The module temperature

A good estimation of the module temperature is essential to predict the occurrence of PID.

Temperature is a stress factor for PID not only because it promotes the migration of sodium ions through the encapsulant (by reducing the resistivity of the encapsulant, as proven experi-mentally in Chapter 6) but also because it is linked to the formation of dew on the module surface.

In the absence of the film of water, when a strong negative field is present between the frame and the solar cell, the PID effect will generally affect only the cells (and the part of the cell) close to the module edge. Conversely, in general the presence of a thin film of water (dew or rain water) over a module’s glass surface evenly distributes the potential from the grounded frame towards the center of the module, aggravating the PID effect. This was experimentally observed in [82], where for a one-cell mini-module installed outdoors sudden drops in the shunt resistance were observed that corresponded to periods when the surface conductivity, measured with a sensor, was higher (i.e. in the presence of dew or rain). The condensation of dew over the module surface will generally occur during the night, or, in sunny days, at dawn and during the evenings, when the module temperature cools below the dew point.

During overcast days a layer of dew (or of rain) can be present as well during daytime. At night, this phenomenon is related as well to the sky temperature. On clear-sky nights, indeed, the sky temperature is generally lower than the earth (or module) temperature. The module (and earth) will then cool down by radiative heat transfer to the sky and its temperature will

5.2. Calculating the module instantaneous nominal power

decrease below the air temperature [1], [64], [25].

A thin layer of water will be present on the module surface:

1. On clear-sky days: in the early and late hours of day when the temperature is below (equal to or just above) the dew point, as long as there is no direct sunshine light on the module surface, which will make the water immediately evaporate;

2. When it rains;

3. On cloudy or overcast days, the film of water formed by rain or by dew can remain for a much longer time over the module surface. We should stress that, during daytime and under this condition, the PV modules will be under tension (V_mpp), so that these are the conditions which will mostly trigger PID degradation.

In Section 5.3.1 we will introduce some thresholds on temperature that are used in the model to discriminate between a wet or dry surface. We continue instead this section presenting the models that we selected from the literature to obtain an accurate calculation of the module temperature at night and during the day. The calculated daily module temperature is then used as an input parameter to estimate the module instantaneous nominal power and to model the evolution of the PID effect.

King model

An empirical relation commonly used to compute the module temperature is that proposed by King in [86]:

T_mod^King= Tair+E_mod

E₀ · exp (a + b · vw), (5.1)

where:

T_mod^Kingis the module temperature, estimated at the module back surface, [^◦C ];

Tairis the ambient air temperature, [^◦C ];

E_modis the plane-of-array irradiance [W/m²];

E₀= 1000 W/m²is the reference solar irradiance on the module;

vw is the wind speed measured at a height of 10 m, [m/s];

a,b are coefficients that depend on the mounting configuration and module type (refer to Table 1 in [86]). For a glass/backsheet module with an open-rack mounting configu-ration, as we consider here, a = −3.56 [-] and b = −0.0750 [-].

Although King’s model gives a good estimation for the module temperature during the day under stable climatic conditions (i.e. not during transients), this relation might overestimate T mod during nighttime by setting for E_mod= 0, Tmod= Tair, which is however still a good approximation for cloudy/overcast nights. For this reason, we consider a second model for the module temperature at night: the Myers/Kempe model.

Myers/Kempe model

In this model, implemented by Kempe (NREL) in [73] using a physical model proposed by Myers in [108], the module temperature is the result of thermal exchange by solar radiation, convection, and thermal radiation to the sky, according to Equation 5.2. The Excel code that implements this model was shared by Mike Kempe for this work. More details about this model are given in reference [73].

T_mod^Kempe=

αEmod+ 2Tairh + ²σ³

T_sky⁴ + T_Gr⁴ ´

2h + ²σT_mod³ , (5.2)

where:

α = ² = 0.6 are, respectively, the module thermal emissivity and absorptivity, [-];

h is the convective heat-transfer coefficient, [-];

σ = 5.6703 · 10⁻8 W/(m²K⁴) is the Stefan-Boltzmann constant;

T_skyis the sky temperature, [^◦C ], computed using the dew point and the atmospheric pressure. We point out that the implementation proposed by Kempe and used here always assumes clear-sky conditions. For more precise estimations, further parameters such as cloud cover factor should be integrated as well, which however are not included in typical meteorological datasets;

TGris the ground temperature, assumed equal to Tair, [^◦C ];

Comparison of models

In order to evaluate the King and Myers/Kempe models, we compare their outputs to module temperature data measured over five months on fielded modules in a PV plant in Greece, shared with us by a private company. The measurements were recorded on the rear side of the modules (with a glass/backsheet structure) with an hourly resolution over several months. We apply the two models using as inputs weather data collected for the same location and period from Solargis. Figure 5.4 shows the results over a restricted period of four days. The yellow line represents the plane-of-array irradiance. As we can see, the measured module temperature

5.2. Calculating the module instantaneous nominal power

(black line) can indeed drop below the dew point (blue dashed line) during the night and early morning hours. The model by Myers/Kempe (green line) is better able to simulate the lower module temperature (compared to Tair) during these hours of the night/day than the model by King (red line), which sets instead the module temperature to the ambient temperature when the irradiance is null. The King model however still gives a better approximation for the daily module temperature when the sun shines.

Figure 5.4: Measured temperature T_modof a module installed in Greece (black line) compared to the outputs of the King model (red line) and the Myers/Kempe model (green line). During the night and the early morning hours (as distinguished by the yellow line of the POA irradiance on the right axis) the module temperature can drop below the dew point (blue dashed curve).

The Myers/Kempe model gives a more realistic prediction of T_modduring such hours, while the King model is more accurate in the daylight hours when the sun shines.

For the same set of data, we then calculate the absolute error between each model and the measured temperature and plot it against the POA irradiance (Figure 5.5), confirming that the Myers/Kempe model is less accurate at high POA irradiance levels.

Figure 5.5: Absolute error with respect to the measured values of the two models used to estimate the module temperature T_mod. The high errors at null irradiance correspond to some outliers in the measured values, probably due to sensor malfunctions.

Module temperature

Based on the above considerations, we calculate the module temperature at each hour i as follows:

• T_mod(i ) = T_mod^Kempe(i ) if POA(i ) < 200 W/m²;

• T_mod(i ) = T_mod^King(i ) otherwise.