Optimizing maintenance scheduling is a major issue to improve the performance of hydropower plants. We study a system of several physical components (turbines, alternators, generators) sharing a common stock of spare parts. Components 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 Interaction Prediction Principle is used to decompose the original large-scale optimization problem into a sequence of independent subproblems of smaller dimension. Each subproblem consists in optimizing the maintenance on a single component. The resulting algorithm iteratively solves the subproblems with a blackbox algorithm and coordinates the components. The maintenance optimization problem is a mixed-integer problem. However, decomposition methods are based on variational techniques, therefore we have to relax the dynamics of the system and the cost functions. Relaxation parameters have an important influence on the optimization and must be appropriately chosen. We apply the decomposition method on a system with 80 components. It outperforms the reference blackbox algorithm applied directly on the original problem.