Electrical and Thermal Load Matching of Thermoelectric Power Generation Systems

Abstract

Thermoelectric power generation systems operate by converting temperature differences directly into electricity. Such systems usually contain a heat source, a thermoelectric generation module (TEG), a heat sink, thermal interface materials, and an electrical load. The equations describing the heat flow and power generation at the electric load are coupled thermoelectric equations that mix the electrical and thermal resistances of different parts of the system. The conditions of maximum power generation require careful analysis of electrical and thermal load matching. We examine the applicability of commonly used electrical load matching conditions (Duham et al. Adv. Heat Transfer 51:299, 2019, Baranowski et al. 115: 126102, 2014, Apertet et al. 97: 28001, 2012, Yazawa and Shakouri 111: 024509, 2012, Moser et al.: 41: 1653, 2012, McCarty 42:1504, 2013, Gomez et al. 113: 174908, 2013, Freunek et al. 38: 1214, 2009, Shakouri (Proceedings of the IEEE, (2006), Angrist (Direct energy conversion 1976)) (1)$R_{load}=R_{el,TEG}$, (2)$R_{load} =R_{el,TEG} \sqrt{1+Z T_{avg}}$ and thermal load matching condition (3)$R_{th,TEG}=R_{th,external}\sqrt{1+Z T_{avg}}$. We find condition (1) is only applicable to the case when the thermal resistances external to the TEG are negligible. For most common applications, the external thermal resistances of the heat source and heat sink are fixed, and the goal is to find the matching thermal resistance of the TEG and the matching electrical load resistance that maximize the power generation. We present experimental results to demonstrate that the temperature difference across the TEG changes in the presence of an electrical load. The load matching conditions are complicated functions of the relevant parameters. In cases of practical interest, where either the heat sink or the heat source is fixed at near room temperature, we find condition (2) to be a good approximation for temperature differences up to about 100 K, but with the caveat that it is only valid when the system is thermally matched. When the system is not thermally matched, condition (2) is no longer valid. We find condition (3) to be a good approximation only for small temperature differences(<20K).