In this article, a novel approach that considers the time-varying load restoration capability is proposed for operational reliability assessment of distribution networks. To evaluate the operational reliability, two indices are firstly defined as the minimal load loss under the worst-case fault contingency in the upcoming time interval. To search for the optimal remedial actions for load restoration, a sequential network reconfiguration (NR) model is then proposed considering the reconfigurability of feeders and capability of emergent power support of energy storage systems (ESSs). Since this model is a complex nonlinear mixed integer programming model, an improved greedy searching-based algorithm is proposed to compute the optimal remedial actions and to further evaluate the risk of load loss. Comparative case studies are presented in this article to demonstrate that the load level, the expectation of the state-of-charge of ESS and the failure duration have the impacts on the system operational reliability. Besides, the proposed sequential NR model can be used to enhance the reliability of distribution networks by enabling an effective sequential load transfer strategy under emergent conditions. Unlike traditional reliability assessment, the proposed method provides the operators with the real-time awareness of the operational reliability level considering the real-time condition of distributed resource equipped feeders and worst-case emergency constraints.