A simplified mathematical model for power output predicting of Building Integrated Photovoltaic under partial shading conditions

•Relationship of shaded proportion with photocurrent and series resistor is studied.•A simplified mathematical model for power output predicting is proposed.•Electrical performance for shaded photovoltaic module is simulated.•More power output when the shadow is parallel with long edges than short edges.•Solutions to maximize output power of Building Integrated Photovoltaic is analyzed. Shadow will make power output loss for Building Integrated Photovoltaic system. Power output predicting of Building Integrated Photovoltaic is always complicated due to multi-parameters, especially under partial shading conditions. In this paper, effects of partial shadow on the photocurrent and series resistor is analyzed, relationship of shaded cell area proportion with photocurrent and series resistor is obtained respectively, and based on this, a simplified mathematical model to describe the relationship between shaded cell area proportion and current-voltage, power-voltage characteristics of a photovoltaic module under partial shading conditions is proposed and verified by experiments. Electrical performance of the photovoltaic module under different shading scenarios is predicted using the simplified mathematical model, and the predicted results have a high consistency with experiments using the monocrystalline silicon photovoltaic module. The results show that under same shaded area proportion, the shadow distributing in parallel with the short edge, which makes photovoltaic modules power output 3 W/m2 under 10% shaded area, has much more negative effects than distributing in parallel with the long edge. The power output of a photovoltaic string protected by one bypass diode depends on the largest shaded cell area proportion, when the largest shaded cell area proportion is around 45%, the photovoltaic string has no contribution to power output of the whole photovoltaic module. Therefore, in order to minimize the influence of shadow on the power output of a photovoltaic module, for Building Integrated Photovoltaic system meeting inevitable shadow with regular shape, the photovoltaic module should be arranged to make the shadow distributed uniformly on the cells protected with one bypass diode; but for Building Integrated Photovoltaic system meeting inevitable shadow with irregular shape, the module of whom every piece of cells parallels a diode is recommended.