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IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 49, NO. 3, AUGUST 2007
Transient Simulation Model for a Lightning Protection System Using the Approach of a Coupled Transmission Line Network Jun Zou, Jaebok Lee, Yafei Ji, Sughun Chang, Bo Zhang, and Jinliang He, Senior Member, IEEE
Abstract—In this paper, a simulation model is proposed to evaluate the electromagnetic transient surge current distribution in a lightning protection system (LPS) due to a direct lightning stroke. The model is based on the coupled transmission line network in the frequency domain combined with the Fourier transform technique. The conductor of the LPS is described using the coupled transmission line model, and can be reduced to an active two-port equivalent circuit. The unknown quantities are the node voltages of the LPS at the physical junction, which leads to a fast solver at each frequency. The validation of the proposed approach is performed by comparing the results with those in the technical literature. The numerical examples show the flexibility, efficiency, and accuracy of the model in the range of practical application of LPS. Index Terms—Lightning protection system (LPS), metallic structures, transmission line model.
I. INTRODUCTION HE LIGHTNING protection system (LPS) of a modern building is usually made of reinforced steel bars. Typical LPSs consist of air terminations, down conductors, and earth terminations. Down conductors usually form a 3-D cage or a mesh of wires. The LPS is installed adjacent to the structure to be protected, or incorporated within the structure. The principal function of the LPS is to receive the stroke, and distribute the lightning current to the earth. During a lightning stroke to an LPS, a surge current with high amplitude and short rise time may cause the unequal highvoltage distribution in the LPS. This may lead to damage of the LPS, danger to the people inside the building, secondary sparks, or electromagnetic disturbances to the sensitive electronic systems resulting in their malfunction or damage. Therefore, the accurate prediction of the surge current distribution in the LPS is essential not only for the protection against the lightning stroke but also for electromagnetic compatibility (EMC) reasons and safety of personnel. The evaluation of the surge current distribution in an LPS has been addressed for decades, resulting in numerous publica-
T
Manuscript received August 24, 2006; revised November 29, 2006, and February 14, 2007. This work was supported by the National Natural Science Foundation of China under Grant 50207005. J. Zou,Y. Ji, B. Zhang, and J. He are with the State Key Laboratory of Control and Simulation of Power Systems and Generation Equipments, Department of Electrical Engineering, Tsinghua University, Beijing 100084, China (e-mail:
[email protected];
[email protected];
[email protected];
[email protected]). J. Lee and S. Chang are with the Electrical Environment and Transmission Group, Korea Electrotechnology Research Institute, Changwon 641600, Korea (e-mail:
[email protected];
[email protected]). Digital Object Identifier 10.1109/TEMC.2007.902188
tions concerning simulation methods [1]–[9] and experimental results [16]. In these papers, there are two basic approaches used to evaluate the surge current distribution in an LPS—the electromagnetic field method and the equivalent circuit method. The LPS modeling technique based on the electromagnetic field method [8], [9], [22] usually employs the frequencydomain mixed potential electric field integral equation (EFIE). The EFIE is solved via the method of moments, and the time domain results are then obtained through the fast Fourier transform (FFT) technique. Numerical modeling based on the EFIE may be the most rigorous way to predict the transients of an LPS. The model can globally account for all electromagnetic phenomena which arise in an LPS environment. However, a large amount of computation is required because the inversion of a fully dense matrix is required at each frequency. Another important simulation modeling technique [1]–[7] is based on circuit theory. In this method, the LPS is simulated by a set of interconnected π circuits which form an equivalent electrical network. The surge current distribution in the network is computed by solving nodal equations or loop equations according to Kirchoff’s Law. In contrast to the approach based on the electromagnetic field method, the approach based on the circuit method is comparatively simple and capable of evaluating the current distribution directly. General-purpose commercial software, such as PSPICE, EMTP (electromagnetic transients program), and Matlab simulink, is readily available to serve as a simulation tool. Time-domain algorithms are used in the aforementioned software, so frequency dependencies of the equivalent circuit parameters are usually neglected. In addition, an approach based on the partial element equivalent circuit (PEEC) technique has been proposed to analyze the transients of the LPS in [10]. In fact, the PEEC modeling approach is a sort of circuit interpretation of an EFIE. In order to take into account the propagation phenomena due to the rapidly varying lightning current, the conductor of the LPS should be divided into longitudinal elements whose length is much less than the wavelength of the highest frequency applied by the lightning current. This results in a large number of unknown quantities (the axis currents in the EFIE model and the π-circuit model). Techniques to minimize the computation time and significantly speed up the overall simulation process are highly desirable. This paper discusses the evaluation of the surge current distribution in an LPS due to a direct lightning stroke. A fast simulation model is proposed in order to evaluate the electromagnetic transient surge current and transient node voltage distribution in
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Fig. 2. Transmission line model of a single conductor with the inductive coupling effects.
Fig. 1. Geometrical configuration of the lightning protection system and the global and local coordinate system.
an LPS due to a direct lightning stroke. The model is based on the coupled transmission line network in the frequency domain combined with the Fourier transform technique. The conductor of the LPS is described by using the coupled transmission line model, and can be reduced to an active two-port equivalent circuit. The model is superior to the existing models as it does not need to divide the conductor of the LPS into a number of elements, and the coupling effects of the LPS are taken into account by using an iterative algorithm. The unknown quantities are only the node voltages at the physical junction of the LPS, which leads to a fast solver at each frequency. II. DEVELOPMENT OF NUMERICAL MODEL A. Active Two-Port Representation for a Single Conductor of the Lightning Protection System The LPS, whose typical geometry is shown in Fig. 1, consists of a set of straight interconnected conductors forming a cage, which is either located outside the structure to be protected or incorporated within it. A global coordinate system is set up in Fig. 1, whose origin is located on the ground plane. For simplicity, the grounding system of the LPS is simulated by a set of lumped ground resistors connected to the down conductors directly, shown as Rg 1 and Rg 2 in Fig. 1. For the conductor of the LPS—the branch between node k and n as shown in Fig. 1—a local coordinate system (o − ξk ) of one dimension is established with respect to the kth conductor, along its axis. The lightning current is applied to a node of the LPS as an ideal current generator. The single conductor of the LPS can be treated by using the transmission line model, which is described by the per-unitlength longitudinal impedance Z and transverse admittance Y . The impedance Z and admittance Y are determined from geometric parameters and material properties of the conductors. The effect of the earth is taken into consideration by using the image method. The complex penetration depth based on Deri’s theory [17] is adopted to determine the location of conductor images. For the horizontal conductors, the formulations for the self- and mutual impedance can be found in [18]. As for the vertical conductors, one may refer to papers on the impedance calculation of the tower [19]. As can be seen from Fig. 1, the conductor between two nodes is treated by using a single uniform
transmission line model that is described by the per-unit-length parameters Z and Y . So, for the vertical conductors whose parameters are varied with respect to the height, in order to apply the transmission line theory, in fact, the average impedance Z and the admittance Y are calculated in this paper to compromise the accuracy and the complexity of the program implantation. There exist mutual inductive and capacitive couplings between any two conductors. The mutual capacitive coupling is neglected in this paper, and the reason will be explained in the following text. The inductive coupling among conductors is modeled by a number of series voltage sources along the axis of the conductor, and the potential of two terminations is determined by the node voltage of the conductor, as shown in Fig. 2. The model shown in Fig. 2 is governed by the telegrapher’s equation; the relationship between the port currents (Ikl , Ikr ) and port voltages (Ukl , Ukr ) is given by l l ∆Ikl −yks ykm Uk Ik = + . (1) Ikr ∆Ikr ykm −yks Ukr The Y-matrix parameter yk s and yk m of the conductor in (1) can be determined by [11] 1 cosh(γk lk ) yks = Z sinh(γ l ) k k k (2) 1 1 ykm = Zk sinh(γk lk ) √ where Zk (Zk = Z /Y ) and γk (γk = Z Y ) are the characteristic impedance and propagation constant of the transmission line, respectively, and lk denotes the length of the kth conductor. ∆Ikl and ∆Ikr are the equivalent current sources representing the inductive coupling effects among the conductors. In order to obtain the expression of ∆Ikl and ∆Ikr , the inductive coupling effects are treated as a set of lumped voltage sources E(ξkn ) applied at ξkn along the transmission line. In terms of (1), ∆Ikl and ∆Ikr are the short circuit port currents when Ukl = Ukr = 0. The conductors are divided into short segments as shown in Fig. 3, and E(ξki ) along conductor 1 due to the other conductors can be given as E(ξki ) =
Nc 2
Mij Ij .
(3)
j =1
∆Ikl and ∆Ikr are given as [11] c1 c2 1 sinh(γk ξi )Mij Ij Zk sinh(γk lk ) i=1 j =1
N
∆Ikr = −∆Ikl =
N
(4)
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Fig. 3.
Fig. 4.
IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 49, NO. 3, AUGUST 2007
Fig. 5.
Inductive coupling between two conductors.
Active π circuit of the coupled transmission line.
where Nc1 is the number of segments of conductor 1, Nc2 denotes the total number of segments of other conductors, and Mij is the mutual impedance of segments i and j in Fig. 3. An alternative representation of the active port model of the transmission line is given by the equivalent π circuit shown in Fig. 4. In the figure, the individual admittance elements of the circuit, Yak , Ybk , and Yck , are given in terms of the admittance matrix parameters yk s and yk m as Yck = ykm (5) Yak = Ybk = yks − ykm.
B. Approach of Coupled Transmission Line Network in the Frequency domain In formulating the solution to the whole LPS, the conductors are treated using the model defined in Fig. 4, and the equivalent coupled transmission line network is formed. A local profile of the equivalent network at node k is shown in Fig. 5. ILtn stands for the known lightning current. Fig. 5 shows a circuit network, and the equation system with respect to nodal voltages is easily obtained and can be written in matrix form as [Y port ][U node ] = [I lightning ] + [∆I(U node )]
(6)
where Y port is the admittance matrix, U node is the unknown vector of nodal voltages to be determined, and I lightning = [0, . . . , 0, ILtn , 0, . . . , 0]T is the lightning current source applied at the node k. ∆I(U node ) is the current source describing the inductive coupling effects as defined in (4), which depends on the solution of U node . Obviously, (6) can not be solved directly due to the dependency of ∆I(U node ) on U node . In order to obtain the solution of (6), an iterative approach is proposed and described as follows.
Model of the coupled transmission line network for LPS.
Step 1 (Initial Node Voltage Calculation): At the first step, the coupling effects are neglected completely, i.e., ∆I(U node ) (0) is set to zero. Solve [Y port ][U node ] = [I lightning ] to obtain the (0) initial node voltage distribution U node of the whole LPS. Step 2 (Voltage Update and Error Estimation): By using the (0) node voltage U node calculated in the previous step, the current distribution along the conductor can be obtained. For the kth conductor, the current Ik (ξ) at ξ in the local coordinate is given as Ik (ξ) =
Ukl cosh[γk (lk − ξ)] − Ukr cosh(γk ξ) . Zk sinh(γk lk )
(7)
In (7), the inductive coupling effects are not included; this will not impact the final accuracy of solution because of the convergent property of the iterative algorithm. Once the current distribution along the conductor is determined, the additional (0) current source ∆I(U node ) can be calculated using (4). The (1) (0) equation [Y port ][U node ] = [I lightning ] + [∆I(U node )] can be (1) solved to obtain a new node voltage distribution U node of the LPS. The error estimation is carried out using (1)
ε = 100
(0)
|U node − U node | (1)
|U node |
(8) (0)
where || · || denotes the infinite norm of a vector. The U node (1) should be updated when the U node is available. Step 3 (Termination of the Iterative Process): The iterative procedure is terminated if the error indicator meets the predefined error requirement. If not, the iteration returns to Step 2. The [Y port ] is a symmetric and strictly diagonally dominant matrix, so the convergence of the iterative procedure is assured theoretically, and has been proved by the following numerical examples. Apparently, the times of the iterative procedure depend on the predefined error more or less. The author would like to make the term “active” more clear in the model shown in Fig. 4. The ∆Ikl and the ∆Ikr that represent the inductive coupling among the conduct segments are not independent current sources at all. However, in each iterative step, the value of ∆Ikl and the ∆Ikr has been determined by using
ZOU et al.: TRANSIENT SIMULATION MODEL FOR A LIGHTNING PROTECTION SYSTEM
the current distribution of the LPS calculated in the previous step. So, the model defined in Fig. 4 can be called as an “active” one with the ∆Ikl and the ∆Ikr acting as the current sources. It should be noted that the π circuit shown in Fig. 4 is the equivalent model for the whole conductor instead of the conductor segment. The unknown quantities are the nodal voltages at the physical junction of the LPS, which leads to a small computational requirement in comparison with those of the segment approach in the EFIE or traditional circuit models. Although the procedure of segmentation is necessary to calculate the inductive coupling, there is no extra matrix inversion due to the iterative approach. C. Transient Responses of the LPS The transient characteristics of the LPS can be obtained by using Fourier transform techniques [12], [13] v(t) = −1 {T (jω)[ilightning (t)]}
(9)
where and −1 are Fourier and inverse Fourier transformations respectively. ilightning (t) is the lightning current injected into the LPS at a node, and v(t) is the response of ilightning (t) in the time domain. T (jω) is the transfer function in the frequency domain, i.e., U node in (6). By referring to the most common case, a stroke with descending negative polarity is considered in this paper. The doubleexponential representation of the lightning current pulse may be inadequate, since it predicts the maximum current derivative at t = 0 while in reality, it occurs near the current peak. However, the aim of this paper is to provide a systematic and fast algorithm to predict the lightning current distribution in the LPS. The representation of lightning current may influence the final numerical results but has no impact on understanding the proposed method. The more accurate lightning model should be adopted, and may be reported in an upcoming paper. With this type of stroke, the temporal trend of the current is taken to be characterized by the double exponential pulse ilightning (t) = KI0 (e−α t − e−β t )
(10)
where K, I0 , α, and β are suitable parameters, and can be determined via a numerical fitting method. The frequency-domain expression of ilightning (t) is given as Ilightning (jω) =
KI0 (β − α) . (α + jω)(β + jω)
(11)
The truncation frequency ωmax of Ilightning (jω) can be estimated using the following equation [15]:
K(β − α)
= −200 dB.
(12) 20 log
(α + jωmax )(β + jωmax )
ωmax can be obtained using a nonlinear equation solver. III. NUMERICAL EXAMPLES A. Comparison With EMTP and Measured Data To verify the results computed by the proposed method, a comparison is carried out between the results reported in [16]
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Fig. 6. Double 24 m × 12 m × 12 m LPS injecting the lightning current at the corner.
and those of the new method. Fig. 6 shows the model of the LPS serving as the validation with dimensions of double 24 m × 12 m × 12 m. The lightning current is characterized by the crest time and half-value time parameters equal to about 1 and 40 µs, respectively. The peak current of the lightning is 100 A. The aforementioned parameters can be defined using the symbols in (10), such that K = 1.08, I0 = 100, α = 1.86 × 104 s−1 , and β = 1.36 × 106 s−1 . The steel bar diameter Φ is 4 mm, and its conductivity σ c is 5.03 × 106 S/m. The earth is assumed to be a perfectly conductive plane, and the bonding resistance between the LPS and the earth is assumed to be zero. The lightning stroke is modeled as an ideal current source, which is injected into the LPS at a corner. In reality, lightning peak currents are typically in the tens of kiloamperes. However, the nonlinear phenomena of the conductor impedance are not considered in this paper, so the results are in proportion to the amplitude of the lightning current. The comparison between the proposed method and the EMTP is made as follows. The EMTP has been widely used to simulate the electromagnetic transient problems related to the lightning in electrical engineering in past decades. In order to use the EMTP in calculating the lightning current distribution in the LPS, the LPS should be modeled as a network of π circuits. The truncation frequency ωmax is approximately 19 MHz for the lightning current with the parameter of 1/40 µs; the corresponding wavelength at 19 MHz is about 15.6 m. The branches of the LPS are divided into a number of short segments, the length of which is shorter than the 1/10 of the wavelength of the maximal frequency. In this example, the length of the segment is set as 1 m to meet the requirement of minimal length. The total number of segments of LPS is about 204. The segmentation of the LPS serves two purposes. In the model proposed in this paper, the inductive coupling effects are calculated by using the current on those segments. Also, an EMTP based π-circuit model can be constructed with those segments. The current partitioning coefficient kc , the ratio between the peak value of the current in the down conductor, and the peak value of the injected current is computed and compared with the measured results. The error is defined as the ratio between the difference in measured and calculated current and the peak value of the injected current. Table I shows the calculated and measured current partitioning coefficients kc on each steel bar. It can be seen that good agreement is achieved between the measured and calculated results. The maximal error is less than
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TABLE I COMPARISON OF THE PARTITIONING COEFFICIENTS OF BRANCH CURRENT BETWEEN THE MEASURED AND CALCULATED RESULTS
Fig. 8. Comparison of the current in branch 12, 4, 8, and 13 with EMTP in the time domain.
Fig. 7. Comparison of the current in branch 1, 7, 10, and 3 with EMTP in the time domain.
3%. In most engineering applications, this error is acceptable, and the results can be taken as the “exact” ones. Figs. 7–9 show the time-domain currents at the middle of each conductor. As a comparison, the corresponding EMTP results are also shown. In the figures, the numbers in the square brackets are the measured data from [16]. The EMTP is based on an algorithm in the time domain, which does not take the frequencydependent impedance into account. Although the peak value of the branch current is quite close, some discrepancies exist between the currents calculated using the proposed methodand EMTP. B. Discussion on the Proposed Model The configuration shown in Fig. 6 is taken as an example to determine the effects of inductive and capacitive coupling, respectively. Fig. 10 shows a comparison of the transient current on branch 1 with and without consideration of the inductive coupling effects. The peak currents are 46.4 A under consideration inductive coupling effects and 52.2 A neglecting the coupling effects, whose error is about 10%. In the proposed method, only the capacitance between the conductor and the earth is taken into account, while the mutual capacitances among conductors are neglected completely. It is
Fig. 9. Comparison of the current in branch 11, 5, 6, and 9 with EMTP in the time domain.
Fig. 10. Comparison of the current in branch 1 with and without inductive coupling.
easy to quantify the impact of this assumption by using the equivalent circuit model shown in Fig. 11. The FFT technique is used to obtain the transient response, so the capacitive coupling effects can be quantified at each frequency. At the maximal frequency of the lightning frequency spectrum, the effects of the mutual capacitive coupling will obviously become largest. As mentioned in Section III-A, the length of each segment is 1 m at the maximal frequency of 19 MHz.
ZOU et al.: TRANSIENT SIMULATION MODEL FOR A LIGHTNING PROTECTION SYSTEM
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Fig. 11. Simplified circuit model at the strike point at 19 MHz. (a) Segmentation. (b) Equivalent circuit.
Fig. 13. floor.
Current partitioning coefficient of the down conductors of the fourth
Fig. 12. floor.
Fig. 14. floor.
Current partitioning coefficient of the down conductors of the first
Current partitioning coefficient of the down conductors of the seventh
Fig. 11(a) shows the segmentation near the strike point, and Fig. 11(b) shows the T-type equivalent circuit model by using the lumped resistance, inductance, and capacitance. In Fig. 11, under the assumption of the quasi-static field, the self-capacitance of a single conductor and the mutual capacitance between two finite-length conductors with an arbitrary angle can be calculated by using the average potential method [11] when the image theory is adopted to take the effect of the earth into account. The amplitude of mutual capacitive reactance is about five times greater than the self-capacitive reactance of each branch, and 40 times greater than the impedance in series in each branch. A lower frequency leads to a weaker influence of mutual capacitive coupling. Considering Table I, and Figs. 10 and 11, one may draw the conclusion that the mutual inductive coupling effects are essential to the accuracy of the results, but the effect of mutual capacitive coupling is trivial, and can be neglected. C. Comparison With the Results of a Seven-Storeyed LPS In [16], the measurements were carried out in models of high structures. Some surge current distributions in vertical elements of seven-storeyed buildings were presented. Figs. 12–14 show the comparisons between the proposed results and the measured data. All parameters of the LPS used in this example are the same as those given in Section III-A. Numbers appearing in
TABLE II COMPARISON OF COMPUTATIONAL EFFICIENCY
square brackets are the measured data. It can be seen that good agreement is achieved for this complex LPS. D. Comparison of Computational Efficiency Using the LPS shown in Fig. 6, the solutions in the time domain are obtained by both the proposed model and the π circuit model with the aid of the FFT technique. The solution time needed at a single frequency is chosen as an index to compare the efficiency of the two models. In the proposed model, the unknown quantities are the node voltages and a 12 × 12 system of equations is established. In the π -circuit model, the unknown quantities are the branch currents and the dimension of the system of equations is 204 × 204. The computer used for calculation has an Intel Pentium 3.0-GHz CPU and 1-GB memory. The programming language is Matlab version 6.5. Table II shows the time needed for each of the two methods at a single frequency. The proposed model is about five times faster than the π-circuit model. It should be noted that the reduction
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TABLE III PARAMETER DEFINITIONS FOR FOUR SCENARIOS
TABLE V INFLUENCE OF THE MAXIMAL NODE VOLTAGE DUE TO THE PARAMETER VARIATION
TABLE IV INFLUENCE OF THE PARTITIONING COEFFICIENTS DUE TO THE PARAMETER VARIATION
maximal node voltage at the striking point, it is easily understood that the derivative of the lightning waveform with respect to time is the most important factor. However, if the quantity of interest is the ground potential rise (GPR), the grounding resistance will play the most important role for that profile. This parameter analysis gives guidelines for designing an LPS. IV. CONCLUSION of total computational time is rather remarkable, because the calculation must be repeated at a large number of frequencies. Recently, an interpolation method in the frequency domain has been proposed [20] by the author, which can hopefully improve the efficiency dramatically. This acceleration approach will be attempted later in the frequency-domain calculation of the LPS. E. Parameter Analysis of the LPS In order to analyze the influence on the LPS due to the variation of parameters, four special scenarios are modeled. The variable parameters are the lightning waveform, the diameter of the conductor, the grounding resistance of the LPS, and the conductivity of the LPS conductor. The basic way to observe each parameter’s influence is to vary one parameter for each scenario. The LPS structure is still the model shown in Fig. 6, and the peak value of the lightning current is 100 A. The other parameters defined in the four cases are given in Table III. The partitioning coefficient of branch 1 and the node voltage of the striking point are the observed quantities of interest. The calculated results are shown in Tables IV and V, respectively. It can be seen from Tables IV and V that the properties of the LPS conductors, i.e., the conductivity and diameter of the conductor, impact the partitioning coefficient and the node voltage greatly. The lightning waveform and the grounding resistance have a relatively weak influence on the observed quantities. It is very interesting that the variation of grounding resistance has almost no influence on the results. Generally speaking
dilightning
L
dt where L is the equivalent inductance of the LPS conductor, is far greater than the grounding resistance of the LPS. For the
In this paper, a coupled transmission line network model is proposed to calculate the surge current distribution of an LPS due to direct lightning stroke. The main advantage of the proposed model is its rather low computational demand. The reasons are as follows. The number of unknown quantities is less than that in the traditional circuit method or EFIE method, which leads to a low rank equation system at each frequency. Also, the inductive coupling effects are taken into account by using an iterative approach, which avoids the inversion of a matrix. The validation of the proposed model has been carried out with measured and computed results available in other literature, and good agreement has been demonstrated. It is worth mentioning that the present study focuses on the direct effect of lightning; however, the model discussed here can be conveniently extended to predict the effect of an indirect effect of lightning. In addition, if the lightning is also equivalent to a transmission line [21], the coupling between the lightning channel and the LPS should be considered carefully. The method proposed in this paper should be revised further if the above mentioned coupling exists. In designing an LPS, the surge current distribution is one of the most essential parameters. After getting the surge current distribution in the LPS, the impulsive magnetic fields around the LPS can be calculated using the Biot–Savart law, which is very important for the analysis of sensitive electronic equipment’s EMC [23], [24]. The proposed method is fast and is a good candidate. If the transient ground potential rise (TGPR) due to lightning is of interest, the proposed method may not be suitable because the conductive coupling of the grounding system is not appropriately included. This is the main limitation of the proposed method, which may be improved in future work. In addition, since the calculations are performed in the frequency domain and the transient responses are obtained by using the
ZOU et al.: TRANSIENT SIMULATION MODEL FOR A LIGHTNING PROTECTION SYSTEM
FFT technology, modeling nonlinear protective devices is not possible in this approach. ACKNOWLEDGMENT The authors would like to thank the anonymous reviewers for their constructive comments and suggestions. The authors wish to acknowledge V. Rawat for his academic discussion and careful proofreading of the paper. REFERENCES [1] S. Cristina and A. Orlandi, “Calculation of the induced effects due to a lightning stroke,” Proc. Inst. Electr. Eng. B, vol. 139, no. 4, pp. 374–380, 1992. [2] A. Orlandi, G. B. Piparo, and C. Mazzetti, “Analytical expressions for current share in lightning protection systems,” Eur. Trans. Electr. Power, vol. 5, no. 2, pp. 107–114, 1995. [3] A. Orlandi and F. Schietroma, “Attenuation by a lightning protection system of induced voltages due to direct strikes to a building,” IEEE Trans. Electromagn. Compat., vol. 38, no. 1, pp. 43–50, Feb. 1996. [4] A. Orlandi, C. Mazzetti, Z. Flisowski, and M. Yarmarkin, “Systematic approach for the analysis of the electromagnetic environment inside a building during lightning strike,” IEEE Trans. Electromagn. Compat., vol. 40, no. 4, pt. 2, pp. 521–535, Nov. 1998. [5] R. Cortina and A. Porrino, “Calculation of impluse current distributions and magnetic fields in lightning protection structure—A computer and its laboratory validation,” IEEE Trans. Magn., vol. 28, no. 2, pp. 1134–1137, Mar. 1992. [6] A. Geri and G. M. Veca, “A complete lightning protection system simulation in the EMI analysis,” in Proc. IEEE 1991 Int. Symp. EMC, pp. 90–95. [7] Q. B. Zhou and Y. Du, “Using EMTP for evaluation of surge current distribution in metallic gridlike structures,” IEEE Trans. Ind. Appl., vol. 41, no. 4, pp. 1113–1117, Jul./Aug. 2005. [8] A. Karwowski and A. Zeddam, “Transient currents on lightning protection systems due to the indirect lightning effect,” Proc. Inst. Electr. Eng., Sci. Meas. Technol., vol. 142, no. 3, pp. 213–222, May 1995. [9] G. Ala and M. L. D. Silvestre, “A simulation model for electromagnetic transients in lightning protection systems,” IEEE Trans. Electromagn. Compat., vol. 44, no. 4, pp. 539–554, Nov. 2002. [10] G. Antonini, S. Cristina, and A. Orlandi, “PEEC modeling of lightning protection systems and coupling to coaxial cables,” IEEE Trans. Electromagn. Compat., vol. 40, no. 4, pt. 2, pp. 481–491, Nov. 1998. [11] F. M. Tesche, M. V. Ianoz, and T. Karlsson, EMC Analysis Methods and Computational Models. New York: Wiley, 1997. [12] E. O. Brigham, The Fast Fourier Transform. Englewood Cliffs, NJ: Prentice-Hall, 1974. [13] L. Grcev and F. Dawalibi, “An electromagnetic model for transients in grounding systems,” IEEE Trans. Power Del., vol. 5, no. 4, pp. 1773– 1781, Oct. 1990. [14] F. Rachidi, M. Ianoz, C. A. M. Nucci, and C. Mazzetti, “Calculation methods of the horizontal component of lightning return stroke electric field,” in Proc. 11th Int. Wroclaw Symp. EMC, Wroclaw, Poland, 1992, pp. 452–456. [15] S. Cristina and A. Orlandi, “Current distribution in lightning stroked structure in presence of nonlinear ground impedance,” in Proc. 20th Int. Conf. Lightning Prot., Interlaken, Switzerland, Sept.1990, pp. 22–28. [16] A. Sowa, “Surge current distribution in building during a direct lightning stroke,” in Proc. IEEE Symp. EMC, Cherry Hill, NJ, pp. 103–105, 1991. [17] 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 App. Syst., vol. PAS-100, no. 8, pp. 3686– 3693, Aug. 1981. [18] E. J. Rogers and J. F. White, “Mutual coupling between finite lengths parallel or angled horizontal earth return conductors,” IEEE Trans. Power Del., vol. 4, no. 1, pp. 103–113, Jan. 1989. [19] A. Ametani, Y. Kasai, J. Sawada, A. Mochizuki, and T. Yamada, “Frequency-dependent impedance of vertical conductors and multiconductor tower model,” Proc. Inst. Electr. Eng., Gener. Transm. Distrib., vol. 141, no. 4, pp. 339–345, Jul. 1994. [20] J. Guo, J. Zou, B. Zhang, J. L. He, and Z. C. Guan, “An interpolation model to accelerate the frequency-domain response calculation of grounding systems using the method of moments,” IEEE Trans. Power Del., vol. 21, no. 1, pp. 121–128, Jan. 2006.
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[21] Working Group 33.01 (Lightning), “Lightning-induced voltages on overhead power lines. Part I: Return-stroke current models with specified channel-base current for the evaluation of the return-stroke electromagnetic fields,” Electra, no. 161, pp. 75–102, Aug. 1995. [22] G. Ala, M. L. D. Silvestre, E. Francomano, and A. Tortorici, “Waveletbased efficient simulation of electromagnetic transients in a lightning protection system,” IEEE Trans. Magn., vol. 39, no. 3, pt. 1, pp. 1257– 1260, May 2003. [23] C. A. F. Sartori, J. R. Cardoso, C. C. B. Oliveira, A. Orlandi, and G. Antonini, “Constrained decision planning applied to field profile optimization in LPS of structures directly struck by lightning,” IEEE Trans. Magn., vol. 38, no. 2, pt. 1, pp. 757–760, Mar. 2002. [24] I. A. Metwally, F. H. Heidler, and W. J. Zischank, “Magnetic fields and loop voltages inside reduced and full scale structures produced by direct lightning strikes,” IEEE Trans. Electromagn. Compat., vol. 48, no. 2, pp. 414–426, May 2006.
Jun Zou was born in Wuhan, China, in January 1971. He received the B.S. and M.S. degrees from Zhengzhou University, Zhengzhou, China, and the Ph.D. degree from Tsinghua University, Beijing, China, in 1994, 1997, and 2001, respectively, all in electrical engineering. In 2001, he joined the Department of Electrical Engineering at Tsinghua University as an Assistant Researcher, where he became an Associate Professor in 2004. His research interests include electromagnetic compatibility in power systems, computational electromagnetics, and analysis of brain electricity.
Jaebok Lee was born in Iri, Korea, in 1962. He received the B.Sc., M.Sc., and Ph.D. degrees from Inha University, Incheon, Korea, in 1985, 1987, and 1999, respectively, all in electrical engineering. In 1987, he joined the Korea Electrotechnology Research Institute (KERI), Changwon, as a Researcher in the Power System Insulation Coordination Laboratory. Currently, he is a Principal Researcher in the electrical environment and transmission group at KERI. His research interests include surge protection and EMC in power systems and electronic systems, and grounding technology. Dr. Lee is a member of the Korean Institute of Electrical Engineers and the Korea Chapter of the International Electrotechnical Commission Technical Committee (IEC TC 77A).
Yafei Ji was born in Zhoukou city of Henan province in China, in 1984. He received the B.Sc. degree in electrical engineering from Xian Jiaotong University, Xian, China, in 2004. Currently, he is a graduate student in the Department of Electrical Engineering, Tsinghua University, Beijing, China. His research interests include electromagnetic compatibility in power systems.
Sughun Chang was born in Seoul, Korea, in 1974. He received the B.Sc. and M.Sc. degrees from Inha University, Incheon, Korea, in 1996 and 1999, respectively, both in electrical engineering. In 2002, he joined the Korea Electrotechnology Research Institute, Changwon, as a Researcher in the electrical environment and transmission group. His research interests include surge protection and electromagnetic compatibility in power systems and electronic systems, and grounding technology. Mr. Chang is a member of the Korean Institute of Electrical Engineers.
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Bo Zhang was born in Datong, China, in 1976. He received the B.Sc. and Ph.D. degrees in theoretical electrical engineering from the North China Electric Power University, Baoding, in 1998 and 2003, respectively. He is currently a Postdoctoral Researcher with the Department of Electrical Engineering, Tsinghua University, Beijing, China. His current research interests include computational electromagnetics, grounding technology, and electromagnetic compatibility in power systems.
Jinliang He (M’02–SM’02) was born in Changsha, China, in 1966. He received the B.Sc. degree from the Wuhan University of Hydraulic and Electrical Engineering, Wuhan, China, the M.Sc. degree from Chongqing University, Chongqing, China, and the Ph.D. degree from Tsinghua University, Beijing, China, in 1988, 1991, and 1994, respectively, all in electrical engineering. Currently, he is the Vice Chief of the High Voltage Research Institute, Tsinghua University. He joined the Department of Electrical Engineering, Tsinghua University, as a Lecturer in 1994, where he became a Professor in 2001. From 1994 to 1997, he was the Head of High Voltage Laboratory, Tsinghua University. From 1997 to 1998, he was a Visiting Scientist in the Korea Electrotechnology Research Institute, Changwon, involved in research on metal-oxide varistors and high-voltage polymeric metal-oxide surge arresters. He is the Chief Editor of the Journal of Lightning Protection and Standardization (in Chinese), and is the author of five books and many technical papers. His research interests include overvoltages and electromagnetic compatibility in power systems and electronic systems, grounding technology, power apparatus, dielectric material, and power distribution automation. Dr. He is a Senior Member of the China Electrotechnology Society, the China Representative of the International Electrotechnical Commission Technical Committee (IEC TC 81), and the Vice Chief of the China Lightning Protection Standardization Technology Committee. He is a member of the International Compumag Society, the Electromagnetic Interference Protection Committee, the Transmission Line Committee of the China Power Electric Society, China Surge Arrester Standardization Technology Committee, the Overvoltage and Insulation Coordination Standardization Technology Committee, and the Surge Arrester Standardization Technology Committee in Electric Power Industry.
