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Lightning protection design of solar photovoltaic systems: Methodology and

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Article in Electric Power Systems Research · June 2019

DOI: 10.1016/j.epsr.2019.105877

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 Lightning Protection Design of Solar Photovoltaic
Systems: Methodology and Guidelines
Yang Zhanga, Hongcai Chenb and Yaping Dua
a
Department of Building Services Engineering, Hong Kong Polytechnic University, Hong Kong.
b
Academy for Advanced Interdisciplinary Studies, Southern University of Science and Technology, Shenzhen, China.

Abstract—Solar photovoltaic (PV) system is one of the promising renewable energy options for substituting the conventional energy. PV
systems are subject to lightning damage as they are often installed in unsheltered areas, and have vulnerable electronic devices. This
paper proposes a partial element equivalent circuit (PEEC) method enhanced with the vector fitting technique for analyzing lightning
transients in the PV systems. The frequency-dependent effects and ferromagnetic properties of structural steel are taken into account.
Models of major components in the PV systems including structure steels, wiring in panels, and PV cells are provided. The non-linear
surge protective device (SPD) is also considered in the modelling. An experiment on a PV panel is presented for the validation of the
proposed method. The proposed procedure is finally applied to investigate lightning transients in a practical PV system. The lightning
failure mode of bypass diodes is identified for the first time. The results can help to design effective lightning protection and select
appropriate parameters of protective devices.

Index - photovoltaic system design; lightning protection; transient analysis; PEEC.

1. Introduction
Solar photovoltaic (PV) systems are regarded as one of the best renewable energy resources for substituting conventional energy
[1, 2]. Different types of grid connected PV systems have been developed [3] and put into commercial use. These systems have
expanded extensively worldwide due to recent technological advancement, demand-driven and policy encouragement. Similar to
other power systems [4-8], PV systems are vulnerable to lightning because they are always installed in unsheltered open areas.
Recent studies on lightning protection of PV systems have drawn much attentions [9]. However, the knowledge of appropriate
design and installation of lightning protection systems (LPS) are still under research.
It has been reported that averagely 26% damage of PV systems is caused by lightning strikes [9]. This figure could be higher in
the areas with severe lightning storms. Furthermore, increasing usage of string inverters or micro-inverters instead of a central
inverter in the modern PV systems leads to a new challenge for choosing the proper lightning surge protection devices (SPDs).
These inverters are more vulnerable to lightning strikes as they are close to the PV modules. The replacement of components
damaged by lightning strikes largely reduces the return of investment because it incurs disassembly cost and transportation cost.
The component failures affect the continuity of the power supply as well. Consequently, effective lightning protection is
indispensable for PV systems.
Lightning transient evaluation of a PV system has been a necessary task in designing effective LPS. Such evaluation has been
addressed experimentally and numerically. Stern and Karner [10] invesigated the induced voltages of a single panel in the laboratory.
An inductive coupling model for PV panels was also proposed to assist the design. Effects of metal frames, integrated bypass diodes
and cell interconnection were discussed. Hernandez et al. [11] introduced scientific background and essential assumptions into the
design of lightning protection systems for PV systems. They emphasized the needs of standardisation that should be addressed in
the near future. Vangala et al. [12] conducted a field measurement on an practical PV system. High-speed dataloggers were used to

1
monitor the voltage at the terminals of two PV arrays. The observed data proves that DC-side protection for PV power electronics
is important. Kokkinos et al. [13] assessed the LPS of a PV system installed at a location with a high ground flash density and high
soil resistivity (2000 Ωm). Laboratory experiments on an isolated PV panel was performed to investigate overvoltages in DC cables.
Tu et al. [14] used a modified mesh current method to calculate the induced voltages of the DC cables in a rooftop PV system.
Systems with and without an external LPS were compared. Various factors were discussed on the design of SPD configurations for
PV systems. Charalambous et al. [15] used CDEGS software to access the external LPS and earthing design options that were
installed in PV systems. Both isolated LPS and non-isolated LPS were investigated respectively. Yonezawa et al. [16] evaluated
the overvoltages between the DC line and the ground line, and the current flow through the SPD using the finite difference time
domain (FDTD) method. Required current withstand capability of SPDs for a PV system is evaluated. Méndez et al. [17, 18]
explored transient effects within the frameless PV system. Circuit models and EMTP-ATP were employed to simulate the system.
The influences of the ground connection of the negative or positive terminal in PV systems were investigated.
It is found that some factors in PV system modelling are underestimated for lightning transient analysis. Firstly, the conductors,
such as structural steels, DC cables, etc. are generally modeled as perfect conductors. The frequency dependent effects of these
conductors are ignored. These conductors are highly frequency dependent under lightning transients. Particularly, the steels are
made of ferromagnetic materials so that they exhibit a strong frequency dependent effect. Secondly, the wiring of PV panels and
the nonlinear characteristic of PV cells are not considered in some studies. All these could lead to inaccurate evaluation results of
lightning voltages and currents in the system. An efficient modelling method for the PV systems would be then necessary in order
to provide effective lightning protection.
This paper presents a comprehensive procedure of PV system modelling for lightning transient analysis. Taking advantage of
the partial element equivalent circuit (PEEC) method, models of various conductors, cables and nonlinear components in the PV
system are presented. With the vector fitting method, the frequency-dependent characteristic of conductors is taken into account in
modelling. The proposed method is verified experimentally, and a practical PV system is simulated to provide guidelines for
effective design. The rest of the paper is organized as follows. Section II presents the modelling method of the supporting steel, DC
cables and the wiring in the PV panel. Section III explains the nonlinear behavior of the PV cell and its model. In section VI, the
laboratory experiment on a PV panel is presented for validation of the proposed method. Finally, lightning transients in a practical
PV system are simulated in Section V.

2. Modelling of conductors and cables

Lightning transient problems can be generally solved using electromagnetic field methods, such as finite difference time domain
(FDTD) method [19-21], method of moment (MoM), etc. The partial element equivalent circuit (PEEC) method [22-24] is
considered as an efficient method for modelling electromagnetic (EM) coupling in a wire structure, and is suitable for modelling
PV systems. The PEEC method [25-27] is derived from the mixed potential formulation of Maxwell equations. The total electric
field on a conductor in free space can be expressed by using both magnetic vector A and electric scalar potential  as

E ( r ,  ) = j A ( r ,  ) + ( r ,  ) (1)

With the free space Green’s function G, (1) can be expressed as

J (r )
0= + j  G ( r , r  ) J ( r  ) dv
 v
(2)

+  G ( r , r  )  ( r  ) ds '
 s'

2
where J is the volume current density at source point,  is the conductor conductivity and  is the surface charge density, v is the
volume of the conductor, r and r are the position vectors. Divide the conductor into a number of small segments, and assume both
conductor current I and line charge q are constant in each segment. Fig. 1 illustrated a typical segment of conductors for modelling.
Integrating (2) along segments yields a set of electrical circuit equations for Nb segments and Nn nodes, as follows:
Nb
Vn − Vn +1 = Rii I i +  j Lij I i
j =1
Nn
(3)
Vn =  pnm qm
m =1

where Rii is the resistance of segment i, and both Lij and pij are the inductance and coefficient of potential between segments i and j,
nodes n and m.
Note that lightning return stroke currents contain high-frequency components. The current in a segment at high frequency is not
uniformly distributed over its cross section due to the eddy current effect. Both resistance and internal inductance then vary with
frequency significantly. They can be determined by surface impedance of the conductor. For a circular conductor with radius a,
both resistance and internal inductance in s domain are expressed with the surface impedance Zii,s [28, 29], as follows:

j I（ R）
Z s ,ii ( s ) =  0 a
2 Ra I（
1 Ra）

Rii ( s) = real  Z s ( s )  (3)

imag  Z s ( s ) 
Lint,ii ( s ) =

where In is modified Bessel functions of the 1st kind at order n with argument Ra=(1+j)a/δ in which δ is skin depth and μ is the relative
permeability. External inductance and coefficient of potential are generally frequency invariant, and are determined by general PEEC
formulas, as follows:
 1
Lext ,ij =
4 
li lj dij
dli dl j
(4)
1 1 1
pnm =
4 ln lm ln lm dnm dln dlm
where dij or dnm is the distance between branches i and j or nodes n and m..
As surface impedance varies significantly with frequency, the vector fitting method [30] is adopted to represent the frequency-
dependent surface impedance with frequency invariant circuit parameters. Given by Z(s) in s domain, this impedance can be
approximated with rational functions in the form of pole-residue terms as follows:
N
s
Z s ( s) = R0 + sL0 +   Rk (5)
k =1 s + Rk / Lk

After all the poles are identified, the impedance of the conductor can be realized with an equivalent cascade circuit consisting of
frequency-invariant resistors and inductors. Because the surface impedance increases with frequency monotonously in the frequency
range of interest, two real-pole rational functions are sufficient to capture the rather smooth frequency behavior of the elements. Fig.
1(b) shows a complete vector-fitting enhanced PEEC model for a segment of the conductor. In this circuit model, all circuit parameters
of the conductors are passive and frequency-independent. Time-domain circuit analysis tools can be applied directly to solve for
lightning transients in a wire structure, such as that built from a PV system. In this paper, the circuit parameters of the wire structure
are calculated with Matlab codes, and transient voltages and currents in the structure are solved with a SPICE solver with the netlist
files generated with the Matlab codes as well [31].

3
 Node n Branch i Node n+1
Vn Ii Vn+1

(a)

Lii,1 Lii,2 𝑑𝐼𝑗

Rii,0 Lii,0
𝐿𝑖𝑗
Vn
𝑑𝑡
𝑗 Vn+1
...
Icn Icn+1
Rii,1 Rii,2

1 𝑝𝑛𝑚 1 𝑝𝑛+1𝑚
𝐼 𝐼
𝑝𝑛𝑛 𝑝𝑛𝑛 𝑐𝑚 𝑝𝑛+1𝑛+1 𝑝𝑛+1𝑛+1 𝑐𝑚
𝑚≠𝑛 𝑚≠𝑛+1

(b)
Figure 1. PEEC model of a conductive segment with the vector-fiting method.(a) A conductor segment (b) Equivalent circuit.

2.1 C Profile Steel

Because of its excellent mechanical performance (high strength, light in weight, easy installation), C profile steel is commonly
used as the supporting structure in PV systems. Fig. 2(a) shows the typical C profile steel use for the PV systems. The steel used in
this paper has the width of 40 mm and the thickness of 3 mm, as seen in Fig. 2(b).

Lm
t= 3 mm
w = 40 mm

Ls Ls

Ls

(a) (b)
Figure 2. Configuration of C profile steel. (a) Overview. (b) Cross section view.

As one kind of ferromagnetic materials, C profile steel exhibits nonlinear characteristics under the excitation of current. While,
the steel is deeply saturated when it carries the lightning current directly. It can be then treated as a linear magnetic material [32]. As
described in early part of Section 2, the C profile steel can be represented by internal impedance and external inductance. The
resistance and internal inductance of the C profile steel are calculated using the cylindrical model with an equivalent radius [33]. As
the thickness of the steel is very small, equivalent radius a of the cylindrical model is determined by its side width as

3w
a= (6)
2

4
Note that the external inductance is associated with the magnetic flux linkage outside the conductor. It is determined only by the
geometric dimensions of the C profile steel. In order to calculate the external inductance, the C profile steel is divided into three thin
tapes as shown in Fig. 2(b). Consequently, the external inductance of the C profile steel can be calculated based on the parallel
connection of three thin tapes, and is expressed as

1
Lext = −1
(7)
 Ls Lm1 Lm 2 
  Lm1 Ls Lm1 
 Lm 2 Lm1 Ls 

where Ls is the external self-inductance of individual thin tapes, and both Lm1 and Lm2 represent the mutual inductances between two
thin tapes orientated in perpendicularly and parallel. These inductances can be obtained using the simplified Hoer’s formulas [34]
as shown in Appendix.
Experimental tests were undertaken to verify the proposed modelling approach. Fig. 3 shows the test setup for extracting the
impedance of the C profile steel. A square loop made of C profile steel with side length of 1 m was constructed in the laboratory. An
impulse current was injected into the loop, and both the impulse voltage across the loop and the injected current were recorded by a
digital oscilloscope. The inverse Fourier transform technique was used to convert the time-domain voltage and current to the
frequency-domain results. Thus, frequency-domain resistance and inductance under the impulse were obtained. Fig. 4 shows
frequency-domain resistance and inductance obtained by both measurement and calculation with (4)-(7) using 𝜎 = 5 × 106 S/m and
𝜇𝑟 = 75. It is found that calculated resistance and inductance using the proposed model match well with the measured results.

Figure 3. Experiment configuration of a C profile steel loop.

(a) (b)
Figure 4. Measured and calculated circuit parameters of a C profile steel loop. (a) Resistance, (b) Inductance.

5
2.2 Wiring of the PV Panel

PV cells in a PV panel are connected in series through galvanized copper wires. There are several types of wires generally used
in industry as listed in Table 1. Because of their thin thickness, the skin effect is neglected in wire modelling. Consequently, the
resistance of the wire is approximated by its DC resistance. Self-inductance is almost equals to its DC inductance and can be calculated
using the Hoer’s formula [34], which is given in Appendix. To verify our assumption, the wire with the width of 1.6 mm, the thickness
of 0.2 mm and the length of 1.8 m is tested. The frequency-dependent curves of resistance and inductance are obtained using a vector
network analyzer (VNA) as shown in Fig. 5. It is found that both the resistance and inductance are almost frequency-invariant and
are coincident with the DC inductance (2.29 H) and DC resistance (150.5 mΩ), respectively.

Tables 1. Dimensions of the wiring.

Dimensions
Conductor
Type Wide(mm) Thickness(mm)
A 1.6 0.2

Wires B 1.8 0.16

C 0.2 0.16

(a) (b)
Figure 5. Measured parameters of the wiring of the PV cells. (a) Resistance, (b) Inductance.

3. Modelling of the PV panel

The circuit models of PV cells have been studied extensively over the years. The single diode model [35], double-diode model,
and modified 3-diode equivalent circuit model [36], are the most commonly adopted for representing the PV cell in circuit simulation
under DC conditions. For lightning transient study in this paper an improved PV model using the single diode model is proposed.
Note that few articles have addressed the transient behavior of the PV cells.

Rs I Ls Rs I

Id Ip
Ig Rsh V Solar cell V

(a) (b)
Figure 6. Equivalent circuit of of a PV cell. (a) Single diode model. (b) Transient model.

6
 Fig. 6(a) shows the diagram of the single diode PV model. Ig is the photocurrent. Both Rs and Rsh represent respectively the series
resistance for the ohmic loss of the wiring, and the shunt resistance for the losses caused by localized shorts at the emitter layer or
perimeter shunts along cell borders, etc. Fig. 6(b) shows the proposed transient PV-cell model for lightning transient analysis. The
diode in the traditional model retains, while the photocurrent is neglected due to its negligible magnitude compared with the lightning
current. Both Ls and Rs are the inductance and resistance of the wiring, respectively. They can be determined with the impulse test as
described in Section 2.1. The V-I relation of the diode is given by
I
V = NVT log( + 1) (8)
Is

where VT is a constant of 26 mV. Both N and Is are the determining factors of the diode D, and are determined by the I-V curve
measured in the laboratory with the least square method. The measurement is similar to that described in Section 2.1. Fig. 7 shows
the V-I curves measured in the experiment and calculated with (9). A good agreement is observed.

Figure 7. Comparison of measured and simulated results.

4. Laboratory verification
To verify the proposed modelling procedure, a simplified PV system was tested in the laboratory as shown in Fig. 8. The system
is a PV unit made of a PV panel and its supporting frame made of the C profile steel. The dimensions of the PV supporting frame
is shown in Fig. 8(b) and listed in Table 2. The configuration of the PV panel is shown in Fig. 8(c). During the test, four leg ends
of the PV frame were connected with copper strips as shown in Fig. 8(b). An impulse current was injected into the top corner of the
frame through a shielded power cable. The impulse current flows back to the impulse generator through the legs of the frame. The
current distributed at each leg and induced open voltage in the DC cable were recorded with a digital oscilloscope.
Transient simulation of the tested system was performed using the proposed method. A system-level model was constructed,
which included the C profile steel, DC cables and the PV cell.

7
 (a)
PT
+
-
1m
OSC
Impulse
1m

0.6 m

0.25 m

CT

copper strips

(b)
112.5 cm

6 cm
+DC
12.5 cm
54 cm

-DC

120 cm

(c)
Figure 8. Simplified PV system for testing. (a) overview of the the laboratory setup. (b) configuration of the test arrangement. (c) configuration of the PV panel.

Table 2. Dimensions of C-profile steels in the PV frame.

Parameters
Items
Quantity Length(mm) Cross-section(mm)
Side Length: 40
Front legs 2 250
Thickness: 3
Side Length: 40
Rear legs 2 600
Thickness: 3
Side Length: 40
Cross girder 2 1000
Thickness:3
Side Length: 40
Oblique girder 2 1000
Thickness: 3

Fig. 9 shows the results of currents in four legs obtained with the measurement and simulation under an 8/20 μs impulse current
of 632 A in peak. It is observed that both simulated and measured currents match well in both magnitude and waveform. Table 3
shows the measured and calculated peak currents in each leg. Good agreements are observed and the errors are less than 4.2 %. Fig.

8
10 shows the measured and simulated induced open voltages in the DC cable. The calculated and measured voltages also match
well in waveform. Therefore, the proposed model is adequate for the analysis of lightning transients in PV systems.

Figure 9. Comparison of current distribution at four legs of the PV panel.

Table 3. Comparison of impulse current peaks in four legs of the PV system.

Value (A)
Position
Meas. Cal. Err.
Leg 1 296 296 0%

Leg 2 82 79.61 2.9%

Leg 3 71 74 4.2%

Leg 4 180 182.7 1.5%

Figure 10. Comparison of te induced open voltage between two DC lines.

9
 5. Simulation of surges in a photovoltaic system
Lightning induced voltages in DC cables is one of the critical issues in lightning protection of PV systems. This voltage may
damage the inverter connected to the DC cable. The induced voltage on the PV panel could damage bypass diodes connected to the
panel as well. In addition, lightning current can cause a potential rise in the grounding grid. The voltage between the
positive/negative lines of the DC cable and the grid may cause breakdown of cable insulation. In this section, transient analysis of
a practical PV system is performed to investigate these voltages under a direct lightning strike.

5.1 Configuration of the PV System

String inverters are commonly used in PV systems due to its high power generation efficiency, installation flexibility and low
maintenance cost. In order to generate a sufficient DC voltage, several PV panels are connected in series as a PV string. The PV
string is then connected to a string inverter to convert the DC power to three-phase AC power. For the system discussed in this
paper, 8 PV panels are installed on a PV supporting frame. Total 24 PV panels on 3 supporting frames are connected in series as a
PV string to output a voltage around 700VDC. At the end of the PV string, the DC cable is connected to an inverter. Fig. 11 shows
the configuration of the system under investigation.

Air terminal rod 1.2 m

120 cm
+ DC
220 cm 2.6 m
- DC
Inverter
Lightning strike
1. 2 m
point
60 cm
185 cm
3.4 m 1m 1.8 m

60 cm 310 cm Horizontal conductor

Grounding grid

(a) (b)
Figure 11. The PV system under investigation. (a) Configuration of the PV panels on a frame. (b) Top view of the PV ststem with the grounding grid.

The PV string in Fig. 11 is protected with a non-isolated LPS. The air terminal rod of 1.2 m is mounted on the PV frame which
is part of the LPS. Fig. 11(a) shows one PV supporting frame considered in the simulation. Fig. 11(b) shows the top view of the
system. The grounding grid is represented with the dash lines. The grid is buried in the ground with the depth of 0.5 m and the size
of 5 m ×15 m. The legs of PV frame are connected to the grounding grid via horizontal bonding conductors in the ground. The length
of the bonding conductors is 1.2 m and they are buried at depth of 0.5 m as well. Both the grounding grid and bonding conductors

are made with 40 × 4 mm2 flat steel.

5.2 Bypass Diodes

In the PV system, a bypass diode is connected in parallel with the PV cell at the output of each module in the reverse direction.
The bypass diode is an important element in the PV module. It can effectively prevent the PV cell from burning out caused by hot
spot effect. For better reference, the represented circuit of a PV cell with 8 PV modules is shown in Fig. 12.

10
 Loop due to wiring
structure in each module

+DC terminal
Loop due to
DC cable
-DC terminal

Solar cell
Bypass diode

Figure 12. Representive circuit of a PV string with 8 PV modules.

Because of the polarity of the lightning return stroke current, there are two scenarios for the induced voltage of the loop. In the
first scenario, the bypass diodes are all in the reverse direction while the solar cells are in forward direction as shown in Fig. 13(a).
Bypass diodes are equivalent to open and the PV string becomes the series connection of PV modules as shown in Fig. 13(b). In
this case, the electromagnetic induction in both the loop of DC cables and the loop of the wiring structure in each module contributed
to the overvoltage at the DC terminal. The overvoltage due to electromagnetic induction in the loop of the wiring structure might
lead to the breakdown of the bypass diodes.

Lightning current Lightning current

+DC terminal +DC terminal

Reverse
direction
-DC terminal -DC terminal

Solar cell Solar cell

Bypass diode Bypass diode

(a) (b)

Figure 13. Representive circuit of a PV string with 8 PV modules with the lightning current in the reverse direction. (a) Original circuit. (b) Equivelaent ciruict.

Lightning current Lightning current

+DC terminal +DC terminal

Forward
direction
-DC terminal -DC terminal

Solar cell Solar cell

Bypass diode Bypass diode

(a) (b)

Figure 14. Representive circuit of a PV string with 8 PV modules with the lightning current in forward direction. (a) Original circuit. (b) Equivelaent ciruict.

11
 In the second scenario, the bypass diodes are all in the forward direction as shown in Fig. 14(a). The wiring structure of the PV
cell in each PV module is shorted by the bypass diode. The loop of the circuit is only contributed by the DC cable as shown in Fig.
14(b). Thus, the induced voltage applied at the DC terminal is smaller than the former one. In this scenario, the bypass diodes will
not suffer from breakdown. For worse case analysis, only the first scenario is considered in the following analysis.

5.3 Ligntning Transient Voltages

The first negative stroke of 1/200 μs and 100 kA in peak is employed in the simulation. This current is represented by the
Heidler’s model specified in IEC Standard 62305 [37]. The open-circuit voltage between the positive and negative lines of the DC
cable is simulated. To investigate the issue of insulation breakdown, the voltages between the positive/negative lines and the ground
are also simulated. The soil resistivity is taken to be 500 Ω∙m, and a high soil resistivity value of 2000 Ω∙m is selected for comparison.
The relative permittivity of soil is assumed to be 10.

Figure 15. Induced voltage between negative and positive DC cables.

Fig. 15 shows the induced voltage between the positive and negative lines. The induced voltage is 64.33 kV when the soil
resistivity is 500 Ω∙m, which exceeds the PV inverter’s capacity as indicated in [38]. While, the induced voltage between DC lines
varies slightly to 65.27 kV when the soil resistivity is changed to 2000 Ω∙m. It can be concluded that the soil resistivity has a little
influence on the voltage between the positive and negative lines of the DC cable.
In order to investigate the influence of the wavefront on the induced voltage between the DC cables, three different lightning
waveforms, 1/200 μs, 2.6/50 μs and 10/350 μs with 100 kA in peak, are conducted in the simulations. Fig. 16 shows obtained
induced voltages between the positive and negative cables under different lightning waveforms. The corresponding peak voltages
are listed in the Table 4. It is found that the induced voltage decreases with increasing front time. This is because the induced voltage
between the DC cables is mainly generated by the magnetic coupling between the conductors in the LPS and the DC cable. It is
determined by the loop area, the magnitude and steepness of the lightning current.

12
 Figure 16. Induced voltage between negative and positive DC cables under different lightning waveforms.

Table 4. Comparison of impulse current peaks in the PV system

Lightning Waveform Peak induced voltage
(s) (kV)
1/200 65.27
2.6/50 25.35
10/350 6.22

Figure 17. Induced voltage between negative/positive cables and the ground terminal.

Fig. 17 shows the voltage between the negative/positive lines and the ground terminal at the inverter with different values of
soil resistivity. It is shown that the voltages have a much longer tail and higher amplitude than the voltage between negative and
positive lines. Such voltages are mainly caused by the rise of ground potential. In addition, the soil resistivity has a significant
influence on the voltages. The peak voltage is increased from 292.4 kV to 1225 kV when the soil resistivity is changed from 500
Ω∙m to 2000 Ω∙m. Such a high voltage can cause insulation breakdown of the LV cables.

+DC

I
-DC

SPD2 SPD1

PE

Figure 18. The configuration of surge protection at DC circuits.

13
 (a) (b)
Figure 19. Surge in the DC cables after installation of SPDs. (a) Induced voltage between negative and positive DC cables. (b) Induced current in negative and
positive DC cables

In order to protect electrical equipment, surge protection devices (SPDs) are provided in the PV system. Fig. 18 shows a typical
configuration of SPD installation for the DC cable. Simulation was performed again to investigate transient voltages of the DC
cable. In this case, the voltage between the DC lines and the ground terminal is suppressed because of the SPDs are installed on
these line. However, the voltage between the negative and positive lines of the DC cable are 4.92 kV as shown in Fig.19 (a). This
voltage still exceeds lightning transient withstand voltage of the PV inverter [38]. Fig.19 (b) shows the current flowing through
each SPD. The current direction is indicated in Fig. 18. Since the DC cables will not be struck directly by lightning, these SPDs are
not subject to the large lightning current (less than 500 A in this case).

Figure 20. The induced voltage of bypass diodes.

The bypass diodes are connected in parallel to the outputs of PV panels as shown in Fig 12. However, these bypass diodes are
often damaged by lightning due to their low withstand voltage. The bypass diodes used in the system have a repetitive peak reverse
voltage of 1 kV and they will suffer permanent breakdown when the impulse voltage exceeds 2 kV. In order to analyze the defection
of the bypass diodes, the voltages induced in the wiring of PV panels are calculated. Fig. 20 shows the induced voltages in two
diodes close to the lightning striking point as shown in Fig. 11(b). Induced voltages without and with SPD installation are evaluated
for comparison. Soil resistivity is chosen as 2000 Ω∙m to represent the worst case. For the system without SPD being installed, the

14
voltages on two diodes are 8.75 kV and 6.75 kV, respectively. For system with SPDs being installed, the voltages are reduced to
7.05 kV and 5.13 kV, respectively. SPDs in the DC circuit can reduce the induced voltage on the bypass diodes. However, the
voltages under these situations still exceed the transient withstand votlage of the bypass diodes.

6. Conclusion
This paper presents a comprehensive modelling procedure for transient analysis of the PV system. Transient voltages and
currents in the PV system are calculated using an enhanced PEEC method. Detailed models of various components in the PV system,
including the C profile steel, the DC cable, and the wiring of PV panels, are provided. Both the frequency-dependent effect and
ferromagnetic properties of steels are taken into account. Meanwhile, the nonlinear PV panel model applicable to lightning transients
is also investigated. The proposed modelling procedure has been verified experimentally by comparing with the measurement in
the laboratory. Finally, lightning transients in a practical PV system with a string inverter are investigated using the proposed method.
Systems with and without SPD installation are performed in the simulation. The results are summarized as followed:
• The induced voltage between negative and positive of the DC cables has a short waveform, and is not sensitive to the soil
resistivity.
• On the contrary, the voltage between the DC cable and ground has a long waveform, and is greatly affected by the soil
resistivity.
• With SPDs installed only between the DC lines and the ground, the voltage between the positive and negative lines can reach
a high level (4.92 kV in our simulation). It may lead to breakdown in the PV inverter. It is recommended installing another
SPD between two lines of the DC cable.
• Overvoltages are observed on the bypass diodes of PV panels although SPDs are installed at the inverter. It will lead to the
failure of the bypass diode. Appropriate lightning protection for these bypass diodes is necessary.

Appendix
The inductance of sheets or plates with zero thickness has been discussed extensively in [32, 34]. For easy reference, these
inductance formulas are presented in this section. For self-inductance of a thin sheet it is given by

0 1  2 l + l 2 + W 2 3
Ls = 
6 W 2 
3W l ln
W
− ( l 2
+ W )
2 2

(9)
W + l2 +W 2 3 
+3l W ln
2
+ l +W 3 
l 

where both W and l are the width and length of the sheet, respectively. For two parallel horizontal planes with sheet spacing of z,
mutual inductance is expressed as

0 1 x y x y
2 1 2' 2'

Lm =  f ( x − x, y − y, z )

4 W 2 x y x y
(10)
1 2 1' 1'

Function f(u,v,w) in (10) is given as

v 2 − w2 u 2 − w2
f ( u , v, w ) = u ln(u + R) + v ln(v + R)
2 2
1  uv 
− ( R 2 − 3w2 ) R − uvw tan −1  
6  wR 

15
and 𝑅 = √𝑢2 + 𝑣 2 + 𝑤 2 .
For two perpendicular planes, the same expression (10) is used except the function f(u,v,w) is replaced by
 v 2 w2   v2 u 2 
f ( u,v,w ) =  -  wln(u + R)+  -  uln(w+ R)
 2 6   2 6 
uw v3 -1  uw 
+uvwln(v + R) - R - tan  
3 6  vR 
vu 2 -1  vw  vw2 -1  vu 
- tan  - tan  
2  uR  2  wR 

Acknowledgement
The work leading to this paper was supported by the grants from the Research Grants Council of the HKSAR (Project No.
152038/15E and 152044/14E).

References
[1] A. Zahedi, "Solar photovoltaic (PV) energy; latest developments in the building integrated and hybrid PV systems," Renewable Energy, vol. 31, no. 5, pp.
711-718, 2006.
[2] A. Kanase-Patil, R. Saini, and M. Sharma, "Integrated renewable energy systems for off grid rural electrification of remote area," Renewable Energy, vol. 35,
no. 6, pp. 1342-1349, 2010.
[3] S. Chatterjee, P. Kumar, and S. Chatterjee, "A techno-commercial review on grid connected photovoltaic system," Renewable and Sustainable Energy Reviews,
vol. 81, pp. 2371-2397, 2018.
[4] K. Yamamoto, T. Noda, S. Yokoyama, and A. Ametani, "Experimental and analytical studies of lightning overvoltages in wind turbine generator systems,"
Electr Pow Syst Res, vol. 79, no. 3, pp. 436-442, 2009.
[5] P. Sarajčev, I. Sarajčev, and R. Goić, "Transient EMF induced in LV cables due to wind turbine direct lightning strike," Electr Pow Syst Res, vol. 80, no. 4,
pp. 489-494, 2010.
[6] R. B. Rodrigues, V. M. F. Mendes, and J. P. S. Catalao, "Protection of wind energy systems against the indirect effects of lightning," Renewable Energy, vol.
36, no. 11, pp. 2888-2896, Nov 2011.
[7] S. Yokoyama, "Lightning protection of wind turbine blades," Electr Pow Syst Res, vol. 94, pp. 3-9, 2013.
[8] Y. M. Hernández, T. E. Tsovilis, F. Asimakopoulou, Z. Politis, W. Barton, and M. M. Lozano, "A simulation approach on rotor blade electrostatic charging
and its effect on the lightning overvoltages in wind parks," Electr Pow Syst Res, vol. 139, pp. 22-31, 2016.
[9] N. I. Ahmad et al., "Lightning protection on photovoltaic systems: A review on current and recommended practices," Renewable and Sustainable Energy
Reviews, vol. 82, pp. 1611-1619, 2018.
[10] H. J. Stern and H. C. Karner, "Lightning induced EMC phenomena in photovoltaic modules," presented at the 1993 International Symposium on
Electromagnetic Compatibility, 1993.
[11] J. C. Hernandez, P. G. Vidal, and F. Jurado, "Lightning and surge protection in photovoltaic installations," IEEE Transactions on power delivery, vol. 23, no.
4, pp. 1961-1971, 2008.
[12] P. Vangala, M. Ropp, K. Haggerty, K. Lynn, and W. Wilson, "Field measurements of lightning-induced voltage transients in PV arrays," presented at the
2008 33rd IEEE Photovolatic Specialists Conference, 2008.
[13] N. Kokkinos, N. Christofides, and C. Charalambous, "Lightning protection practice for large-extended photovoltaic installations," presented at the 2012
International Conference on Lightning Protection (ICLP), 2012.
[14] Y. Tu, C. Zhang, J. Hu, S. Wang, W. Sun, and H. Li, "Research on lightning overvoltages of solar arrays in a rooftop photovoltaic power system," Electr Pow
Syst Res, vol. 94, pp. 10-15, 2013.
[15] C. A. Charalambous, N. D. Kokkinos, and N. Christofides, "External lightning protection and grounding in large -scale photovoltaic applications," IEEE
Transactions on Electromagnetic Compatibility, vol. 56, no. 2, pp. 427-434, 2014.
[16] K. Yonezawa, S. Mochizuki, Y. Takahashi, T. Idogawa, and N. Morii, "Evaluation of SPDs for a PV system using the FDTD method taking concrete
foundations into consideration," presented at the 2014 International Conference on Lightning Protection (ICLP), 2014.
[17] Y. M. Hernández, D. Ioannidis, G. Ferlas, E. G. T. Tsovilis, Z. Politis, and K. Samaras, "An experimental approach of the transient effects of lightning currents
on the overvoltage protection system in MW-class photovoltaic plants," in 2014 International Conference on Lightning Protection (ICLP), 2014, pp. 1972-
1977.
[18] Y. Mendez, I. Acosta, J. C. Rodriguez, J. Ramirez, J. Bermudez, and M. Martinez, "Effects of the PV-generator's terminals connection to ground on
electromagnetic transients caused by lightning in utility scale PV-plants," presented at the 2016 33rd International Conference on Lightning Protection (ICLP),
2016.
[19] T. Noda, A. Tatematsu, and S. Yokoyama, "Improvements of an FDTD-based surge simulation code and its application to the lightning overvoltage calculation
of a transmission tower," Electr Pow Syst Res, vol. 77, no. 11, pp. 1495-1500, 2007.
[20] H. Chen, Y. Du, M. Yuan, and Q. H. Liu, "Analysis of the Grounding for the Substation Under Very Fast Transient Using Improved Los sy Thin-Wire Model
for FDTD," Ieee T Electromagn C, vol. 60, no. 6, pp. 1833 - 1841, 2018.
[21] H. Chen, Y. Du, M. Yuan, and Q. H. Liu, "Lightning-Induced Voltages on a Distribution Line With Surge Arresters Using a Hybrid FDTD–SPICE Method,"
IEEE Transactions on Power Delivery, vol. 33, no. 5, pp. 2354-2363, 2017 2018.
[22] P. Yutthagowith, A. Ametani, F. Rachidi, N. Nagaoka, and Y. Baba, "Application of a partial element equivalent circuit method to lightning surge analyses,"
Electr Pow Syst Res, vol. 94, pp. 30-37, 2013.
[23] H. Chen, Y. Du, and M. Chen, "Lightning Transient Analysis of Radio Base Stations," IEEE Transactions on Power Delivery, vol. 33, no. 5, pp. 2187-2197,
2018.

16
[24] H. Chen and Y. Du, "Lightning Grounding Grid Model Considering Both the Frequency-Dependent Behavior and Ionization Phenomenon," Ieee T
Electromagn C, vol. 61, no. 1, pp. 157-165, 2019.
[25] A. E. Ruehli, "Inductance Calculations in a Complex Integrated-Circuit Environment," Ibm J Res Dev, vol. 16, no. 5, pp. 470 - 481, 1972.
[26] A. E. Ruehli and P. A. Brennan, "Efficient Capacitance Calculations for 3-Dimensional Multiconductor Systems," Ieee T Microw Theory, vol. 21, no. 2, pp.
76-82, 1973.
[27] D. Gope, A. Ruehli, and V. Jandhyala, "Solving Low-Frequency EM-CKT Problems Using the PEEC Method," IEEE Transactions on Advanced Packaging,
vol. 30, no. 2, pp. 313-320, 2007.
[28] Y. Du and J. Burnett, "Current distribution in single-core cables connected in parallel," IEE Proceedings - Generation, Transmission and Distribution, vol.
148, no. 5, pp. 406-412, 2001.
[29] A. E. Ruehli, G. Antonini, and L. J. Jiang, "Skin-Effect Loss Models for Time- and Frequency-Domain PEEC Solver," Proceedings of the IEEE, vol. 101,
no. 2, pp. 451-472, Feb 2013.
[30] B. Gustavsen and A. Semlyen, "Rational approximation of frequency domain responses by vector fitting," IEEE Transactions on Power Delivery, vol. 14, no.
3, pp. 1052-1061, Jul 1999.
[31] H. Chen, Z. Qin, Y. Du, Q. Wang, and Y. Ding, "TAES: A PEEC-based tool for transient simulation," presented at the 7th Asia-Pacific International
Symposium on Electromagnetic Compatibility (APEMC), Shenzhen, China, 2016.
[32] H. Chen and Y. Du, "Model of ferromagnetic steels for lightning transient analysis," IET Science, Measurement & Technology, vol. 12, no. 3, pp. 301-307,
2018.
[33] J. Brown, J. Allan, and B. Mellitt, "Calculation and measurement of rail impedances applicable to remote short circuit fault currents," in IEE Proceedings B
(Electric Power Applications), 1992, vol. 139, no. 4: IET, pp. 295-302.
[34] C. Hoer and C. Love, "Exact inductance equations for rectangular conductors with applications to more complicated geometries," Journal of Research of the
National Bureau of Standards, Section C: Engineering and Instrumentation, vol. 69, no. 2, pp. 127-137, 1965.
[35] K. Leban and E. Ritchie, "Selecting the accurate solar panel simulation model," presented at the Nordic Workshop on Power and Industrial Electronics
(NORPIE/2008), Helsinki, Finland, 2008.
[36] K. Nishioka, N. Sakitani, Y. Uraoka, and T. Fuyuki, "Analysis of multicrystalline silicon solar cells by modified 3-diode equivalent circuit model taking
leakage current through periphery into consideration," Solar Energy Materials and Solar Cells, vol. 91, no. 13, pp. 1222-1227, 2007.
[37] IEC 62305-1: Protection against lightning: Part I General principles, 2010.
[38] IEC 62109-1: Safety of power converters for use in photovoltaic power systems – Part 1: General requirements, 2010.

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