**1. Introduction**

The use of static energy conversion devices such as static converters and others has increased during the last years [1,2]. Because all are made up of power semiconductors, they absorb a current with a non-sinusoidal. These are considered as non-linear and non-symmetrical loads for the power grid. In addition to the fundamental component, the non-sinusoidal waveform exposes a harmonic content, which can be considered very important under certain circumstances [3]. These harmonics can flow from the load to the grid and generate harmonic pollution for the power grid, resulting in a degradation of power quality. The most common e ffects of this pollution are [4]: the destruction of capacitors or circuit breakers under the e ffect of strong harmonic currents increased by resonances; the heating of neutral conductors and transformers and the long-term e ffects that explain by an advanced devastation of the wired equipment at the common connection point [5,6]. There are certain processes that can be used to reduce the harmonic pollution generated by these converters. Among the

most widespread and e ffective are filtering, which has two main task: to minimize harmonic pollution, namely passive filtering, known as resonant and/or damped, which prevents harmonic currents from flowing into the electrical networks; and to compensate for reactive power. Despite this, passive filtering has some problems such as lack of adaptability when the impedance of the network or load changes, which is a major disadvantage that may be unbearable in these particular circumstances. The other filtering method is active filtering. This is the best known and most used in research to improve the quality of electrical energy. Its principle consists in injecting a compensation current in phase opposition and of the same amplitude with the harmonic currents generated by the non-linear load, in order to render the current of a sinusoidal shape at the connection point and thus limit the di ffusion of harmonic currents in the power grid network. There are several active filter structures according to the desired performance criteria. Active filters can be in parallel [7], in series [8], or hybrid [9], i.e., the combination of an active filter and a passive filter. There is also a combination of a serial active filter and a parallel active filter called universal power quality conditioner [10]. The filter can have a current design or a voltage design depending on the type of element used as its energy source [11,12]. A hybrid power filter is deployed to solve passive filter problems in addition to active power filters. In this document a hybrid active power filter controlled by the backstepping control is exposed. The controller is an essential tool for a proper operation of the HAPF, so for this reason the backstepping control [13] was chosen. The HAPF combines the best performances of the active and passive filters: the active filter allowing to attenuate the harmonics of the source current, and the passive filter considered at the fundamental frequency as a high impedance, and at the tuning frequency as a low impedance. The use of our approach can lead to a more symmetrical waveform, thus avoiding problems to the power grid. To demonstrate the e ffectiveness of the proposed backstepping-controlled HAPF approach for harmonic currents compensation and power quality improvement, a comparison of the three control methods, i.e., the classical PI [13], the fuzzy logic [14] and backstepping control is presented in this work. The proposed backstepping controller applied to the HAPF provides a better response time to maintain the DC bus voltage *Vdc* at its reference value, and a significantly reduced THD according to standards, whereas the conventional PI controller has a very high response time and an error between the setpoint and its reference value. Finally, the fuzzy logic control presents a 5% response time lower than the PI controller, but the system remains slower. The above reflects that the proposed approach achieves the desired performance.
