Mathematical Modeling Application in Energy Conversion and Energy Storage

Abstract

This article reviews mathematical modeling applications in energy conversion and energy storage. In the first section, the primary emphasis is on energy conversion, mainly focusing on solar cells and fuel cells' structure and methods of modeling and prediction of their performances. Modeling of Perovskite solar cell modules is one of the major components responsible for the proper functioning of PV systems. Modeling provides ways to understand PV modules' current, voltage, and power relationships. However, the estimation of models is affected by various intrinsic and extrinsic factors, which ultimately influence current and voltage behavior. Therefore, perfect modeling is essential to estimate the performance of PV modules in different environmental conditions. In the second section, the major emphasis is on energy storage focuses on modeling the structure and performance of batteries and supercapacitors. Supercapacitors and batteries are electrochemical energy storage devices that can be charged in a matter of seconds to minutes. This efficient storage of energy is based on the adsorption of an electrolyte to a high-surface-area electrode. These marvelous properties led to extensive concerted research into the nature of the storage mechanism, electrode design, and especially new optimized materials. Mathematical modeling has become an effective method in energy storage science, contributing to the development and optimization of electric generators and energy storage devices. It is thus a suitable method for analyzing a battery and supercapacitor’s performance and investigating its mechanism. The simulation is performed in two steps because of the multi-physics nature of energy conversion and storage systems. In the first step, the semiconductor equations are applied, and the electrical response of the electrochemical device is modeled. The second step calculates the thermal equations, while the heat generated in the first step is used as the heat source.