  Wind power is one of the most important sources of renewable energy. A large
part of the wind energy cost is due to the cost of maintaining the wind power
equipment. To further reduce the maintenance cost, one can improve the design
of the wind turbine components. One can also reduce the maintenance costs by
optimal scheduling of the component replacements. The latter task is the main
motivation for this paper.
  When a wind turbine component fails to function, it might need to be replaced
under less than ideal circumstances. This is known as corrective maintenance.
To minimize the unnecessary costs, a more active maintenance policy based on
the life expectancy of the key components is preferred. Optimal scheduling of
preventive maintenance activities requires advanced mathematical modeling.
  In this paper, an optimization model is developed using the renewal-reward
theorem. In the multi-component setting, our approach involves a new idea of
virtual maintenance which allows us to treat each replacement event as a
renewal event even if some components are not replaced by new ones.
  The proposed optimization algorithm is applied to a four-component model of a
wind turbine and the optimal maintenance plans are computed for various initial
conditions. The modeling results showed clearly the benefit of PM planning
compared to pure CM strategy (about 8.5% lower maintenance cost). When we
compare it with another state-of-art optimization model, it shows similar
scheduling with a much faster CPU time. The comparison demonstrated that our
model is both fast and accurate.
