**7. Conclusions**

A direct power model developed from Park's reference frame for the SCES systems has been presented in this study. The direct power model controls instantaneous active and reactive powers regardless of the SCES system without employing typical phase-Locked-Loop. A PI-PBC approach was used to control the SCES system because it takes advantage of the pH structure of the SCES system to propose a control law that guarantees the stability of the system and exploits proportional-integral actions. The proposed controller demonstrates better performance in relieving the active and reactive power oscillations generated by wind generation considering imbalance when compared to the IDA-PBC approach.

**Author Contributions:** Conceptualization and writing—review and editing, W.G.-G. and O.D.M.; and supervision, writing—review and editing, F.M.S., C.A.R. and C.O.-H. All authors have read and agreed to the published version of the manuscript.

**Acknowledgments:** This work was partially supported by the National Scholarship Program Doctorates of the Administrative Department of Science, Technology and Innovation of Colombia (COLCIENCIAS), by calling contest 727-2015.

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