## 5 Conclusions  
Most equations and models of photovoltaics (PVs) are based on the assumption that such devices are flat. The classical models based on flat PV devices do not consider the possibility of the local variations of cosine losses in the active area of PV devices and the mismatching losses in flat devices caused by this variation. Another misleading aspect is that the aperture area may be the same as the active area of flat PV devices, but this is not true for curved PV devices. The fundamental formula of PV devices, (Output) = (Device Active Area) \(\times\) (Irradiance) \(\times\) (Power Conversion Efficiency), is suitable for flat PV devices but incorrect for curved PV devices. Moreover, we do not have clear definitions of the area of the curved PV devices, including whether the projected or total active area should be used. This is an issue that the international web meeting groups, consisting of experts and researchers from research institutes, testing laboratories, and the PV and automotive industries, have discussed. The global meeting group was upgraded to an official international project team (PT600) under the umbrella of the International Electrotechnical Commission (IEC) in April 2021 and is continuing discussions for the goal of fair and scientifically correct international standards in this field. The actual performance of nonplanar PV devices should be investigated and developed. In this study, outdoor monitoring was developed, and algorithms were validated based on vector computations. The measurement methods were also developed independently of this study by an international collaboration with testing laboratories for reproducible indoor test protocols. Note that reproducible tests were established for flat PV devices. Still, developing reproducible testing methods, including the additional testing equipment requirements, was challenging because most testing methods and instruments were designed for flat PV devices and did not work with sufficient reproducibility for curved PV devices. In parallel with the above activities, we developed two models (Figures 1 and 2). Both were based on differential geometry and were essentially the same. Still, the first one is more general and can be applied to the 3D movement of PV devices, such as an aircraft PV device (pitch, roll, and yaw rotations), but with more computation time. The second one is quick but can be applied to simple string configurations (all in series). It is limited to yaw movement and is suitable for vehicle applications. Also, note that the unusual behavior of the curved PV devices was enhanced on clear-sky days when the solar irradiance mainly consisted of direct and collimated sunlight, as anticipated. The developed models help us to understand the dramatic differences in the behaviors on clear-sky days from indoor-tested results. Conceptualization, K.A. ; methodology, K.A. and Y.O. ; software, K.A. ; validation, K.A. and Y.O. ; formal analysis, K.A. ; investigation, K.A. ; resources, K.A. and Y.O. ; data curation, K.A. ; writing--original draft preparation, K.A. ; writing--review and editing, K.A. ; visualization, K.A. ; supervision, K.N. ; project administration, K.N. ; funding acquisition, K.A. and K.N. All authors have read and agreed to the published version of the manuscript. **Funding:** This research was funded by the New Energy and Industrial Technology Development Organization (NEDO) of Japan (project number JPNP20015). **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** The data presented in this study are available on request from the corresponding author. **Acknowledgments:** Many scientists and testing engineers worldwide have performed standardization. Although not included in the author list, it is apparent that many other contributors have worked behind the scenes. The Ministry of Economy, Trade, and Industry (METI) of Japan were entrusted with the standardization of VIPVs.