**6. Conclusions**

This paper mainly studies the opportunistic maintenance strategy of wind turbines. The economic correlation, random correlation, and structural correlation among subsystems and carbon emissions can be considered in the proposed maintenance model. The stochastic correlation coefficient matrix is constructed by a failure chain to describe the reliability of the subsystems, and the structural correlation coefficient is used to describe the downtime loss cost in order to present the opportunistic maintenance model. Moreover, the operation energy consumption of wind turbines increases with their performance degradation. The environmental benefits are combined in the maintenance model of wind turbines. The working age fallback factor and failure rate increasing factor are introduced to establish the carbon emission model and the total expected cost model. This paper further considers the reduction effect of wind turbines recovery on cost and emission. The benefits of wind turbines can introduce recovery and emissions of maintenance activities into the proposed model by adopting the dynamic failure rate function and carbon emission function. The total expected maintenance cost could be described as the objective function for the proposed opportunistic maintenance model, including maintenance preparation cost, maintenance

adjustment cost, shutdown loss cost, and operation cost. The operation cost is related to the energy consumption of wind turbines. Finally, a case study is provided to analyze the performance of the proposed model. Compared with preventive maintenance, the proposed model demonstrates better performance on wind turbines maintenance problems and can obtain a relatively good solution in a short computation time. The method proposed in this paper provides certain significance for guiding the selection of a wind turbine maintenance strategy.

The proposed model does not consider the complex external operation environment and external impacts. Thus, the joint optimization model between the carbon emission model and condition-based maintenance that considers the external operation environment and effect needs to be developed in the future.

**Author Contributions:** Conceptualization, Q.L. and Z.L.; methodology, T.X.; investigation, Q.L.; resources, J.L.; data curation, Z.L. and J.L.; writing—original draft preparation, Q.L.; writing—review and editing, Z.L.; supervision, T.X.; funding acquisition, M.H. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China (No. 71840003 and 51875359), the Natural Science Foundation of Shanghai (No. 19ZR1435600 and 20ZR1428600), the Humanity and Social Science Planning foundation of the Ministry of Education of China (No. 20YJAZH068), the science and technology development project of the University of Shanghai for Technology and Science (No. 2020KJFZ038) and the National Key R&D Program of China(2021YFF0900400).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The authors are indebted to the reviewers and the editors for their constructive comments, which greatly improved the contents and exposition of this paper.

**Conflicts of Interest:** The authors declare no conflict of interest.
