Distribution System Operation With Renewables and Energy Storage: A Linear Programming Based Multistage Robust Feasibility Approach

Distribution systems are operated with an increasing level of uncertainty. Energy storage is playing an important role in shaving the peak load and mitigating uncertainty. This paper proposes a multistage robust optimization model for distribution system operation with energy storage under uncertainty. Unlike the conventional robust optimization paradigm which minimizes the worst-case cost, the proposed formulation optimizes the cost in the nominal scenario. In analogy to dynamic programming, we define dynamic robust feasible regions in a recursive manner. In each period, the dynamic robust feasible region is shown to be polyhedral, and a linear programming based projection algorithm is developed to compute such regions offline. In the online stage, the method is executed following a rolling horizon manner: renewable output is observed at the beginning of each period, and the cost of remaining periods in the forecast scenario is to be minimized subject to operation constraints and dynamic robust feasible regions, giving rise to a linear program. In this way, the dispatch strategy ensures multistage operation security regardless of future realizations of renewable power. In numeric tests on a modified IEEE 33-bus distribution system, the dynamic robust feasible regions are visualized and analyzed, and the proposed method is compared with two prevailing robust optimization methods, verifying its advantages in terms of optimality and robustness.