The energy yield of vehicle-integrated photovoltaics (VIPV) differs from that of standard photovoltaics (PV). It is mainly by the difference of the solar irradiance onto the car roof and car bodies as well as its curved shape. Both meaningful and practical modeling and measurement of solar irradiance for VIPV need to be established, rather than the extension of the current technologies. The solar irradiance is modeled by a random distribution of shading objects and car orientation with the correction of the curved surface of the PV modules. The measurement of the solar irradiance onto the car roof and car body is done using five pyranometers in five local axes on the car for one year. The measured dynamic solar irradiance onto the car body and car roof is used for validation of the solar irradiance model in the car.

For modeling the energy generation of three-dimensional car roof photovoltaic (PV) panels, it is essential to define a scientifically accurate method to model the amount of solar irradiance received by the panel. Additionally, the average annual irradiance incident on car roofs must be evaluated, because the PV module is often shaded during driving and when parked. The curve-correction factor, which is a unique value depending on the three-dimensional curved shape of the PV module, is defined in this paper. The curve-correction factor was calculated using a ray-trace simulator. It was found that the shape of the curved surface affected the curve-correction factor. The ratio of the projection area to the curved surface area of most car roofs is 0.85–0.95, and the annual curve-correction factor lies between 0.70 and 0.90. The annual irradiance incident on car roofs was evaluated using a mobile multipyranometer array system for one year (September 2017–August 2018). It is estimated that the effective annual solar radiation for curved PV modules is 2.53–3.52 kWh m⁻²/day.

In this article, we measured and estimated the outputs of car-mounted PV panels under actual driving conditions and different effective shading angles. On a sunny day, the performance ratio (PR) decreased to 0.99, despite the decrease in module temperature caused by the increased wind speed when driving. The PR decreased because of the effect of partial shading over the PV module. Public infrastructure could have led to dynamic partial shading passing across the PV module at high speeds. Furthermore, the effective shading angle being close to the sun's altitude could also have led to static partial shading. In contrast, on an overcast day the PR value was almost the same ($>$1) under both driving and parking conditions; this was because of the low module temperature and the spectrum effect.

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.