Three-dimensional mathematical modelling and dynamic analysis of freestanding triboelectric nanogenerators

Abstract Energy harvesting system based on triboelectric nanogenerators (TENGs) has aroused wide interest from many researchers since it integrates multiple disciplines together including electromagnetics, electric circuit theory, materials science and mechanical engineering. Accurate modeling of a TENG is an indispensable part for revealing the relationships and interactions among physical quantities from different areas. Here, a three-dimensional mathematical model of a contact-mode freestanding TENGs (CF-TENGs) is built with a combination of physical abstraction and geometry configuration, which makes it possible to dynamically analyze the variations of the field and circuit quantities. An accurate Norton’s equivalent circuit model that consists of a current source in parallel with a pure capacitive reactance is proposed. Based on this model the reason for identifying the displacement current as the driving force of TENGs is elucidated, and quantitatively determine the current flowing through the external load resistor and the internal equivalent capacitor. More importantly, a universal dynamic simulation model consisting of a quasi-electrostatic model and a circuit model for the TENG-based energy harvesting system is presented. The presented composite model exhibits an obvious advantage in terms of revealing the dynamic output of TENGs with arbitrary geometry and charge distribution. Finally, based on the characteristics of linearity and time-invariance of the CF-TENG, general optimization strategies are pinpointed, which allow us to accurately predict the maximum output efficiency (close to 82.5%).