Power computation for the triboelectric nanogenerator

TL;DR

This paper provides a mathematical analysis of power generation in contact-mode triboelectric nanogenerators, deriving formulas for mean power, current waveforms, and harmonic distribution, validated by numerical comparisons.

Contribution

It introduces a differential equation model with periodic coefficients to analyze the power output of triboelectric nanogenerators, offering new analytical and computational methods.

Findings

Derived approximate mean power formulas

Analyzed current waveforms and harmonic distribution

Validated analysis with numerical simulations

Abstract

We consider, from a mathematical perspective, the power generated by a contact-mode triboelectric nanogenerator, an energy harvesting device that has been well studied recently. We encapsulate the behaviour of the device in a differential equation, which although linear and of first order, has periodic coefficients, leading to some interesting mathematical problems. In studying these, we derive approximate forms for the mean power generated and the current waveforms, and describe a procedure for computing the Fourier coefficients for the current, enabling us to show how the power is distributed over the harmonics. Comparisons with accurate numerics validate our analysis.