Mohammed, Nouralden Mohammed Jadalla2024-01-292024-01-292024https://hdl.handle.net/10539/37466A thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy to the Faculty of Science, School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg, 2023This research explores the use of stochastic optimization in finding the optimal size of hybrid renewable energy systems that combine two or more renewable energy sources. The goal is to achieve an optimal balance between system size, cost, and reliability. We have used mathematical models and algorithms to find the optimal sizing of the system by minimizing costs while ensuring reliability. Specifically, we propose an optimal-sized hybrid renewable energy system that uses stochastic programming to minimize the cost of the system based on the reliability percentage. We have formulated the hybrid renewable energy sizing problem using two-stage stochastic programming and developed an algorithm using the three-block Alternating Direction Method of Multipliers (ADMM) to solve this problem. The theoretical convergence of the proposed algorithm was established, and the results were compared with state-of-the-art methods in the literature, demonstrating the superior performance of our proposed approach. Also, we have applied the proposed algorithm to a rural area in South Africa- as a case study- to find the optimal sizing of the hybrid renewable system for the geographic location. Moreover, we have developed a differential equations-based model for the deterministic version of the stochastic programming problem for optimal sizing. This model enables the design of the renewable system as we progress in time instead of building the entire system at the beginning of the project. The dynamical-based model has shown superiority over the three-block ADMM in terms of capital cost, where it decreased the capital costs of the renewable components by a significant amount. Finally, we have incorporated machine learning techniques to model wind turbine power curves and solar power predictions using climatic data. We have found that ensemble models outperformed parametric models by having better accuracy. Overall, this research provides new insights into the optimal sizing of hybrid reiii newable energy systems and presents innovative algorithms and techniques for their design and optimization.enHybrid renewable energyTwo-stage stochastic programmingProgressive hedgingThesis