Optimal Sizing of Hybrid Renewable Energy System Using Two-Stage Stochastic Programming

Stochastic programming has become increasingly vital in energy applications, especially in the context of the growing need for renewable energy solutions. This paper presents a significant advancement in this field by introducing an efficient and robust algorithm for optimally sizing hybrid renewable energy systems. Utilizing a two-stage stochastic programming approach, the proposed algorithm addresses the challenges posed by the unpredictability of renewable energy sources. The proposed solution leverages the three-block alternating direction method of multipliers (ADMM), a cutting-edge technique that facilitates parallel computation and enhances computational efficiency. The distinctiveness of this method lies in its ability to solve complex stochastic optimization problems without compromising the mathematical integrity of the model. This is achieved by applying first-order optimality conditions, ensuring both robustness and efficacy. To demonstrate the practical applicability and superiority of the algorithm, a case study was conducted in a rural area of South Africa. The proposed algorithm was applied to design an optimal hybrid renewable energy system, and its performance was compared against traditional methods such as progressive hedging and Monte Carlo techniques. Results affirm the superiority of the approach, saving approximately 8.16% capital cost when compared to progressive hedging. In addition, the proposed algorithm outperforms the Monte Carlo method both in terms of CPU time and the number of cost function evaluations.