Partial shading detection and hotspot prediction in photovoltaic systems based on numerical differentiation and integration of the P − V curves

Abstract Hotspot phenomenon is an expected consequence of long‐term partial shading condition (PSC), which results in early degradation and permanent damage of the shaded cells in the photovoltaic (PV) systems. Hence, partial shading detection and estimation of its intensity is a significant factor to predict the possibility of hotspotting process and its occurrence time for PV system protection. In this paper, two partial shading detection indices are introduced based on the extracted power‐voltage (P−V$P - V$) curves. The first P−V$P - V$ characteristic is related to the real shaded PV system and the second P−V$P - V$ curve is numerically obtained from the equivalent single‐diode circuit model. The proposed PSC detection indices are established according to the difference between the numerical differentiation and integration of the P−V$P - V$ curves from the real PV system and the virtual reference model. These techniques have the advantages to distinguish between temporary and permanent PSC. Moreover, it is possible to estimate the intensity of the shading level and predict the hotspot occurrence time, accordingly. The performance of these methods are confirmed using some simulations and an experimental setup. The results verify the capabilities of the methods for partial shading detection without the requirement of an extra physical cell/module as a reference model