# Application of Thermoelectric Generators for Low-Temperature-Gradient Energy Harvesting
## 4 Efficiency Determination of the Best Combination of TEG + DC/DC Converter  
This section discusses in detail the efficiency of the best combination of TEG + DC/DC converter, that is, TEG #1 + DC/DC converter #1. For this, the assembly shown in Figure 7 is analyzed, which corresponds to a realistic situation. The TEG #1 + DC/DC converter #1 combination is mounted on a stainless steel tubular hollow conductor with an inner diameter of 120 mm and a wall thickness of 0.4 mm. Using this configuration, the steady-state performance of TEG #1 + DC/DC converter # 1 is studied. To calculate the efficiency of the entire TEG #1 + DC/DC converter #1 system \(\eta_{TEG+DC/DC}\), the individual efficiencies of the TEG \(\eta_{TEG}\) and the DC/DC converter \(\eta_{DC/DC}\) are required. According to IEEE Std. 605 [41] describing the design of busbars in air insulated substations, indoors and under steady state conditions, the heat gain per unit length due tooule losses must compensate the terms of heat loss per unit length due to convective and radiative cooling as,  
\[I_{RMS}^{2}r_{ac}(T)=p_{c}+p_{r}\left[\mathrm{W/m}\right] \tag{8}\]  
where \(I_{RMS}\) (A) is the current through the busbar, \(r_{ac}(T)\left[\mathrm{\Omega/m}\right]\) is the ac resistance of the conductor per unit length at the operating temperature \(T\), and \(p_{c}\left[\mathrm{W/m}\right]\) and \(p_{r}\left[\mathrm{W/m}\right]\) are, respectively, the losses due to natural convection and radiation. The ac resistance per unit length of the conductor, \(r_{ac}\left[\mathrm{\Omega/m}\right]\), was measured according to the method described in [7; 13]. This method requires measuring the voltage drop \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Measured Values** \\ \hline Ambient temperature (\({}^{\circ}\)C) & 21.5 \\ Cold side temperature (\({}^{\circ}\)C) & 57.8 \\ Hot side temperature (\({}^{\circ}\)C) & 67.7 \\ Open circuit voltage (V) & 0.79 \\ Short-circuit current (mA) & 99.56 \\ Maximum power point voltage (V) & 0.40 \\ Maximum power point current (mA) & 50.39 \\ Resistance at the maximum power point (\(\mathrm{\Omega}\)) & 6.00 \\ Maximum power (mW) & 20.25 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parameters of the analyzed TEG module. Figure 7: Experimental setup to characterize the performance of TEG #1 + DC/DC converter #1 mounted on a tubular conductor. [V] between two points of the conductor surface separated by 1 m, the ac current \(I\) [A] flowing through the conductor, the phase shift \(\varphi\) [rad] between the voltage drop and the current, and the conductor temperature \(T\) [\({}^{\circ}\)C],  
\[r_{ac}(T)=\frac{\Delta V_{\text{1m}}}{I}\times\cos\varphi\left[\Omega/\text{m}\right] \tag{9}\]  
To calculate the efficiency of entire system, including the TEG and the DC/DC converter, \(\eta_{TEG+DC/DC}\), the individual efficiencies of the TEG, \(\eta_{TEG}\), and the DC/DC converter, \(\eta_{DC/DC}\), are needed. The efficiency of the TEG \(\eta_{TEG}\) can be calculated as the ratio between the electrical power generated by the TEG, \(P_{electric,TEG}\) [W], and the Joule heat generated by the conductor in the area of the TEG (80 mm \(\times\) 40 mm), \(P_{Joule,TEG-area}\) [W], as,  
\[\eta_{TEG}=\frac{P_{electric,TEG}}{P_{Joule,TEG-area}} \tag{10}\]  
\(P_{Joule,TEG-area}\) can be calculated as,  
\[P_{Joule,TEG-area}=P_{Joule,conductor}\times\frac{A_{TEG}}{A_{Conductor}}\ \ \ [\text{W}] \tag{11}\]  
where \(A_{TEG}\) [m\({}^{2}\)] and \(A_{Conductor}\) [m\({}^{2}\)] are the area of the outer surfaces of the TEG and conductor, respectively, while \(P_{Joule,conductor}\) [W] is the heat generated in the conductor. The efficiency of the DC/DC converter can be calculated as,  
\[\eta_{DC/DC}=\frac{V_{out}\times I_{out}}{V_{inp}\times I_{inp}}\ \ \ [-] \tag{12}\]  
where \(V_{out}\), \(I_{out}\), \(V_{inp}\), and \(I_{inp}\) are, respectively, the output and input voltages and currents of the DC/DC converter.