414
IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 48, NO. 2, MAY 2006
Magnetic Fields and Loop Voltages Inside Reducedand Full-Scale Structures Produced by Direct Lightning Strikes Ibrahim A. Metwally, Senior Member, IEEE, Fridolin H. Heidler, and Wolfgang J. Zischank
Abstract—This paper presents a numerical electromagnetic analysis of magnetic fields and loop voltages inside reduced- and full-scale lightning protection systems (LPSs) “structures” resulting from direct lightning strikes. The method of moments is employed to model the whole structure in three dimensions except the lightning channel. The lightning channel is simulated by the wellknown transmission-line model (TL model), where the influence of the lightning-channel generated electric and magnetic fields are taken into account. Three distinct LPSs were modeled, namely, reduced-scale model with return conductors (RSRC), reducedscale model with lightning channel (RSLC), and full-scale model with lightning channel (FS). The computed results of magnetic fields and magnetic-field derivatives were verified versus some experimental results for the RSRC model. In addition, the scale factor for all the measured quantities were also checked as functions of the geometrical scale factor for the positive and the negative first stroke currents. The lightning shielding performance with and without bonding was investigated for three distinct lightning stroke types, namely, the negative first, the negative subsequent, and the positive strokes. The voltages and currents generated in loops located inside the struck FS LPS were computed with and without bonding and grounding resistance and for different lightning current waveforms, locations and inclination of the lightning channel, and return stroke velocity. Index Terms—Buildings, lightning, magnetic shielding, numerical analysis, transient analysis.
NOMENCLATURE c f (Hx , Hy , Hz ) Htot H˙ tot i(t, z) Iˆl
Speed of light, m/s. Frequency, Hz. Components of magnetic field in x-, y- and z-directions, A/m. Resultant magnetic field, A/m. Resultant magnetic-field time derivative, A/m µs. Time-varying current propagating along the return stroke channel in z-direction, kA. Peak of the simulated lightning current waveform, kA.
Manuscript received June 14, 2005; revised January 12, 2006. I. A. Metwally is with the Department of Electrical and Computer Engineering, College of Engineering, Sultan Qaboos University, Muscat, Sultanate of Oman, and also with Faculty of Electrical Engineering, University of the Federal Armed Forces–Munich, EIT 7, Werner-Heisenberg-Weg 39, D-85577 Neubiberg, Germany (e-mail:
[email protected]). F. H. Heidler and W. J. Zischank are with the Faculty of Electrical Engineering, University of the Federal Armed Forces–Munich, EIT 7, WernerHeisenberg-Weg 39, D-85577 Neubiberg, Germany (e-mail: fridolin.heidler@ unibw-muenchen.de;
[email protected]). Digital Object Identifier 10.1109/TEMC.2006.873852
Iµ kg kt kI kdI /dt kH kdH /dt kU Rg sµ t t f , tt U v x, y z z∗ ∆f φ η λ τ1 , τ2 ω EM EMC EMFs FS LEMP LPS LPZ MoM pu RSLC RSRC TL
Current in the µth segment of the lightning channel, kA. Geometrical scale factor, pu. Time scale factor, pu. Current scale factor, pu. Current derivative scale factor, pu. Magnetic field scale factor, pu. Magnetic-field derivative scale factor, pu. Voltage scale factor, pu. Grounding resistance, Ω. Length of segment µ on the lightning channel, m. Time. Front and tail times, µs. Peak of the roof-to-floor voltage, kV. Return stroke velocity, m/µs. Coordinates in a horizontal plane, m. Coordinate directed outward from the ground, m. Height of the striking point, m. Frequency step, Hz. Channel inclination angle to the vertical and projected to the east end, ◦ . Constant. Wave length, m. Time constants, µs or ns. Angular frequency, rps. Electromagnetic. Electromagnetic compatibility. Electric and magnetic fields. Full-scale model with lightning channel. Lightning electromagnetic pulses. Lightning protection system. Lightning protection zone. Method of moments. Per unit. Reduced-scale model with lightning channel. Reduced-scale model with return conductors. Transmission line. I. INTRODUCTION
EARBY and direct lightning strikes to a LPS produce socalled LEMP that induce overvoltages on wires and cables inside it. Nearby lightning strikes radiate EMFs whose effects
N
0018-9375/$20.00 © 2006 IEEE
METWALLY et al.: MAGNETIC FIELDS AND LOOP VOLTAGES INSIDE REDUCED- AND FULL-SCALE STRUCTURES
are similar to those of the direct strikes, but with lower amplitudes [1], [2]. Lightning represents a severe threat to the sensitive electrical or electronic equipment located inside a struck structure. Nowadays, as a result of the ever-increasing use of highly sophisticated microelectronic circuits having very low signal levels, the equipment becomes more susceptible to electromagnetic interferences. The control of electromagnetic interferences has become the dominant task of lightning protection. The lightning phenomenon involves frequencies up to several megahertz [3], [4]. The evaluation of the EMFs inside a struck structure is essential for the EMC of the electrical and electronic systems [5], [6]. In spite of the shielding efficiency of the LPS, the interference voltages may be of magnitudes that are dangerous for control units and instruments [7]. In addition, if the magnetic field exceeds certain levels, electronically stored data can be erased [8]. Direct lightning strikes may involve a variety of current waveforms from slow-rising impulse currents of positive strokes with amplitudes up to 200 kA to fast rising currents of negative subsequent strokes with front times in the range of a few 100 ns and current peak values up to 50 kA [9]. Such currents flowing through LPS conductors to the ground may cause [3]–[6], [10], [11] 1) damage in the LPS due to thermal and electromagnetic forces, 2) secondary sparks, which might lead to fire or explosion hazard, 3) unequal high-voltage distribution, which may cause dangerous events for persons inside the struck structure, and 4) interference and malfunctioning of the electronic communications, control, and measuring systems inside the struck structure by high-magnitude disturbances. Moreover, the main reason of inadvertent outages of overhead power lines is not only due to direct lightning strikes to the lines but also due to the direct strikes to control buildings of indoor substations [12], [13], where overvoltages are produced at the input/output (I/O) ports of electronic equipment. Analyses of the EM environment inside a building during a lightning event were addressed by many authors in different ways. The fundamental works of Uman et al. [14]–[16] addresses the evaluation of the EM field due to lightning channel knowing the current distribution along the channel. Their model has also been used to compute the EM field radiated by the down conductors [6], [17]. The EM field depends on the currents flowing in the down conductors of the LPS. Prediction models for the current sharing in the down conductors include numerical [18] and analytical models [19], e.g., based on transmission line models [20] and lumped circuit models [10]. For nearby lightning strikes, electric field integral equations based methods are more suitable for the evaluation of the induced currents and EM field inside the building [4], taking into account both the LPS configuration [12] and the shielding performances of pillars and reinforced concrete walls [21]. The knowledge of magnetic fields and induced voltages inside a building in case of a direct lightning strike is crucial for the design of lightning protection measures from the EMC point of view. In the present analysis, all Maxwell’s equations are solved using the MoM to compute the transient lightning magnetic fields and their derivatives, and voltages and currents in loops
415
inside the struck LPS. The excitation of the structure under study is simulated by the TL model. Theoretical investigations into the factors affecting the lightning shielding performance are introduced and interpreted in the light of a computational EMF analysis by MoM combined with TL model. Because of the limited size, in high voltage laboratories it is not possible to build up full size structures like the LPS of buildings. Therefore, scaled models are used with reduced dimensions. Such scale modeled structures have been set up in the High Current Laboratory of the University of the Federal Armed Forces in Munich (UAFM), using a scale factor of 1:6. The measurements at scaled models necessitate that not only the geometry but also all relevant physical quantities have to be scaled. The current tests further require an injection rod to simulate the lightning channel and a current return path arrangement in order that the current flows back to the impulse current generator. Of course, this return path does not exist in reality, e.g., when a building is struck by lightning. Therefore, in the laboratory tests a quasi-coaxial arrangement of return path rods is used to minimize the influence on the test object. The objectives of the present paper are as follows. 1) A 1:6 scaled-down LPS tested in the laboratory is simulated with a computer model to validate the experimental results. 2) In a second modified computer model, the return path arrangement is removed and the current injection rod is substituted by a simulated lightning channel. This model is also based on a scaling factor of 1:6 to compare the LPS with and without return path arrangement. 3) With a third full-scale 1:1 model, a real sized structure is simulated to check the scaling factors. This full-scale model also simulates loop structures placed inside the LPS in order to investigate the induction effects in installation loops. Finally, the influence of additional quantities is examined, like the bonding and grounding of the LPS, the return stroke velocity, and the inclination of the lightning channel. II. TRANSMISSION-LINE MODEL The analysis and modeling of EMC problems is often difficult in dealing with complex environments where interacting objects of arbitrary shape are present. The TL method requires significantly more computer memory per node, but it generally does a better job of modeling complex boundary geometries. This is because both the EMFs are calculated at every boundary node, and complex nonlinear materials are readily modeled. Impulse responses and the time-domain behavior of systems are determined explicitly. The MoM, which is in widespread use, calculates charge and current distributions on such boundaries. MoM approach permits the incorporation of the treatment of large free space regions with very high efficiency. The goal of the hybrid method is to combine the advantages of the space discretizing TL method and the advantages of the MoM, thereby overcoming the limitations of both the methods and a significant reduction of computation time, which enables analysis of complex structures.
416
IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 48, NO. 2, MAY 2006
results in i(t, z) =
Iˆ1 [Exp(−(t − (z − z ∗ )/ν)/τ1 ) η − Exp(−(t − (z − z ∗ )/ν)/τ2 )].
(3)
The TL model is transferred to the frequency domain, using the time shifting theorem of the Fourier analysis. Dividing the lightning channel into segments of the length sµ , the current Iµ in the µth segment can then be determined, where sµ designates the length of the lightning channel between the starting point of the current wave and the middle of segment µ. Both the basic assumption of the TL model and the link to the MoM computer code (CONCEPT) are summarized in [24]. III. COMPUTATIONAL APPROACH
Fig. 1.
Traveling of a current wave along the return stroke channel.
The injected double-exponential lightning current to the attachment/striking point il (t) is simulated by Iˆ1 [Exp(−t/τ ) − Exp(−t/τ )], t ≥ 0 (1) 1 2 i1 (t) = η 0, t
