^{1}

^{2}

Solar cells are widely used to generate electric energy even at homes. It surely has a great advantage of sustainability. However, the potential induced degradation has been found to be an obstacle problem for practical use. It was reported that the main cause is the dielectric breakdown in the glass covered over the solar cells triggered by the thunderstroke. In this paper, the effects of the parameters such as the position of thunderstroke, the wave form, the peak value and the front duration of the lightning current, were examined by means of numerical calculation. For the lightning current, a step-like waveform and an impulse waveform were examined. The effect of the induced voltage was found to be independent of the waveform. The peak value, the front duration of the lightning current greatly affects the induced voltage.

Nowadays, solar cells are widely used to generate electricity without any environmental disturbance such as thermal or atomic power generation of electricity [

Recently, it was recognized that solar cells are degraded slowly for years. This degradation attracted much attention after Swanson et al. reported that the degradation reached 30%. This is a big problem for the practical use. The degradation is now known as a potential induced degradation (PID) [

Our group assumes that PID is induced by a thunderstroke. In Japan, there are several thunderstrokes in a year. Since usually solar cells are exposed in the air, thunderstroke directly affects the solar cell system. In our previous paper, we reported the effect of lightning current on a solar cell by means of simulation [

In this paper, we study the effects of four kinds of parameters on the induced electric field in the glass. They are the waveform, peak value, the front duration and the position of the lightning current because they are the basic parameters.

The well-known Maxwell’s electromagnetic equations are shown here.

with the help of B = μH, D = εE and J = σE,

are obtained. These equations were transformed to difference equations. We applied the well-known Yee algorithm [

All the spatial finite differences Δx, Δy and Δz should be under the tenth of the wave length. As for the time finite difference Δt, it should be consistent with the Courant condition that is

The readers should refer to the literature [

The solar cell panel treated here is described.

The analytical model of the solar cell panel is shown in

We describe here the model of lightning current where only the indirect thunder stroke was considered. The lightning current was located at the point P in

Glass | PET,EVA | Water | |
---|---|---|---|

ε_{r} | 4.4 | 4.3 | 80.4 |

μ_{r} | 1.0 | 1.0 | 0.999992 |

σ | 1.0E−12 | 1.0E−10 | 0.01 |

Analytical space was in the area of 1.6 m × 1.6 m × 0.4 m. The differences of Δx, Δy and Δz are 10 mm, 10 mm, and 1 mm, respectively. In order to satisfy the Courant condition, the time difference was set to 1 ps. We took the 300,000 time steps that are far larger than the head voltage width.

We assume the voltages V1, V2, and V3 as shown in

We first consider the waveform of lightning current. _{1} has a step waveform while I_{2} has an impulse one. The maximum value was 20 kA in common. For the impulse waveform, the front duration of the current was was 0.1 μs and the time to half value of the current was 1 μs. Both of LX and LY were 0.3 m.

_{1} in the vicinity of an aluminum frame. The blue and the sky blue lines represent the step like and the impulse current responses, respectively. The maximum spikes in both cases are very similar that surpass 20 kV. From this fact, the height of the spike should be determined by the very head part of the lightning current within 0.1 μs. So the difference between I_{1} and I_{2} do not affect the induced voltage. It suggests that the step like current is valid for the numerical simulation for this kind of analysis.

Next we discuss the dependence of the height of the lightning current with a step like form. Both of LX and LY were 0.3 m, and the front duration of the current was 0.1 μs. The peak heights of the current were chosen to be 20, 50, 70, and 100 kA. The simulation results are shown in _{1} in the vicinity of an aluminum frame. The maximum spike was respectively about 21, 50, 60, and 85 kV. The maximum spike rises monotonically with the current, almost linearly.

The difference in the front duration is discussed here. The results for the four front durations of 0.1, 0.3, 1, and 8 μs are shown in

V_{1} was calculated in the vicinity of the aluminum frame. As the front duration becomes the longer, the peak maximum of the spike in the induced voltage reduces. Also it is recognized that the high frequency component is less dominant when the duration is large. But the lightning current is a natural phenomenon, and then it may be quite difficult to control the current anyway. If possible, the current should be varied slowly to protect from the dielectric breakdown.

Finally we see the dependence of the position of the lightning current. The step like current was characterized with the maximum value of 20 kA and the front duration of 0.1 μs. The position of LX and LY were simultaneously varied 0.2, 0.3, 0.4, and 0.5 m. The induced voltage V_{1} was also calculated in the vicinity of the aluminum frame. The results are shown in

LX and LY ranges from 0.2 to 0.5 m where the dimension of solar cell was 0.5 m. These are the same order of magnitude. In this range, no significant difference in the effect was observed. But the peak maximum of the induced voltage was slightly greater when the position of the lightning current was nearer to the solar cell.

We performed the numerical calculation of the induced voltage across the glass covering the solar cell unit in the case that thunderstroke hit near the solar cell panel. The calculation was based on the fundamental Maxwell’s electromagnetic equations. The parameters of the wave form, the peak value, the front duration and the position of the lightning current were varied and the peak maximum of the induced voltage was examined. Our results showed that the prominent difference was not seen if the lightning current had an impulse or a step like form. The peak maximum of the voltage depended mainly on the front duration of the current. The current magnitude linearly affected the peak maximum of the voltage. The position that ranged in the same order of the dimension of the solar cell panel, the triggered effect was not so noticeable.

Ohmukai, M. and Tsuyoshi, A. (2017) Effect of Parameters on Potential Induced Degradation of Solar Cell. Journal of Power and Energy Engineering, 5, 36-42. https://doi.org/10.4236/jpee.2017.56003