3D Solar Irradiance Model for Non-Uniform Shading Environments Using Shading (Aperture) Matrix Enhanced by Local Coordinate System

Abstract

Building-integrated photovoltaics (BIPVs) and vehicle-integrated photovoltaics (VIPVs) receive solar irradiance through non-uniform shading objects. Standard scalar calculations cannot accurately determine the solar irradiance of BIPV and VIPV systems. This study proposes a matrix model using an aperture matrix to accurately calculate the horizontal and vertical planes affected by non-uniform shading objects. This can be extended to the solar irradiance on a VIPV by applying a local coordinate system. The 3D model is validated by a simultaneous measurement of five orientations (roof and four sides, front, left, tail, and right) of solar irradiance on a car body. An accumulated logistic function can approximate the shading probability. Furthermore, the combined use of the 3D solar irradiance model is effective in assessing the energy performance of solar electric vehicles in various zones, including buildings, residential areas, and open spaces. Unlike standard solar energy systems, the energy yield of a VIPV is affected by the shading environment. This, in turn, is affected mainly by the location of vehicle travel or parking in the city rather than by the climate zones of the city.