Chaos-Theoretic Models for Nonlinear Dynamics in Renewable Energy Harvesting Systems

Abstract

Solar-piezoelectric hybrids, wind-driven oscillators and thermoelectric devices belong to renewable energy harvesting systems, and they are nonlinear inherently because of the complexity of the turbulence, stochastic environmental forces, vibrational dynamics and multi-physics coupling. These irregularities cannot be represented through the traditional linearized models and thus the correct prediction of the performance of the system under actual fluctuating conditions cannot be obtained. Here we introduce a detailed chaos-theoretic modeling approach to the study and prediction of the nonlinear behavior of renewable energy harvesting systems. The suggested approach along with mathematical uses of nonlinear dynamics, including the bifurcation theory, the Lyapunov exponent analysis, the Poincare mapping, and the phase space reconstruction, allows revealing the existence of the chaotic regimes that significantly influence the efficiency of the system, its stability, and long-term reliability. MATLAB /Simulink simulations of hybrid solar- piezoelectric harvesters and wind-driven oscillatory systems in situations with varying excitation frequencies and stochastic environmental perturbations represented by Lorenz chaotic attractors, were thoroughly detailed. The results lead to the fact that periodic-chaotic transitions during a bifurcation bring about significant changes in the amount of power harvested, with uncontrolled chaos incurring efficiency losses of up to about 12%. However, a mixture of chaos-based control schemes, such as delayed feedback and nonlinear redistribution of energy can diminish detrimental chaotic vibrations and apply broadband chaotic excitations to increase energy conversion. Comparing this model to the conventional linear models reveals that the above model enhances the energy that is captured by up to 17 percent in the conditions of fluctuation and intermittency which is clearly encouraging in the aspect of high variability and intermittency. Along with the performance advantages, the study also develops a roadmap to the design of resilient and adaptive renewable energy harvesters that employ chaos-aware modeling to forecast instability, optimization of control and robustness. The gained lessons suggest that it is necessary to adopt the chaos-theoretic methods in mathematical modeling of renewable energy systems, in order to add nonlinear dynamics to sensible engineering resolutions to sustainable energy production.