3.1.2. Modeling of Lightning Current

The heat source was given as a large current in the multi-physical field numerical simulation model. The lightning current used in lightning transient calculation can be divided into three categories: double exponential model, Heidler model and pulse function model [29]. In 1941, Bruce and Golde put forward the double exponential function model of lightning current [30]. The concise mathematical expression can describe the typical lightning current waveform, which has been widely used in the field of lightning protection. The expression form is expressed in Equation (14).

$$\dot{a}(t) = \frac{I\_0}{\eta} \left( \mathbf{e}^{-at} - \mathbf{e}^{-\beta t} \right) \tag{14}$$

In which *I*0 is the peak current; *η* indicates the peak correction coefficient; *α* = 1/*T*1, *β* = 1/*T*2, *T*1 is the wave head time and *T*2 is the wave tail time.

In the simulation, the mathematical model of lightning current adopts double exponential model, the amplitude of lightning current is 10–100 kA, the peak correction coefficient is 0.998, the current waveform is 10/350 μs standard lightning wave. According

to the results of Section 2.2.3, the maximum electric field strength on the surface of PV module is set as the lightning injection point.

## 3.1.3. Simulation Result and Analysis

The methodology of Section 3.1.1 can be used to verify the transient state of current distribution and lightning energy withstand capability of BIPV module unit. Figure 9 shows the transient distribution of lightning current at six times. Lightning current flows from attachment point of the metal frame to the grounding point. From 0 μs to 14 μs, the current density instantly increases and reaches a peak value of 4.16 × 10<sup>9</sup> A/m2. At the half peak time of 350 μs, the current density gradually decreases to 2.06 × 10<sup>9</sup> A/m2, and then tends to 0. Because the simulated lightning current waveform is 10/350 μs with a short rising edge, the current density reaches the maximum in a short time. There is no current passing through the solar cells in the whole process, so it is noted that the metal frame can effectively protect the solar cells.

**Figure 9.** Current transient distribution of BIPV at different times (**a**) 0 μs; (**b**) 2 μs; (**c**) 14 μs; (**d**) 350 μs; (**e**) 1000 μs; (**f**) 1500 μs.

In addition, the temperature rise effect of BIPV during lightning striking is shown in Figure 10. After 1200 μs, the amplitude of lightning current is reduced to 10% Iimp. The resistivity of the metal frame is very low and the whole process is transient. Therefore, the temperature rise tends to be stable after 1200 μs. The maximum temperature rise only increases from 0.17 ◦C to 16.07 ◦C with increasing lightning current from 10 kA to 100 kA. This temperature rise is easy for the metal frame to withstand without causing any damage.

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**Figure 10.** Temperature rise of BIPV at different time and current amplitude. (**a**) The temperature rise of BIPV (**b**) The lightning impulse current waveform.
