# Application of Thermoelectric Generators for Low-Temperature-Gradient Energy Harvesting
## 4 Efficiency Determination of the Best Combination of TEG + DC/DC Converter
### Steady State Performance of TEG #1  
Using the setup shown in Figure 7, a second experiment was carried out on the 120 mm diameter tubular conductor to characterize the steady state performance of TEG #1. Five levels of current (136 A, 169 A, 194 A, 226 A and 254 A) were injected to heat the tubular conductor to steady state.  
Figure 8a shows the evolution of the temperature with time of the hot side and the cold sides of TEG #1, while Figure 8b shows the evolution with time of the output electrical power of TEG #1 and DC/DC converter #1.  
To determine the \(I_{RMS}^{2}r_{ac}(T)\) Joule heating in (8), \(r_{ac}\) as a function of temperature is required. For this purpose, an offline experiment was carried out, measuring the voltage drop, the current flowing through the tubular conductor, the conductor temperature and \(\cos\varphi\). The results obtained are summarized in Table 5.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**T** (\({}^{\circ}\)**C) & \(\Delta V_{\text{1m}}\) (**V\({}_{\text{RMS}}\)**) & **Current** (**A\({}_{\text{RMS}}\)**) & **cos\(\varphi\)** & \(r_{ac}\) (**uT\(\Omega\)/m**) \\ \hline
25 & 1.4735 & 280 & 0.9997 & 5267 \\
30 & 1.4845 & 279 & 0.9997 & 5319 \\
35 & 1.4913 & 277 & 0.9997 & 5378 \\
40 & 1.5085 & 277 & 0.9997 & 5441 \\
45 & 1.5148 & 275 & 0.9997 & 5501 \\
50 & 1.5200 & 274 & 0.9997 & 5545 \\
55 & 1.5290 & 273 & 0.9997 & 5591 \\
60 & 1.5313 & 271 & 0.9997 & 5635 \\
65 & 1.5353 & 271 & 0.9997 & 5657 \\ \hline \end{tabular}
\end{table}
Table 5: Dependence of \(r_{ac}\) with the temperature of the tubular conductor.  
Table 6 summarizes the results obtained with the entire system, including the tubular bus bar, TEG #1 and DC/DC converter #1. It shows that when current applied is, for example, \(I\) = 254 A\({}_{rms}\), the steady state temperature difference between the hot side of TEG #1 and the ambient is \(\Delta T_{Hot\_Ambient}\) = 43.7 \({}^{\circ}\)C, while the temperature difference between the hot and cold sides of TEG #1 is \(\Delta T_{Hot\_Cold}\) = 5.67 \({}^{\circ}\)C. In this steady-state condition, the output power of TEG #1 and DC/DC converter#1 are, respectively, \(P_{electric\_TEG}\) = 11.2 mW and \(P_{DC/DC}\)= 0.84 mW. They correspond to efficiencies of TEG #1, \(\eta_{TEG}\), and TEG#1 + DC/DC #1, \(\eta_{TEG+DC/DC}\), of 0.36% and 0.027%, respectively. Although the overall efficiency is quite low, the output power of the whole system, which is in the order of 0.84 mW for \(\Delta T_{Hot\_Cold}\) = 5.67 \({}^{\circ}\)C, is enough to supply low power WSs. According to a previous study [12], and supposing a communication cycle of 5 s using a Bluetooth low energy module and three sensors (temperature, current and voltage), on average, each communication cycle consumes an energy of 0.16 J. Therefore, according to Table 6, when \(\Delta T\) = 5.05 \({}^{\circ}\)C, \(P_{DC/DC}\) = 0.66 mW, so in 1 h, about 2.4 J are harvested, so, this energy is enough to supply low power WSs.  
Figure 8: (**a**) Hot side, heat sink and ambient temperatures measured by T-type thermocouples. (**b**) Electrical output power of TEG and DC/DC converter, and temperature difference between hot side and ambient.  
for 10-15 communication cycles per hour. This is not a problem in many applications, because WS typically operate in an intermittent on-off pattern [42].