## 2 Methods
### Curve-Shape Measurements and Indoor Tests  
To identify the unusual behavior of the curved PV modules and validate the computational model, we conducted a series of measurements using a commercial curved PV module and the solar roof of the Toyota Prius 40 series (Toyota, Japan). Because the optical and performance characteristics of the curved module are sensitive to angle errors and because we considered it essential to set the module at equal angles, we prepared a module carrier (holding fixture). The module was set throughout the manufacturing process, storage, and transportation (Figure 3). Curved PV devices should be held on a stable contact plane to prevent deflection, gravity distortion, and stress from the holders. The holding fixture did not shade the solar cells in the module. Figure 2: The simplified algorithm flowchart for computing the power output of a curved PV module [(69)]. The frame was attached externally to prevent deflection and deformation of the curved PV devices and damage caused by dropping or handling. An example is shown in Figure 3. The frame should satisfy the following conditions for holding curved PV modules:  
* The reference bottom surface (bracket or frame bottom surface) is flat across the bottom. As a criterion for assessment, it should be placed on a surface plate that is larger than the frame, and a force should be applied to at least three corners to ensure adequate tightness. The permissible deflection is 10 mm using a 100 N load force. * The frame, bracket, and enveloping holder surfaces are outside the envelope surface of the module outline. * At least three holders are provided to hold the modules. * The holder's height is lower than that of the neighboring cells. * To prevent module deformation (twisting) during fastening, all the holders have an angle-adjustment function to follow the variations in the curved surface shape (purple plates on the four corners and a center point of a side in Figure 3). * The central tilt angle for the angle adjustment of the holder (Figure 3) is designed based on the aspects of the module. Specifically, the module is placed on a horizontal surface plate (there is no need to compensate for deflection owing to its weight). The angle of inclination of the edge of the module at the point where it is fixed with a holder is measured using a protractor or a small inclinometer. The center angle of the holder (14\({}^{\circ}\) in Figure 3) is determined according to the estimated value. * To prevent the glass cover from cracking during fastening, the fastening part is sandwiched between 3 mm thick urethane plates. Furthermore, the fastening torque is controlled (e.g., 2-M4 fastening torque of 1 Nm). * The surface viewed from the light-receiving surface is matte black in color. Any surface treatment method such as black alumite treatment, black dyeing, black chromate treatment, black nickel plating, or matte painting can be used. The surfaces concealed behind the module are not black. Non-black surfaces such as screw heads and machined surfaces may remain if these are negligible in terms of the projected area of the frame. Figure 3: Carrier for the curved PV module. It was designed to keep angles equal during the following measurement steps: (1) coordinate measurements, (2) indoor performance tests, and (3) outdoor performance tests. * The module is attached to a rail for convenience. For example, in a series of set operations such as removing the upper holding portion of the holder, placing the module, adjusting the position, and tightening the upper holding portion, the module does not slip or need to be held temporarily. * Specifically, the frame is placed on the surface plate, the top is removed, a part of the holder is pressed, the module is enabled to stand, and the distance from the plate surface to the lower end of the module (mechanical contact plane) is set as an equal distance. The module is fine-tuned by shifting it in the \(x\) and \(y\) directions.