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Research on lightning overvoltages of solar arrays in a rooftop photovoltaic power system
Electric Power Systems Research 94 (2013) 10–15
Contents lists available at SciVerse ScienceDirect
Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr
Research on lightning overvoltages of solar arrays in a rooftop photovoltaic power system Youping Tu a , Chunxia Zhang a , Jun Hu b,∗ , Shunchao Wang b , Wei Sun c , Hongjun Li c a b c
School of Electrical & Electronic Engineering, North China Electric Power University, Beijing 102206, China State Key Lab of Power System, Department of Electrical Engineering, Tsinghua University, Beijing 100084, China Schneider Electric, No. 3000 Longdong Avenue, Pudong, Shanghai 201203, China
a r t i c l e
i n f o
Article history: Available online 26 July 2012 Keywords: Lightning overvoltage Solar array Photovoltaic power system Thin-wire Time-domain method
a b s t r a c t Lightning overvoltages threaten the safe operation of the photovoltaic (PV) power system. This document uses the generalized modified mesh current method and establishes a time-domain multiport model of thin-wire system to simulate the lightning transient process of the solar arrays in a rooftop PV power system with and without the external lightning protection system. Different factors of the PV power system are simulated in order to study the effects of these factors on the induced lightning overvoltages. The simulation results show that the induced lightning overvoltage of the solar arrays in a rooftop PV power system is highly dependent on the lightning striking position, the lightning current amplitude, the building’s height, the soil resistivity, and the distance to the external protection system. Therefore, when choosing the SPD configuration for a PV power system, the factors mentioned above should be considered comprehensively. © 2012 Elsevier B.V. All rights reserved.
1. Introduction Comparing to the traditional power system, the layout of a PV power system is more spacious, and is often located in a high place. Therefore, it is easier to be struck by lightnings. In the solar arrays of a rooftop PV power system, there are many thinwire conductors: the input and output cables in the junctions, the metal frame and bracket of the solar modules, the grounding system, the lightning terminals of the buildings and so on. These conductors are not only the important carriers of energy, but also the main coupling channels of electromagnetic interference. Numerical methods have been made to study the lightningcaused electro-magnetic transients on thin-wire structures [1–3]. There are two types of numerical methods to model a thin-wire structure: transmission-line models and full-wave models. The former one includes Bergeron [4], multi-conductor transmission lines [5,6] and time-domain finite element method [7]. These methods can be easily used to analyze the lightning transient when nonlinear components exist, such as arresters and surge protective devices. However, this method usually neglects the coupling among conductors, therefore might give rise to inaccurate results. The latter one is based on electromagnetic field integral equation method [8].
∗ Corresponding author. Tel.: +86 10 62795423; fax: +86 10 62784709. E-mail address: [email protected] (J. Hu). 0378-7796/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.epsr.2012.06.012
Since the integral-equation based methods are much more easier to solve in the frequency domain than in the time domain, most of the softwares, this method is usually implemented in the frequency domain. However, the frequency domain method always has a disadvantage: it cannot be interfaced with external circuits straight forwardly. It is hard to be applied to the circuit simulation software. Recently, the finite-difference time-domain (FDTD) method has been used to simulate the thin-wire structure lightning transients [9,10]. One advantage of the FDTD method is that it can handle multiple media around the conductor. However, the FDTD method will lead to a large number of unknowns, and it cannot consider nonlinear components conveniently. In realistic scenarios, most of the thin-wire structures have both above and below-ground parts. The above-ground structure gets struck by the lightning and the below-ground part dissipates lightning current into ground. The two parts affect electromagnetic transients from each other. Aiming at this situation, [11,12] raised the time-domain simulation of small thin-wire structures above and buried in lossy ground using the generalized modified mesh current method (MMC) to solve it. MMC method introduces radial branches to the original circuit topology and uses node charges as extra state-variables, therefore it is capable of modeling all the electromagnetic coupling mechanisms in soil or air. The final form of MMC method is a system of state space equations, which can be solved easily in the time domain. The details of this methods can be found in [11,12].
Y. Tu et al. / Electric Power Systems Research 94 (2013) 10–15
Fig. 1. The equivalent model of the solar module.
Based on the generalized modified mesh current method, we calculated and analyzed the induced lightning overvoltage of the solar arrays in a rooftop PV power system. This paper is the extended version of our paper [13] in APL2011. 2. Numerical analysis model The first step of simulation is to establish the geometrical structure of the solar module. According to the basic structure of the solar module, the solar cells in series are equivalent to a straight wire, and both ends of the line stand for the positive and negative electrodes, respectively. All the solar modules in the solar arrays can be modeled as straight wires in series-parallels. At the ends of the wires, two terminal lines are extracted as the positive and negative electrodes of the solar arrays, as Fig. 1 shows. According to the actual size and location of the solar array, the 3D solar array model is built in Gmsh software as Fig. 2 shows. The outlines of the solar module are the metal frame and bracket of the solar module, and they are connected to the grounding system. The parallel metal wires in the middle are many solar modules in series-parallels. And then, by duplicating these thin-wire models, the whole solar arrays model is formed as Fig. 3 shows. There are 6 rows of solar arrays in total and each line has 10 solar modules in series. 12 output wires, which are labeled as OW1-OW12, are extracted from these 6 rows of solar arrays. And in the following calculation, the induced overvoltages on these 12 output wires will be calculated. The whole solar arrays are located on the building rooftop. For a building, there may be or may not be an external lightning protection system When there is not, it is possible that the lightning strikes the solar modules directly. In order to protect the solar arrays from direct strike, lightning rods are always installed near the solar arrays. It aims to lead the lightning current through the lightning rod to the earth safely. However, when a large lightning current flows through the lightning rod, the current will produce a strong electromagnetic radiation. Because of the electromagnetic
Fig. 2. The thin-wire structure of the solar array.
11
Fig. 3. The thin-wire structure of the whole solar arrays.
radiation, overvoltages will be induced on the solar arrays. The thinwire structures of the PV power system with or without an external lightning protection system are shown in Fig. 4. For a PV system without an external lightning protection as shown in Fig. 4(a), the highest spots on the solar arrays frames are chosen as the striking spots. Totally 18 lightning striking spots from P1 to P18 as shown in Fig. 3 are selected. For a PV system with an external lightning protection, the lightning rods are chosen as the lightning striking spots, which are labeled from N1 to N8 as shown in Fig. 4(b). In this paper, the waveform of the lightning current is represented by the Heilder equation as below: i(0, t) = I0 x(t)y(t), x(t) =
(t/1 )
n
1 + (t/2 )
n,
t
y(t) = exp −
2
(1)
where I0 is the peak value of the lightning current, t is the time, i is the lightning current value at time t, x(t) is the rise time function, y(t) is the delay time function, 1 is the rise time constant, 2 is the delay time constant, and n is the factor about current rise speed. In our simulation, the rise time and delay time are assumed to be 1 s and 35 s, respectively. In addition, if not mentioned specifically, the peak value of lightning current is set to 20 kA, the soil’s resistivity and relative permittivity are set to 100 m and 10, respectively. The height of the building is 20 m.
Fig. 4. The thin-wire structure of the whole solar arrays on the building rooftop: (a) without an external lightning protection system; (b) with an external lightning protection system.
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Y. Tu et al. / Electric Power Systems Research 94 (2013) 10–15
Fig. 5. The waveforms of induced overvoltages when spot P1 of the solar arrays without external protection is stroked.
3. Lightning overvoltages without an external protection system 3.1. Effect of lightning striking spot The lightning current is injected into the chosen lighting spots, and the corresponding overvoltage on each output wire of the solar arrays is calculated. When lightning strikes the PV power system, the lightning current will flow through the conductor to the earth, and cause the grounding potential rise. Because of the rising grounding potential, the waveforms of the absolute induced overvoltage and the relative induced overvoltage (with the grounding potential rise substracted) are different. When the spot P1 is struck by the lightning with a current of 20 kA, the waveforms of induced overvoltages on the output wire OW1 are shown in Fig. 5, including the rising grounding potential, the absolute induced overvoltage based on infinity point and the relative induced overvoltage excluding the rising grounding potential. From Fig. 5, it can be seen that there is a maximal peak value of the overvoltage. In the following calculated examples, the peak value of the absolute induced overvoltage based on infinity point is labeled as Va , and that of the relative induced overvoltage excluding the rising grounding potential is labeled as Vb . In addition, the induced overvoltage between the positive and negative electrodes of the same row of solar arrays is also considered, whose peak value is labeled as Vd . Figs. 6–8 show the absolute induced overvoltage Va , the relative induced overvoltage Vb , and the induced overvoltage Vd between the positive and negative electrodes, respectively, when the spots P1–P6 gets struck by the lightning current of 20 kA.
Fig. 6. The absolute induced overvoltage of the solar arrays without external protection.
Fig. 7. The relative induced overvoltage of the solar arrays without external protection.
From above figures, it can be seen that the waveforms and peak values of the absolute induced overvoltage Va , and the relative induced overvoltage Vb are closely related to the location of the lightning striking spot. When the lightning striking spot is near the output wires and the metal frame of the solar array, the corresponding induced overvoltages Va and Vb have large peak values. For example, the overvoltages induced by the lightning current injected into the spot P3 or P4 are much larger than those induced by the lightning current injected into the spot P1 or P6. When the spots P3 are P4 get struck, the induced overvoltages on output wires OW1 and OW2 are larger than those on OW11 and OW12, because the spot P3 are P4 is nearer to the solar array with OW1 and OW2 than that with OW11 and OW12. 3.2. Effect of lightning current amplitude The amplitudes of lightning currents are always different from case to case. The overvoltages of the solar arrays induced by lightning currents of different amplitudes (20 kA and 50 kA) are calculated. When the lightning currents are injected into spots P1–P18, respectively, the maximal overvoltages appeared on each output wire are listed in Table 1. It can be seen that all induced overvoltages on the output wires of the solar arrays, including Va , Vb and Vd , are directly proportional to the peak value of lightning current. 3.3. Effect of building height Considering the solar arrays are located on the building rooftop, the induced overvoltages of the solar arrays on the rooftops of
Fig. 8. The induced overvoltage between the positive and negative electrodes of the solar arrays without external protection.
Y. Tu et al. / Electric Power Systems Research 94 (2013) 10–15
13
Table 1 The overvoltages of the solar arrays induced by different amplitudes of lightning currents. Output wire (OW)
1
2
3
4
5
6
7
8
9
10
11
12
Ipeak = 20 kA VaI20 (kV) VbI20 (kV) VdI20 (kV)
290 250
295 253
293 250
289 248
287 248
294 246
293 245
286 247
284 249
292 243
286 237
280 245
Ipeak = 50 kA VaI50 (kV) VbI50 (kV) VdI50 (kV)
725 625
VaI50 /VaI20 VbI50 /VbI20 VdI50 /VdI20
9.8
7 738 632
731 625
24 2.5 2.5
14 722 620
717 621
17 2.5 2.5
2.5 2.5
2.5
14.5 735 616
733 612
34 2.5 2.5
2.5 2.5
2.5
20 715 618
710 624
36 2.5 2.5
2.5 2.5
2.5
21 731 608
714 592
49 2.5 2.5
2.5 2.5
2.5
700 614 51
2.5 2.5
2.5 2.5
2.5
2.5 2.5 2.5
Table 2 The induced overvoltages of the solar arrays on the rooftops of the buildings with different heights. Output wire (OW)
1
2
3
4
5
6
7
8
9
10
11
12
H = 20 m Vah20 (kV) Vbh20 (kV) Vdh20 (kV)
290 250
295 253
293 250
289 248
287 248
294 246
293 245
286 247
284 249
292 243
286 237
280 245
H=5m Vah5 (kV) Vbsh5 (kV) Vdsh5 (kV)
123 71
9.8
7 127 76
8
125 74
14 122 70
126 72
7
the buildings with different heights (20 m and 5 m) are calculated. When the lightning current with peak value of 20 kA is injected into spots P1–P18, respectively, the maximal overvoltages appeared on each output wire are listed in Table 2. It can be seen that the induced overvoltages Va and Vb become much smaller when the building height becomes lower. However, the induced overvoltages Vd between the positive and negative electrodes of some output wires become much smaller, while the induced overvoltages Vd of other output wires only decrease in a small extent. It is known that the higher the building is, the greater the impedance of the thin-wire conductors consisting the building structure model would be. When the lightning current flows through the thin-wire conductors, the voltage of the thin-wire inductance will also be larger. Therefore, if the building height increases, the output induced overvoltages of the solar arrays located on the rooftop of the building will increase too.
14.5 130 81
13
130 80
20 125 73
13
129 74
21 134 83
14
129 78
127 71 15
than the spots of the solar arrays. Figs. 9–11 show the absolute induced overvoltage Va , the relative induced overvoltage Vb , and the induced overvoltage Vd between the positive and negative electrodes, when the spots N1–N8 in the protection system gets
3.4. Effect of soil resistivity The resistivity of the soil where the building is located depends on the local geological condition. The induced overvoltages of the solar arrays on the rooftops of the buildings with different soil resistivity (100 m and 200 m) are calculated. When the lightning current with peak value of 20 kA is injected into spots P1–P18, respectively, the maximal overvoltages appeared on each output wire are listed in Table 3. When the solid resistivity increases from 100 m to 200 m, the grounding potential will significantly increase from 94 kV to about 169 kV. Thus the absolute induced overvoltages Va will also increase with the same degree. But the relative induced overvoltages Vb and the induced overvoltages Vd between the positive and negative electrodes will almost remain unchanged.
Fig. 9. The absolute induced overvoltage of the solar arrays with external protection.
4. Lightning overvoltages with an external protection system 4.1. Effect of lightning striking spot In a PV system with external protection, the lightning current would strike the lightning rods in the protection system rather
Fig. 10. The relative induced overvoltage of the solar arrays with external protection.
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Y. Tu et al. / Electric Power Systems Research 94 (2013) 10–15
Table 3 The induced overvoltages of the solar arrays on the rooftops of the buildings with different solid resistivities. Output wire (OW)
1
2
3
4
5
6
7
8
9
10
11
12
soil = 100 ˝ m Vas100 (kV) Vbs100 (kV) Vds100 (kV)
290 250
295 253
293 250
289 248
287 248
294 246
293 245
286 247
284 249
292 243
286 237
280 245
soil = 200 ˝ m Vas200 (kV) Vbs200 (kV) Vds200 (kV)
321 250
9.8
7 326 253
10
324 250
14 320 248
317 248
7
14.5 324 246
14
323 245
20 316 247
14
313 249
21 321 243
314 237
20
309 245 20
struck by the lightning current of 20 kA, respectively. The distance between the solar arrays and the protection system is 1.5 m. From above figures, it can be seen that the absolute induced overvoltage Va , the relative induced overvoltage Vb are also closely related to the location of the lightning striking spot. When the lightning striking spot is near the output wires and the metal frame of the solar array, the corresponding induced overvoltages Va and Vb will be large. For example, N8 is the closest lightning striking spot to the output wires of the solar arrays, thus the overvoltages induced by the lightning current injected into the spot N8 are much larger than those induced by the lightning currents injected into other spots.
1.5 m far away from the external protection system, respectively. N8 is assumed to be the lightning striking spot and the peak value of the lightning current is set as 20 kA. According to the calculated results, when the distance between the solar arrays and the protection system becomes larger, the corresponding induced overvoltages Va , Vb and Vd will all decrease. However, it should be mentioned that a larger distance means a higher lightning rods is required for the effectively protecting the solar arrays from the lightning strike.
4.2. Effect of distance to protection system
According to the actual lightning statistics in different areas, the statistical probability of induced lightning overvoltages of the solar arrays in a special PV system can be obtained. Here, the cumulative
The distance between the solar arrays and the external protection system will also affect the induced overvoltages. Figs. 12–14 show the influence of the different distances on the induced overvoltages of the solar arrays, which are 0.25 m, 0.5 m, 0.75 m and
Fig. 11. The induced overvoltage between the positive and negative electrodes of the solar arrays with external protection.
Fig. 12. The effect of distance to protection system on the absolute induced overvoltage of the solar arrays.
5. Statistical study of induced lightning overvoltages
Fig. 13. The effect of distance to protection system on the relative induced overvoltage of the solar arrays.
Fig. 14. The effect of distance to protection system on the induced overvoltage between the positive and negative electrodes of the solar arrays.
Y. Tu et al. / Electric Power Systems Research 94 (2013) 10–15
Fig. 15. The cumulative probability curves of the induced voltage on the solar array output wires.
15
The induced overvoltages Va and Vb are quite small when the building height is low. However, the induced overvoltages Vd between the positive and negative electrodes of some output wires become much smaller, while the induced overvoltages Vd of other output wires only decrease in a small extent. When the soil resistivity increases, the absolute induced overvoltages Va will also increase with the same extent. But the relative induced overvoltages Vb and the induced overvoltages Vd between the positive and negative electrodes almost remain unchanged. When the distance between the solar arrays and the protection system becomes larger, the corresponding induced overvoltages Va , Vb and Vd will all decrease. Since the induced lightning overvoltage of the solar arrays in a rooftop PV power system is highly dependent on the abovementioned factors, they should be considered comprehensively in choosing the SPD configuration for the PV power system. References
probability function of lightning current amplitude in Beijing as below is used: P(> I) =
1 1 + (I/33.9)
2.9
(2)
where I is the lightning current amplitude, and P is the cumulative probability of all lightning currents with amplitude less than I. Thousands of lightning events with random amplitudes, whose probability distribution fits the above function, randomly strike one of the eight lightning rods N1–N8. In each case, the peak value of the absolute induced overvoltages appeared on the output wires of the solar arrays are counted. As shown in Fig. 15, the cumulative probability curve of the maximal absolute induced overvoltages for the special PV system sample in this paper can be drawn. 6. Conclusion Through numerical simulations, the influence of different factors of the PV power system on the induced lightning overvoltages of the solar arrays are analyzed in this paper. These factors include the lightning striking spot, the lightning current amplitude, the building height, the soil resistivity, and the distance between the solar arrays and the external protection system. The absolute induced overvoltage Va and the relative induced overvoltage Vb are closely related to the location of the lightning striking spot. When the lightning striking spot is near the output wires and the metal frame of the solar array, the corresponding induced overvoltages Va and Vb will be large. All induced overvoltages on the output wires of the solar arrays, including Va , Vb and Vd , are directly proportional to the peak value of lightning current.
[1] J. He, Y. Gao, R. Zeng, J. Zou, X. Liang, B. Zhang, J. Lee, S. Chang, Effective length of counterpoise wire under lightning current, IEEE Transactions on Power Delivery 20 (April) (2005) 1585–1591. [2] A. Geri, Behavior of grounding systems excited by high impulse currents: the model and its validation, IEEE Transactions on Power Delivery 14 (July) (1999) 1008–1017. [3] L. Grcev, F. Dawalibi, An electromagnetic model for transients in grounding systems, IEEE Transactions on Power Delivery 5 (October) (1990) 1773–1781. [4] J. Liu, B. Zhao, X. Cui, Analysis of transient response of complex thin wire structures by using time domain integral equation approach, Proceedings of the CSEE 29 (2009) 116–122 (in Chinese). [5] T. Lu, X. Cui, Numerical analysis of wave processes for buses without load in substations using FDTD, Proceedings of the CSEE 20 (2000) 39–42 (in Chinese). [6] L. Qi, T. Lu, X. Cui, Transient analysis for nonuniform multiconductor transmission lines based on the FDTD method, Proceedings of the CSEE 23 (2003) 102–106 (in Chinese). [7] L. Liu, X. Cui, L. Qi, Transients analysis of transmission line by time domain finite element method, Proceedings of the CSEE 28 (2008) 112–118 (in Chinese). [8] L. Lee, The application of time-domain integral equation method in calculating transient response of thin wire conductor, M. CHN. Thesis, North China Electric Power University Indian Institute of Science, Beijing, China, December 2006. [9] T. Noda, A. Tatematsu, S. Yokoyama, Improvements of an FDTD-based surge simulation code and its application to the lightning overvoltage calculation of a transmission tower, Electric Power Systems Research 77 (2007) 1495–1500. [10] Y. Baba, N. Nagaoka, A. Ametani, Modeling of thin wires in a lossy medium for FDTD simulations, IEEE Transactions on Electromagnetic Compatibility 47 (February) (2005) 54–60. [11] S. Wang, J. He, B. Zhang, R. Zeng, Z. Yu, A time-domain multiport model of thin-wire system for lightning transient simulation, IEEE Transactions on Electromagnetic Compatibility 52 (February) (2010) 128–135. [12] S. Wang, J. He, B. Zhang, R. Zeng, Time-domain simulation of small thin-wire structures above and buried in lossy ground using generalized modified mesh current method, IEEE Transactions on Power Delivery 26 (January) (2011) 369–377. [13] C. Zhang, Y. Tu, J. Hu, S. Wang, W. Sun, H. Li, Study of induced overvoltage onsolar arrays, in: The Proceeding of 7th Asia-Pacific International Conference on Lightning (APL 2011), November, 2011.
Contents lists available at SciVerse ScienceDirect
Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr
Research on lightning overvoltages of solar arrays in a rooftop photovoltaic power system Youping Tu a , Chunxia Zhang a , Jun Hu b,∗ , Shunchao Wang b , Wei Sun c , Hongjun Li c a b c
School of Electrical & Electronic Engineering, North China Electric Power University, Beijing 102206, China State Key Lab of Power System, Department of Electrical Engineering, Tsinghua University, Beijing 100084, China Schneider Electric, No. 3000 Longdong Avenue, Pudong, Shanghai 201203, China
a r t i c l e
i n f o
Article history: Available online 26 July 2012 Keywords: Lightning overvoltage Solar array Photovoltaic power system Thin-wire Time-domain method
a b s t r a c t Lightning overvoltages threaten the safe operation of the photovoltaic (PV) power system. This document uses the generalized modified mesh current method and establishes a time-domain multiport model of thin-wire system to simulate the lightning transient process of the solar arrays in a rooftop PV power system with and without the external lightning protection system. Different factors of the PV power system are simulated in order to study the effects of these factors on the induced lightning overvoltages. The simulation results show that the induced lightning overvoltage of the solar arrays in a rooftop PV power system is highly dependent on the lightning striking position, the lightning current amplitude, the building’s height, the soil resistivity, and the distance to the external protection system. Therefore, when choosing the SPD configuration for a PV power system, the factors mentioned above should be considered comprehensively. © 2012 Elsevier B.V. All rights reserved.
1. Introduction Comparing to the traditional power system, the layout of a PV power system is more spacious, and is often located in a high place. Therefore, it is easier to be struck by lightnings. In the solar arrays of a rooftop PV power system, there are many thinwire conductors: the input and output cables in the junctions, the metal frame and bracket of the solar modules, the grounding system, the lightning terminals of the buildings and so on. These conductors are not only the important carriers of energy, but also the main coupling channels of electromagnetic interference. Numerical methods have been made to study the lightningcaused electro-magnetic transients on thin-wire structures [1–3]. There are two types of numerical methods to model a thin-wire structure: transmission-line models and full-wave models. The former one includes Bergeron [4], multi-conductor transmission lines [5,6] and time-domain finite element method [7]. These methods can be easily used to analyze the lightning transient when nonlinear components exist, such as arresters and surge protective devices. However, this method usually neglects the coupling among conductors, therefore might give rise to inaccurate results. The latter one is based on electromagnetic field integral equation method [8].
∗ Corresponding author. Tel.: +86 10 62795423; fax: +86 10 62784709. E-mail address: [email protected] (J. Hu). 0378-7796/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.epsr.2012.06.012
Since the integral-equation based methods are much more easier to solve in the frequency domain than in the time domain, most of the softwares, this method is usually implemented in the frequency domain. However, the frequency domain method always has a disadvantage: it cannot be interfaced with external circuits straight forwardly. It is hard to be applied to the circuit simulation software. Recently, the finite-difference time-domain (FDTD) method has been used to simulate the thin-wire structure lightning transients [9,10]. One advantage of the FDTD method is that it can handle multiple media around the conductor. However, the FDTD method will lead to a large number of unknowns, and it cannot consider nonlinear components conveniently. In realistic scenarios, most of the thin-wire structures have both above and below-ground parts. The above-ground structure gets struck by the lightning and the below-ground part dissipates lightning current into ground. The two parts affect electromagnetic transients from each other. Aiming at this situation, [11,12] raised the time-domain simulation of small thin-wire structures above and buried in lossy ground using the generalized modified mesh current method (MMC) to solve it. MMC method introduces radial branches to the original circuit topology and uses node charges as extra state-variables, therefore it is capable of modeling all the electromagnetic coupling mechanisms in soil or air. The final form of MMC method is a system of state space equations, which can be solved easily in the time domain. The details of this methods can be found in [11,12].
Y. Tu et al. / Electric Power Systems Research 94 (2013) 10–15
Fig. 1. The equivalent model of the solar module.
Based on the generalized modified mesh current method, we calculated and analyzed the induced lightning overvoltage of the solar arrays in a rooftop PV power system. This paper is the extended version of our paper [13] in APL2011. 2. Numerical analysis model The first step of simulation is to establish the geometrical structure of the solar module. According to the basic structure of the solar module, the solar cells in series are equivalent to a straight wire, and both ends of the line stand for the positive and negative electrodes, respectively. All the solar modules in the solar arrays can be modeled as straight wires in series-parallels. At the ends of the wires, two terminal lines are extracted as the positive and negative electrodes of the solar arrays, as Fig. 1 shows. According to the actual size and location of the solar array, the 3D solar array model is built in Gmsh software as Fig. 2 shows. The outlines of the solar module are the metal frame and bracket of the solar module, and they are connected to the grounding system. The parallel metal wires in the middle are many solar modules in series-parallels. And then, by duplicating these thin-wire models, the whole solar arrays model is formed as Fig. 3 shows. There are 6 rows of solar arrays in total and each line has 10 solar modules in series. 12 output wires, which are labeled as OW1-OW12, are extracted from these 6 rows of solar arrays. And in the following calculation, the induced overvoltages on these 12 output wires will be calculated. The whole solar arrays are located on the building rooftop. For a building, there may be or may not be an external lightning protection system When there is not, it is possible that the lightning strikes the solar modules directly. In order to protect the solar arrays from direct strike, lightning rods are always installed near the solar arrays. It aims to lead the lightning current through the lightning rod to the earth safely. However, when a large lightning current flows through the lightning rod, the current will produce a strong electromagnetic radiation. Because of the electromagnetic
Fig. 2. The thin-wire structure of the solar array.
11
Fig. 3. The thin-wire structure of the whole solar arrays.
radiation, overvoltages will be induced on the solar arrays. The thinwire structures of the PV power system with or without an external lightning protection system are shown in Fig. 4. For a PV system without an external lightning protection as shown in Fig. 4(a), the highest spots on the solar arrays frames are chosen as the striking spots. Totally 18 lightning striking spots from P1 to P18 as shown in Fig. 3 are selected. For a PV system with an external lightning protection, the lightning rods are chosen as the lightning striking spots, which are labeled from N1 to N8 as shown in Fig. 4(b). In this paper, the waveform of the lightning current is represented by the Heilder equation as below: i(0, t) = I0 x(t)y(t), x(t) =
(t/1 )
n
1 + (t/2 )
n,
t
y(t) = exp −
2
(1)
where I0 is the peak value of the lightning current, t is the time, i is the lightning current value at time t, x(t) is the rise time function, y(t) is the delay time function, 1 is the rise time constant, 2 is the delay time constant, and n is the factor about current rise speed. In our simulation, the rise time and delay time are assumed to be 1 s and 35 s, respectively. In addition, if not mentioned specifically, the peak value of lightning current is set to 20 kA, the soil’s resistivity and relative permittivity are set to 100 m and 10, respectively. The height of the building is 20 m.
Fig. 4. The thin-wire structure of the whole solar arrays on the building rooftop: (a) without an external lightning protection system; (b) with an external lightning protection system.
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Y. Tu et al. / Electric Power Systems Research 94 (2013) 10–15
Fig. 5. The waveforms of induced overvoltages when spot P1 of the solar arrays without external protection is stroked.
3. Lightning overvoltages without an external protection system 3.1. Effect of lightning striking spot The lightning current is injected into the chosen lighting spots, and the corresponding overvoltage on each output wire of the solar arrays is calculated. When lightning strikes the PV power system, the lightning current will flow through the conductor to the earth, and cause the grounding potential rise. Because of the rising grounding potential, the waveforms of the absolute induced overvoltage and the relative induced overvoltage (with the grounding potential rise substracted) are different. When the spot P1 is struck by the lightning with a current of 20 kA, the waveforms of induced overvoltages on the output wire OW1 are shown in Fig. 5, including the rising grounding potential, the absolute induced overvoltage based on infinity point and the relative induced overvoltage excluding the rising grounding potential. From Fig. 5, it can be seen that there is a maximal peak value of the overvoltage. In the following calculated examples, the peak value of the absolute induced overvoltage based on infinity point is labeled as Va , and that of the relative induced overvoltage excluding the rising grounding potential is labeled as Vb . In addition, the induced overvoltage between the positive and negative electrodes of the same row of solar arrays is also considered, whose peak value is labeled as Vd . Figs. 6–8 show the absolute induced overvoltage Va , the relative induced overvoltage Vb , and the induced overvoltage Vd between the positive and negative electrodes, respectively, when the spots P1–P6 gets struck by the lightning current of 20 kA.
Fig. 6. The absolute induced overvoltage of the solar arrays without external protection.
Fig. 7. The relative induced overvoltage of the solar arrays without external protection.
From above figures, it can be seen that the waveforms and peak values of the absolute induced overvoltage Va , and the relative induced overvoltage Vb are closely related to the location of the lightning striking spot. When the lightning striking spot is near the output wires and the metal frame of the solar array, the corresponding induced overvoltages Va and Vb have large peak values. For example, the overvoltages induced by the lightning current injected into the spot P3 or P4 are much larger than those induced by the lightning current injected into the spot P1 or P6. When the spots P3 are P4 get struck, the induced overvoltages on output wires OW1 and OW2 are larger than those on OW11 and OW12, because the spot P3 are P4 is nearer to the solar array with OW1 and OW2 than that with OW11 and OW12. 3.2. Effect of lightning current amplitude The amplitudes of lightning currents are always different from case to case. The overvoltages of the solar arrays induced by lightning currents of different amplitudes (20 kA and 50 kA) are calculated. When the lightning currents are injected into spots P1–P18, respectively, the maximal overvoltages appeared on each output wire are listed in Table 1. It can be seen that all induced overvoltages on the output wires of the solar arrays, including Va , Vb and Vd , are directly proportional to the peak value of lightning current. 3.3. Effect of building height Considering the solar arrays are located on the building rooftop, the induced overvoltages of the solar arrays on the rooftops of
Fig. 8. The induced overvoltage between the positive and negative electrodes of the solar arrays without external protection.
Y. Tu et al. / Electric Power Systems Research 94 (2013) 10–15
13
Table 1 The overvoltages of the solar arrays induced by different amplitudes of lightning currents. Output wire (OW)
1
2
3
4
5
6
7
8
9
10
11
12
Ipeak = 20 kA VaI20 (kV) VbI20 (kV) VdI20 (kV)
290 250
295 253
293 250
289 248
287 248
294 246
293 245
286 247
284 249
292 243
286 237
280 245
Ipeak = 50 kA VaI50 (kV) VbI50 (kV) VdI50 (kV)
725 625
VaI50 /VaI20 VbI50 /VbI20 VdI50 /VdI20
9.8
7 738 632
731 625
24 2.5 2.5
14 722 620
717 621
17 2.5 2.5
2.5 2.5
2.5
14.5 735 616
733 612
34 2.5 2.5
2.5 2.5
2.5
20 715 618
710 624
36 2.5 2.5
2.5 2.5
2.5
21 731 608
714 592
49 2.5 2.5
2.5 2.5
2.5
700 614 51
2.5 2.5
2.5 2.5
2.5
2.5 2.5 2.5
Table 2 The induced overvoltages of the solar arrays on the rooftops of the buildings with different heights. Output wire (OW)
1
2
3
4
5
6
7
8
9
10
11
12
H = 20 m Vah20 (kV) Vbh20 (kV) Vdh20 (kV)
290 250
295 253
293 250
289 248
287 248
294 246
293 245
286 247
284 249
292 243
286 237
280 245
H=5m Vah5 (kV) Vbsh5 (kV) Vdsh5 (kV)
123 71
9.8
7 127 76
8
125 74
14 122 70
126 72
7
the buildings with different heights (20 m and 5 m) are calculated. When the lightning current with peak value of 20 kA is injected into spots P1–P18, respectively, the maximal overvoltages appeared on each output wire are listed in Table 2. It can be seen that the induced overvoltages Va and Vb become much smaller when the building height becomes lower. However, the induced overvoltages Vd between the positive and negative electrodes of some output wires become much smaller, while the induced overvoltages Vd of other output wires only decrease in a small extent. It is known that the higher the building is, the greater the impedance of the thin-wire conductors consisting the building structure model would be. When the lightning current flows through the thin-wire conductors, the voltage of the thin-wire inductance will also be larger. Therefore, if the building height increases, the output induced overvoltages of the solar arrays located on the rooftop of the building will increase too.
14.5 130 81
13
130 80
20 125 73
13
129 74
21 134 83
14
129 78
127 71 15
than the spots of the solar arrays. Figs. 9–11 show the absolute induced overvoltage Va , the relative induced overvoltage Vb , and the induced overvoltage Vd between the positive and negative electrodes, when the spots N1–N8 in the protection system gets
3.4. Effect of soil resistivity The resistivity of the soil where the building is located depends on the local geological condition. The induced overvoltages of the solar arrays on the rooftops of the buildings with different soil resistivity (100 m and 200 m) are calculated. When the lightning current with peak value of 20 kA is injected into spots P1–P18, respectively, the maximal overvoltages appeared on each output wire are listed in Table 3. When the solid resistivity increases from 100 m to 200 m, the grounding potential will significantly increase from 94 kV to about 169 kV. Thus the absolute induced overvoltages Va will also increase with the same degree. But the relative induced overvoltages Vb and the induced overvoltages Vd between the positive and negative electrodes will almost remain unchanged.
Fig. 9. The absolute induced overvoltage of the solar arrays with external protection.
4. Lightning overvoltages with an external protection system 4.1. Effect of lightning striking spot In a PV system with external protection, the lightning current would strike the lightning rods in the protection system rather
Fig. 10. The relative induced overvoltage of the solar arrays with external protection.
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Y. Tu et al. / Electric Power Systems Research 94 (2013) 10–15
Table 3 The induced overvoltages of the solar arrays on the rooftops of the buildings with different solid resistivities. Output wire (OW)
1
2
3
4
5
6
7
8
9
10
11
12
soil = 100 ˝ m Vas100 (kV) Vbs100 (kV) Vds100 (kV)
290 250
295 253
293 250
289 248
287 248
294 246
293 245
286 247
284 249
292 243
286 237
280 245
soil = 200 ˝ m Vas200 (kV) Vbs200 (kV) Vds200 (kV)
321 250
9.8
7 326 253
10
324 250
14 320 248
317 248
7
14.5 324 246
14
323 245
20 316 247
14
313 249
21 321 243
314 237
20
309 245 20
struck by the lightning current of 20 kA, respectively. The distance between the solar arrays and the protection system is 1.5 m. From above figures, it can be seen that the absolute induced overvoltage Va , the relative induced overvoltage Vb are also closely related to the location of the lightning striking spot. When the lightning striking spot is near the output wires and the metal frame of the solar array, the corresponding induced overvoltages Va and Vb will be large. For example, N8 is the closest lightning striking spot to the output wires of the solar arrays, thus the overvoltages induced by the lightning current injected into the spot N8 are much larger than those induced by the lightning currents injected into other spots.
1.5 m far away from the external protection system, respectively. N8 is assumed to be the lightning striking spot and the peak value of the lightning current is set as 20 kA. According to the calculated results, when the distance between the solar arrays and the protection system becomes larger, the corresponding induced overvoltages Va , Vb and Vd will all decrease. However, it should be mentioned that a larger distance means a higher lightning rods is required for the effectively protecting the solar arrays from the lightning strike.
4.2. Effect of distance to protection system
According to the actual lightning statistics in different areas, the statistical probability of induced lightning overvoltages of the solar arrays in a special PV system can be obtained. Here, the cumulative
The distance between the solar arrays and the external protection system will also affect the induced overvoltages. Figs. 12–14 show the influence of the different distances on the induced overvoltages of the solar arrays, which are 0.25 m, 0.5 m, 0.75 m and
Fig. 11. The induced overvoltage between the positive and negative electrodes of the solar arrays with external protection.
Fig. 12. The effect of distance to protection system on the absolute induced overvoltage of the solar arrays.
5. Statistical study of induced lightning overvoltages
Fig. 13. The effect of distance to protection system on the relative induced overvoltage of the solar arrays.
Fig. 14. The effect of distance to protection system on the induced overvoltage between the positive and negative electrodes of the solar arrays.
Y. Tu et al. / Electric Power Systems Research 94 (2013) 10–15
Fig. 15. The cumulative probability curves of the induced voltage on the solar array output wires.
15
The induced overvoltages Va and Vb are quite small when the building height is low. However, the induced overvoltages Vd between the positive and negative electrodes of some output wires become much smaller, while the induced overvoltages Vd of other output wires only decrease in a small extent. When the soil resistivity increases, the absolute induced overvoltages Va will also increase with the same extent. But the relative induced overvoltages Vb and the induced overvoltages Vd between the positive and negative electrodes almost remain unchanged. When the distance between the solar arrays and the protection system becomes larger, the corresponding induced overvoltages Va , Vb and Vd will all decrease. Since the induced lightning overvoltage of the solar arrays in a rooftop PV power system is highly dependent on the abovementioned factors, they should be considered comprehensively in choosing the SPD configuration for the PV power system. References
probability function of lightning current amplitude in Beijing as below is used: P(> I) =
1 1 + (I/33.9)
2.9
(2)
where I is the lightning current amplitude, and P is the cumulative probability of all lightning currents with amplitude less than I. Thousands of lightning events with random amplitudes, whose probability distribution fits the above function, randomly strike one of the eight lightning rods N1–N8. In each case, the peak value of the absolute induced overvoltages appeared on the output wires of the solar arrays are counted. As shown in Fig. 15, the cumulative probability curve of the maximal absolute induced overvoltages for the special PV system sample in this paper can be drawn. 6. Conclusion Through numerical simulations, the influence of different factors of the PV power system on the induced lightning overvoltages of the solar arrays are analyzed in this paper. These factors include the lightning striking spot, the lightning current amplitude, the building height, the soil resistivity, and the distance between the solar arrays and the external protection system. The absolute induced overvoltage Va and the relative induced overvoltage Vb are closely related to the location of the lightning striking spot. When the lightning striking spot is near the output wires and the metal frame of the solar array, the corresponding induced overvoltages Va and Vb will be large. All induced overvoltages on the output wires of the solar arrays, including Va , Vb and Vd , are directly proportional to the peak value of lightning current.
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