## 2 Materials and Methods
### Construction of Operation Mode Factor (OMF)  
The construction operational mode factor (OMF) was obtained by remodeling the thermal efficiency model as shown in Equation (1) to the thermal efficiency results in [13]. Joule heating is involved in the results. As the previous results were carried out outdoors with the wind loss effect due to wind convection, it was then added back to the system to become the without wind loss effect (ideal condition). Figure 2 shows the model analysis of the current PVT system: a simple solar energy balance during PVT-mode is shown in Figure 2a and its thermal simplification in Figure 2b. The analysis assumed that (1) the hysteresis effect was neglectable due to the system being in a steady state, (2) the surface temperature, \(T_{S}\) (\({}^{\circ}\)C) was consistent throughout the glass layer area, (3) the glass layer did not permeate the sun's heat, (4) the layer of the backside absorber was appropriately insulated, (5) the adhesive had excellent electrical insulation  
and thermal conduction [27], (6) the \(\tau\alpha\) was considered unchanged for T-mode and PVT-mode, and (7) the temperature of a silicon solar cell was constant along the direction perpendicular to the glass plate. For overviews, there are differences in addressing PV cells as a reference. [PERSON] [7] treated the PV cells as the absorber, and included the radiation effect between the glass plate and the other surface forming the flow passage and the convection effect between the surface and the collector fluid. As assumed, no heat transfer occurred via the PV cells. It may give lower heat transport from the fin to the tube to lower the efficiency. The thermal resistance reduces, while thermal conductivity increases, in the absorber. These increase the electrical and thermal conversion into usable heat and release it to the water fluid \(Q_{th}\). It is changed into electricity and channeled to the load \(Q_{e}\). The remaining losses leave the system (W) and never become absorbed by reflection \(Q_{ref}\) and by radiation \(Q_{rad}\), discharged to the air as convection loss \(Q_{conv}\). Figure 1: Previous outdoor experiment [13]: (a) Experiment setup, (b) PVT array \(2\times 2\), (c) PVT construction. Here,  
\[Q_{s}=Q_{pot}+Q_{l,tot} \tag{2}\]  
where \(Q_{pot}\) is the PVT solar conversion and \(Q_{l,tot}\) as the total losses. Here, \(Q_{pot}\) is the total solar conversion by the PV layer \(Q_{pv}\) and the thermal layer \(Q_{th}\), so  
\[Q_{pot}=Q_{th}+Q_{pv} \tag{3}\]  
In this analysis, the \(Q_{pv}\) generates both \(Q_{e}\) and \(Q_{th}\). \[Q_{pv}=Q_{e}+Q_{th} \tag{4}\]  
Both PVT and T-mode, the electrical-internal heat, \(Q_{ih}\), consequently enter the PVT system as the usable heat \(Q_{ih,th}\) or as the loss heat \(Q_{ih,l}\), so  
\[Q_{ih}=Q_{ih,th}+Q_{ih,l} \tag{5}\]  
Then, the total energy losses \(Q_{l,tot}\) is expressed as  
\[Q_{l,tot}=Q_{rad}+Q_{conv}+Q_{ref}+Q_{ih,l} \tag{6}\]  
Figure 2: Model analysis: (**a**) simple energy balance, (**b**) thermal simplification. Here, the energy balance for the PVT collector from the source of solar cell energy, with a size \(A_{c}\) of 1 m\({}^{2}\), can be expressed as follows:  
\[Q_{th}+Q_{e}=A_{c}I\tau\alpha \tag{7}\]  
From Figure 2, the PVT collector expresses heat balance at the silicon solar cell as follows:  
\[Q_{th}=Q_{u,th}+Q_{ih,th}+Q_{l,tot} \tag{8}\]  
where \(Q_{th}\) is the thermal energy absorbed by the surface of PVT collector \(A_{c}\) (m\({}^{2}\)), with the heat transfer coefficient from the surface to an absorber of PVT collector \(K_{SA}\) (W/m\({}^{2}\).C) and the temperature difference between the surface and fluid of PVT, \(T_{S}\) and \(T_{f}\) (\({}^{\circ}\)C), respectively. Here, in steady state, the absorber temperature \(T_{A}=T_{f}\).