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• 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]