Optimal working conditions for maximal thermoelectric generation via radiative cooling

Thermoelectric generation via radiative cooling holds promise as a renewable electricity source. However, the governing mechanisms have not been fully explained, and the optimal operating conditions are yet to be identified. To address this issue, detailed parametric analyses of the most basic, passive configuration are presented here, where the cold side of the thermoelectric generator is coupled to a radiative cooling surface and the hot side collects heat from the ambient surroundings. We note that the operation deviates significantly from the constant temperature conditions because the radiative cooling power under realistic conditions is not large enough to act as a cold reservoir. The system is thus considered as imperfectly coupled to the reservoirs with a finite thermal conductance. In this regime, the contributions of both electrical and thermal conduction within the thermoelectric generator, along with their interdependence, must be carefully treated to describe the steady-state behaviour. An analytical solution is derived, as an explicit function of system parameters such as the radiative cooling surface area, the degree of thermal insulation of the radiative cooling surface, and the heat transfer coefficient at the hot side. As a result, electrical and thermal impedance matching conditions are presented for the generation of maximum electrical power in terms of these parameters. Our findings serve as a design guide for renewable thermoelectric generation based on the temperature difference between the ambient and the coldness of the sky.