2.2.3. Experimental Results and Analysis

According to the experiment method in Section 2.2.2, the long gap arc was attached to the metal frame of Sample A seven times. The arc was attached to the solar cells and flashed over the surface to the metal frame 13 times. Consequently, the interception efficiency of the metal frame was 35%. Figure 8a,b show the successful and failed interception of the discharge arc of Sample A. Under the same experimental conditions, it was noted that the arc attached to the metal frame of Sample B for 15 times. The other five discharge arcs flashed over the surface of solar cells. Then the interception efficiency is 75%. Figure 8c,d show the successful and failed interception of the discharge arc of Sample B. Compared with the electric field distribution and the experimental results, the location of lightning attachment point is very close to simulation results in Section 2.1.3, which can be used to check the effectiveness of the simulation method.

**Figure 8.** Lightning connection of different PV modules (**a**) Lightning connection of metal frame of Sample A; (**b**) Surface flashover of Sample A; (**c**) Lightning connection of metal frame of Sample B; (**d**) Surface flashover of Sample B.

It is noted that under the impulse 1.2/50 μs standard lightning voltage, the metal frame of Sample B was easier to attract the discharge arc generated by the rod electrode than the metal frame of Sample A. The interception efficiency is increased by 114%. That is to say, the metal frame of the BIPV module has better lightning interception performance, which can protect the solar cells from lightning damage more effectively.

#### **3. Study of Lightning Energy Withstand Capability to BIPV Modules**

*3.1. Numerical Simulation and Analysis*

3.1.1. Thermoelectric Coupling Theory

In the process of flowing through BIPV modules, lightning current converted to Joule heat acts on BIPV modules. Studying the temperature field distribution plays a crucial role in the lightning energy withstand capability of BIPV modules. In this section, the thermoelectric coupling analysis model of BIPV modules is established. The solution of the model is based on the law of charge conservation and the law of conservation of energy.

According to the law of charge conservation, the governing equation of electric field in conductor is as follows,

$$\int\_{s} \mathbf{J} \bullet \mathbf{n} dS = \int\_{v} r\_{c} dV \tag{8}$$

where *S* is cross sectional area of unit; *V* is unit volume; **n** is normal vector; *J* is current density; and *rc* is charge density per unit volume.

Based on Ohm's law, current density can be defined as Equations (9),

$$J = \sigma \bullet E = -\sigma \bullet \nabla \Phi \tag{9}$$

where *σ* is the conductivity; *E* is the electric field strength; and Φ is the electrical potential. The governing equation in the finite element is obtained as Equations (10),

$$\int \nabla \delta \Phi \bullet (\sigma \bullet \nabla \Phi)dV = \int\_{V} \delta \Phi r\_{\varepsilon}dV + \int\_{S} \delta \Phi \mathsf{J}dS \tag{10}$$

According to Joule's law, the current flowing through the conductor will be converted into Joule heat, as shown in the following relationship.

$$P\_{\text{cc}} = \mathbf{J} \bullet \mathbf{E} = (\sigma \bullet \mathbf{E}) \bullet \mathbf{E} \tag{11}$$

$$
\sigma = \eta\_v P\_{\infty} \tag{12}
$$

where *P*ec is the power loss density; *ηv* is the energy conversion factor; and *r* is the thermal density.

The governing equation of heat conduction is obtained as Equations (13),

$$
\int\_{v} \rho \mathbf{C}\_{v} \frac{\partial \theta}{\partial t} \partial \theta dV + \int\_{v} \nabla \partial \theta \bullet (K \bullet \nabla \theta) dV = \int\_{v} \delta \theta r dV + \int\_{s} \delta \theta q dS \tag{13}
$$

where *θ* is the temperature; *K* is the solid thermal conductivity; *ρ* is the solid density; *Cv* is the specific heat capacity; and *q* is the heat flux density.

Equations (10) and (13) describe the governing equations of thermoelectric coupling problem. When studying lightning current withstand capability of BIPV modules, the potential, current and temperature can be calculated in the multi-physical field numerical simulation.
