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Application of the FDTD-based simulation code VSTL REV to the lightning surge analysis of a nuclear power plant
Electric Power Systems Research 178 (2020) 106040
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Application of the FDTD-based simulation code VSTL REV to the lightning surge analysis of a nuclear power plant
T
⁎
Akiyoshi Tatematsua, , Hideki Motoyamaa, Akihiro Tanigawab a b
Electric Power Engineering Research Lab., Central Research Institute of Electric Power Industry, 2-6-1 Nagasaka, Yokosuka, Kanagawa 240-0196, Japan Projects Development Dep., The Japan Atomic Power Company, 1-1 Kandamitoshirocho, Chiyoda-ku, Tokyo 101-0053, Japan
A R T I C LE I N FO
A B S T R A C T
Keywords: Electromagnetic transient analysis Finite-difference time-domain method Grounding Lightning Lightning protection system
The installation of effective lightning protection is necessary to protect power equipment and sensitive electronic devices and guarantee human safety in nuclear power plants. To evaluate the effectiveness of countermeasures against lightning, it is necessary to predict lightning surge phenomena. Recently, the finite-difference timedomain (FDTD) method, which is one of the full-wave numerical approaches, has been applied for analyzing electromagnetic transient phenomena in three-dimensional structures such as lightning protection systems and buildings or grounding structures such grounding grids. In this study, we model buildings and grounding structures of a nuclear power plant using the FDTD-based surge simulation code VSTL REV, and we study the effect of soil resistivities on the step voltages around the reactor building and the voltages induced on grounding buses drawn into an auxiliary building and the metal sheaths of coaxial cables in the case of a direct lightning strike to the nuclear power plant.
1. Introduction To protect power equipment and sensitive electronic devices and guarantee human safety in nuclear power plants (NPPs), it is necessary to design lightning protection measures properly [1]. In a design process, the prediction of lightning surge phenomena is very useful for evaluating the effectiveness of lightning protection measures. Traditionally, transmission-line (TL) based electromagnetic transient analysis has been employed for predicting lightning surge phenomena. On the other hand, full-wave numerical approaches such as the finite-difference time-domain (FDTD) method [2] and the method of moments (MoM) [3] are now widely used for analyzing electromagnetic transient phenomena in three-dimensional or grounding structures (e.g. Refs. [4–7]). Compared with other full-wave numerical approaches, the FDTD method is advantageous in terms of its capability of handling inhomogeneous soil parameters, nonflat ground surfaces such as mountainous terrains, and, in particular, nonlinear characteristics such as those of surge protective devices and back-flashover phenomena at TL towers [8–10]. Several techniques have been developed to apply the FDTD method to surge analysis, for example, for representing thin wires such as electrical wires and grounding wires [11,12]; thus the FDTD method has been applied to the lightning surge analysis of power plants, transmission lines, distribution lines, substations, grounding ⁎
systems, and buildings. Central Research Institute of Electric Power Industry (CRIEPI) has been developing an FDTD-based surge simulation code called VSTL REV (Virtual Surge Test Lab. Restructured and Extended Version) based on the three-dimensional FDTD method along with the development of simulation techniques [13,14]. The simulation code was applied for calculating the transient response of a grounding grid of a high-voltage substation class, lightning electromagnetic pulses inside a real-scale building for direct and indirect striking, and so forth (e.g. Refs. [15,16]). In our previous study [17], we presented FDTD-based lightning surge simulations of an NPP by taking into account its practical configuration. Using VSTL REV, we modeled buildings, a grounding grid, grounding buses, and a lightning protection system (LPS) in an advanced pressurized water reactor (APWR) NPP. By simulating a direct lightning strike to the LPS of the reactor building (R/B) or turbine building (T/B), we studied the ground potential rises (GPRs) of the grounding grid, the induced voltages on the grounding buses and the metal sheaths of control cables drawn into the auxiliary building (A/B), and step voltages around the R/B, and then evaluated the effect of the configuration of the LPS. In this work, we study the effect of soil resistivities in the area of the building models on the step voltages and induced voltages. Note that the abbreviations mainly used through this paper will be summarized in Fig. 1.
Corresponding author. E-mail address: [email protected] (A. Tatematsu).
https://doi.org/10.1016/j.epsr.2019.106040 Received 20 March 2019; Received in revised form 7 September 2019; Accepted 19 September 2019 Available online 03 October 2019 0378-7796/ © 2019 Elsevier B.V. All rights reserved.
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Fig. 1. Calculation model of an APWR nuclear power plant [17].
Fig. 2. Plan view of the nuclear power plant model [17].
Fig. 3. Reactor building model [17].
Fig. 4. Connecting wires between the buildings and between the buildings and the grounding grid [17]: (a) EL = 9 m and (b) EL = −3 m.
2. Modeling of a nuclear power plant this study, owing to the limitation of cell sizes, we set the separation of the thin wires representing the beams, columns, and floors of the building models uniformly to 10 m by considering the layouts of the steel-structure parts of the buildings. In the right figure of Fig. 1, the parts of the buildings colored in red correspond to the basements. As shown in Fig. 3, each R/B has four stories above the ground and a twostory basement, where a space corresponding to a reactor containment vessel in each R/B is also included inside the building model. The height, length, width, and depth of each R/B are 63 m, 90 m, 70 m, and 15 m, respectively. As shown in Fig. 1, the A/B is located between the two R/Bs and has four stories above the ground and a one-story
2.1. Buildings and grounding grid Fig. 1 shows the calculation arrangement of the APWR NPP, which is mainly composed of two R/Bs (#1 and #2), a T/B, an A/B, a grounding grid, and an LPS based on the blueprint of Tsuruga Power Station Units 3 and 4 under planning in Japan. Fig. 2 shows its plan view. The beams, columns, and floors of the buildings are simulated by combining thin wires with a radius of 0.23 m, whereas the basements of the buildings are considered to be inside the soil. Although some parts of the buildings in NPPs have reinforced concrete (RC) structures, in
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Fig. 5. Connecting wires between the cut-off wall and the sea walls and between the cut-off wall and the grounding grid [17].
Fig. 8. Layout of culvert and utility tunnel below the grounding grid: (a) plane view and (b) plan view.
Fig. 6. Configuration of conductors placed in the soil at the back of the reactor buildings and auxiliary building and connected to the grounding grid [17].
Fig. 9. Analysis space simulated in the FDTD method [17].
basement. The height, width, length, and depth of the A/B are 32 m, 100 m, 60 m, and 6 m, respectively. The T/B, with three stories above the ground and a two-story basement, is located next to the R/Bs and A/ B. The height, length, width, and depth of the T/B are respectively 39 m, 90 m, 220 m, and 16 m. The grounding grid is composed of thin wires with a radius of 8.92 mm close to the buildings and a radius of 6.91 mm in other areas, and is placed 1 m below the ground surface at an elevation level (EL) of 9 m. Note that the ground surface, except for the hill at the back of the R/Bs and A/B, which will be explained later, corresponds to an EL of 10 m. As shown in Fig. 4, the buildings are electrically connected to each other by grounding wires at ELs of 9 m and −3 m, and the buildings are connected to the grounding grid by grounding wires at an EL of 9 m. As shown in Figs. 1 and 2, in addition to the buildings and the
Fig. 7. Layout of a ground bus drawn into the auxiliary building [17].
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Fig. 10. Modeling of the resistivities of the soil.
Fig. 12. Integration path for obtaining the GPR of the grounding grid.
Fig. 11. Distribution of the peak values of the ground potential rises of the grounding grid for strikes R and T in case I [17]: (a) Strike R and (b) Strike T.
Fig. 13. Calculation positions of voltages induced on the ground buses.
grounding grid, sea walls electrically connected to the grounding grid are simulated by conductors to represent the reinforcing bars of the sea walls. A cut-off wall, which is placed inside the soil and below the grounding grid to prevent water from invading the plant, is also represented by a conductor with a thickness of 1 m. The height of the cutoff wall is in the range from 14 m to 36 m, and the upper surface of the cut-off wall is positioned at an EL of 4 m. As shown in Fig. 5, the sea walls are connected to the cut-off wall by six grounding wires with a radius of 8.92 mm, and the cut-off wall is connected to the grounding grid by six grounding wires with the same radius. As shown in Figs. 1, 2, and 6 , some conductors with radii of 8.92 mm and 6.91 mm are placed inside the soil at the back of the R/Bs and A/B and are connected to the grounding grid. The length of the conductors buried in the soil ranges from 100 m to 200 m. As shown in Fig. 1, the LPS is composed of
conductor plates with a width of 1 m and thin wires with radii of 5.64 mm and 3.48 mm, where the conductors and wires are placed 2 m away from the building models. The thin wires of the LPS are connected to the grounding grid at an EL of 9 m, 1 m below the ground surface. As shown in Fig. 7, a ground bus connected to the grounding grid on the side of R/B #1 is buried inside the soil and is drawn into the A/B. The top ends of the branched ground bus in the A/B are positioned at an EL of 20 m on the third floor. Another ground bus is symmetrically placed from the grounding grid on the side of R/B #2. To simulate a ground bus of an insulated vinyl wire, the ground buses modeled by thin wires are placed inside lossless dielectric materials with a cross section of 2 × 2 m2 to simulate air, and the relative permittivities are set to 1. As shown in Fig. 8, two conductors simulating RC structures #1 and #2, inside which cables are installed in practice, are placed below 4
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Fig. 14. Calculated waveforms of the voltages induced on the ground bus at position A-1: (a) Case I-B and (b) Case II-B.
Fig. 15. Calculated waveforms of the voltages induced on the ground bus at position A-2: (a) Case I-B and (b) Case II-B.
Fig. 16. Calculated waveforms of the voltages induced on the ground bus at position A-3: (a) Case I-B and (b) Case II-B.
Table 1 Peak values of the voltages induced on the ground buses. Case
I-A I-B I-C II-A II-B II-C
Strike
R T R T R T R T R T R T
Peak values of induced voltages [kV/kA] A-1
A-2
A-3
2.42 0.72 6.83 3.28 9.10 4.54 0.36 0.32 1.06 0.97 1.45 1.29
2.71 0.81 7.63 3.61 10.14 4.97 0.40 0.36 1.13 1.12 1.55 1.50
0.33 0.42 1.13 3.16 1.75 4.59 0.27 0.23 0.83 0.72 1.21 0.95
Fig. 17. Calculation positions of step voltages around the reactor building model #1.
the grounding grid, and the conductor of RC structure #1 is electrically connected to the thin wires simulating the beams and columns of the T/ B below the ground surface, whereas the conductor simulating RC structure #2 is similarly connected to R/B #1. Thin wires to simulate the metal sheaths of cables in RC structures #1 and #2, which are respectively referred to as wires A and B, are located inside the two conductors, and one end of each thin wire is also connected to the structure of the A/B model to simulate a condition that the metal sheath of a control cable is grounded at one end inside a building.
2.2. FDTD-based surge simulations As shown in Fig. 9, in our FDTD-based surge simulations, the abovedescribed calculation model is placed in an analysis space, which has a volume of 1613 m × 1891 m × 1100 m. The bottom space with a thickness of 510 m is treated as soil, and the inhomogeneous resistivity distribution of the soil is taken into account. As shown in Fig. 10, the plant area is divided into six subareas, which have different resistivities. To study the effect of the soil resistivities, the resistivity in the area of 5
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Fig. 18. Calculated waveforms of the step voltages around the reactor building model #1 at position R-1: (a) Case I-B and (b) Case II-B.
Fig. 19. Calculated waveforms of the step voltages around the reactor building model #1 at position R-2: (a) Case I-B and (b) Case II-B.
Fig. 20. Calculated waveforms of the step voltages around the reactor building model #1 at position R-3: (a) Case I-B and (b) Case II-B.
counterpoise with a pulse generator (Model 360, Velonex). Although the relative permittivity used in this study is a little larger than typical values of 5–15 [18], the same value was used in the previous FDTD simulations of the transient response of grounding structures [15,19], which will be mentioned later. The area colored in blue corresponds to the sea with a depth of 25 m, whose resistivity and relative permittivity are set to 0.2 Ωm and 80, respectively. All the external surfaces of the analysis space are treated as absorbing boundaries of the second-order Liao’s formulation [20] to assume an open space. In this study, the lightning striking point is assumed to be the LPS of R/B #1 (strike R) or the T/B (strike T), and, as shown in Fig. 9, the vertical and straight lightning channel is represented by a TL model, which is composed of phased-array current sources placed along the channel to control the propagation speed of the current [21]. The lightning current has a triangular waveform, whose front time and time to half value are respectively set to 1 μs and 70 μs. A lightning current with the same waveform is widely applied when designing the lightning protection of power plants and substations in Japan [22]. In this study, the peak lightning current is normalized to 1 kA. In the FDTD method, thin wires are represented by thin-wire representation techniques, which have been developed for the application of the FDTD method to surge analysis and have been successfully and widely employed for analyzing electromagnetic transient phenomena [11,12]. In this study, to reduce the calculation time and the required memory capacity, the analysis space is divided into 959 × 1129 × 353 nonuniform cells, where the size of the cells is changed considering the calculation arrangement. The size of the cells close to the calculation model of the NPP is set to 1 m, whereas the size of the other cells increases away from the calculation model and ranges from 2 m to 10 m.
Table 2 Peak values of the step voltages. Case
I-A I-B I-C II-A II-B II-C
Strike
R T R T R T R T R T R T
Peak values of step voltages [kV/kA] R-1
R-2
R-3
0.06 0.05 0.10 0.07 0.11 0.08 0.07 0.06 0.12 0.09 0.13 0.10
0.26 0.04 0.50 0.07 0.58 0.09 0.05 0.04 0.12 0.08 0.14 0.10
0.37 0.04 1.01 0.13 1.34 0.20 0.05 0.05 0.23 0.14 0.40 0.22
the buildings (R/Bs, T/B, and A/B) is set to 100 Ωm, 525.1 Ωm, or 1000 Ωm. Note that the difference in the soil resistivity of less than 1 Ωm in areas A to E has very little effect on the calculated results, although the estimated results of the soil resistivity in the corresponding area, except for the values of 100 Ωm and 1000 Ωm in area A, are used as they are here. On the other hand, the relative permittivity of the soil is set uniformly to 30 on the basis of a comparison of the current flowing through a horizontal electrode with a length of 60 m and a depth of 0.5 m, simulated by the FDTD method, with the current measured with a current probe (CT411, Pearson) when a step voltage with a rise time of about 20 ns was applied to the end of the
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Fig. 21. Calculated waveforms of the voltages induced on wire A: (a) Case I-B and (b) Case II-B.
Fig. 22. Calculated waveforms of the voltages induced on wire B: (a) Case I-B and (b) Case II-B.
The time discretization is set to 0.96 ns, which is identical to half the limit of Courant’s condition. In this study, the FDTD-based surge simulations are carried out using VSTL REV [13,14], which has been developed on the basis of the three-dimensional FDTD method. Compared with conventional TLbased simulation methods, the FDTD method requires a longer calculation time and a larger memory capacity. However, thanks to the recent development of high-performance computing techniques, particularly GPU computing, the FDTD method can be employed for analyzing electromagnetic transient phenomena taking into account a complex and practical configuration. VSTL REV can also be executed on a GPU-based parallel computer using CUDA (Compute Unified Device Architecture) and MPI (Message Passing Interface), which can markedly reduce the calculation time. In previous studies [15,19], we confirmed the applicability of VSTL REV to the electromagnetic transient analysis of grounding structures by comparing the GPRs of a grounding structure (a grounding electrode with a length of 60 m or a grounding grid with a size of 60 m × 30 m) and the currents flowing it, calculated using VSTL REV, with the measured results. In this study, the FDTD simulations are performed on a parallel computer equipped with 24 GPUs (P100, NVIDIA corp.), and the calculation time is about 55.5 min when the observation time is 20 μs, and the required memory capacity is about 27 GB. Using the aforementioned calculation arrangement, we calculate the GPRs of the grounding grid, the step voltages around R/B #1, and the voltages induced on the ground buses and wires A and B in the case of a direct lightning strike to the LPS of R/B #1 or the T/B (strikes R and T in Fig. 2). The above calculation arrangement is referred to as case I hereafter. To evaluate the effect of the LPS configuration, FDTD simulations are also performed by connecting the LPS to the building structure at the striking point for strikes R and T, which is referred to as case II. For both cases I and II, the soil resistivity in subarea A is set to 100 Ωm, 525.1 Ωm, or 1000 Ωm, referred to as cases K–A, K–B, and K–C (K = I and II), respectively.
Table 3 Peak values of the voltages induced on Wires A and B. Case
I-A I-B I-C II-A II-B II-C
Strike
R T R T R T R T R T R T
Peak values of induced voltages [kV/kA] Wire A
Wire B
0.27 0.13 0.32 0.21 0.33 0.24 0.26 0.14 0.29 0.22 0.31 0.24
0.39 0.12 1.19 0.18 1.67 0.25 0.47 0.14 1.36 0.20 2.08 0.25
3. Calculated results 3.1. GPRs, step voltages, and induced voltages Fig. 23. Modification of the configuration of the LPS [17].
In our previous study [17], using the aforementioned calculation model of the NPP, first, we calculated the GPRs of the grounding 7
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Fig. 24. Calculated waveforms of the voltages induced on the ground bus at position A-1 for the modified LPS: (a) Case I-B and (b) Case II-B.
Fig. 25. Calculated waveforms of the voltages induced on the ground bus at position A-2 for the modified LPS: (a) Case I-B and (b) Case II-B.
Fig. 26. Calculated waveforms of the voltages induced on the ground bus at position A-3 for the modified LPS: (a) Case I-B and (b) Case II-B.
surface at an EL of 10 m is the extension of the straight line between point S under the striking point and the calculation point of the GPR. As shown in Fig. 11, the peak-value distributions have their maximum values at the back of the R/B model for strike R and on the side of the T/ B model for strike T, and the peak value of the GPR of the grounding grid for strike R is about 20% larger than that for strike T. This is because there are fewer grounding wires installed at the back of the R/B model. Voltages induced on the ground buses placed from the grounding grid into the A/B model, as shown in Fig. 7, are calculated in cases I-A to II-C for both strikes R and T. As shown in Fig. 13, the induced voltages, that is, the voltage differences between the building structure and the ground buses, are calculated at three positions, which correspond to the ends of the branched ground buses on the third floor in the A/B model and are referred to as positions A-1–A-3. As an example of the calculated waveforms, Figs. 14–16 show the calculated induced voltages at positions A-1, A-2, and A-3, respectively, in cases I-B and II-B for strikes R and T. Table 1 summarizes the peak induced voltages on the ground buses. As shown Figs. 14–16, the waveforms of the induced voltages oscillate mainly owing to the effect of the lightning current propagating through the LPS and the voltages propagating through the ground buses. In all the cases, the peak values for strike R are larger than those for strike T, although the differences between the peak values for strikes R and T in case II are much smaller than those in case I, and the differences between the maximum peak values of the three positions for strike R and those for strike T range from 51% to 70% in case I and from 3% to 10% in case II. Table 1 shows that the peak induced voltages have a tendency to be larger for higher resistivities in
Table 4 Peak values of the voltages induced on the ground buses for the modified LPS. Case
I-A I-B I-C II-A II-B II-C
Strike
R T R T R T R T R T R T
Peak values of induced voltages [kV/kA] A-1
A-2
A-3
0.27 0.14 0.85 0.36 1.24 0.50 0.26 0.15 0.99 0.42 1.45 0.58
0.30 0.15 0.86 0.37 1.24 0.49 0.26 0.16 0.96 0.41 1.40 0.55
0.17 0.13 0.44 0.35 0.61 0.47 0.17 0.15 0.40 0.38 0.56 0.53
structure when the striking point is assumed to be the LPS of the R/B model (strike R) or the turbine building model (strike T). Fig. 11 shows the calculated distributions of the peak values of the GPRs of the grounding grid in case I-B for both strikes R and T, where the peak values of the GPRs are normalized by 5.30 kV/kA, corresponding to the maximum peak value of the GPRs in case I. Here, the GPR at each point is calculated by integrating the electric fields on the ground surface from the calculation point to the external surface on the side of the analysis space, where the reference point of the voltage is assumed to be positioned on the ground surface at the side surface of the analysis space. As shown in Fig. 12, the integration path projected on the ground 8
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Fig. 27. Calculated waveforms of the step voltages around the reactor building model #1 at position R-1 for the modified LPS: (a) Case I-B and (b) Case II-B.
Fig. 28. Calculated waveforms of the step voltages around the reactor building model #1 at position R-2 for the modified LPS: (a) Case I-B and (b) Case II-B.
Fig. 29. Calculated waveforms of the step voltages around the reactor building model #1 at position R-3 for the modified LPS: (a) Case I-B and (b) Case II-B.
to II-C for strikes R and T. Figs. 18–20 show the calculated waveforms of the step voltages at positions R-1, R-2, and R-3 in cases I-B and II-B, respectively. Table 2 summarizes the peak step voltages. The waveforms of the step voltages at positions R-2 and R-3, which have larger peak values, highly oscillate owing to the effect of the lightning current propagating through the LPS. As shown in Figs. 18–20 and Table 2, it is confirmed that the peak step voltages for strike R are larger than those for strike T and the ratios of the maximum peak values of the three positions for strike R to those for strike T range from 6.7 to 7.6 in case I and from 1.2 to 1.8 in case II. The above results also confirm that the step voltages are larger for higher resistivities. The step voltages at position R-3 are severer than those at the other positions, particularly for higher resistivities, since the structure of each R/B is not connected to the surrounding grounding grid by wires on this side of the R/B as shown in Fig. 4. In case II, the injected lightning current is distributed to the structure of the R/B model in addition to the LPS from the striking point, and thus the voltage differences between the R/B model and the grounding grid are decreased, and the step voltages in case II are suppressed compared with those in case I for the three resistivities. The maximum peak step voltages in each of cases I-A, I-B, and I-C are reduced by 70%–82% in case II. Voltages induced on wires A and B, both ends of which are connected to the structure of the A/B, are calculated in cases I-A to II-C for both strikes R and T. Figs. 21 and 22 respectively show the calculated waveforms of the induced voltages on wires A and B, that is, the voltage differences between the far ends of the wires from the A/B and the grounding grid, in cases I-B and II-B. Table 3 summarizes the peak voltages induced on wires A and B. The main part of the oscillation of the induced voltages on wires A and B arises from the propagation of
Table 5 Peak values of the step voltages for the modified LPS. Case
I-A I-B I-C II-A II-B II-C
Strike
R T R T R T R T R T R T
Peak values of step voltages [kV/kA] A-1
A-2
A-3
0.06 0.05 0.10 0.07 0.11 0.08 0.07 0.06 0.12 0.09 0.13 0.10
0.13 0.02 0.18 0.03 0.19 0.04 0.04 0.03 0.05 0.04 0.06 0.04
0.14 0.02 0.17 0.03 0.18 0.03 0.04 0.02 0.06 0.03 0.07 0.04
cases I and II for both strikes R and T. The ratios of the maximum peak induced voltages in cases I-A and II-A to those in cases I-B and II-B are approximately 2.8, whereas the ratios of the maximum peak values in cases I-B and II-B to those in cases I-C and II-C are from 1.3 to 1.4. The peak induced voltages in case II are smaller than those in case I irrespective of the striking points and the soil resistivities in the building area, since the injected lightning current flows into both the LPS and the structure of the building models, and thus the GPRs of the connecting points of the ground buses are suppressed in case II. Step voltages around the R/B model (#1) are calculated at three positions specified by R-1, R-2, and R-3 as shown in Fig. 17 in cases I-A
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Fig. 30. Calculated waveforms of the voltages induced on wire A for the modified LPS: (a) Case I-B and (b) Case II-B.
Fig. 31. Calculated waveforms of the voltages induced on wire B for the modified LPS: (a) Case I-B and (b) Case II-B.
A-3 (see Fig. 13), respectively, in cases I-B and II-B for strikes R and T, and Table 4 summarizes the peak induced voltages in cases I-A to II-C. Figs. 27–29 respectively show the calculated waveforms of the step voltages at positions R-1, R-2, and R-3 (see Fig. 17) around the R/B model in cases I-B and II-B for strikes R and T, and Table 5 shows the peak step voltages in the case of the modified LPS for cases I-A to II-C. Figs. 30 and 31 show the calculated voltages induced on wires A and B, respectively, in cases I-B and II-B for strikes R and T using the modified LPS, and Table 6 summarizes the peak induced voltages on wires A and B in cases I-A to II-C. These results show that the above-described change in the configuration of the LPS is not effective for lowering the peak voltages induced on wires A and B. However, by modifying the LPS, we can suppress the GPRs at the connecting points of the ground buses and the voltages induced on the ground buses. In particular, the improvement is significant in case I, and the peak induced voltages are reduced by 81%–90% for the three soil resistivities. Furthermore, we can suppress the voltage differences between the building structures and the grounding grid by applying the modified LPS, and reduce the peak step voltages. The maximum peak step voltages in each case is reduced by 47%–86% except in case II-A, where the step voltages are originally smaller than those in the other cases.
Table 6 Peak values of the voltages induced on wires A and B for the modified LPS. Case
I-A I-B I-C II-A II-B II-C
Strike
R T R T R T R T R T R T
Peak values of induced voltages [kV/kA] Wire A
Wire B
0.27 0.13 0.32 0.21 0.36 0.24 0.26 0.14 0.29 0.23 0.31 0.26
0.41 0.12 1.04 0.18 1.56 0.26 0.47 0.15 1.34 0.21 2.04 0.25
the voltages through the wires. In all the cases, the voltages induced on wires A and B are larger for strike R than for strike T. As shown in Table 3, the peak voltages induced on wire B are larger than those on wire A in all the cases for strike R, and the induced voltages on wire B are highly dependent on the resistivities in the building area.
4. Conclusion
3.2. Effect of the configuration of the LPS
In this study, we presented lightning surge simulations of an APWR NPP in a three-dimensional arrangement using the FDTD-based surge simulation code VSTL REV developed by CRIEPI and studied the effect of the soil resistivities in the building area on step voltages around a reactor building and the voltages induced on ground buses drawn into an auxiliary building and wires simulating the metal sheaths of cables in the case of a direct lightning strike to an NPP. Taking into account various soil resistivities, we confirmed that the voltages induced on the ground buses and the step voltages around the reactor building can be suppressed by connecting down-conductors to the grounding grid far from the connection point of the ground buses to the grounding grid and by connecting the down-conductors of the LPS to the grounding grid and the building structure at multiple points.
Here, to evaluate the effect of the configuration of the LPS on the voltages induced on the wires and the step voltages by taking into account the three resistivities in the building area, we modify the configuration of the LPS in the following two ways. (i) Four down-conductors below the horizontal conductor of the LPS near the connecting points of the ground buses drawn into the A/B building are removed, where the positions of the removed downconductors are denoted by the red points in Fig. 23. (ii) The down-conductors of the LPS are electrically connected to the surrounding grounding grid at the positions specified by the green points in Fig. 23.
References
Using the aforementioned modified LPS, we calculate the induced voltages on the wires and the step voltages. Figs. 24–26 show the calculated voltages induced on the ground buses at positions A-1, A-2, and
[1] P. Duquerroy, C. Trouilloud, Evolution of lightning protection of nuclear power
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[2]
[3] [4] [5]
[6]
[7]
[8]
[9]
[10]
[11]
[12] Y. Baba, N. Nagaoka, A. Ametani, Modeling of thin wires in a lossy medium for FDTD simulations, IEEE Trans. Electromagn. Compat. 47 (1) (2005) 54–60. [13] A. Tatematsu, Development of a surge simulation code VSTL REV based on the 3D FDTD method, Proc. Joint IEEE Int. Symp. EMC and EMC Europe, Dresden, Germany, August 16–22, 2015, pp. 1111–1116. [14] A. Tatematsu, Overview of the three-dimensional FDTD-based surge simulation code VSTL REV, Proc. 2016 Asia-Pacific Int. Symp. on Electromagn. Compat, Shenzhen, China, Paper SS04-02, May 18–21, 2016. [15] A. Tatematsu, K. Yamazaki, K. Miyajima, H. Motoyama, A study on induced voltages on an aerial wire due to a current flowing through a grounding grid, IEEJ Trans. Power Energy Soc. 129 (10) (2009) 1245–1251. [16] A. Tatematsu, F. Rachidi, M. Rubinstein, Analysis of electromagnetic fields inside a reinforced concrete building with layered reinforcing bar due to direct and indirect lightning strikes using the FDTD method, IEEE Trans. Electromagn. Compat. 57 (3) (2015) 405–417. [17] A. Tatematsu, H. Motoyama, A. Tanigawa, Lightning surge analysis of a PWR nuclear power plant using the three-dimensional FDTD method, Proc. 2018 International Conference on Lightning Protection (ICLP), Rzeszow, Poland, September 2–7, 2018. [18] E.F. Vance, Coupling to Shielded Cables, John Wiley & Sons, Australia, 1978. [19] A. Tatematsu, T. Noda, H. Motoyama, Simulation of induced voltages on an aerial wire due to a current through a buried bare wire using the FDTD method, Proc. 2006 International Conference on Lightning Protection (ICLP), Kanazawa, Japan, Paper III-2, September 18–22, 2006, pp. 459–464. [20] Z.P. Liao, H.L. Wong, B.P. Yang, Y.F. Yuan, A transmitting boundary for transient wave analysis, Sci. Sinica Ser. A 27 (10) (1984) 1063–1076. [21] Y. Baba, V.A. Rakov, On the transmission line model for lightning return stroke representation, Geophys. Res. Lett. 30 (24) (2003) 2294. [22] Subcommittee for power stations and substations, study committee on lightning risk, Guide to Lightning protection design of power stations, substations and underground transmission lines (rev.2011), CRIEPI Report, no. H06, 2012.
plants: an overview of EDF’s experience, Proc. CIGRE Session 2018, Paris, France, Paper C4-213, August 26–31, 2018. K.S. Yee, Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media, IEEE Trans. Antennas Propag. 14 (3) (1966) 302–307. R.F. Harrington, Field Computation by Moment Methods, Macmillan Co., New York, 1968. Working Group C4.501, Guideline for numerical electromagnetic analysis method and its application to surge phenomena, Cigre report, no. 543, 2013. Y. Baba, V.A. Rakov, Applications of the FDTD method to lightning electromagnetic pulse and surge simulations, IEEE Trans. Electromagn. Compat. 56 (6) (2014) 1506–1521. A. Tatematsu, Y. Baba, M. Ishii, S. Okabe, T. Ueda, N. Itamoto, Development of Surge Simulation Techniques Based on the Finite Difference Time Domain Method and Its Application to Surge Analysis, Cigre Session 2016, Paris, France, Paper C4302, August 21–26, 2016. E. Bachelier, F. Issac, D. Prost, C. Miry, E. Amador, P. Duquerroy, Protection against lightning of reinforced concrete buildings, Proc. 2014 International Conference on Lightning Protection (ICLP), Shanghai, China, October 11–18, 2014, pp. 452–457. A. Tatematsu, T. Noda, Three-dimensional FDTD calculation of lightning-induced voltages on a multiphase distribution line with the lightning arresters and an overhead shielding wire, IEEE Trans. Electromagn. Compat. 56 (1) (2014) 159–167. M. Namdari, M.K. Farsani, R. Moini, S.H.H. Sadeghi, An efficient parallel 3-D FDTD method for calculating lightning-induced disturbances on overhead lines in the presence of surge arresters, IEEE Trans. Electromagn. Compat. 57 (6) (2015) 1593–1600. A. Tatematsu, T. Ueda, FDTD-based lightning surge simulation of an HV air-insulated substation with back-flashover phenomena, IEEE Trans. Electromagn. Compat. 58 (5) (2016) 1549–1560. T. Noda, S. Yokoyama, Thin wire representation in finite difference time domain surge simulation, IEEE Trans. Power Deliv. 17 (3) (2002) 840–847.
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Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr
Application of the FDTD-based simulation code VSTL REV to the lightning surge analysis of a nuclear power plant
T
⁎
Akiyoshi Tatematsua, , Hideki Motoyamaa, Akihiro Tanigawab a b
Electric Power Engineering Research Lab., Central Research Institute of Electric Power Industry, 2-6-1 Nagasaka, Yokosuka, Kanagawa 240-0196, Japan Projects Development Dep., The Japan Atomic Power Company, 1-1 Kandamitoshirocho, Chiyoda-ku, Tokyo 101-0053, Japan
A R T I C LE I N FO
A B S T R A C T
Keywords: Electromagnetic transient analysis Finite-difference time-domain method Grounding Lightning Lightning protection system
The installation of effective lightning protection is necessary to protect power equipment and sensitive electronic devices and guarantee human safety in nuclear power plants. To evaluate the effectiveness of countermeasures against lightning, it is necessary to predict lightning surge phenomena. Recently, the finite-difference timedomain (FDTD) method, which is one of the full-wave numerical approaches, has been applied for analyzing electromagnetic transient phenomena in three-dimensional structures such as lightning protection systems and buildings or grounding structures such grounding grids. In this study, we model buildings and grounding structures of a nuclear power plant using the FDTD-based surge simulation code VSTL REV, and we study the effect of soil resistivities on the step voltages around the reactor building and the voltages induced on grounding buses drawn into an auxiliary building and the metal sheaths of coaxial cables in the case of a direct lightning strike to the nuclear power plant.
1. Introduction To protect power equipment and sensitive electronic devices and guarantee human safety in nuclear power plants (NPPs), it is necessary to design lightning protection measures properly [1]. In a design process, the prediction of lightning surge phenomena is very useful for evaluating the effectiveness of lightning protection measures. Traditionally, transmission-line (TL) based electromagnetic transient analysis has been employed for predicting lightning surge phenomena. On the other hand, full-wave numerical approaches such as the finite-difference time-domain (FDTD) method [2] and the method of moments (MoM) [3] are now widely used for analyzing electromagnetic transient phenomena in three-dimensional or grounding structures (e.g. Refs. [4–7]). Compared with other full-wave numerical approaches, the FDTD method is advantageous in terms of its capability of handling inhomogeneous soil parameters, nonflat ground surfaces such as mountainous terrains, and, in particular, nonlinear characteristics such as those of surge protective devices and back-flashover phenomena at TL towers [8–10]. Several techniques have been developed to apply the FDTD method to surge analysis, for example, for representing thin wires such as electrical wires and grounding wires [11,12]; thus the FDTD method has been applied to the lightning surge analysis of power plants, transmission lines, distribution lines, substations, grounding ⁎
systems, and buildings. Central Research Institute of Electric Power Industry (CRIEPI) has been developing an FDTD-based surge simulation code called VSTL REV (Virtual Surge Test Lab. Restructured and Extended Version) based on the three-dimensional FDTD method along with the development of simulation techniques [13,14]. The simulation code was applied for calculating the transient response of a grounding grid of a high-voltage substation class, lightning electromagnetic pulses inside a real-scale building for direct and indirect striking, and so forth (e.g. Refs. [15,16]). In our previous study [17], we presented FDTD-based lightning surge simulations of an NPP by taking into account its practical configuration. Using VSTL REV, we modeled buildings, a grounding grid, grounding buses, and a lightning protection system (LPS) in an advanced pressurized water reactor (APWR) NPP. By simulating a direct lightning strike to the LPS of the reactor building (R/B) or turbine building (T/B), we studied the ground potential rises (GPRs) of the grounding grid, the induced voltages on the grounding buses and the metal sheaths of control cables drawn into the auxiliary building (A/B), and step voltages around the R/B, and then evaluated the effect of the configuration of the LPS. In this work, we study the effect of soil resistivities in the area of the building models on the step voltages and induced voltages. Note that the abbreviations mainly used through this paper will be summarized in Fig. 1.
Corresponding author. E-mail address: [email protected] (A. Tatematsu).
https://doi.org/10.1016/j.epsr.2019.106040 Received 20 March 2019; Received in revised form 7 September 2019; Accepted 19 September 2019 Available online 03 October 2019 0378-7796/ © 2019 Elsevier B.V. All rights reserved.
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Fig. 1. Calculation model of an APWR nuclear power plant [17].
Fig. 2. Plan view of the nuclear power plant model [17].
Fig. 3. Reactor building model [17].
Fig. 4. Connecting wires between the buildings and between the buildings and the grounding grid [17]: (a) EL = 9 m and (b) EL = −3 m.
2. Modeling of a nuclear power plant this study, owing to the limitation of cell sizes, we set the separation of the thin wires representing the beams, columns, and floors of the building models uniformly to 10 m by considering the layouts of the steel-structure parts of the buildings. In the right figure of Fig. 1, the parts of the buildings colored in red correspond to the basements. As shown in Fig. 3, each R/B has four stories above the ground and a twostory basement, where a space corresponding to a reactor containment vessel in each R/B is also included inside the building model. The height, length, width, and depth of each R/B are 63 m, 90 m, 70 m, and 15 m, respectively. As shown in Fig. 1, the A/B is located between the two R/Bs and has four stories above the ground and a one-story
2.1. Buildings and grounding grid Fig. 1 shows the calculation arrangement of the APWR NPP, which is mainly composed of two R/Bs (#1 and #2), a T/B, an A/B, a grounding grid, and an LPS based on the blueprint of Tsuruga Power Station Units 3 and 4 under planning in Japan. Fig. 2 shows its plan view. The beams, columns, and floors of the buildings are simulated by combining thin wires with a radius of 0.23 m, whereas the basements of the buildings are considered to be inside the soil. Although some parts of the buildings in NPPs have reinforced concrete (RC) structures, in
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Fig. 5. Connecting wires between the cut-off wall and the sea walls and between the cut-off wall and the grounding grid [17].
Fig. 8. Layout of culvert and utility tunnel below the grounding grid: (a) plane view and (b) plan view.
Fig. 6. Configuration of conductors placed in the soil at the back of the reactor buildings and auxiliary building and connected to the grounding grid [17].
Fig. 9. Analysis space simulated in the FDTD method [17].
basement. The height, width, length, and depth of the A/B are 32 m, 100 m, 60 m, and 6 m, respectively. The T/B, with three stories above the ground and a two-story basement, is located next to the R/Bs and A/ B. The height, length, width, and depth of the T/B are respectively 39 m, 90 m, 220 m, and 16 m. The grounding grid is composed of thin wires with a radius of 8.92 mm close to the buildings and a radius of 6.91 mm in other areas, and is placed 1 m below the ground surface at an elevation level (EL) of 9 m. Note that the ground surface, except for the hill at the back of the R/Bs and A/B, which will be explained later, corresponds to an EL of 10 m. As shown in Fig. 4, the buildings are electrically connected to each other by grounding wires at ELs of 9 m and −3 m, and the buildings are connected to the grounding grid by grounding wires at an EL of 9 m. As shown in Figs. 1 and 2, in addition to the buildings and the
Fig. 7. Layout of a ground bus drawn into the auxiliary building [17].
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Fig. 10. Modeling of the resistivities of the soil.
Fig. 12. Integration path for obtaining the GPR of the grounding grid.
Fig. 11. Distribution of the peak values of the ground potential rises of the grounding grid for strikes R and T in case I [17]: (a) Strike R and (b) Strike T.
Fig. 13. Calculation positions of voltages induced on the ground buses.
grounding grid, sea walls electrically connected to the grounding grid are simulated by conductors to represent the reinforcing bars of the sea walls. A cut-off wall, which is placed inside the soil and below the grounding grid to prevent water from invading the plant, is also represented by a conductor with a thickness of 1 m. The height of the cutoff wall is in the range from 14 m to 36 m, and the upper surface of the cut-off wall is positioned at an EL of 4 m. As shown in Fig. 5, the sea walls are connected to the cut-off wall by six grounding wires with a radius of 8.92 mm, and the cut-off wall is connected to the grounding grid by six grounding wires with the same radius. As shown in Figs. 1, 2, and 6 , some conductors with radii of 8.92 mm and 6.91 mm are placed inside the soil at the back of the R/Bs and A/B and are connected to the grounding grid. The length of the conductors buried in the soil ranges from 100 m to 200 m. As shown in Fig. 1, the LPS is composed of
conductor plates with a width of 1 m and thin wires with radii of 5.64 mm and 3.48 mm, where the conductors and wires are placed 2 m away from the building models. The thin wires of the LPS are connected to the grounding grid at an EL of 9 m, 1 m below the ground surface. As shown in Fig. 7, a ground bus connected to the grounding grid on the side of R/B #1 is buried inside the soil and is drawn into the A/B. The top ends of the branched ground bus in the A/B are positioned at an EL of 20 m on the third floor. Another ground bus is symmetrically placed from the grounding grid on the side of R/B #2. To simulate a ground bus of an insulated vinyl wire, the ground buses modeled by thin wires are placed inside lossless dielectric materials with a cross section of 2 × 2 m2 to simulate air, and the relative permittivities are set to 1. As shown in Fig. 8, two conductors simulating RC structures #1 and #2, inside which cables are installed in practice, are placed below 4
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Fig. 14. Calculated waveforms of the voltages induced on the ground bus at position A-1: (a) Case I-B and (b) Case II-B.
Fig. 15. Calculated waveforms of the voltages induced on the ground bus at position A-2: (a) Case I-B and (b) Case II-B.
Fig. 16. Calculated waveforms of the voltages induced on the ground bus at position A-3: (a) Case I-B and (b) Case II-B.
Table 1 Peak values of the voltages induced on the ground buses. Case
I-A I-B I-C II-A II-B II-C
Strike
R T R T R T R T R T R T
Peak values of induced voltages [kV/kA] A-1
A-2
A-3
2.42 0.72 6.83 3.28 9.10 4.54 0.36 0.32 1.06 0.97 1.45 1.29
2.71 0.81 7.63 3.61 10.14 4.97 0.40 0.36 1.13 1.12 1.55 1.50
0.33 0.42 1.13 3.16 1.75 4.59 0.27 0.23 0.83 0.72 1.21 0.95
Fig. 17. Calculation positions of step voltages around the reactor building model #1.
the grounding grid, and the conductor of RC structure #1 is electrically connected to the thin wires simulating the beams and columns of the T/ B below the ground surface, whereas the conductor simulating RC structure #2 is similarly connected to R/B #1. Thin wires to simulate the metal sheaths of cables in RC structures #1 and #2, which are respectively referred to as wires A and B, are located inside the two conductors, and one end of each thin wire is also connected to the structure of the A/B model to simulate a condition that the metal sheath of a control cable is grounded at one end inside a building.
2.2. FDTD-based surge simulations As shown in Fig. 9, in our FDTD-based surge simulations, the abovedescribed calculation model is placed in an analysis space, which has a volume of 1613 m × 1891 m × 1100 m. The bottom space with a thickness of 510 m is treated as soil, and the inhomogeneous resistivity distribution of the soil is taken into account. As shown in Fig. 10, the plant area is divided into six subareas, which have different resistivities. To study the effect of the soil resistivities, the resistivity in the area of 5
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Fig. 18. Calculated waveforms of the step voltages around the reactor building model #1 at position R-1: (a) Case I-B and (b) Case II-B.
Fig. 19. Calculated waveforms of the step voltages around the reactor building model #1 at position R-2: (a) Case I-B and (b) Case II-B.
Fig. 20. Calculated waveforms of the step voltages around the reactor building model #1 at position R-3: (a) Case I-B and (b) Case II-B.
counterpoise with a pulse generator (Model 360, Velonex). Although the relative permittivity used in this study is a little larger than typical values of 5–15 [18], the same value was used in the previous FDTD simulations of the transient response of grounding structures [15,19], which will be mentioned later. The area colored in blue corresponds to the sea with a depth of 25 m, whose resistivity and relative permittivity are set to 0.2 Ωm and 80, respectively. All the external surfaces of the analysis space are treated as absorbing boundaries of the second-order Liao’s formulation [20] to assume an open space. In this study, the lightning striking point is assumed to be the LPS of R/B #1 (strike R) or the T/B (strike T), and, as shown in Fig. 9, the vertical and straight lightning channel is represented by a TL model, which is composed of phased-array current sources placed along the channel to control the propagation speed of the current [21]. The lightning current has a triangular waveform, whose front time and time to half value are respectively set to 1 μs and 70 μs. A lightning current with the same waveform is widely applied when designing the lightning protection of power plants and substations in Japan [22]. In this study, the peak lightning current is normalized to 1 kA. In the FDTD method, thin wires are represented by thin-wire representation techniques, which have been developed for the application of the FDTD method to surge analysis and have been successfully and widely employed for analyzing electromagnetic transient phenomena [11,12]. In this study, to reduce the calculation time and the required memory capacity, the analysis space is divided into 959 × 1129 × 353 nonuniform cells, where the size of the cells is changed considering the calculation arrangement. The size of the cells close to the calculation model of the NPP is set to 1 m, whereas the size of the other cells increases away from the calculation model and ranges from 2 m to 10 m.
Table 2 Peak values of the step voltages. Case
I-A I-B I-C II-A II-B II-C
Strike
R T R T R T R T R T R T
Peak values of step voltages [kV/kA] R-1
R-2
R-3
0.06 0.05 0.10 0.07 0.11 0.08 0.07 0.06 0.12 0.09 0.13 0.10
0.26 0.04 0.50 0.07 0.58 0.09 0.05 0.04 0.12 0.08 0.14 0.10
0.37 0.04 1.01 0.13 1.34 0.20 0.05 0.05 0.23 0.14 0.40 0.22
the buildings (R/Bs, T/B, and A/B) is set to 100 Ωm, 525.1 Ωm, or 1000 Ωm. Note that the difference in the soil resistivity of less than 1 Ωm in areas A to E has very little effect on the calculated results, although the estimated results of the soil resistivity in the corresponding area, except for the values of 100 Ωm and 1000 Ωm in area A, are used as they are here. On the other hand, the relative permittivity of the soil is set uniformly to 30 on the basis of a comparison of the current flowing through a horizontal electrode with a length of 60 m and a depth of 0.5 m, simulated by the FDTD method, with the current measured with a current probe (CT411, Pearson) when a step voltage with a rise time of about 20 ns was applied to the end of the
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Fig. 21. Calculated waveforms of the voltages induced on wire A: (a) Case I-B and (b) Case II-B.
Fig. 22. Calculated waveforms of the voltages induced on wire B: (a) Case I-B and (b) Case II-B.
The time discretization is set to 0.96 ns, which is identical to half the limit of Courant’s condition. In this study, the FDTD-based surge simulations are carried out using VSTL REV [13,14], which has been developed on the basis of the three-dimensional FDTD method. Compared with conventional TLbased simulation methods, the FDTD method requires a longer calculation time and a larger memory capacity. However, thanks to the recent development of high-performance computing techniques, particularly GPU computing, the FDTD method can be employed for analyzing electromagnetic transient phenomena taking into account a complex and practical configuration. VSTL REV can also be executed on a GPU-based parallel computer using CUDA (Compute Unified Device Architecture) and MPI (Message Passing Interface), which can markedly reduce the calculation time. In previous studies [15,19], we confirmed the applicability of VSTL REV to the electromagnetic transient analysis of grounding structures by comparing the GPRs of a grounding structure (a grounding electrode with a length of 60 m or a grounding grid with a size of 60 m × 30 m) and the currents flowing it, calculated using VSTL REV, with the measured results. In this study, the FDTD simulations are performed on a parallel computer equipped with 24 GPUs (P100, NVIDIA corp.), and the calculation time is about 55.5 min when the observation time is 20 μs, and the required memory capacity is about 27 GB. Using the aforementioned calculation arrangement, we calculate the GPRs of the grounding grid, the step voltages around R/B #1, and the voltages induced on the ground buses and wires A and B in the case of a direct lightning strike to the LPS of R/B #1 or the T/B (strikes R and T in Fig. 2). The above calculation arrangement is referred to as case I hereafter. To evaluate the effect of the LPS configuration, FDTD simulations are also performed by connecting the LPS to the building structure at the striking point for strikes R and T, which is referred to as case II. For both cases I and II, the soil resistivity in subarea A is set to 100 Ωm, 525.1 Ωm, or 1000 Ωm, referred to as cases K–A, K–B, and K–C (K = I and II), respectively.
Table 3 Peak values of the voltages induced on Wires A and B. Case
I-A I-B I-C II-A II-B II-C
Strike
R T R T R T R T R T R T
Peak values of induced voltages [kV/kA] Wire A
Wire B
0.27 0.13 0.32 0.21 0.33 0.24 0.26 0.14 0.29 0.22 0.31 0.24
0.39 0.12 1.19 0.18 1.67 0.25 0.47 0.14 1.36 0.20 2.08 0.25
3. Calculated results 3.1. GPRs, step voltages, and induced voltages Fig. 23. Modification of the configuration of the LPS [17].
In our previous study [17], using the aforementioned calculation model of the NPP, first, we calculated the GPRs of the grounding 7
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Fig. 24. Calculated waveforms of the voltages induced on the ground bus at position A-1 for the modified LPS: (a) Case I-B and (b) Case II-B.
Fig. 25. Calculated waveforms of the voltages induced on the ground bus at position A-2 for the modified LPS: (a) Case I-B and (b) Case II-B.
Fig. 26. Calculated waveforms of the voltages induced on the ground bus at position A-3 for the modified LPS: (a) Case I-B and (b) Case II-B.
surface at an EL of 10 m is the extension of the straight line between point S under the striking point and the calculation point of the GPR. As shown in Fig. 11, the peak-value distributions have their maximum values at the back of the R/B model for strike R and on the side of the T/ B model for strike T, and the peak value of the GPR of the grounding grid for strike R is about 20% larger than that for strike T. This is because there are fewer grounding wires installed at the back of the R/B model. Voltages induced on the ground buses placed from the grounding grid into the A/B model, as shown in Fig. 7, are calculated in cases I-A to II-C for both strikes R and T. As shown in Fig. 13, the induced voltages, that is, the voltage differences between the building structure and the ground buses, are calculated at three positions, which correspond to the ends of the branched ground buses on the third floor in the A/B model and are referred to as positions A-1–A-3. As an example of the calculated waveforms, Figs. 14–16 show the calculated induced voltages at positions A-1, A-2, and A-3, respectively, in cases I-B and II-B for strikes R and T. Table 1 summarizes the peak induced voltages on the ground buses. As shown Figs. 14–16, the waveforms of the induced voltages oscillate mainly owing to the effect of the lightning current propagating through the LPS and the voltages propagating through the ground buses. In all the cases, the peak values for strike R are larger than those for strike T, although the differences between the peak values for strikes R and T in case II are much smaller than those in case I, and the differences between the maximum peak values of the three positions for strike R and those for strike T range from 51% to 70% in case I and from 3% to 10% in case II. Table 1 shows that the peak induced voltages have a tendency to be larger for higher resistivities in
Table 4 Peak values of the voltages induced on the ground buses for the modified LPS. Case
I-A I-B I-C II-A II-B II-C
Strike
R T R T R T R T R T R T
Peak values of induced voltages [kV/kA] A-1
A-2
A-3
0.27 0.14 0.85 0.36 1.24 0.50 0.26 0.15 0.99 0.42 1.45 0.58
0.30 0.15 0.86 0.37 1.24 0.49 0.26 0.16 0.96 0.41 1.40 0.55
0.17 0.13 0.44 0.35 0.61 0.47 0.17 0.15 0.40 0.38 0.56 0.53
structure when the striking point is assumed to be the LPS of the R/B model (strike R) or the turbine building model (strike T). Fig. 11 shows the calculated distributions of the peak values of the GPRs of the grounding grid in case I-B for both strikes R and T, where the peak values of the GPRs are normalized by 5.30 kV/kA, corresponding to the maximum peak value of the GPRs in case I. Here, the GPR at each point is calculated by integrating the electric fields on the ground surface from the calculation point to the external surface on the side of the analysis space, where the reference point of the voltage is assumed to be positioned on the ground surface at the side surface of the analysis space. As shown in Fig. 12, the integration path projected on the ground 8
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Fig. 27. Calculated waveforms of the step voltages around the reactor building model #1 at position R-1 for the modified LPS: (a) Case I-B and (b) Case II-B.
Fig. 28. Calculated waveforms of the step voltages around the reactor building model #1 at position R-2 for the modified LPS: (a) Case I-B and (b) Case II-B.
Fig. 29. Calculated waveforms of the step voltages around the reactor building model #1 at position R-3 for the modified LPS: (a) Case I-B and (b) Case II-B.
to II-C for strikes R and T. Figs. 18–20 show the calculated waveforms of the step voltages at positions R-1, R-2, and R-3 in cases I-B and II-B, respectively. Table 2 summarizes the peak step voltages. The waveforms of the step voltages at positions R-2 and R-3, which have larger peak values, highly oscillate owing to the effect of the lightning current propagating through the LPS. As shown in Figs. 18–20 and Table 2, it is confirmed that the peak step voltages for strike R are larger than those for strike T and the ratios of the maximum peak values of the three positions for strike R to those for strike T range from 6.7 to 7.6 in case I and from 1.2 to 1.8 in case II. The above results also confirm that the step voltages are larger for higher resistivities. The step voltages at position R-3 are severer than those at the other positions, particularly for higher resistivities, since the structure of each R/B is not connected to the surrounding grounding grid by wires on this side of the R/B as shown in Fig. 4. In case II, the injected lightning current is distributed to the structure of the R/B model in addition to the LPS from the striking point, and thus the voltage differences between the R/B model and the grounding grid are decreased, and the step voltages in case II are suppressed compared with those in case I for the three resistivities. The maximum peak step voltages in each of cases I-A, I-B, and I-C are reduced by 70%–82% in case II. Voltages induced on wires A and B, both ends of which are connected to the structure of the A/B, are calculated in cases I-A to II-C for both strikes R and T. Figs. 21 and 22 respectively show the calculated waveforms of the induced voltages on wires A and B, that is, the voltage differences between the far ends of the wires from the A/B and the grounding grid, in cases I-B and II-B. Table 3 summarizes the peak voltages induced on wires A and B. The main part of the oscillation of the induced voltages on wires A and B arises from the propagation of
Table 5 Peak values of the step voltages for the modified LPS. Case
I-A I-B I-C II-A II-B II-C
Strike
R T R T R T R T R T R T
Peak values of step voltages [kV/kA] A-1
A-2
A-3
0.06 0.05 0.10 0.07 0.11 0.08 0.07 0.06 0.12 0.09 0.13 0.10
0.13 0.02 0.18 0.03 0.19 0.04 0.04 0.03 0.05 0.04 0.06 0.04
0.14 0.02 0.17 0.03 0.18 0.03 0.04 0.02 0.06 0.03 0.07 0.04
cases I and II for both strikes R and T. The ratios of the maximum peak induced voltages in cases I-A and II-A to those in cases I-B and II-B are approximately 2.8, whereas the ratios of the maximum peak values in cases I-B and II-B to those in cases I-C and II-C are from 1.3 to 1.4. The peak induced voltages in case II are smaller than those in case I irrespective of the striking points and the soil resistivities in the building area, since the injected lightning current flows into both the LPS and the structure of the building models, and thus the GPRs of the connecting points of the ground buses are suppressed in case II. Step voltages around the R/B model (#1) are calculated at three positions specified by R-1, R-2, and R-3 as shown in Fig. 17 in cases I-A
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Fig. 30. Calculated waveforms of the voltages induced on wire A for the modified LPS: (a) Case I-B and (b) Case II-B.
Fig. 31. Calculated waveforms of the voltages induced on wire B for the modified LPS: (a) Case I-B and (b) Case II-B.
A-3 (see Fig. 13), respectively, in cases I-B and II-B for strikes R and T, and Table 4 summarizes the peak induced voltages in cases I-A to II-C. Figs. 27–29 respectively show the calculated waveforms of the step voltages at positions R-1, R-2, and R-3 (see Fig. 17) around the R/B model in cases I-B and II-B for strikes R and T, and Table 5 shows the peak step voltages in the case of the modified LPS for cases I-A to II-C. Figs. 30 and 31 show the calculated voltages induced on wires A and B, respectively, in cases I-B and II-B for strikes R and T using the modified LPS, and Table 6 summarizes the peak induced voltages on wires A and B in cases I-A to II-C. These results show that the above-described change in the configuration of the LPS is not effective for lowering the peak voltages induced on wires A and B. However, by modifying the LPS, we can suppress the GPRs at the connecting points of the ground buses and the voltages induced on the ground buses. In particular, the improvement is significant in case I, and the peak induced voltages are reduced by 81%–90% for the three soil resistivities. Furthermore, we can suppress the voltage differences between the building structures and the grounding grid by applying the modified LPS, and reduce the peak step voltages. The maximum peak step voltages in each case is reduced by 47%–86% except in case II-A, where the step voltages are originally smaller than those in the other cases.
Table 6 Peak values of the voltages induced on wires A and B for the modified LPS. Case
I-A I-B I-C II-A II-B II-C
Strike
R T R T R T R T R T R T
Peak values of induced voltages [kV/kA] Wire A
Wire B
0.27 0.13 0.32 0.21 0.36 0.24 0.26 0.14 0.29 0.23 0.31 0.26
0.41 0.12 1.04 0.18 1.56 0.26 0.47 0.15 1.34 0.21 2.04 0.25
the voltages through the wires. In all the cases, the voltages induced on wires A and B are larger for strike R than for strike T. As shown in Table 3, the peak voltages induced on wire B are larger than those on wire A in all the cases for strike R, and the induced voltages on wire B are highly dependent on the resistivities in the building area.
4. Conclusion
3.2. Effect of the configuration of the LPS
In this study, we presented lightning surge simulations of an APWR NPP in a three-dimensional arrangement using the FDTD-based surge simulation code VSTL REV developed by CRIEPI and studied the effect of the soil resistivities in the building area on step voltages around a reactor building and the voltages induced on ground buses drawn into an auxiliary building and wires simulating the metal sheaths of cables in the case of a direct lightning strike to an NPP. Taking into account various soil resistivities, we confirmed that the voltages induced on the ground buses and the step voltages around the reactor building can be suppressed by connecting down-conductors to the grounding grid far from the connection point of the ground buses to the grounding grid and by connecting the down-conductors of the LPS to the grounding grid and the building structure at multiple points.
Here, to evaluate the effect of the configuration of the LPS on the voltages induced on the wires and the step voltages by taking into account the three resistivities in the building area, we modify the configuration of the LPS in the following two ways. (i) Four down-conductors below the horizontal conductor of the LPS near the connecting points of the ground buses drawn into the A/B building are removed, where the positions of the removed downconductors are denoted by the red points in Fig. 23. (ii) The down-conductors of the LPS are electrically connected to the surrounding grounding grid at the positions specified by the green points in Fig. 23.
References
Using the aforementioned modified LPS, we calculate the induced voltages on the wires and the step voltages. Figs. 24–26 show the calculated voltages induced on the ground buses at positions A-1, A-2, and
[1] P. Duquerroy, C. Trouilloud, Evolution of lightning protection of nuclear power
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[2]
[3] [4] [5]
[6]
[7]
[8]
[9]
[10]
[11]
[12] Y. Baba, N. Nagaoka, A. Ametani, Modeling of thin wires in a lossy medium for FDTD simulations, IEEE Trans. Electromagn. Compat. 47 (1) (2005) 54–60. [13] A. Tatematsu, Development of a surge simulation code VSTL REV based on the 3D FDTD method, Proc. Joint IEEE Int. Symp. EMC and EMC Europe, Dresden, Germany, August 16–22, 2015, pp. 1111–1116. [14] A. Tatematsu, Overview of the three-dimensional FDTD-based surge simulation code VSTL REV, Proc. 2016 Asia-Pacific Int. Symp. on Electromagn. Compat, Shenzhen, China, Paper SS04-02, May 18–21, 2016. [15] A. Tatematsu, K. Yamazaki, K. Miyajima, H. Motoyama, A study on induced voltages on an aerial wire due to a current flowing through a grounding grid, IEEJ Trans. Power Energy Soc. 129 (10) (2009) 1245–1251. [16] A. Tatematsu, F. Rachidi, M. Rubinstein, Analysis of electromagnetic fields inside a reinforced concrete building with layered reinforcing bar due to direct and indirect lightning strikes using the FDTD method, IEEE Trans. Electromagn. Compat. 57 (3) (2015) 405–417. [17] A. Tatematsu, H. Motoyama, A. Tanigawa, Lightning surge analysis of a PWR nuclear power plant using the three-dimensional FDTD method, Proc. 2018 International Conference on Lightning Protection (ICLP), Rzeszow, Poland, September 2–7, 2018. [18] E.F. Vance, Coupling to Shielded Cables, John Wiley & Sons, Australia, 1978. [19] A. Tatematsu, T. Noda, H. Motoyama, Simulation of induced voltages on an aerial wire due to a current through a buried bare wire using the FDTD method, Proc. 2006 International Conference on Lightning Protection (ICLP), Kanazawa, Japan, Paper III-2, September 18–22, 2006, pp. 459–464. [20] Z.P. Liao, H.L. Wong, B.P. Yang, Y.F. Yuan, A transmitting boundary for transient wave analysis, Sci. Sinica Ser. A 27 (10) (1984) 1063–1076. [21] Y. Baba, V.A. Rakov, On the transmission line model for lightning return stroke representation, Geophys. Res. Lett. 30 (24) (2003) 2294. [22] Subcommittee for power stations and substations, study committee on lightning risk, Guide to Lightning protection design of power stations, substations and underground transmission lines (rev.2011), CRIEPI Report, no. H06, 2012.
plants: an overview of EDF’s experience, Proc. CIGRE Session 2018, Paris, France, Paper C4-213, August 26–31, 2018. K.S. Yee, Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media, IEEE Trans. Antennas Propag. 14 (3) (1966) 302–307. R.F. Harrington, Field Computation by Moment Methods, Macmillan Co., New York, 1968. Working Group C4.501, Guideline for numerical electromagnetic analysis method and its application to surge phenomena, Cigre report, no. 543, 2013. Y. Baba, V.A. Rakov, Applications of the FDTD method to lightning electromagnetic pulse and surge simulations, IEEE Trans. Electromagn. Compat. 56 (6) (2014) 1506–1521. A. Tatematsu, Y. Baba, M. Ishii, S. Okabe, T. Ueda, N. Itamoto, Development of Surge Simulation Techniques Based on the Finite Difference Time Domain Method and Its Application to Surge Analysis, Cigre Session 2016, Paris, France, Paper C4302, August 21–26, 2016. E. Bachelier, F. Issac, D. Prost, C. Miry, E. Amador, P. Duquerroy, Protection against lightning of reinforced concrete buildings, Proc. 2014 International Conference on Lightning Protection (ICLP), Shanghai, China, October 11–18, 2014, pp. 452–457. A. Tatematsu, T. Noda, Three-dimensional FDTD calculation of lightning-induced voltages on a multiphase distribution line with the lightning arresters and an overhead shielding wire, IEEE Trans. Electromagn. Compat. 56 (1) (2014) 159–167. M. Namdari, M.K. Farsani, R. Moini, S.H.H. Sadeghi, An efficient parallel 3-D FDTD method for calculating lightning-induced disturbances on overhead lines in the presence of surge arresters, IEEE Trans. Electromagn. Compat. 57 (6) (2015) 1593–1600. A. Tatematsu, T. Ueda, FDTD-based lightning surge simulation of an HV air-insulated substation with back-flashover phenomena, IEEE Trans. Electromagn. Compat. 58 (5) (2016) 1549–1560. T. Noda, S. Yokoyama, Thin wire representation in finite difference time domain surge simulation, IEEE Trans. Power Deliv. 17 (3) (2002) 840–847.
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