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• A novel generator start-up sequence optimization strategy is proposed in this work, taking the integration time of wind-solar hybrid systems into account. • The proposed model requires fewer variables compared with other models, therefore the computational efficiency can be greatly improved. • The confidence gap decision theory based generator start-up sequence strategy is proposed to address the generation uncertainty of wind-solar hybrid systems. • Better generator start-up sequence solutions with higher computational efficiency and less conservatism can be attained by employing the proposed strategy. A reasonable start-up sequence of generators considering renewable energy generation integration can effectively improve the restoration efficiency of the power system concerned. The restoration strategy of generators is time-sensitive, however, the computation procedure of existing methods is not fast enough to meet the requirements of practical applications. In this paper, the generator start-up sequence optimization (GSSO) problem is addressed with the integration of wind-solar hybrid systems (WSSs) considered in bulk power systems. Specifically, a deterministic model for GSSO is formulated to maximize the total generation capability during the restoration procedure, in which fewer auxiliary variables are required to promote the computational efficiency. On this basis, in order to deal with the inherent and significant uncertainties of WSSs, a confidence gap decision theory (CGDT) based approach is proposed combining the advantages of stochastic optimization and the information gap decision theory based method while considering the worst-case realization of unknown probability distributions, so that a chance-constrained robust generator start-up solution is thereby attained. Moreover, the formulated CGDT based model is transformed into a mixed integer linear programming problem. Finally, the IEEE 39-bus power system and a modified version of an actual power system in China are employed to demonstrate the feasibility and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

• A load restoration scheme is proposed to coordinate the transmission, distribution, and gas systems. • The coordinated load restoration is achieved in a distributed manner to respect the information privacies. • The line-packs caused by slow gas slow dynamics is exploited to assist in load restoration. • An efficient algorithm is proposed to solve the distributed load restoration scheme with excellent calculation performance. Recent electricity systems have witnessed many power outage events, and the interrupted loads must be restored as soon as possible to reduce the enormous outage losses. However, the ever-increasing interdependencies of the transmission, distribution, and gas systems cause the restoration behaviors of a system to inevitably influence the others, which brings about new impacts on the load restoration decisions. Moreover, the different velocities of power and gas flows cause additional complexities in making load restoration decisions for the whole system. To address these problems, this paper proposes a new load restoration scheme coordinating transmission, distribution, and gas systems. Firstly, to respect the information privacy of individual energy subsystems, a distributed load restoration coordination structure is proposed with the interactions of different energy systems and corresponding load restoration models considering pipeline gas storage capacity caused by slow gas flow dynamics. Based on the distributed restoration coordination structure and considering that discrete variables in load restoration models hinder the efficient calculation, a projection function-based adaptive alternating direction method of multipliers is then proposed with iterative relaxation and projection of discrete variables. Finally, simulation results in the T118-D33-N56 test system and a real-world system in China demonstrate that coordination of transmission, distribution, and gas systems and considering pipeline gas storage capacity can shorten the load restoration time. The proposed solution method also shows good computational performance. [ABSTRACT FROM AUTHOR]