Simulation of large photovoltaic arrays

Large photovoltaic arrays are becoming common as the world moves to replace fossil-fuelled electricity generators. As the array size and project cost increase, it becomes increasingly important to know accurately what the array's performance will be before it is built. Large arrays inevitably contain modules with a spread of performance characteristics such as short-circuit current and open-circuit voltage, and suffer from temperature differences between modules. In this first study of these problems, a model has been developed that accurately predicts the behaviour of a photovoltaic array subject to variability between modules and inhomogeneity of cell temperature across the array. The model was applied to a real rooftop array consisting of 912 modules (298 kW nominal peak power). Based on measured string currents, the predicted average string temperature was compared the temperature measured by a radiometric survey using a drone-mounted IR camera and matched very well. The five-parameter model of cell characteristics was fitted to manufacturer's data, with highest weighting given to the region around the maximum-power point (MPP) where a real array should operate via active MPP tracking. The model was used to explore separately the effects of a spread in module characteristics arising in the manufacturing process and of temperature inhomogeneity across the array. The current in each module of a string was constrained to be the same, and the voltage of every parallel-connected string was also constrained to be the same. These constraints lead to greater power loss than is predicted based on an average module at an average temperature. Compared to a hypothetical array assembled from identical average modules at the same average temperature, variability caused a loss of power of about 2%, depending on the detailed form of the distribution function chosen to represent the spread of characteristics in the manufacturer's tolerance band. As a rule of thumb, de-rating the maximum power to the lower end of the manufacturer's tolerance band is recommended to account for module variability during the design phase. The effect of temperature inhomogeneity is more serious, because temperature affects V-oc strongly, causing parallel-connected strings to be pulled away from their ideal operating points to obey the constraint of equal voltage. A modest 10 degrees C temperature gradient across the studied array was predicted to cause about a 4% loss of power at the MPP. Much higher real temperature differences could be expected in summer and were observed. The study confirmed that temperature inhomogeneity poses a serious design problem for large arrays, requiring careful thermal design to achieve not only acceptably low average array temperature, but also the least possible temperature spread.