ROBUST OPTIMAL SIZING OF A STAND-ALONE HYBRID RENEWABLE ENERGY SYSTEM

Abstract

This dissertation explores three novel frameworks for robust optimal sizing of a stand-alone hybrid renewable energy system composed of wind turbines, photovoltaic panels, a battery bank, and a diesel generator under supply and demand uncertainty. First, an adaptive robust approach that uses dynamic uncertainty sets (DUS), which account for temporal auto-correlations in the wind and solar energy outputs, is proposed. The DUSs are constructed based on time series models selected through a statistical framework to have the best description of the energy supply behavior. Moreover, vector auto-regressive and neural network models within DUSs are proposed to capture the cross-correlation between uncertain parameters, i.e., load demand, wind, and solar output power. By exploiting the correlative information of the data, tight DUSs are constructed, thus leading to less conservative and higher quality solutions than those obtained from their corresponding static uncertainty sets. Second, two robust satisficing models, scenario-based and stochastic-free, are developed for a reliability-constrained version of the problem and are compared to classical adaptive robust optimization. It is shown that robust satisficing is a promising approach for the problem when parameter uncertainty and system reliability are both considered. Finally, two scenario-based approaches are proposed to alleviate scenario-reduction errors when extracting power supply and demand scenarios from historical data: a robust-stochastic optimization model that handles uncertainty about the cluster/scenario center, and a phi-divergence-based distributionally-robust optimization model to deal with uncertain probabilities of scenarios. Both models outperformed classical stochastic Programming (SP) and robust optimization (RO) in out-of-sample experiments. Iterative column-and-constraint generation algorithms are developed to solve the adaptive robust and robust-stochastic optimization problems. A genuine case study of an isolated community in northern Ontario, Canada, is used as a testbed. Extensive numerical experiments have demonstrated the significant improvements achievable via the proposed approaches versus classical methods like SP and RO since they enable more information to be extracted from data and incorporated into the design process while being hedged against over-reliance on small data samples. Hence, this work makes significant contributions towards breaking some barriers in adopting RO by practitioners in energy systems, namely its overconservatism and insufficient use of the available data.