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This paper proposes a new parallel algorithm for unit commitment including optimal power flow constraints. The algorithm employs a new Augmented Lagrangian method that involves the Variable Duplication technique. By using the Auxiliary Problem Principle, we can convert the primal problem to its dual problem and get the separate structure of the Augmented Lagrangian which allows its implementation in parallel computers. With preliminary implementations of the algorithm, we have been able to solve the IEEE118 and IEEE300 problems reliably. Meanwhile the calculation speed is increased sufficiently by using parallel computation.