## 2 Materials and Methods
The P and N elements incorporated in this module offer excellent heat transfer capability in a 40 \(\times\) 40 mm configuration. According to the manufacturers, with the usual temperatures in PVTs, some 2W could be expected as a maximum, with a voltage match of 1.0 V and a current match of 2 A (internal resistance = 0.5 Ohm)  
The integration of TEG modules inside the PVT panel must be made that the TEG sides are set between two sources of different temperatures. In this way, electricity can be produced. The two selected heat sources are mass inlet flow as the cold side and outlet mass flow as the hot side of the thermoelectrical modules. The hot side of the TEG must have excellent contact with the heat sources, the outlet collector pipe of the PVT panel. This pipe is inside the panel between the absorber and isolation layer. It is the pipe where hot water production is collected before leaving the panel and entering into the water tank. The cold side of the TEG module must be in thermal contact and compressed against a heat exchanger in order to dissipate heat from this surface. With the increase of the temperature gradient between the TEG sides, the electric production will be more significant. In a conventional PVT panel, inlet and outlet pipes are distanced. To a successful integration of the thermoelectrical modules in the hybrid panel, a modification in the inlet pipe has been made. The inlet pipe has been derivated, and before the water enters the panels, water flows inside a pipe set at the back of the panel. This part is where TEGs are integrated. Copper laminas are employed between TEGs and pipes to maximize the heat exchanger and the thermal contact. Furthermore, clamping plates were installed for a consistent subjection between TEGs modules and copper fins. The 19 TEG modules have been connected electrically in series. The positive pole is located on the side of the hybrid panel, and the negative pole is set on the opposite side. Solar energy (\(E_{s}\)) is the energy input in the studied PVT with integrated TEG modules system, and it is stated according to  
\[E_{s}=I\;*\;A_{C} \tag{1}\]  
where \(I\) is solar irradiance in W/m\({}^{2}\) and \(A_{C}\) is the gross area of working PVT collectors measured in m\({}^{2}\). Furthermore, the useful thermal energy production of PVT collectors (\(Q_{PVT}\)) is the result of the product between the solar energy that comes from the sun and the thermal performance of the PVT ( \(\eta_{th\_PVT}\)) that depends on the model of the panel. \[Q_{PVT}=\;\eta_{th\_PVT}*Q_{s} \tag{2}\]  
\[\eta_{th\_PVT}=\;\eta_{0}-\;a_{1}\;*\;G\;-\;a_{2}\;*\;G\;*\;(T_{m}\;-\;T_{amb}) \tag{3}\]  
where \(\eta_{th\_PVT}\)[44] represents the solar thermal performance of the PVT panel, \(\eta_{0}\) is the optical efficiency of the solar hybrid collector, \(a_{1}\) is the heat loss coefficient in W/m\({}^{2}\)K and \(a_{2}\) is the temperature dependence of thermal heat loss coefficient in W/m\({}^{2}\)K\({}^{2}\). These parameters are provided by the manufacturer of PVTs. Temperatures are given in \({}^{\circ}\)C. \(T_{m}\) is the average temperature of the PVT panels, and it is defined by the average between the inlet (\(T_{in}\)) and outlet (\(T_{out}\)) temperatures of the working fluid. \(T_{amb}\) is ambient temperature, and G can be calculated as  
\[G\;=\;(T_{m}\;-\;T_{amb})/I \tag{4}\]  
where \(I\) represents global solar irradiance. The electrical production of a conventional PVT is calculated as  
\[W_{PVT}=\;\frac{P_{n}}{1000}\;*\;[1-\gamma\;*\;(T_{cell}-25)] \tag{5}\]  
where \(P_{n}\) is peak power of the module in \(W\), \(\gamma\) is the temperature coefficient losses given by the manufacturer and \(T_{cell}\) is the cell temperature measured in \({}^{\circ}\)C. In photovoltaic-thermal panels, \(T_{cell}\) can be assumed equal as \(T_{m}\). In this paper, the integration of TEG modules on a PVT panel is studied. Therefore, the electrical efficiency of TEGs must be considered as well.