# Measurement and Modeling of 3D Solar Irradiance for Vehicle-Integrated Photovoltaic
## 1 Introduction  
Let us think about a solar engine car, considering the recent development and success of EVs (electric vehicles) and PHVs (plug-in hybrid vehicles). Photovoltaic (PV) technologies will be game-changing in the automobile industry. It may be a dream now, but it is worth challenging [1].  
The case study of the photovoltaic (PV) driven cars was conducted both by car manufacturers [2] and a think tank [3], and both reached the same conclusion in 2017. About 70% of a vehicle can run exclusively by solar energy on a different calculation basis [2, 3]. The calculation base is published, namely: projected area of PV is 3.23 m\({}^{2}\), temperature loss is 9%, Maximum power point tracking (MPPT) loss is 5%, DC-to-DC converter (DC is direct current) loss is 10%, battery charging and discharging loss is 5%, Electronic Control Unit (ECU) loss is 0.12 kWh/day, mileage is 12.5 km/kWh for electric vehicles (EVs), 10 km/kWh for plug-in hybrid vehicles (PHVs), and the battery size is 40 kWh to EVs and 10 kWh to PHVs. Then, the requirement of the car roof PV is 1 kW. As a result, 70% of cars (runs less than 30 km/day) are expected to run by solar energy [2, 3, 4]. When we multiply 71 million vehicles (annual sales in 2017), the expected sales are 50 GW/year (50,000,000 kW/year) [5]. The above calculations assume that the solar cells are stabilized with no or negligible degradation. However, some solar cells degrade with time, and this should be considered, in case such type of solar cells such as, amorphous Si [6], perovskite [7], crystalline Si [8], and Si module [9] are used. The photovoltaic is also useful for auxiliary powers and range-extension of other low-carbon energies, like hybrid vehicles [10], electric vehicles [11], as well as researches on innovation of the usage of solar energy [12] like, auxiliary power [13], charging [14], and support for fuel cells [15].  
The efficiency and power rating, as well as energy prediction under the curved surface affected by the shading objects, are critical. For example, the car roof is three-dimensionally curved, and its curvature may induce power loss by increased cosine loss and self-shading loss [1]. This activity is mainly done by an international web-meeting which targets standardization of the vehicle-integrated photovoltaic and regularly publishes almost every half-year with the progress of arguments [16; 17; 18; 19; 20]. The irradiance and temperature of the car roof are different from that of the roof top or the ground mounting systems [16]. The expected energy yield should be different.  
Car roofs are often shaded, resulting in significant losses by string mismatching [1]. It may be improved by the introduction of a power distribution circuit for compensating the mismatch in view of dynamic shading [21], alignment issue [22], and sampling interval [23]. However, due to the limited area and allowed thickness on the car roof, the most practical approach increases the number of series-connected strings [24].  
Another aspect is that the car roof PV is not in the installation of the standard slope angle and orientation. The orientation of the car roof changes with time without correlation to the sun direction. Surrounding buildings and other objects (trees and signals) often shade PV panels, and the variety of the curved shapes has a complicated impact. Such interaction needs to be taken into account [1].  
The development of meaningful testing and modeling methods is done by an international group using the web-meeting mentioned above [16; 17; 18; 19; 20]. The three dimensional (3D) model of photovoltaic power generation developed initially in the car roof PV, namely VIPV (vehicle integrated photovoltaic), can be extended to VIPV applications with curved PV using a flexible one.  
This article covers the modeling and measurement of the solar irradiance of the car body for accurate, meaningful, and non-biased estimation of the energy yield of automobile mounting PV modules.