Adaptive Characteristic Modeling of Long-Period Uncertainties: A Multi-Stage Robust Energy Storage Planning Approach Based on the Finite Covering Theorem

An accurate planning decision relies on the careful consideration of short-term operations. However, exactly modeling the operation of the entire planning horizon is generally computationally intractable. To address this issue, existing methods usually use typical days to estimate the expected operational process, while formulating an uncertainty set to capture short-term operational uncertainties during the entire planning horizon. However, different typical days may exhibit distinct characteristics in short-term uncertainties, e.g., the photovoltaic curve may vary in temporal and spatial characteristics across different seasons. It means that a single uncertainty set cannot precisely describe short-term uncertainties of different characteristics. Motivated by these challenges, this paper develops a new uncertainty set formation approach based on the Theorem of Finite Covering. The main idea is to adaptively optimize several uncertainty sets to cover the uncertainties. Short-term uncertainties with different characteristics are carefully formulated in individual uncertainty sets, which together cover the uncertainty during the entire planning horizon. Based on the proposed uncertainty sets, a multi-stage robust optimization planning model is established. Extensive case studies are tested on an IEEE-33 bus distribution system and compared with two popular existing methods. Results verify the effectiveness of the proposed method.