A distributionally robust approach for the optimal protection of power networks with endogenous uncertainty

Abstract

Power networks are among the most important infrastructures in any society, and protecting them from a large variety of disruptive events is an essential task. Finding an optimal protection plan often takes the form of a multilevel optimization problem. Recently, approaches based on distributionally robust optimization (DRO) have gained the attention of many scholars. In fact, DRO allows protecting the decision-maker from the ambiguity arising from the imprecisely identified probability distributions of the failure scenarios. In this framework, the probability distribution of the failure scenarios is assumed to be known ambiguously, and contained in an ambiguity set defined by moment-based conditions. In practice, some decisions taken in the protection plan affect the conditions of the ambiguity set. We refer to this situation as DRO with endogenous uncertainty. In this paper, we study the impact of the endogenous uncertainty on the optimal protection plan of a power network, using a numerical example built upon the IEEE 14-bus system with a traditional moment-based ambiguity set.