An Adaptive Distributionally Robust Optimization Approach for Optimal Sizing of Hybrid Renewable Energy Systems

Hybrid renewable energy systems (HRESs) that integrate conventional and renewable energy generation and energy storage technologies represent a viable option to serve the energy demand of remote and isolated communities. A common way to capture the stochastic nature of demand and renewable energy supply in such systems is by using a small number of independent discrete scenarios. However, some information is inevitably lost when extracting these scenarios from historical data, thus introducing errors and biases to the design process. This paper proposes two frameworks, namely robust-stochastic optimization and distributionally robust optimization, that aim to hedge against the resulting uncertainty of scenario characterization and probability, respectively, in scenario-based HRES design approaches. Mathematical formulations are provided for the nominal, stochastic, robust-stochastic, distributional robust, and combined problems, and directly-solvable tractable reformulations are derived for the stochastic and the distributional robust cases. Furthermore, an exact column-and-constraint-generation algorithm is developed for the robust-stochastic and combined cases. Numerical results obtained from a realistic case study of a stand-alone solar-wind-battery-diesel HRES serving a small community in Northern Ontario, Canada reveal the performance advantage, in terms of both cost and utilization of renewable sources, of the proposed frameworks compared to classical deterministic and stochastic models, and their ability to mitigate the issue of information loss due to scenario reduction.