**5. Conclusions**

In this paper, an MPC method with an enhanced AV2R was proposed for a two-level grid-connected inverter. First of all, three existing MPC methods and the corresponding AV2Rs were analyzed and discussed. Thereafter, to improve the steady-state performance of the MPC method, a formal mathematical methodology was studied in terms of duty-ratio calculation, in which the well-known Lagrange multipliers method and the Hessian matrix were applied. The AV2R of the proposed MPC method and an SVM-based PWM generation strategy were elaborated as well. Finally, the experimental results of the proposed MPC were presented. Moreover, to prove the effectiveness of the proposed method, three mentioned MPC methods were conducted. The comparative results verified that the proposed MPC method can improve the steady-state performance and retain the excellent dynamic performance of the classic MPC method simultaneously. Furthermore, the grid-connected operation under non-unity power factor conditions can also be realized using the proposed art, ensuring that the V2G system is characterized with excellent performance under different desired power factor.

**Author Contributions:** Conceptualization, L.X. (Lie Xia), L.X. (Lianghui Xu), F.Y.; Methodology, L.X. (Lie Xia); Software, L.X. (Lie Xia); Validation, L.X. (Lie Xia), L.X. (Lianghui Xu) and Q.Y.; Formal Analysis, L.X. (Lie Xia) and Q.Y.; Investigation, L.X. (Lie Xia); Resources, L.X. (Lianghui Xu) and Q.Y.; Data Curation, L.X. (Lie Xia) and L.X. (Lianghui Xu); Writing-Original Draft Preparation, L.X. (Lie Xia); Writing-Review & Editing, F.Y. and S.Z.; Visualization, L.X. (Lie Xia), L.X. (Lianghui Xu) and Q.Y.; Supervision, S.Z. Project Administration, S.Z.; Funding Acquisition, Q.Y. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Key Research and Development Program of China (2018YFB1500705).

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