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Distributed generations (DGs) introduce significant uncertainties to restoration of active distribution networks, in addition to roughly estimated load demands. An adjustable robust restoration optimization model with a two-stage objective is proposed in this paper, involving the uncertain DG outputs and load demands. The first stage generates optimal strategies for recovery of outage power and the second stage seeks the worst-case fluctuation scenarios. The model is formulated as a mixed-integer linear programming problem and solved using the column-and-constraint generation method. The feasibility and reliability of the strategies obtained via this robust optimization model can be guaranteed for all cases in the predefined uncertainty sets with good performance. A technique known as the uncertainty budget is used to adjust the conservativeness of this model, providing a tradeoff between conservativeness and robustness. Numerical tests are carried out on the modified PG&E 69-bus system and a modified 246-bus system to compare the robust optimization model against a deterministic restoration model, which verifies the superiority of this proposed model.
Chen et al. (2015) studied this question.