Optimal sizing of hybrid renewable energy systems using quasi-optimal control

Abstract

This paper addresses the critical challenge of sizing hybrid renewable energy systems over their lifespan while accounting for uncertainties in energy sources and load demands. By leveraging stochastic programming, we introduce a novel modeling technique that ensures robust optimization without compromising numerical tractability. Unlike conventional methods, which determine system parameters for the entire project duration upfront, our approach enables annual adjustments to the renewable components’ sizing. This dynamic strategy alleviates early-stage under-utilization, aligning system capacity with evolving demand patterns. Central to our approach is the reformulation of the two-stage stochastic program as a quasi-optimal control. This reduces the number of optimization variables significantly, simplifying the solution process. Moreover, thousands of constraints are replaced with a system of differential equations, enhancing computational efficiency. By minimizing capital costs and dynamic operating expenses, we achieve an optimal system size. Through a real-world application in a rural area of South Africa, we demonstrate the effectiveness of our approach. The results showed a remarkable improvement in problem-solving efficiency, reduced under-utilization, and heightened adaptability to unpredictable weather conditions. This innovative framework represents a substantial leap forward in hybrid renewable energy systems design, offering a more agile and efficient solution for sustainable energy generation.