Thresholds

PID at daytime vs nighttime

At night, when when there is no built-up voltage in the module, we assume that the module undergoes a temperature-dependent regeneration (this mechanism was analyzed in Chapter 4.2.2). Night is defined as any time interval in which module nominal power P_nomis zero.

Daytime: PID degradation vs regeneration

As we showed in Chapter 4, the module performance can undergo a certain extent of regener-ation not only during the night, when there is no potential difference between the cells and the module frame, but also during the day, provided that specific weather conditions are met (typically, during hot and dry periods). During daytime, two phases of PID can thus occur: a degradation and a daytime regeneration. We model here the trade-off between degradation and regeneration by assuming an alternation between the two processes.

The surface conductivity of the glass is a key factor for PID, and it is increased by a high ambient relative humidity. The dependency of module power loss on the relative humidity was investigated through accelerated tests in Chapter 4. In Figure 4.6), the mini-modules power loss after 192 h was plotted against the RH level of the test and fitted with a polynomial curve.

Such curve indicated that the value of RH = 40% seems to provide a threshold of humidity above which power degradation starts to be observed. In our simulations of outdoors PID we therefore assume that, during daily hours, power degradation occurs whenever the ambient relative humidity is RH > 40%, otherwise daytime regeneration occurs.

Other authors apply different thresholds. In [44], for instance, degradation is applied when it rains or when the relative humidity is above 95%, otherwise regeneration is assumed (thermally-driven, with no voltage bias assumed).

Threshold on wet module surface

The dew point T_D.P.is defined as the air temperature, at a fixed vapor pressure p_H2O, such that the saturation vapor pressure at T_D.P.equals the actual vapor pressure, i.e. p_H^sat

2O(T_D.P.) = pH2O

[123]. From the definitions of dew point and of relative humidity it follows that if, at a fixed pressure p_H2O, the air temperature is lower than the dew point then RH> 100%, i.e. liquid water is also present in addition to saturated vapor (with formation of dew, or frost if the dew point is below the freezing point of water). As mentioned, we can thus assume that condensation occurs over the module surface when T_mod< TD.P.. However, the transition phase between the condensed state and the dry state is typically not immediate, and a dew layer may remain over the module surface for a certain time after the module temperature has increased above the dew point, at least as long as there is no direct light impinging on the surface o f the module. This period can have a considerable extension, e.g. in cloudy and

overcast days, or, for modules affected by shading, during the full year or during parts of the year (typically in winter) and for the early/late hours of the day.

Defining when the module surface is wet starting from weather data is therefore not straight-forward. This aspect was investigated by Peter Hacke et al. in a paper of 2016 [34], where they analyze different indicators for the surface wetness of a c-Si module. One criterion that they identify is that the module surface is wet whenever the module temperature satisfies T_mod< TD.P.+ 10^◦C.

Figure 5.6 shows time-lapse photographs we took on a commercial PV module installed in our outdoors testing facility in Neuchâtel, Switzerland, on 15/11/2017 during morning hours. In parallel, the ambient and module temperature, relative humidity and irradiance were monitored. The dew point was calculated from the ambient temperature and relative humidity, using Arden Buck equation to calculate the saturation vapor pressure (see Figure 5.7a). Before the sunrise the module was fully covered with frost (not dew in this case as it was a cold day), as shown in Figure 5.6 (a). The module temperature increases above the dew point at about 08:30 (see the zoom-in at the early morning hours in Figure 5.7b). However, the module surface does not immediately dry as one could expect. Instead, a phase change from frost to liquid state occurred starting 1h 34min later (see (b) and (c)), and the module surface was completely dry only at 10:02 (d). By comparing with the calculated dew point in Figure 5.7b, we see that a water film is present on the module surface until the module temperature is ∼10^◦C to ∼15^◦C above the dew point, consistent with what found by Hacke et al. [34].

Figure 5.6: Time-lapse photographs of a PV module installed in PV-Lab’s outdoors facility in Neuchâtel. (a) The surface is initially covered by dew/frost, (b) and (c) a phase change from frost to liquid occurs starting from 09:34, and (d) at 10:02 the module is completely dry. The photos were taken by Jarle Austbø as part of his Master’s project at PV-Lab [5].

5.3. Applying the PID model to field modules

(a) (b)

Figure 5.7: (a) Irradiance and module temperature values over one winter day for the commer-cial module in Figure 5.6. (b) The first hours of the morning show the correspondence with the phase changes observed in Figure 5.6. The module temperature drops below the dew point over night, leading to the formation of frost (Figure 5.6 (a)); it then increases as the sun rises and at 10:00 its value is ∼15^◦C above the dew point. Only at this time is the module surface completely dry (Figure 5.6 (d)).

This threshold does not consider the presence of direct sunlight, but it provides a reasonable assumption. We therefore adopt it in our model and assume in our simulations that conden-sation is present over the module surface, and set RH= 100% in Equation 4.3, if at least one of the following conditions is satisfied:

1. Rain;

2. T_mod< TD.P.+ 10^◦C.

These thresholds provide a more accurate description of the situation of a wet module surface than what we found in other works. In [82], for instance, the presence of dew is assumed for each hour of the morning and in general the module surface is assumed to be wet whenever the relative humidity exceeds 70%. The threshold in point 2, instead, is able to capture the transient dew behavior as the module temperature increases from its overnight condition.

The flowchart Block B.1b, in Figure 5.8, illustrates the meteorological data representing the stress factors for PID (both degradation and regeneration). Such data constitute some of the inputs in the final simulations for PID as shown in Block B.3 (Figure 5.9).

Threshold for daily degradation/regeneration

Ambient RH

Input to Block B.3

Simulating PID in outdoors conditions Input meteorological data

Stress factors for PID

Dew point Precipitation Block B.1b

TMY dataset of the specific location

Threshold for wet module surface Module

temperature [Block B.1a]

Figure 5.8: Block B.1b flow chart showing the meteorological data used as input stress factors in our simulations of PID for PV modules exposed outdoors (see Block B.3 in Figure 5.9).