Optimizing maintenance scheduling is a major issue to improve the performance of hydropower plants. We study a system of several physical components of the same family: either a set of turbines, a set of transformers or a set of generators. The components share a common stock of spare parts and experience random failures that occur according to known failure distributions. We seek a deterministic preventive maintenance strategy that minimizes an expected cost depending on maintenance and forced outages of the system. The Auxiliary Problem Principle is used to decompose the original large-scale optimization problem into a sequence of independent subproblems of smaller dimension while ensuring their coordination. Each subproblem consists in optimizing the maintenance on a single component. Decomposition-coordination techniques are based on variational techniques but the maintenance optimization problem is a mixed-integer problem. Therefore, we relax the dynamics and the cost functions of the system. The resulting algorithm iteratively solves the subproblems on the relaxed system with a blackbox method and coordinates the components. Relaxation parameters have an important influence on the optimization and must be appropriately chosen. An admissible maintenance strategy is then derived from the resolution of the relaxed problem. We apply the decomposition algorithm on a system with 80 components. It outperforms the reference blackbox method applied directly on the original problem.