A novel mathematical optimization method to obtain the maximum-power electrical configuration of thermoelectric generators for energy harvesting

Waste thermal energy recovery with thermoelectric generators has been widely studied as a method to make systems that produce hot exhaust gases, such as aircrafts, ground vehicles and factories, more sustainable. In this type of applications, the mismatch in hot and cold side temperatures of thermoelectric modules (TEMs) creates a mismatch in the electrical output. For each situation, there is a certain electrical interconnection between the modules that gives the maximum global power output. Three optimization models to find what is the best way of connecting the TEMs without a trial-and-error process, as usually done in previous literature, based on mathematical programming are proposed: single branch of series-connected TEMs, multiple parallel-connected branches of series-connected TEMs, and multiple groups of independent series-connected TEMs. The main novel contributions of this paper are: i) a mathematical optimization approach that provides how to connect the thermoelectric modules one by one, ii) the application of the above-mentioned method in a common case study: an automotive thermoelectric generator, iii) information about how the optimal connection between modules changes if the heat source changes its operation iv) a method for selecting a fixed optimal connection even when the heat source operation changes, e.g. different operation modes in a thermal engine, based on introducing weighting parameters in the optimization mathematical model. The optimization approach followed here is novel and has not been applied before to thermoelectric generators.