IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 31, NO. 4, NOVEMBER 1989 393

TABLE I CURRENT DIVISION OF THE LAUNCH TOWER MODEL (%)

Swingam 1 2 3 4 5 6 7 8 9 10

2.74 1.46 1.23 Calculated value 5.158 3.267 2.276 1;084 0.973 0.1624 -0.278 2.922 1.781 0.5538 Experimental value 5.38 2.58 1.19 0.24

Tower foot I 11 I11 IV Elevator Cable 2-tube 5-tube Vehicle tank tray

Calculated value 10.78 11.66 12.23 11.24 17.32 7.145 5.94 4.53 17.9 Experimental value 12.1 14.2 18.3 15.5 8.17 4.33 5.99 6.33 18.0

Tsinghua Univ., Beijlng, China, TH87001 Sci. Rep., no. 195, July

D. K. Reitan and T. J. Higgins, “Accurate determination of the capacitance of a thin rectapgular,” AZEE Trans., vol. 75, pt. 1, pp.

1987, pp. 1-11. [8]

761-766, 1956.

Electroexplosive Devices

THOMAS A. BAGINSKI, MEMBER, IEEE

Abstract-Overhead transmission lines and stations generate electric and magnetic fields. The purpose of this investigation and analysis is to determine whether these fields pose a hazard to electroexplosive devices (EED’s).

I. INTRODUCTION

(a) (b) Power transmission lines and substations can operate at high voltage and current levels. The high voltages result in substantial electric fields, and large line currents produce magnetic fields. Both the electric and magnetic fields can induce currents in a conductor.

Fig. 8. Waveforms of current of the top left swingam: (a) experimental value; (b) computed value.

In order to consider the presence of high-frequency components in the waveforms, the tower is discretized as many isolated segments; thus, each segment has a discretized potential, and the capacitances of these isolated segments can be calculated by a multiconductor system capacitance coefficient algorithm. The waveforms calculated are also consistent with those obtained from the model test.

REFERENCES

[l] F. A. Fisher, “Analysis of lightning effects on launch vehicle ground support electrical cables,” in Proc. Conf. Lightning Static Electricity (Royal Aeronautical S o c . , Abirgdon, Berks, England), Apr. 1975, pp.

C. F. Wagner and A. R. Hileman, “A new approach to the calculation of the lightning performance of transmission lines III-A simplified method: Stroke to tower,’’ AIEE Trans., pt. 3, vol. 79, pp. 589-603, 1960. W. A. Chisholm and Y. L. Chow, “Lightning surge response of transmission tower,” ZEEE Trans. Power App. Syst., vol. PAS-102, no. 9, pp. 3232-3242, 1983.

[4] L. R. Neuman and P. L. Karantarov, Theory Fundamental of Electricity. Moscow: National-Energy , 1954.

[5] F. W. Grover, Inductance Calculations. New York: Dover, 1962. [6] L. Zhang, “Research on lightning surge response of a launch tower,”

Undergraduate work, Dept. Elec. Eng., Tsinghua Univ., Beijing, China, June 1986.

[7] G. Zhou, S . Wang, and L. Gong, “Algorithms of subareas of calculating the partial capacitance of a multiconductor system,”

14-17. [2]

[3]

Typical electroexplosive devices (EED’s) consist of a conductor (wire), a resistive heating element (bridgewire), and a flammable mix, as shown in Fig. 1. EED’s are used in a variety of ordnance such as impulse cartridges, rockets, and initiators. It is inevitable that during transport, the ordnance will be exposed to the electric and magnetic fields of power transmission lines. The purpose of this investigation is to determine whether these fields can induce hazardous currents in EED’s. The following analysis examines worse-case conditions for both electric and magnetic coupling, and as such, the analysis is restricted to unshielded EED’s. The analysis deals only with electrical igniters and does not concern itself with any electronics utilized to initiate the EED’s.

11. ELECTRIC FIELD COUPLING

The electric field is a vector quantity defined by its space components along three orthogonal axes. For steady-state sinusoidal fields, each space component is a phasor that may be expressed as an rms value Exy,z( V / m ) and a phase ( C # J ~ ~ , ~ ) . The total electric field

Manuscript received September 30, 1988; revised May 13, 1989. This work was supported by the HERO group at the Naval Surface Warefare Center under contract N60921-87-D-A315.

The author is with the Electrical Engineering Department, Auburn University, Auburn, AL 36849.

IEEE Log Number 8930250.

0018-9375/89/1100-0393$01 .MI 0 1989 IEEE

394 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 31, NO. 4, NOVEMBER 1989

T F l o m m o b l e Mix r,-----

I ~ :-- - ' I I * _ , - - i ;I

I . - 0 .# I - 1 ' . I

Conductor (wire)

Fig. 1. Schematic of typical electroexplosive device.

TABLE I VALUES FOR E,,

Voltage # (kV)

345

520

Measured Gradient (Emu kV/m)

7.5

8.5

765 9.0

may be expressed as

where p is the displacement charge density. Thus

[ , D - d S = I Y pdu (7)

where px , p y , and p, are unit vectors along the x , y , and z axes and where

ex(t) = Ex cos (ut + 4x)

ey(t) = Ey cos (ut + + y )

e,(t) = E, cos (ut + 4,).

(2)

(3)

(4)

Since the analysis considers worst-case conditions, only the maximum magnitude E,, of the electric field need be considered. Typical measured values for E,, corresponding to various line voltages are shown in Table I. A free body, self-contained electric field meter was utilized for the measurements shown in Table I. The theory and operational characteristics of the meter are discussed in 113.

Since E,, induces a current in a conductor, the starting point in the analysis is to determine the maximum induced current Z, associated with the electric displacement vector D, where D = eOE, and eo is the permittivity of free space (equal to 8.84 x lo-'' F/m). In addition.

Z, = dQ/dt (5 )

where Q is the displacement charge resulting from the displacement vector D and

DS= Q (8)

where the surface area of the conductor excited by the electric field is represented by S, and D is the component of the electric displacement vector that is normal to S .

The electric displacement can be represented by a phasor express- ing the maximum amplitude and time dependency. For a worst-case analysis

D,, = eoE,,eJwr.

In addition, Q,, is the maximum displacement charge, and hence, substituting Q,, into (5 ) yields

Z, = dQ-/dt (9)

Z, = jueoEm,eJwfS (10)

or

I Zsc 1 = OEOE,,S. (1 1)

Typical values of E,, and S can be used to carry out a preliminary calculation of the maximum induced displacement current flowing between a conductor and ground. Two cases will be examined. The first is for an arbitrary conductor of 1 m2 surface area. The second is for a variety of antenna arrays. In both cases, a worst-case value of the voltage gradient is chosen as 9 kV/m [2]. Substituting this value into (1 1) yields

IZscI =30x A.

Power companies have made measurements of IZ,l for various antenna configurations. Typical antenna, mast, and guy-wire config- urations tested are shown in Fig. 2.

Fig. 3 shows induced antenna current as a function of antenna height for the various configurations. These figures have been copied directly from [2] for the convenience of the reader. Additional test data is also contained in [2]. It is sufficient for the analysis to utilize the highest induced current, which is approximately 0.7 pA/(V/m) 121.

Assuming again a maximum voltage gradient of 9 kV/m yields

IZ,I =6.3 mA.

It is noted that several worst-case assumptions were made in arriving at this figure. First, the analysis assumes the igniter (EED) is connected directly as a load element between an antenna and ground. Second, the line voltage chosen was extremely high. Third, the analysis assumes the antenna is practically in physical contact with the power line.

III. MAGNETIC INDUCTION

The time-varying line current induces a magnetic field in the vicinity of the transmission line. This time-varying field can induce voltages on a loop of wire. Since the analysis once again considers worse-case conditions, the magnetic flux @ will be represented by a phasor of maximum magnitude amax with a time dependency of dw':

@ = @,,eJwf. (12)

(6) The induced voltage Von a loop is given by the time rate of change of p d v = Q

IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 31, NO.

A B C D E No.of m m m m IOJm Ekmls

N ch. 6 1.m 1.83 1.58 0.019 9.55 5 TV d ch. 3.80 2.04 1.84 0.254 9.55 28 FM ‘s’ 0.765 1.19 - - 9.55 2

Antenna dlmenclonr.

T +ltf

I .53m

+ m A I I f I f I f f f f 1 f f f 1 1 f 1 f f l l l l l l

Fig. 2. Antenna, mast, and guy-wire configurations tested

I .oo 0.80

0.60 - E 5 0.40 - - a y 0.30 2 z 0.20 t- z w a U 3 0.10 U

9 0*08 5 0.06 I- z a 0.04

0.03 ---GUY WIRE S MAST GROUNDED .

0.02 2 3 4 6 8 1 0 20

ANTENNA HEIGHT ABOVE GROUND - rn Fig. 3. I,, TV all channels.

magnetic flux density B encompassed by the loop. Or

and

+=BS (15)

4, NOVEMBER 1989 395

where B is the component of the magnetic flux density that is perpendicular to surface S. In addition,

B = poH

where po is the relative permeability of free space (po = 4~ x lo-’ H/m). Combining (12)-( 15) yields

V = jupoHS. (16)

A worst-case estimate is chosen for H = 14.34 A h [2]. This value assumes an 800-kV line operating at 2000 A of current. The surface area S is chosen as 0.1 m2. Substituting these values into (16) yields

I VI =0.677 mV.

Assuming this entire voltage is developed across an EED resistance of 1 n

V (EED resistance) zsc =

Z,=0.677 mA.

To induce even this level, the following assumptions are made. First, the loop is ungrounded. Second, the coupling area is extremely high (0.1 m2). Third, the large coupling area has an EED as the only load. Fourth, the EED is directly under an 800-kV line.

Iv . DISCUSSION AND CONCLUSION

Under worst-case conditions, the maximum induced current in an EED resulting from power-line coupling is approximately 6.3 mA for the case of electric field coupling and 0.67 mA for the case of magnetic field coupling.

A wide variety of military standards exist that discuss hazards of electromagnetic radiation to ordnance (HERO) including MIL-STD- 1377 (Navy) and MIL-STD-1385B (Navy). Although neither of these standards deal specifically with power-line frequencies, they provide a general guide to safety margins. Usually, an EED is judged safe if the maximum induced current does not exceed 15 percent of the no-fire level (MIL-STD-1385B). It is thus necessary to compare the no-fire current of an EED to the calculated values to determine if a hazard exists.

The no-fire current is a device parameter measured by the manufacturer. Parameters for some pyrotechnic devices are not publically available due to the sensitive nature of the associated ordnance system.

The no-fire levels of numerous devices including, but not limited to, impulse cartridges, blasting caps, detonations, flares, switches, and pressure cartridges were compared to determine the most sensitive. Extensive manufacturers files at the HERO facility of the Naval Surface Warfare Center (in Dahlgren, VA) were utilized for the study. The lowest no-fire current was found to be 50 mA. The maximum induced current from a power line is only 12 percent of this value.

It is concluded that worst-case coupling assumed in the previous analysis is insufficient to induce a hazardous current level in an EED.

REFERENCES [l] D. W. Den0 and L. E. Zaffanella, “Electrostatic and electromagnetic

effects of ultrahigh-voltage transmission lines,” Electric Power Re- search Inst. Palo Alto, CA, ERRI Research Project 566-1, Final Report, EL-802, June 1978.

[2 ] Transmission Line Reference Book. Palo Alto, CA: Electric Power Research Inst., ch. 8, pp. 329-379.