Curve correction of vehicle-integrated photovoltaics using statistics on commercial car bodies

Typically, car roofs are curved, which means that vehicle-integrated photovoltaics (VIPVs) are also curved along the roof surface. The performance of the PV module is influenced by the local cosine loss and self-shadowing loss due to the curved surface. The ratio between the solar irradiances of curved and flat surfaces is defined as the curve correction factor, and it widely varies with the shape of the curved surface. When the curve correction factor is less than unity, the PV on a curved car roof performs worse than the PV on a flat plate. Understanding the typical range of the curve correction factor is important for the estimation of the energy generated by VIPV. We investigated the curved shapes of 100 lines of cars and 200 cases. The curved shapes were then used to extract eight nondimensional geometric parameters, and the distributions and correlations among the parameters were investigated. The parent population of the curved surfaces was estimated via a Monte Carlo simulation based on an analysis of the statistical characteristics. The distribution of curve correction factors for the car population was calculated via differential geometry weighted by the distribution of incident angles of sunlight (direct and diffused) affected by shading along the streets, which was obtained from 1 year of driving data for Miyazaki City, Japan. The curve correction factors were highly skewed, but the average value was 0.92. This means that VIPV requires a 10% boost in performance to compensate for the inherent loss due to the geometry of curved roofs.