**5. Conclusions**

In this document, we have implemented and investigated an HAPF with a backstepping control technique. This control technique allows to ensure the stability of the closed loop system with better speed and accuracy compared to the classical PI controller and fuzzy logic controller. It is able to maintain the THD of the current within the limits indicated by the IEEE-519 standard, and to require a desired dynamic attitude.

The simulation results obtained illustrate the high performance of the HAPF using the backstepping controller for harmonic compensation. The proposed control strategy applied to the HAPF therefore has an important theoretical impact to improve the THD in a typical way, and to strengthen the power quality of the grid, by improving the stability, speed and precision of the system. The proposed backstepping controller has an advantage that does not require a mathematical model and achieves the desired performance, but the PI controller requires a precise mathematical model, and has a significant response time, which implies a degradation of speed. Also the fuzzy logic controller has a degraded speed and precision. The HAPF can also be spread to other electronic power converter topologies.

Taking into account the above methods, the proposed controller, which is applied on a hybrid HAPF filter, is an appropriate choice for improving the quality of electrical energy in the transmission and distribution of energy. An additional experimental test bench is being developed for the realization and testing of the proposed control scheme in our laboratory.

**Author Contributions:** Conceptualization, N.D.; Methodology, N.D.; Software, N.D.; Validation, N.D., F.G.M. and Y.D.; Formal analysis, N.D.; Investigation, N.D.; Resources, N.D.; Data curation, N.D.; Writing—Original draft preparation, N.D.; Writing—Review and editing, N.D. and F.G.M.; Visualization, N.D.; Supervision, N.D., F.G.M., N.A. and Y.D.; Project administration, N.D.; Funding acquisition, F.G.M.

**Funding:** This research received no external funding.

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