In response to the need for robust black-start strategies in modern smart grids during blackouts

this paper proposes a two-stage black-start model that integrates wind turbines (WT)

photovoltaic generators (PV)

and energy storage systems (ESS). The system restoration path model in the first stage utilizes the Dijkstra algorithm to create a skeleton network and formulate a post-outage generator start-up plan. The second stage involved a load pick-up model

structured as a mixed-integer linear programming problem

aimed at restoring the load with the assistance of the ESS. This stage was designed for computational efficiency

allowing solutions to be obtained using standard commercial solvers. The performance and efficacy of the proposed model were demonstrated through its application to modified IEEE 39/118-bus transmission systems

with the results affirming its high efficiency and effectiveness in power system restoration scenarios.