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A large penetration of renewable energy sources with volatile power generation imposes new challenges for efficient restoration of the power system after a blackout. Prolonged power outages are also characterized be uncertain load conditions due to cold load phenomena. To meet this challenge, this paper deals with the problem of how to restore a transmission system after a blackout under uncertain load conditions and volatile power generation. The main contribution is a approximate method which minimizes the expected dissipated power under random current injection and maximizes the short circuit power under random generator generator introduction. The method is demonstrated in a numerical example on the Nordic32 400 kV transmission system.