possible to choose an average curve corresponding, for instance, to a dip angle of 67" in order to define a normalized peak current value.

Based on this last remark and on the considerations concerning the dominant horizontal polarization, the calculations for the rest of the pulse parameters as rise time, pulse width, or


Fig. 18. Probability

1

P

0.8

0.6

0.4 1 - h-100 k m

2 - h-400 k m 0.2

0 0 20 40 60 ao deg

functions for elevation angles for heights of burst o f 100 and 400 km

time to peak, decay time and total charge have been performed with a complete horizontal polarized wave, permitting the definition of three classes of conducted environment which will be proposed for the civil EMP standard.

APPENDIX PROBABILITY FUNCTION OF THE ELEVATION ANGLES

In order to determine the probability function of the elevation angles, the earth can be assumed to be a sphere with a radius r and the center at 0 (Fig. 17).

An observer situated at A at a height h above the ground will see an overhead line situated at point B on the earth’s surface under an angle a. The elevation angle is formed by the tangent to the earth surface at B contained in the plane AOB and the straight line from A to B.

The probability function of this elevation angle is given by

FQ(z ) = Prob (’$ 5 x ) . (AI)

Assuming that the surface density of the potential victims is constant over the ground surface

Surf. spher. zone BCC’B’ Fq(z) Surf, spher. zone DCC’

and

The above surfaces are given by rh S(DCC’) = 2 m -

r + h S(BCC’B’) = S(DCC‘) - S(DBB’)

=2m- [ ~ rh - D E ] . r + h

The sine theorem in the triangle OAB reads

r r + h from where

cos (x) sin(a) = ~

d . h ’

As the angle AOB = 7 ~ / 2 - a - x and as

D E = r[1 - sin (u + x)] (A81

the probability function of the elevation angles reads

This function is represented in Fig. 18 for two heights of the burst 100 km and 400 km.

It can be seen that the differences between the two functions are larger for small elevation angles. An important conclusion is also that the probability is very different for different elevation angles, which means that on a surface on the earth which is seen from a burst point, the elevation angles are not equally distributed.

REFERENCES

Advisory Committee on Electromagnetic Compatibility (ACEC), Un- confirmed Minutes of the Meeting held in Geneva on Dec. 12 and 13, 1988, Doc. (Central Ofice) 9, Jan. 1989. Sub-committee 77C: “Immunity to high altitude nuclear electromagnetic pulse (HA-NEMP),” Doc. 77C (Secretariat)l, Mar. 1992. C. E. Baum, “From the electromagnetic pulse to high-power electro- magnetics,” in Proc. IEEE, vol. 80, pp. 789-817, June 1992. Bell Laboratories, “EMP engineering and design principles,” Bell Tele- phone Laboratories, .Inc., Techn. Publ. Dept., Whippany, NJ, 1975. F. M. Tesche and P. R. Barnes, “Development of a new high altitude EMP (HEMP) environment and resulting overhead line responses,” Electromag., vol. 8, no. 2-4, pp. 213-240, 1988. C. L. Longmire, R. M. Hamilton, and J. M. Hahn, “A nominal set o f high-altitude EMP environments,” Oak Ridge National Laboratory,

A. K. Agrawal, H. J. Price, and S. Gurbaxani, “Transient response of a multiconductor transmission line excited by a nonuniform electromagnetic field,” IEEE Trans. Electromag. Compat., vol. 22, pp. 119-129, May 1980. F. M. Tesche, “An overview of transmission line analysis,” in Proc. EMCEXPO’87, Int. Con$ on EMC, San Diego, CA, May 19-21, 1987. M. Ianoz, C. A. Nucci, and F. M. Tesche, “Transmission line theory for field-to-transmission line coupling calculations,” Electromag., vol. 8, no. 2 4 , pp. 171-211, 1988. P. Degauque and A. Zeddam, “Remarks on the transmission-line approach to determining the current induced on above-ground cables,” ZEEE Trans. Electromag. Compat., vol. 30, pp. 17-79, Feb. 1988. F. M. Tesche and P. R. Barnes, “A multiconductor model for determining the response of power transmission and distribution lines to a high altitude electromagnetic pulse,” IEEE Trans. Power Delivery, vol. 4, July 1989.

ORNL/S~b/86-18417/1, 1987.

IANOZ et al.: MODELING OF AN EMP CONDUCTED ENVIRONMENT 413

M. Rubinstein, A. Y. Tzeng, M. A. Uman, P. J. Medelius, and E. W. Thomson, “An experimental test of a theory of lightning-induced voltages on an overhead wire,” ZEEE Trans. Electromag. Compat., vol. 31, pp. 376-383, Nov. 1989. C. A. Nucci, F. Rachidi, M. Ianoz, and C. Mazzetti, “Lightning-induced voltages on overhead lines.” IEEE Trans. Electromag. Compat., vol. 3.5, pp. 75-86, Feb. 1993. -,“Comparison of two coupling models for lightning-induced over- voltage calculations,” ZEEE Trans. Power Delivery, vol. 10, pp. 33S339, Jan. 1995.

ibility, transient phenoml overvoltages.

Michel Ianoz (SM’8.5-F‘96) was born in 1936. He received the B.S. degree in electrical engineering in 1958 from the Politechnical Institute Bucharest Romania and the Ph.D. degree in 1968 from the Moscow University.

He has worked on magnetic field calculations for particle accelerators and focusing devices in different nuclear research centers, among them the European Center for Nuclear Research (CERN) in Geneva. In 197.5 he joined the Power Network Laboratory of the Swiss Institute of Technology

in Lausanne, Switzerland, where he is presently teaching electromagnetic compatibility as a Professor of the Electrical Department. He is engaged in research activities concerning the calculation of electromagnetic fields, transient phenomena, lightning, and EMP effects on power and telecommunication networks. His research on EMP has been performed since 1978; on lightning since 1986. The lightning research was performed in collaboration with the universities of Bologna and Rome (Italy) and the University of Florida. He has organized and has lectured in different postgraduate courses on EMP and EMC in different countries. He is coauthor of a book on high voltage engineering, editor of a hook on electromagnetic compatibility and author or coauthor of about 100 scientific papers.

Prof. Ianoz is President of the Swiss Committee of the URSI, member of the Study Committee 36 “Electromagnetic Compatibility” of CIGRE and of the WGI of the TC77 (EMC), of the International Electrotechnical Commission (IEC). He is also an Associate Editor of the IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY and an EMP Fellow.

Bogdan I. C. Nicoara was born in Bucharest, Romania, in 1949. He received the B.Sc. degree (magna cum laude) in power engineering in 1972 and the Ph.D. in high voltage engineeiring in 1987, both from the Polytechnic Institute of Bucarest (PIB), today University “Politehnica.”

In 1972 he joined the Department of Electrical Networks of the PIB, where he is still working as an Assistant Professor lecturing on transients in power systems and high voltage engineering. His research interests include electromagnetic compat- ma in power networks, and statistics on switching

William A. Radasky (S’68-M’73-SMY92) received the B.S. degree with a double major in electrical engineering and engineering science from the U.S. Air Force Academy in 1968. He also received the M.S. and Ph.D. degrees in electrical engineering from the University of New Mexico in 1971 and the University of California, Santa Barbara in 1981, respectively.

From 1968 to 1972, he was a Research En- gineer at the Air Force Weapons Laboratory in Albuquerque, NM, working on the theory of the

electromagnetic pulse (EMP) generated by nuclear bursts. From 1972to 1984, he worked at Mission Research Corporation and JAYCOR in Santa Barbara, CA. In 1984, he founded Metatech Corporation in Goleta, CA, where he is currently President and Managing Engineer. His current interests include geomagnetic storms, electrostatic discharge, TEM cell testing issues, EMP coupling, and the development of EMC standards.

Dr. Radasky is Chairman of IEC Subcommittee 77C, which it; developing HEMP protection and test standards for civil systems. He is also an EMP fellow and a member of Eta Kappa Nu and Tau Beta Pi.

Documents

Modeling of an EMP conducted environment