###### Abstract  
Power system restoration must be accomplished as soon as possible after a blackout. In this process, available black-start (BS) units are used to provide cranking power to non-black-start (NBS) units so as to maximize the overall power system generation capacity. This procedure is known as the generation start-up problem, which is intrinsically combinatorial with complex non-linear constraints. This paper presents a new mixed integer linear programming (MILP) formulation for the generation start-up problem that integrates non-conventional renewable energy sources (NCRES) and battery energy storage systems (BESS). The main objective consists of determining an initial starting sequence for both BS and NBS units that would maximize the generation capacity of the system while meeting the non-served demand of the network. The nature of the proposed model leads to global optimal solutions, clearly outperforming heuristic and enumerative approaches, since the latter may take higher computational time while the former do not guarantee global optimal solutions. Several tests were carried out on the IEEE 39-bus test system considering BESS as well as wind and solar generation. The results showed the positive impact of NCRES in the restoration processes and evidenced the effectiveness and applicability of the proposed approach. It was found that including NCRES and BESS in the restoration process allows a reduction of 24.4% of the objective function compared to the classical restoration without these technologies. 2021 2021  
the initial power necessary to start up the NBS units. At the same time, as new units are started up increasing the availability of power generation, the loads are reconnected to maintain the stability of the power system [9]. Power system restoration following a blackout is one of the most important tasks of power system operators at control centers. It is a complex process aimed at setting the system back to normal operation after an extensive outage. The experience learned from historical blackouts has demonstrated that an efficient power system restoration plan is of utmost importance [10]. Generally, a common approach to the restoration process consists of three phases: the start-up of generators, the re-energizing of the network, and the restoration of load. The common thread linking each of these stages is the generation availability at each restorative stage. Researchers have worked towards new models and solutions to solve the optimal generation start-up sequence, which is the most important feature of the restoration problem. In [11], an ant colony optimization algorithm is proposed to determine the optimal generation start-up sequence during bulk power system restoration. In this case, the authors intend to maximize the system generation capacity over the restoration period considering the characteristics of different types of generation units and system constraints. In [12], a firefly optimization algorithm is implemented to find the optimal starting generation sequence that minimizes the overall restoration time of a power system. In [13], a genetic algorithm is used to obtain the optimal unit restoration sequence taking into account a decreasing trend of unit start-up efficiency. In [14], a backtracking algorithm is adopted to determine the best unit restarting sequence considering a two-layer restoration process. The aforementioned heuristic methods provide good solutions to the restoration problem; nonetheless, their computational complexity require more time than the available during the restoration process; also, the achievement of a global optimal solution is not guaranteed. On the other hand, knowledge-based system approaches such as the ones presented in [15; 16] require special software tools for which the maintenance and support are often impractical for the power industry. Some conventional optimization methods have also been proposed to provide more accurate solutions to the optimal restoration problem of power systems.