In distribution networks, N-1 contingencies are the main threats to load loss. To reduce the risk from power system threats, the energy storage (ES) can be applied to mitigate the load loss after the N-1 contingencies. However, for a given number of ESs, different location of ESs may have different mitigation results. This article first proposes a bi-level optimization model to find an optimal allocation of ESs for distribution networks, where the upper-level model is to minimize the total risk of all N-1 contingencies and the lower-level model is to compute the load loss for each contingency. Then, the proposed bilevel model is equivalently transformed into a single-level model using Karush–Kuhn–Tucker conditions. The simulation results on two test systems show the effectiveness of the proposed model.