# Measurement and Modeling of 3D Solar Irradiance for Vehicle-Integrated Photovoltaic
## 2 Model
### Angular Distribution Model  
The angular distribution of the solar irradiance is calculated by the weighted histogram of the angular distribution. The angular distribution model is crucial both to the validation of the 3D solar irradiance model around the car body and optimization design of the high-performance static concentrator module (CPV) on the car roof [2]. For example, a new type of static concentrators consists of an array of dielectric lenses [28], its optimization algorithm for VIPV [29], combination to high-efficiency on Si tandem solar cells enhanced by an innovative partial concentrator configuration [30], its prototype [31], and demonstration to VIPV application [32]. In case the high-efficiency multi-junction cells are used for VIPV, it is essential to consider the spectrum impact correctly of the cross effect between the spectrum and angular distribution of the solar irradiance [33]. For example, a detailed spectrum energy model for the tandem solar cell was developed at the University of Miyazaki and recently published [34]. The model, as mentioned above, was expanded to the design of the future high-efficiencysolar cell for VIPV application in the worst-case combination of atmospheric parameters [35] and realistic atmospheric parameters and measured spectrum [36]. The atmospheric parameters that impact performance of high-efficiency solar cells are identified using a statistical approach [37] and also to concentrator photovoltaic (CPV) [38] that is recently considered as a right candidate [39], fine-tuning of the bandgap design for VIPV application based-on the model as mentioned above [40], prediction of the energy yield with consideration of the spectrum and angular issues [41], and the rating method of the VIPV with consideration of above issues [42]. The detailed information of the high-efficiency PV modules used for the validation of the model is found in the article by [PERSON] [43]. The angular distribution model is also useful for this purpose, but it is essential to note that it is deeply coupled with the spectrum variation that is not covered by this article. For the application of the angular model to the spectrum-sensitive tandem cells or CPV, it is indispensable to develop the 3D solar irradiation model further.  
The meteorological data and irradiance data are given by the solar irradiance database, specifically, families of MEteorological Test data for PhotoVoltaic system (METPV), specifically, METPV-3 [44], METPV-11 [45], and METPV-ASIA [46]. It provides both direct and diffused irradiance every hour. The discrete sampling also makes the distribution shaggy, and to make it continuous, the event time is shifted in the range of plus or minus 30 min, also given by the random number under the ranged uniform distribution. The variance of the reflectance by the road and buildings (or mountains, etc.) also fluctuates the direction of the leading solar beam to the car. The modulation of the reflectance is also given by the random number, precisely, 0.10 to 0.40 for vertical reflection (building or trees), and 0.00 to 0.14 for the horizontal reflection (road).  
However, the measurement system defined in Figure 3 does not have enough angular resolution. Instead, the measurement of the incident angle of the main beam is done by the ratio of the vertical irradiance (car roof) and the highest two irradiances of the car side, specifically, in Equation (10). The validation of the model in the angular distribution in this article is done by comparison of the weighted histogram of the main beam of the solar irradiance using Equation (10).