Statistical analysis of back surface vs. cell temperatures of c-Si modules using measurement error models

The thermal characteristics of photovoltaic (PV) modules have a significant impact on the performance of PV systems. Numerous models have been proposed to estimate the module operating temperature for predicting energy production. King et. al. [1] pointed out the uncertainty associated with thermal models. Direct measurement of module temperatures, the paper argues, can improve the accuracy of performance models for continuously predicting expected system performance. The accuracy of the direct measurement is equally critical. The back surface temperature is often measured, and then corrected to cell temperature by adding a correction factor. There is no standard guideline for determining the correction factor. As a result, module temperatures may vary from one reporting entity to another, with serious effect on manufacturer's the bottom line. As an example, the nominal operating cell temperature (NOCT) value is used in various incentive programs, including that of the California Energy Commission (CEC). A difference of 2°C could lead to a huge loss of revenues. In this paper, we used a statistical procedure to (1) examine the back-to-cell temperature correction for crystalline silicon modules at a reference irradiance level of 1 W/m², and (2) derive the relationship between the temperature difference and the irradiance. In doing so, we obtain a confidence bound for the correction factor, and quantify the impact on the NOCT value.