FDTD-Based Lightning Surge Simulation of a Microwave Relay Station

Transcription

1 214 International Conference on Lightning Protection (ICLP), Shanghai, China FDTD-Based Lightning Surge Simulation of a Microwave Relay Station Akiyoshi Tatematsu, Kenichi Yamazaki, and Hirokazu Matsumoto Electric Power Engineering Research Laboratory Central Research Institute of Electric Power Industry Yokosuka, Japan akiyoshi@criepi.denken.or.jp Abstract In electric power systems, microwave relay stations are employed to exchange information using electromagnetic radio waves to control the systems. Some microwave relay stations are built on tops of mountains, which causes a high incidence of lightning strikes to microwave towers, and the lightning strikes may result in disturbances of microwave radio equipment. To protect microwave radio equipment from lightning, it is required to analyze surge phenomena in microwave relay stations and evaluate the effectiveness of lightning protection methodologies. Nowadays, the finite-difference time-domain (FDTD) method to solve Maxwell s equations directly, has been widely and successfully applied to the surge analysis of three-dimensional structures and grounding structures. In this study, setting up a reduced-scale microwave relay station model with a microwave tower of 1 m height, we calculate the distribution of lightning impulse currents in the model and compare the calculated results with measured ones for validation. Secondly, we calculate the magnetic fields inside the microwave relay station in the case of direct lightning strikes to the microwave tower to study the effect of the layout of the microwave relay station and the effectiveness of the reinforcing bars used for grounding. Keywords-lightning surges; microwave relay stations; FDTD I. INTRODUCTION In electric power systems, microwave relay stations are employed to exchange information using electromagnetic radio waves to control the systems. Some microwave relay stations are built on tops of mountains, which causes a high incidence of lightning strikes to microwave towers, and the lightning strikes may result in disturbances of microwave radio equipment. To protect microwave radio equipment from lightning [1], it is required to analyze surge phenomena in microwave relay stations and evaluate the effectiveness of lightning protection methodologies [2], [3]. Although circuittheory-based simulation techniques have been traditionally applied to surge analysis, they cannot rigorously simulate surge phenomena in three-dimensional structures such as microwave towers and grounding structures, since they have been developed on the assumption of the transverse electromagnetic (TEM) mode. Recently, thanks to the development of numerical techniques and affordable high-performance computers, full-wave numerical approaches such as the finitedifference time-domain (FDTD) method [4] and the method of moments (MoM) [5], [6], which do not require the assumption of the TEM mode, have been widely and successfully put to use for analyzing surge phenomena in distribution and transmission lines, substations, buildings, and so forth. Among the full-wave numerical approaches, the FDTD method has the advantages of being capable of taking into account the electrical parameters of the soil, non-flat ground surfaces, and nonlinear phenomena such as surge protective devices. In this study, we set up a reduced-scale model of a microwave relay station, which has a microwave tower of 1 m height and a reinforced-concrete building, in Akagi Testing Center of Central Research Institute of Electric Power Industry (CRIEPI). Using a three-dimensional FDTD-based surge simulation code, we calculate the current distributions in the microwave relay station model by taking into account the complex configuration such as the reinforcing bars of the building, and then compare the calculated results with measured ones for validation. Secondly, we calculate the magnetic fields inside the microwave relay station in the case of direct lightning strikes to the microwave tower to study the effect of the layout of the microwave relay station and the effectiveness of the reinforcing bars used for grounding. II. OVERVIEW OF MICROWAVE RELAY STATION MODEL In this section, we give an outline of the reduced-scale model of a microwave relay station installed for validating FDTD simulations and its calculation model simulated by an FDTD-based surge simulation code, the details of which are presented in [7]. A. Reduced-Scale Model of a Microwave Relay Station As shown in Fig. 1, the reduced-scale model of a microwave relay station mainly comprises a microwave tower of 1 m height, a reinforced-concrete building of 2 m height, a waveguide, a ring earth electrode, and a deep earth electrode of 65 m length. In this study, as shown in Fig. 1, the foundation of the building is called foundation A. To simulate representative layouts of microwave relay stations, the microwave tower can be mounted on the roof of the building or the reinforcedconcrete foundation (called foundation B) next to the building, which are respectively referred to as type I-a and type I-b layouts hereafter. A ladder is placed in the microwave tower,

2 Image 4.5 m Reinforced concrete foundation for the microwave tower (foundation B) Current injection wire 1 m 2 m Ground level 9 m Deep earth electrode 3.5 m 3.5 m Waveguide Microwave tower Reinforced concrete building Ring earth electrode (depth :.4 m) Reinforced concrete foundation of the building (foundation A) Ring earth electrodes are disconnected in type I-a. (a) Microwave tower on a building (type I-a) (b) Microwave tower next to a building (type I-b) Fig. 1. Reduced-scale model of microwave relay station (adapted from [7]). microwave radio equipment. In addition to metal box A, another metal box (called metal box B), a ground bus, and a wire to simulate the grounded core of a DC power source cable (called the grounded DC wire) are installed in the building. Metal box B represents the metal frame of a dehydrator, which is used to flow dry air into a waveguide in practice, and a copper tube is inserted between the waveguide and metal box B. As shown in Fig. 2, the copper tube has three loops to simulate the case that a waveguide has some loops for future use. B. Calculation Model and FDTD-Based Simulation Code Fig. 3 shows a calculation model to simulate in detail the microwave relay station model presented in the previous section. The microwave tower and its inside ladder are modeled by combining numerous small lossless conductor plates. The circular structure at the top of the tower, the waveguide, the ring earth electrode, the reinforcing bars, the ground bus, and the grounded DC wire are simulated by lossless thin wires on the basis of thin-wire representation techniques [8], [9]. Metal boxes A and B and the deep earth electrode are simulated by lossless rectangular conductors. The three loops of the copper tube between metal box B and the waveguide are simulated by a lumped-parameter inductance [1] of 1.1 μh, which was obtained by an impedance analyzer (HP4294A, Hewlett-Packard). The concrete is represented by a lossy dielectric material with a conductivity of.52 S/m and relative permittivity of 8.6, which refer to the values at DC estimated by fitting a Debye model to measured frequency characteristics of concrete with a moisture content of 5.5% [11], although the concrete has very little influence on the current distributions in this arrangement. Note that the concrete of the foundations is ignored on the assumption that its electrical parameters are similar to those of the soil. The current distributions and magnetic fields in the microwave relay station model are calculated using the threedimensional surge simulation code developed on the basis of the FDTD method by CRIEPI, which is called Virtual Surge Fig. 2. Layout inside the building (adapted from [7]). and the waveguide along the vertical center axis of the microwave tower is fixed on the ladder at some points, where insulation rubbers are inserted between the waveguide and ladder. To simulate an actual condition, the top end of the waveguide is electrically connected to the frame of the microwave tower. As shown in Fig. 2, the waveguide is drawn into the building, and it is connected to a rectangular conductor (called metal box A), which simulates the metal frame of Fig. 3. Calculation model of the microwave relay station model (adapted from [7]).

3 Test Lab. Restructured and Extended Version (VSTL REV) [12]. In VSTL REV, we can employ some of the techniques developed to apply the FDTD method to surge analysis and to simulate various objects such as thin wires [8], [9], surge arresters [13], lightning channels [14], and so forth. III. COMPARISON OF CALCULATED AND MEASURED CURRENT DISTRIBUTIONS To inject lightning impulse currents into the top of the microwave tower described in Section II.A, a current injection wire, which is a bare copper wire with a cross section of 8 mm 2, is connected to the top of the tower, while the other end of the current injection wire is connected to an impulse generator placed about 266 m away from the ring earth electrode of the reduced-scale microwave relay station model. The height of the current injection wire is 12 m and 1 m in types I-a and I-b, respectively. Injecting lightning impulse currents with a peak value of about 4 A into the top of the tower, we measured the current distributions in the microwave relay station model, the layout of which is set to type I-a or I-b, denoted by cases A- 1 and A-2, respectively. The specifications of the equipment used for measuring the current distributions are summarized in [7]. In cases A-1 and A-2, the reinforcing bars of the building are employed for grounding, and the outside ground wire of the waveguide is connected to the reinforcing bars of the building as shown in Fig. 2. The inside ring ground bus is connected to the reinforcing bars at the four corners inside the building in both cases. Note that some experiments were also carried out for the case that the reinforcing bars were not used for grounding, for example, the ground wire of the waveguide outside the building and the inside ground bus were directly connected to the outside ring earth electrode (see [7] for details) via electrical wires. Here, in both cases A-1 and A-2, the ground wire between the ring earth electrode and deep earth electrode is removed, unlike the cases presented in [7]. Fig. 4 shows the calculation arrangement used to simulate the above-described experimental setup in the FDTD method. In the analysis space, the volume of which is 675 m 46.5 m m, the bottom space with a thickness of m is treated as the soil. As shown in Fig. 4, the resistivity of the soil is set to values estimated by comparing measured results of the m 212 m Fig. 4. Calculation arrangement used for obtaining the current distributions (adapted from [7]). ground potential rises of the ground structure with results calculated by the FDTD method on the basis of the resistivity distribution estimated by the four-point Wenner test. The relative permittivity of the soil is set uniformly to 3, as obtained in a previous study [15]. To assume an open space, all the external surfaces of the analysis space are treated as absorbing boundaries using Liao s formulation of the second order [16]. To reduce the memory capacity necessary for simulations and the calculation time, the analysis space is divided into nonuniform cells, the size of which ranges from.25 m to 2 m, and the time discretization is set to.24 ns. In the analysis space, the calculation model of the microwave relay station model is set up, and, in addition, a thin wire to simulate the current injection and a voltage source to simulate the impulse generator are also included. Fig. 5 shows the calculated and measured peak values of the currents flowing through the microwave relay station model in case A-1, where the peak value of the current injected into the microwave tower is normalized to 1%. Figs. 6a through 6d respectively show the waveforms of the currents flowing at the injection point at the tower top, through the waveguide before the grounding point of the waveguide outside the building (P-1 in Fig. 2), through the waveguide at the top of metal box A (P-2 in Fig. 2), and through the ground wire of metal box A (P-3 in Fig. 2). Figs. 7 and 8 show the calculated and measured peak values and waveforms of the flowing currents in case A-2, respectively. As shown in Figs. 5 through 8, although a small amount of the injected current flows into the waveguide for both types I-a and I-b, the distributions of the peak values and waveforms calculated by the FDTD method agree well with the measured ones, and thus we confirmed the applicability of the FDTD method to lightning simulations of microwave relay stations by taking into account their practical and complex configurations. In addition, we also found good agreement between the calculated and measured current distributions in the case that the deep earth electrode was connected to the ring earth electrode and the reinforcing bars of the building were not used for grounding [7]. IV. CALCULATION OF MAGNETIC FIELDS INSIDE THE BULDING FOR DIRECT LIGHTNING STRIKES In this section, using the microwave relay station model, we calculate the magnetic fields inside the building for direct lightning strikes to the top of the microwave tower for the first and subsequent stroke currents. Fig. 9 shows the calculation arrangement used for the subsequent stroke cases. The dimensions of the analysis space are 49 m 46.5 m m, and the bottom space with a thickness of m corresponds to the soil, which has a uniform electrical parameter with a conductivity of.1 S/m and relative permittivity of 1. All the external surfaces are treated as Liao s absorbing boundaries of the second order. In the analysis space, the microwave relay station model is installed, and to represent a lightning channel, the transmission line (TL) model [14] is attached to the top of the tower, and the negative currents are injected into the tower top for both first and subsequent stroke cases. The top end of the TL model is connected to the upper surface of the analysis space. The

4 (Side view) Microwave tower 1. / 1. Calculated Measured result [%] result [%] -:No measured results (Side view) Calculated Measured result [%] result [%] -:No measured results Microwave tower 1. / / 1.4 Building.84 / 2.1 Ring earth electrode.67 / / /.3 (Top view) Ring earth electrode 1.8 / / / / 4. Current flowing into metal box A, which represents microwave radio equipment, through the waveguide.35 /.8.55 / 1.4 (Top view) 3.7 / / / /.7 Ring earth electrode 12.3 / / / / / -.29 / - Ring ground bus Metal box A.12 / -.2 / - Ring ground bus Metal box A Foundation for the microwave tower (foundation B) 2.1 / /.6.2 / -.28 / -.12 / -.21 / / / / / / 9.9 Deep earth electrode The deep earth electrode is disconnected from the earth electrode in this case. 4.3 / 3.2 Deep earth electrode 19.9 / 18.5 Ring earth electrode The deep earth electrode is disconnected from the earth electrode in this case. Fig. 5. Comparison of the measured and calculated peak values of the currents in case A-1. Fig. 7. Comparison of the measured and calculated peak values of the currents in case A (a) Injected current (b) Current flowing through P (a) Injected current (b) Current flowing through P (c) Current flowing through P-2 (d) Current flowing through P-3 Fig. 6. Calculated and measured waveforms of the currents in case A (c) Current flowing through P-2 (d) Current flowing through P-3 Fig. 8. Calculated and measured waveforms of the currents in case A-2. current waveforms are given by Heidler s equation specified in the IEC Standard regarding lightning protection [17]. The wave front times of the first and subsequent stroke currents are set to 1 μs and.25 μs, respectively, and the peak values of both currents are normalized to 1 ka. The propagation speed of the return stroke current is set to 1 m/μs. In the case of the first stroke currents, the height of the analysis space is extended by 75 m. The analysis space is divided into nonuniform cells and nonuniform cells, which have sections of.25 m to 1 m, for the first and subsequent strike cases, respectively. The magnetic fields inside the building are calculated for the following four layouts of the microwave relay station model, which are referred to as cases B-1 through B-4. The layout of the model is set to type I-a (Fig. 1a) in cases B-1 and B-2, while it is set to type I-b (Fig. 1b) in cases B-3 and B-4. In cases B-1 through B-4, the deep earth electrode and the ground wire between it and the ring earth electrode are removed. Note that, unlike cases A-1 and A-2, in cases B-1 through B-4, the grounded DC wire is connected to the inside ground bus, not to the outside ring earth electrode, to simulate a more practical condition as shown in Fig. 9. In cases B-1 and B-3, similarly to cases A-1 and A-2, the reinforcing bars of the building and foundations are used for grounding, and the outside ground wire of the waveguide and the inside ring ground bus are connected to the reinforcing bars, which are electrically connected to the ring earth electrode. On the other hand, in cases B-2 and B-4, the reinforcing bars are not employed for grounding, and the outside ground wire of the waveguide and the inside ring ground bus (which is not ring-

5 .5 m.75 m Metal box B m 762 m Metal box A Doorway.6 m Reinforcing bar y Calculation point z x Fig. 12. Calculation points of magnetic fields inside the building (top view). Fig. 9. Calculation arrangement for obtaining the magnetic field distributions inside the building (adapted from [7]) Fig. 13. Calculated peak values of the magnetic fields [A/m/kA] in case B-1. Fig. 1. Ground wire of the waveguide and the feet of the microwave tower in cases B-2 and B-4. Fig. 14. Calculated peak values of the magnetic fields [A/m/kA] in case B-2. Fig. 11. Layout of grounded DC wire and ground bus in cases B-2 and B-4. shaped in cases B-2 and B-4 as shown in Fig. 11) are directly connected to the outside ring earth electrode as shown in Figs. 1 and 11. As shown in Fig. 1, although each foot of the microwave tower is connected to the reinforcing bars of the ceiling via thin wires to simulate anchors in all the cases, in cases B-2 and B-4, where the reinforcing bars are not employed for grounding, the ground wire of each foot is also connected to the ring earth electrode with thin wires with a cross section of 6 mm 2. Note that in cases B-1 and B-2, where the layout of the microwave relay station model is set to type I- a, foundation B in Fig. 1 and part of the ring earth electrode surrounding foundation B are removed, and only the ring earth electrode around the building foundation is considered. Using the aforementioned calculation arrangement, we calculate the magnetic fields at 23 points 1 m above the floor for both first and subsequent stroke currents in cases B-1 through B-4, where the calculation points are shown in Fig. 12. Figs. 13 and 14 show the peak values of the magnetic fields inside the building in cases B-1 and B-2, respectively, where the microwave tower is mounted on the roof of the building (type I-a). Figs. 15 and 16 show the peak magnetic fields in cases B-3 and B-4, respectively, where the microwave relay station is mounted on foundation B next to the building. In all the cases, the magnetic fields are relatively larger near the bottom left corner, where the building model has an aperture with a size of.6 m 1.5 m to correspond to a doorway. Except for case B-2, the peak values of the magnetic fields for the first stroke currents are similar to those for the subsequent stroke currents. The main reason for the differences between the peak magnetic fields for the first and subsequent stroke currents in case B-2 is the current flowing through the ground wire, which connects the ground bus to the earth electrode, arising from the different transient ground potential rises between the building foundation and ring earth electrode in the subsequent stroke case. Figs. 17 and 18 show the difference in the ground potential rises between the building foundation and ring earth electrode and the current flowing through the ground bus at P-4 in Fig. 11, respectively. For both layouts of the microwave relay station, the peak values of the magnetic fields are reduced by using the reinforcing bars for grounding [18]. In particular, in case B-4, compared with case B-3, the magnetic fields around metal box A used to represent

6 reinforcing bars are not employed for grounding, compared with the case of the first lightning stroke current, in the subsequent lightning stroke current case, the magnetic fields are larger due to the current in the ground wire between the inside ground bus and outside ring earth electrode arising from the transient potential differences between the building foundation and the ring earth electrode. Fig. 15. Calculated peak values of the magnetic fields [A/m/kA] in case B microwave radio equipment are highly intensified since the amount of the current flowing into the building through the waveguide is larger in case B-4, which was confirmed in our previous study [7]. V. CONCLUSIONS Fig. 16. Calculated peak values of the magnetic fields [A/m/kA] in case B-4. Potential diff. [kv/ka] Fig. 17. Differences in the ground potential rises between the building foundation and the ring earth electrode. 5 1 In this study, setting up a reduced-scale model of a microwave relay station, we measured the current distributions in the model when the microwave tower is mounted on the building roof and next to the building, which are representative layouts of microwave relay stations. Then, simulating the complex configuration of the model in detail by the surge simulation code developed on the basis of the threedimensional FDTD method, we calculated the current distributions and confirmed that the calculated results are in good agreement with the measured ones. Secondly, we calculated the magnetic field distributions inside the building for direct lightning strikes to the microwave tower. The calculated results indicate that the magnetic fields are reduced by employing reinforcing bars for grounding and that the magnetic fields are highly intensified by the current flowing into the building via the waveguide, particularly when the microwave tower is mounted next to the building and the reinforcing bars are not used for grounding. When the microwave tower is mounted on the building roof and the Current [A/kA] 1 Fig. 18. Waveform of the current flowing through P-4. REFERENCES [1] D. W. Bodle, Lightning protection of microwave relay stations, IEEE Trans. Communication and Electronics, vol. 83, no. 74, pp , Sep [2] H. Kono, M. Fujino, M. Yokoyama, K. Yonezawa, Y. Takahashi, C. Isokawa, and A. Tatematsu, Applying FDTD simulation to lightning surge route analysis in microwave relay stations, J. International Council on Electrical Engineering, vol. 1, no. 1, pp. 6-66, 211. [3] M. Bandinelli, F. Bessi, S. Chiti, M. Infantino, and R. 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