Geometry optimization of two-stage thermoelectric generators using simplified conjugate-gradient method

Thermoelectric devices can convert thermal energy directly into electrical energy. The aim of this study was to develop an approach for integrating computer-aided analysis with an optimization method that could be applied to the design and optimization of thermoelectric generators. The optimization framework consisted of a model generator, a direct solver, and a numerical optimizer. The simplified conjugate-gradient method (SCGM) was used to build the optimizer, and the general-purpose finite-element code was used for the direct solver and model generator. This approach was applied to the multi-objective and multi-parameter optimization of geometric thermoelectric generators to design an optimal structure for both a two-stage bismuth-telluride (BiTe)-based and skutterudite-based thermoelectric generator (TEG) module. The leg length and the ratio between the cross-sectional areas (i.e., footprint) of the semiconductor columns and the TEG module were found to significantly affect the TEG performance; hence, all were incorporated into the present optimization study. Multi-objective optimization was used to realize a design that properly balanced the power output and conversion efficiency so that both improved simultaneously.