A Kelly Criterion-Based Optimal Approach for Renewable Energy Integration in Energy Systems to Maximize Total Returns

Abstract

While renewable energy integration is essential for sustainable modern energy systems and might provide higher overall returns, its variability, insufficient infrastructure, and intermittency lead to profit uncertainty, in contrast to stable but polluting and depletable conventional sources. Therefore, a profit-maximizing energy system should balance conventional energy storage and renewable investment. This paper reviews a series of optimization models for renewable energy integration in energy systems. Subsequently, a mathematical framework based on the Kelly Criterion is proposed to quantify the optimal allocation of renewable energy investments and derive specific results. Treating conventional energy as stable assets and renewables as risky assets, the framework identifies optimal capital distribution under fluctuating returns. Furthermore, by integrating the fractional Kelly criterion into the framework to adjust the original Kelly fraction, this method can address the uncertainty inherent in the return values of renewable energy investments to a certain extent. Finally, this study presents the optimal results derived from the proposed framework through case studies based on energy system data from existing reports and essays and then draws conclusions and suggests directions for future research.