Optimization and comparison of two-stage thermoelectric generators considering the influence of temperature variation on materials for waste heat utilization

Abstract

Thermoelectricity technology, as a kind of cost-effective and pollution-free power generation solution, is often used for waste heat recovery and utilization. In this paper, the temperature distribution of a Two-stage Thermoelectric Generator (TTEG) under constant temperature conditions has been studied using a one-dimensional heat conduction model. Moreover, by combining the obtained temperature distribution with the three-dimensional size of TTEG, a calculation formula of resistance and voltage was developed based on the calculus method. When the sum of cross-sectional areas of all the PN-type thermoelectric arms respectively in high- and low-temperature layers is constant, the optimal ratio between cross-sectional areas of a single PN-thermoelectric arm respectively in high- and low-temperature layers can be calculated using the proposed formula in this study to achieve the maximum output power. Results also showed the relationship between the heights of PN-type thermoelectric arms and the temperature distributions in high- and low-temperature layers. Using PbTe as the medium temperature thermoelectric material and Bi ${}_2$ Te ${}_3$ as the low temperature thermoelectric material, a case study was conducted on the PN-type thermoelectrics with the same total height and the same total cross-sectional area. The theoretical calculation results showed that the bigger of maximum output power between the two-stage thermoelectric generator and that of the Segmented Thermoelectric Generator (STEG) is related to the hot and cold end temperature.