Non-linear continuous analytical model for performance degradation of photovoltaic module arrays as a function of exposure time

The performance of photovoltaic (PV) module arrays versus time is currently modeled by using linear functions of time having different slopes in consecutive time intervals. Slopes are denoted as degradation rates and used to express array-performance degradation. Since degradation rates are determined by using measured data, this approach does not allow modeling array performance in time intervals, where measurements are not available. Moreover, it does not allow distinguishing the influence of non-linear degradation modes on array degradation. We present a continuous non-linear approach to model array performance at any time without using degradation rates. Array-performance degradation is expressed as a product of three continuous non-linear functions of time, two of which simulate three sets of degradation modes reported in the literature and the third simulates degradation modes affecting module-junction boxes. This allows analyzing the influence of different degradation factors. Data of efficiency versus time of six PV-arrays are fitted. In one of the arrays, the non-linear model allows calculating degradation rates to be used in the aforementioned discontinuous linear model. The lifetime of arrays is calculated. Lifetime is determined by module failure in two of the studied arrays with lifetime of 29.87 and 38.29 years and module discoloration in the remaining ones having lifetime of 31.9, 41.31, 49.35, and 58.96 years. In one of the arrays, light-induced efficiency degradation of 2.8 % after 72 hours of exposure to sunlight is detected. The performance ratio (PR) of the arrays is calculated. A possible reverse dependence of PR on two model parameters is observed. Since it uses degradation curves instead of degradation rates, the presented model appears to meet the need reported in the literature to adopt array-degradation models based on degradation curves to apply more sophisticated economic models.