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Influence of Building Structures on the Lightning Return Stroke Current Y. Du and M. L. Chen
Abstract—This paper addresses the influence of building structures on the lightning return stroke current. An equivalent circuit model of the lightning channel is set up using the coupled -type circuit. This model is then integrated with the building structure via the lightning attachment and the mutual coupling. With this integrated circuit model, the lightning current in the building is evaluated using EMTP. It is found that the building generally behaves like a transmission line at its rooftop and on the ground. The rooftop current is the result of the incident lightning current and its subsequent reflected currents on the ground. The propagation parameters of the building can be determined numerically using the integrated model. These parameters vary with the structure type, size, and others. In general, the impedance of typical buildings lies between the channel impedance and grounding impedance, and the lightning current on the lower floors is higher. It is also found that excluding the mutual coupling in the integrated circuit model alters the waveform of the lightning current. Index Terms—Building, equivalent circuit model, lightning return stroke current, transmission line model.
I. INTRODUCTION IGHTNING to buildings is a severe threat to both occupants and properties. It has the power to rip through rooftops, explode walls of brick and concrete and ignite deadly fires. Lightning also generates transient electromagnetic fields and surges on the power and communication circuits in the buildings. These disturbances can cause the malfunction of or damage to the sensitive equipment installed in the buildings. It is known that the damage to the properties and the injury to the occupants are primarily caused by the considerable lightning discharge current in the return stroke phase. To reduce the degree of lightning damage and to design effective protection measures, it would be necessary to investigate whether and how the lightning return stroke current can be altered by the metal structure of the buildings. The ground objects have some influence on the lightning current during a direct strike. In the past decades the waveform of natural lightning currents at tall towers has been observed all around the world [1], [2]. These observations have revealed that the lightning current at the top of a tall tower was a superposed current from the transmitted and reflected currents within the tower, and was affected by the tower height and the reflection coefficients at its two ends [2]–[6]. In [7] it has been found that
L
Manuscript received July 05, 2009. First published December 15, 2009; current version published December 23, 2009.This work was supported in part by the Research Committee of the Hong Kong Polytechnic University, and in part by the Research Grants Council of the Hong Kong Special Administrative Region under Project 515805 and Project 516008. Paper no. TPWRD-00198-2009. The authors are with the Department of Building Services Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong (e-mail:
[email protected];
[email protected]) Digital Object Identifier 10.1109/TPWRD.2009.2035420
the lightning current could be restricted if the resistance at the base of the lightning channel was increased. It has been noted that the electrostatic charge was accumulated on the metal structure of a building under the thundercloud [8]. The charge on the building would affect the lightning current in the building. In literature, however, the study of the building structure impact on the lightning return stroke current has not been addressed significantly. The lightning return stroke itself has been studied for many years. Different models have been developed for the investigation of physical characteristics of lightning, and were summarized in [9]. One of these models, the distributed-circuit model, is favored in this paper as this model can be integrated with the building for the analysis of lightning currents. In the distributed-circuit model, the lightning channel is represented by a transmission line with distributed parameters of inductance, capacitance and resistance. The distributed capacitance of the lightning channel is pre-charged by the preceding stepped leaders. The return stroke is then considered as the discharge of the charged transmission line. Generally speaking, the distributed-circuit parameters are the functions of time and space [10], [11], which arise from the variations of radius and electron density of the channel core, and from the neutralization of the corona sheath that surrounds the channel core and contains the bulk of the channel charge. In [12]–[14] linear distributed-circuit parameters were originally proposed for the return stroke model. The channel nonlinearity using simplified assumptions were taken into account in [15]–[18]. This paper discusses the possible influence of building structures on the lightning return stroke current in the building using an equivalent circuit approach. In this approach the lightning channel is modeled by a set of coupled -type circuits. It is integrated with the building structure via mutual coupling. The lightning current in the integrated circuit model is solved using the Electromagnetic Transient Program. A simple transmission line model for the building structure is presented, as well as its numerical validation. Propagation characteristics of building structures during a direct strike are investigated, and the impact of structure configurations is addressed. The effect of the charge on the building structure arising under a thundercloud is addressed as well in the paper. II. INTEGRATED MODEL FOR THE RETURN STROKE TO A BUILDING A. Model of a Lightning Channel Modeling of a lightning return stroke has been studied extensively although the integration of a building into the stroke model is seldom addressed [5], [9]. The distributed-circuit
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Fig. 1. Equivalent circuit model of a lightning channel (a) Physical model (b) Equivalent circuit model.
model in the form of a lumped-parameter ladder network is the suitable one for the study of the lightning current in a building. This model simulates the mechanism of discharge current generation, and can be integrated with the building structure for current analysis. The distributed-circuit model, however, does not take into account mutual coupling between the lighting channel and the building structure. To include the coupling with the structure on the ground, a similar model using the equivalent circuit modeling approach is adopted in this paper. In this modeling approach the lightning channel in the return stroke phase is divided into a number of small conductive segments. Each of these segments is represented by a -type circuit with longitudinal impedance R and L, and transverse capacitance C. There is mutual inductance and capacitance between any two segments (including those for the building), as illustrated in Fig. 1. Without loss of generality, a straight channel vertically oriented is selected for modeling. In this circuit model, the distributed capacitances are charged by the preceding stepped leaders. The return stroke is equivalent to the neutralization of the charge deposited on the lightning channel with the opposite charge on the ground in the case of a lightning attachment to the ground. For the discussion of the building structure impact, the circuit parameters in each segment are considered constant. These parameters may vary with the height of the lightning channel. Generally the capacitance and impedance of a conductive branch are determined by the geometrical and material properties of the branch as well as the ground. In the return stroke phase the core of a lightning channel is the primary path of the return stroke current, and is the medium determining the longitudinal impedance. The corona sheath of the lightning channel contains a large amount of charge. For simplicity the capacitance is determined by assuming all the charge is deposited on the outer surface of the corona sheath. The formulas for the coupled cylindrical shells [19], [20] are used to calculate the circuit parameters of the channel.
Fig. 2. Metal structures of modern buildings (a) Wire-grid building structure (b) Wire-plate building structure.
The lightning channel in a negative cloud-ground lightning flash has a typical length of a few kilometers. By using the typical figures for the channel length and the cloud charge, 5 km and 50 C [7], it can be found that the cloud has an approximate negative potential of 50 MV to the ground [13]. The lightning channel prior to the lightning attachment has the same potential as the cloud. It is noted that the return stroke channel has a radius of 1–10 mm [21], and that the lightning channel sheath has a radius varying from a few meters to several tens of meters [17]. The core radius was selected to be 3 mm, and the sheath radius 1 m at the channel base and 20 m at the cloud base. The channel is divided into small segments with the length of 10 m. Using the inductance and capacitance formulas in [19], [20], it is found that the average inductance and capacitance of the and 7.7 pF/m. These figures lightning channel are are comparable to the results from [11]. With the reference to was selected for the core resistance. [9] a value of B. Model of Building Structures The structural metalwork of a modern building is the skeleton of the building. It is usually used to enhance the mechanical strength of building components or directly support the load of the building itself and others. It also serves as the down conductor of a lightning protection system when it is connected to an air terminal(s) and runs vertically to the ground. If the building is struck directly by lightning, the lightning return stroke current is drained into the earth via the structural metalwork of the building.
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Fig. 3. Integrated circuit model for the lightning return stroke to a building.
Traditionally, reinforcing steel bars in columns and beams are the major part of structural metalwork. These components are interconnected, or welded together in some situations. As the span of these components is much greater than their crosssectional dimensions, they form a conductive wire grid, as seen in Fig. 2(a). Recently large metal plates have been introduced in buildings for the purpose of floor slab construction. These plates are embedded in the concrete slabs, and may cover the whole floor area. These plates are usually joined together with the columns in the buildings, and a wire-plate structure is then formed, as illustrated in Fig. 2(b). The wire-plate model can, however, be converted into a wire-grid model by replacing the plates with a number of horizontal current cells joining at the potential cells [26]. These current cells look like the branches joining at nodes in the wire grid. The detailed discussion is given in the Appendix . The equivalent circuit model of a wire-grid structure has been discussed extensively [22]–[24]. Each branch of the wire grid is divided into short elementary segments in order to take propagation phenomena into account. In a similar way to the lightning channel, each segment is modeled as a -type circuit, which is coupled with other segments, as shown in Fig. 1. For segments of a thin wire the current is represented by a filament current. The circuit parameters are calculated by using the formulas in [19], [20]. For segments of the plate, the formulas given in the Appendix are used. Thus, a highly-coupled lumped electrical network is established to represent the building structure for the analysis of lightning currents.
C. Integration of the Lightning Channel and the Building Structure The lightning channel and the building structure are represented by two sets of conductive segments. Obviously mutual coupling exists between any two segments from these two groups. Mutual inductance and capacitance between the lightning channel and building structure are then introduced. They are primarily determined by the separation distance of the segments, and become negligible if the distance is much greater than the segment dimensions. Mutual inductance and coefficient of potential between the segments in the lighting channel and building structure can be calculated by using the formulas in [19], [20] for thin wires, and the formulas in the Appendix for plate cells. Note that the mutual inductance and capacitance are not affected significantly
by the channel radii as the radii are much less than the separation distance. The mutual capacitance is charged by the preceding downward leaders, and holds the negative charge on the channel and positive charge on the building structure. Therefore, the charge on the building is already included in the model if the capacitance of the lightning channel is pre-charged. The lightning channel is connected to the building structure via the upward moving streamer channel in the return stroke phase. The upward moving streamer channel is modeled by a serials switch with T-type circuits, as shown in Fig. 3. The length of this channel is in the order of several tens of meters, and was assumed to be 25 m in this paper. The closing operation of the switch mimics the “final jump” in the lightning attachment, and initiates the return stroke process. The circuit parameters are determined with the parameters of the lightning channel core. is added in the upward moving Time-variant resistance streamer channel for simulating the wave front of the lightning current [4]. It is proportional to the inverse of time (in s), and and a minimum value of has a maximum value of . III. SIMULATION OF LIGHTING RETURN STROKE CURRENTS WITH THE INTEGRATED MODEL A. Simulation Approach A lightning return stroke to a ground object, such as a building, is represented by a highly coupled electrical circuit. The return stroke current is generated when the switch to the ground object is closed. Electrical equations for such a circuit can be set up using circuit analysis techniques, and the lightning current in the building be solved using a time-domain procedure. The parameters of the circuit components are determined by using the established formulas at the principal frequency [25]. In the all simulations made for this paper, the principal frequency was set to be 250 kHz. The Electromagnetic Transient Program (EMTP) is a universal program for digital simulation of the transient phenomena. It solves lumped circuit problems in time domain efficiently. The equivalent lumped circuit for the lightning return stroke to a building was already available. EMTP was then applied to simulate the return stroke process and to compute the lightning current at different locations in the building and along the lightning channel. As EMTP did not have any procedure of calculating circuit parameters of short conductive segment or cells, separate circuit parameter procedures were developed on the platform of MATLAB to generate network parameter files and EMTP input files.
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Fig. 5. Lightning discharge currents at the bottom and top of a 400 m-tall tower.
Fig. 4. Lightning currents at the different heights of the channel.
B. Model Validation The model of a lightning channel shown in Fig. 1 was evaluated first before it was applied for the discussion of the structure impact. For this evaluation the lightning return stroke terminated on the ground directly or on a 400 m tall tower with the . grounding resistance of Fig. 4 shows the lighting currents at different heights of the channel when the return stroke terminates on the ground in a negative lightning flash. It is noted that both the peak current and the rate of change of the current rising front decrease negatively with increasing the channel height. At the channel base, , and the rate the peak current is approximately equal to s. At the 100 m of current change in the wave front is height, these parameters turn to be and s. As shown in [9], [21] a few percent of negative first return stroke currents are expected to exceed 100 kA. The 1st return stroke current measured at the ground level rises to an initial peak of typically about 30 kA (the median value) in some microseconds and decays to a half-peak value in some ten microsecond. By using measured electric field derivatives and the simple transmission line model to obtain crude estimates of the lighting current, the average value of the peak of di/dt waveform for the s. These values of the peak curfirst return stroke is rent and steepness of current wave front evidence that the lightning channel model used is reasonable and generally matches the physical characteristics of a lightning return stroke. Fig. 5 shows the rooftop and ground currents when the return stroke terminates on a 400 m tall tower. In the simulation the tower was represented by a 400 m-long cylindrical conductor. This long cylinder was divided into 40 segments, and those segments were modeled as a set of coupled -type circuits similar to the circuits for the building structure. The ground current has a wave front similar to the current on the tower top, but it has a higher negative peak value. A reflected current is generated at the ground level, and travels back to the tower top to create the 2nd peak. The reflection of the lighting current at the tower bottom and top is clearly observed. This pattern of the lighting
current waveforms is similar to that of the current waveforms measured at the towers [2]–[5]. Non-zero values of the ground current are observed in the early time. This is primarily due to the use of a coupled lumpedcircuit model for the simulation. In a lumped circuit the voltage or current responds without any delay when the circuit is excited. The non-zero values are immediately generated even at the far end of the circuit. In the coupled model, the voltage across a segment is contributed by both self-impedance and mutual-impedance components. At the far end of the circuit, the voltage coupled from other segments can increase negatively fast than the total voltage in a negative flash. This leads to an increase of the segment current, that is, a current with positive values at the early time. IV. INFLUENCE OF THE BUILDING STRUCTURE ON THE LIGHTNING CURRENT A. Reference Building A 100 m-tall building with the floor dimensions of was selected for the investigation. In the analysis the building was substituted with either the wire-grid structure or the wire-plate structure. Such a structure was made of four vertical conductors as well as one full-size plate or mesh on each floor, as shown in Fig. 6. The vertical conductors and the conductors in the mesh were modeled as thin wires with the radius of 10 mm. The conductive plate was 2 mm thick. These conductive elements were divided into small segments with the length of 6 m. The earth resistivity was assumed to be . Ground terminations were made at four corners with each [29]. They a low-frequency grounding resistance of were represented by pure resistance as the principal frequency was less than a few of MHz [30]. The effect of the pre-deposited charge on the building structure was already taken into account in the integrated model. B. Propagation and Reflection of the Lightning Current in the Building Fig. 7 shows the lightning currents in the 9-storey building with the wire-plate structure during a negative return stroke.
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Fig. 7. Lightning currents at the rooftop and on the ground.
Fig. 8. Distribution of the peak current (magnitude) on the floor in the building.
C. Transmission Line Model Fig. 6. Configurations of the lightning return stroke to a building (a) Wire-grid building structure (b) Wire-plate building structure.
These currents were measured at the attachment point (building rooftop) and on the ground (ground termination). It is noted that the current on the ground has a wave front similar to that at the rooftop, but has a time delay and a larger peak value. This indicates that the lightning current transmitted into the building propagates downward, and part of the current is reflected on the ground. Because the grounding impedance is small the positive reflection of the lightning current is observed. This reflected current continues to propagate upward to the roof, and generates the 2nd peak of the current at the rooftop, as seen in Fig. 7. The rooftop current is a superposed current from the transmitted lightning current and its subsequent reflected currents from the ground. Such propagation and reflection of the lightning current were also observed in towers via physical measurement [1], [2]. Because of the low grounding impedance the lightning current on lower floors are usually higher during a direct strike. Fig. 8 shows the distribution of the peak current on the floor against floor No. within the building. The waveform of these currents at two extreme ends of the building, that is, the roof and the bottom are illustrated in Fig. 7.
As the lightning current propagates and reflects within the building, it is reasonable to represent the building with a transmission line. Fig. 9 shows a simple transmission line model for the generation of the lightning current within the building. The model is characterized by characteristic impedances and of the channel and building, and grounding impedance . The values of these impedances are determined numerically via the simulation using the integrated circuit model. According to the reflection of the current wave on the ground, characteristic of the building can be calculated with the folimpedance lowing formula: (1)
where and are the incident current and transmitted current at the ground level, as illustrated in Fig. 9. The incident current is simply determined by measuring the ground current when the grounding impedance is set to zero. Characteristic impedance of the lightning channel can be determined in a similar way. The current wave propagates and attenuates along the building. The attenuation coefficient is obtained by dividing the 1st peak current on the ground by that at the rooftop. The propagation velocity of the current wave is estimated by
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TABLE III PROPAGATION PARAMETERS OF THE BUILDING WITH WIRE-GRID AND WIRE-PLATE STRUCTURES (Building Height = 100 m)
Fig. 9. Transmission line model of a lightning return stroke to a building with reflection coefficients and at the rooftop and on the ground.
TABLE IV PROPAGATION PARAMETERS OF THE BUILDING WITH THE WIRE-GRID STRUCTURE HAVING DIFFERENT BUILDING HEIGHTS (Floor Height = 10 m)
TABLE I TYPICAL PARAMETERS OF THE TRANSMISSION LINE MODEL
TABLE V PROPAGATION PARAMETERS OF THE BUILDING WITH THE WIRE-GRID STRUCTURE HAVING DIFFERENT FLOOR NUMBERS (Building Height = 100 m)
TABLE II COMPARISON OF CURRENT PARAMETERS DETERMINED WITH TWO DIFFERENT MODELS
D. Propagation Parameters of Building Structures
measuring the time delay of the current wave at 10% of the 1st peak current between the roof and the ground. Table I shows the propagation parameters of the transmission line model for the lightning channel and building mentioned above. Using these given parameters the transmission line model was tested by comparing the rooftop currents calculated using the integrated circuit model and the transmission line model, respectively. In the transmission line model, the incident current wave in the lightning channel is determined by the current at the base when the channel is shorted at its base. For simplicity, only the 1st and 2nd peaks of the rooftop current and the time delay of these two peaks are selected for comparison. Table II shows these parameters of the rooftop current. It is clearly seen that the results calculated from two models match well. It is noted in the Fig. 7 that the ground current oscillates with s approximately. This oscillation is the time period of mainly caused by the reflection of the lightning current within the building. Note the reflection for the currents at the rooftop and on the ground are negative and positive, respectively. The two successive reflected current waves from the rooftop have alternative “ ” and “ ” signs. This causes the ground current to change from the hill to the valley in one round trip. The complete s using the traveling time for one cycle is found to be figure in Table II, which is comparable to the time measured from Fig. 7.
The lightning current in the building is primarily determined by the lightning channel, but is affected by the building structure due to its propagation and reflection within the building. Characteristic parameters of the transmission line model of the building are then critical in determining the lightning current waveform. Currently there is no simple solution to these parameters. The numerical simulation with the integrated model becomes necessary in order to find out the parameter values for the building. Table III shows the calculated values of characteristic impedance, propagation velocity and wave attenuation of the 9-storey building with different structure configurations. It is noted that the values of these parameters associated with the wire-grid structure are higher. When the floor size is increased ) the impedance becomes less, the attenuation (e.g., coefficient higher, and the propagation slower in both cases. The building height also affects the characteristic parameters. Table IV shows the calculated characteristic parameters of the wire-grid building with different heights. It is found that the impedance increases with increasing the building height. Table V shows the propagation parameters of the 100 m-tall building with different floor numbers. There is no much difference of propagation velocity and attenuation when the floor number increases, but the characteristic impedance increases with increasing the floor number. The results in Tables III–V indicate that the characteristic impedance of a building is greater than the grounding impedance. The characteristic impedance varies more significantly than other parameters, and it plays a significant role in determining the lightning current within the building. Generally speaking, the building with higher characteristic impedance or
DU AND CHEN: INFLUENCE OF BUILDING STRUCTURES ON THE LIGHTNING RETURN STROKE CURRENT
Fig. 10. Lightning currents in the building with the wire-plate structure using (a) the coupled model and (b) the uncoupled model.
less wave attenuation will lead to larger lightning currents in the building according to the transmission line theory. E. Effect of Mutual Coupling With the Building Structure In the traditional analysis of lightning currents [22]–[24], the return stroke is modeled as an independent current source. This current source is directly connected to the building, and the inductive/capacitive coupling with the building structure is not considered. In reality such mutual coupling does exist physically. In the integrated circuit model this coupling is modeled by mutual capacitance and inductance. To reveal the coupling effect from the building structure, the lightning currents are analyzed in two models, that is, (a) retaining the mutual coupling link (coupled model) and (b) removing the mutual coupling links (uncoupled model). In model (a) the mutual capacitance retains the cloud voltage prior to the lightning attachment, and holds the negative charge on the channel and positive charge on the building structure. In model (b) no charge is on the building structure. All the charge for neutralization in the lightning channel comes from the ground. The lightning currents at the rooftop of the reference building described previously as well as on the ground were simulated, and are given in Fig. 10. It is noted that the waveforms of the rooftop currents in two cases are similar. The rooftop current in the uncoupled model has a relatively lower negative value of the 1st peak. The higher negative peak current in the coupled model is primarily due to the additional charge on the mutual capacitance between the lightning channel and the building. Because the mutual capacitance is relatively small, the change of the lightning current in the building is not so significant. By examining the waveforms of the ground currents it is found that the uncoupled-model current has a larger peak current and a shorter traveling time. The faster velocity and large ground current result in the increase of the rooftop current in magnitude around the 2nd peak, and the increase of the peak currents within the building. The difference of the peak currents within the building is found to be around 10%.
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V. CONCLUSION This paper presented the equivalent circuit approach for simulating the lightning current in a building, and the evaluation of the building structure influence on the lightning current during a direct strike. The lightning channel formed by the downward stepped leaders was represented by a set of charged and coupled -type circuits. The metal structure of the building was modeled as the coupled -type circuits as well. A special modeling technique was adopted to tackle the non-uniform distribution of the plate current. These two sub-networks were linked together via the lightning attachment as well as the inductive/capacitive coupling. This integrated circuit model allowed the use of EMTP for calculating the lightning currents in the building. The building structure is a three-dimensional conductive structure. It behaves approximately like a transmission line at its rooftop and on the ground during a direct strike. The transmitted lightning current from the channel propagates downward with attenuation, and reflects on the ground. The total rooftop current and the total ground current are the results of the incident current and its subsequent reflected currents. Propagation parameters of the building structure can be determined numerically using the integrated circuit model. They are affected by structure details, such as size and type. Both characteristic impedance and propagation velocity vary with structure configurations. In general, the impedance of typical buildings lies between the channel impedance and grounding impedance, and the lightning current on the lower floors is generally higher than that on the upper floors. The mutual coupling between the lightning channel and building structure does have some effect on the lightning current within the building. The model excluding the mutual coupling leads to the propagation of a current wave with less attenuation and higher velocity, subsequently the waveform distortion around the 1st peak and/or 2nd peak of the lightning currents within the building. An accurate lightning channel model certainly helps to determine exact lightning currents in the building. Considering the difficulty in having such a model for integration with the building structure, a charged coupled-circuit model was employed. This model exhibits general patterns of the lightning current, and was found to be suitable for the discussion of building structure impact. In fact, accurate parameters of the distributed circuit were not critical in the discussion of lightning characteristics of the building structure. APPENDIX The plate in the wire-plate structure has a thickness much less than other characteristic dimensions. It is reasonable to assume the current within the plate flows in the horizontal plane [26]. The plate can be then represented by a set of potential cells, as illustrated in Fig. 11. The current cells are therefore formed by taking the volume between the centers of these adjacent potential cells, as illustrated in Figs. 11(b) and 11(c). Fig. 11 shows the cells of a plate in a local Cartesian coordinate system with , and axes. Both current and charge in the current and potential cells are considered constant. The current density in a current cell of the plate, however, may vary significantly across its thickness
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capacitance matrix is then obtained by inverting potential matrix . A similar procedure for plate modeling was described in [26]. REFERENCES
Fig. 11. Potential and current cells of a plate (a) Potential cells (b) s-dir. current cells (c) t-dir. current cells.
because of the skin effect. The current density in an infinitely large plate can be expressed analytically [27], and is adopted for the current in the current cell. The density distribution function along the axis is given by (2) , and is the skin depth of the plate. where Both and are the cell width and depth, respectively. is the total current in the current cell. As the separation distance of two adjacent plates is much greater than plate thickness, the proximity effect is ignored in (2). By using the relationship of electrical scale and magnetic vector potentials on the cells and using the average potential method [19], both inductance and coefficient of potential between and source cell are calculated by observation cell (3) (4) where and are respectively the points located in surface of the observation cell and the surface (or volume ) of and are the areas of corresponding the source cell. surfaces. Both and are the plate conductivity and angular frequency. The resistance of the cell is determined by (5) and are the width and length of surface . Equawhere tions (3) and (4) do not take the ground influence into account, but can be modified by adding the image terms in (2) and (3) using the complex image method [28]. After applying (3)–(5) for all segments of the building structure, full resistance, inductance and potential matrices ( , and ) are established. The
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DU AND CHEN: INFLUENCE OF BUILDING STRUCTURES ON THE LIGHTNING RETURN STROKE CURRENT
[24] S. Kuramoto, M. Sato, and M. Ohta, “Surge current and voltage distribution in a reinforced concrete building caused by direct lightning stroke,” in IEEE Int. Symp. EMC., Aug. 1991, pp. 84–91. [25] Protection Against lightning—Part IV: Electrical and Electronic Systems Within Structures, IEC 623501–4, 2006. [26] Y. Du, M. Chen, and Q. Zhou, “Lightning-induced magnetic fields in the building with large metallic plates,” Atmosph. Res., vol. 91, pp. 574–581, 2009. [27] N. Ida, Numerical Modeling for Electromagnetic Non-Destructive Evaluation. New York: Chapman & Hall, 1995. [28] A. Deri, G. Tevan, A. Semlyen, and A. Castanheria, “The complex ground return plane: A simplified model for homogeneous and multilayer earth return,” IEEE Trans. Power Appar. Syst., vol. PAS-100, no. 8, pp. 3686–3693, Aug. 1981. [29] Protection Against Lightning—Physical Damage to Structures and Life Hazard, IEC 62305–3, 2006. [30] L. Grcev, “Impulse efficiency of simple grounding electrode arrangements,” in Proc. 18th Zurish Symp. EMC, Munich, 2007, pp. 325–328. Y. Du received the B.Sc and M.Sc degrees in electrical engineering from Shanghai Jiao Tong University, in 1984 and 1987, respectively, and the Ph.D. degree from the University of Southern California, Los Angeles, in 1994. He is currently an Associate Professor with the Department of Building Services Engineering, the Hong Kong Polytechnic University. His research interests are electromagnetic environments in buildings, lightning protection, and power quality in low-voltage distribution systems.
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He is a member of the Institution of Electrical Engineers, U.K., and a Chartered Engineer, U.K.
M. L. Chen received the B.Sc. degree in physics from Lanzhou University in 1985, the M.Sc. degree in geophysics from Chinese Academy of Sciences, Beijing, in 1988, and the Ph.D. degree in electrical and electronic information from Gifu University, Japan, in 2000. He is currently an Assistant Professor with the Department of Building Services Engineering, The Hong Kong Polytechnic University. His research interests include lightning physics, lightning detection, and structural lightning protection.
