Hierarchical Programming for Worst-Case Analysis of Power Grids

The aim of the present paper is to provide (n-l)-reliability to a power grid, guaranteeing nominal operation after the failure of any one out of n present grid components. Building on previous work (Fliscounakis et al., IEEE Transactions on Power Systems, 2013), a hierarchical programming problem is proposed to characterize the worst-case behavior of a power grid under a given contingency. The formulation is a mixed-integer linear generalized semi-infinite program with a max-min program embedded. The different levels correspond to the choice of preventive actions, realization of uncertainties in the power supply and demand, and the choice of corrective actions. In order to model active components of the grid, models are proposed for load balancing and the behavior of phase-shifting transformers. Since no rigorous solution approaches are published for the problem at hand, the possibility of extending generalized semi-infinite programming approaches to the present problem is discussed.