**5. Conclusions**

To meet the demand bridging the gap between low-cost linear formulation with unsatisfactory accuracy and the high-accuracy nonlinear models, such as large eddy simulation, featuring excessive computational costs, a simplified nonlinear wake model based on the momentum theory is proposed in this study to o ffer a reasonable balance between accuracy requirements and numerical expense. The numerical robustness of the proposed model further enables the establishment of an economic approach for long-term wind farm power prediction that provides the required information for the

financial evaluation of wind farm development. The proposed model was first validated with the offshore measurement of Horns Rev wind farm for a given wind speed of 8 m/s alongside three wind directions. Except for the wind direction of 312◦, the proposed approach delivered good agreemen<sup>t</sup> with the measurements, as well as a comparable accuracy level to the LES results. The in-house code WIFA3D only requires about one percent of the computational cost of the LES approach to predict the mean power delivered by a wind farm. This study also verifies that a reduced computational domain based on the symmetry of wind turbine arrays gives a significant computational advantage without sacrificing the prediction accuracy. This paper also proposes an e fficient approach to predict the yearly capacity factor based on the characteristic wind conditions, where the required computational cost is possibly reduced by two orders of magnitude when compared with the traditional serial approach. The proposed approach can favorably forecast the yearly capacity factor of a wind farm with an average error of less than 5%, but the power variation across the wind turbine array is inevitably smoothed due to an averaging nature in time and space. The advantage of the simplified actuator disk model is demonstrated in its numerical robustness, as well as in the prediction accuracy of the mean power, whereas the time-accurate power behavior and the significant power variation among the wind turbines is unable to be captured by the proposed model due to its steady nature.

**Author Contributions:** Methodology, S.-W.C.; validation, Y.-C.H.; formal analysis, Y.-C.C.; writing—original draft preparation, Y.-C.C.; writing—review and editing, S.-W.C.; visualization, Y.-C.C., Y.-C.H. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Ministry of Science and Technology, Taiwan, gran<sup>t</sup> number MOST 107-3113-E-002-010- and MOST 108-3116-F-006-004-CC1.

**Acknowledgments:** The authors thank the Taiwan Power Company for providing relevant operation information of the investigated wind farms.

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