In recent years, the field of power electronics has seen a notable development mainly due to industrial applications using electrical systems [
1,
2,
3]. However, every revolution comes with its benefits and drawbacks. In fact, any load based on power electronics devices has a so-called “nonlinear” behavior [
4] because they create significant disturbances which degrade the optimal functioning of the installation and its overall efficiency, this also causes current deformation and creates additional losses and heating in the electrical equipments. In this context, three-phase nonlinear loads [
5] lead, on the one hand, to a regular increase in the harmonic rate by producing harmonic currents whose frequencies are integer multiples of the fundamental frequency. By the other hand, they cause current imbalance and high consumption of reactive power. We can find these disturbance problems mainly in the industrial environment, in hospitals or others (control of rotating machines by inverters or rectifiers) [
6,
7]. To reduce the THD of currents delivered by these equipments and to ensure the performance of the dynamical system [
8], power electronics have undergone significant technological development [
9,
10]. Those that best meet industrial constraints today are the parallel active filters. Thus, active filtering tends to cancel out harmonic currents by injecting signals with identical amplitudes but in phase opposition into the disturbing source, this one becomes sinusoidal after filtering. Indeed, a measurement of the nonlinear load current makes it possible to know the harmonic current to supply. The author of [
11,
12] explains the working principle of the active filters in depth. He reports several regulatory structures in his works, including an improved version of the RST, the latter demonstrates the limits of application of the classical RST. Several studies of SAPFs based on conventional inverters having a switching frequency between 12 and 16 kHz and consisting of two voltage level topology associated to a first-order output filter have been carried out; we note that this structure is expensive and very difficult to design. In contrast, the control of this structure is very easy to implement. The second structure represented in [
13], which is based on the same conventional inverter associated, in this case, with an LCL output filter, is very easy to carry out but difficult to control. However, some scientific obstacles remain and need to be raised such as the hybrid control of hybrid dynamical systems (HDS) explicitly and simultaneously involving continuous and discrete behaviors. With a reduced number of switching inputs and a large number of variable states [
14,
15], these systems contribute to the improvement of the filtering function. The performance of these systems was demonstrated for a 4-cell inverter connected to an inductive load. Introduced in the 1980s and 1990s in [
16], this structure constitutes a new solution: it consists of the design of new conversion architectures from the serial association of several switching cells. These associations allow the reduction of the constraints on switches providing multilevel output voltages with better quality compared to traditional architectures. The output signal is characterized by optimal spectral quality noted from the importance of the apparent switching frequency which increases to the value of the frequency of switching multiplied by the number of cells. These combinations of switching cells are made from energy storage elements which are floating capacitors. Their energy management is carried out according to the different states of each association so that their voltages remain always balanced around a fraction of the input voltage. This is ensured by following the principle of direct torque control (DTC) which was patented in [
17]. This control is based on the principle of hysteresis control. It was initially reserved for asynchronous machines, then, advanced studies allow to use it for synchronous machines. The method of Pulse Width Modulation (PWM) is an extension of the DTC concept [
18,
19]. It is a conventional method associated with multicellular converters. The most used strategy is Phase Shifted modulation (PS) based on the PWM principle. Indeed, the regular phase shift between the control signals allows to increase the apparent frequency of the output voltage. This allows, therefore, to repel the harmonics of the output voltage, thus reducing the constraints related to the sizing of the output filter. Several works have been carried out for the development of the serial multicellular converters. Then, the authors of [
20,
21,
22] have developed these structures and found adequate control strategies considering that this type of converters requires an in-depth study, especially with regard to the charges and discharges of floating capacitors [
1,
23,
24]. The works of Guillaume Gateau led to two essential problems characterizing this type of converters, which are the saturation of the controls and the controllability of the floating voltages. Based on these principles, many recent studies have been treated. Compared to the traditional voltage source converters, the authors of [
25,
26] give an increasing attention to both of serial and parallel multicellular structures owing to their ability to synthesize signals with a better harmonic analysis. They focused their studies on observability and control based on sliding mode techniques represented in [
27]. Recently, the authors in References [
28,
29] applied a control strategy based on Petri Nets representation to a multicellular converter. The main contribution of this strategy is the robust control of this type of inverter ensuring current regulation and voltage balancing. Appearing in 1962 as the subject of the doctoral thesis of Carl Adam Petri [
30], PNs is considered as an alternative to automata models; it is a graphical and mathematical modeling language used as an approach for the description and the verification of the dynamical behavior of distributed Discrete Event Systems (DES) [
3,
31]. In this context, the authors in References [
32,
33] provide a viewpoint of the development of the field of DES. Furthermore, a control strategy based on two PNs representation is proposed to regulate simultaneously the capacitor voltages and the output current. To make sufficient conditions of control, a stability analysis is treated using Lyapunov method [
34]. The main objective of using the FCMI within the SAPF is to increase the apparent switching frequency of the structure in order to give the possibility of reducing the value and consequently the volume, weight,.. of the inductance of the output filter. However, a second advantage of this structure is that the voltage applied to the power electronics components is lower than the overall voltage, which increases the operational reliability of the active filter. Note that increasing the number of components, compared to a conventional structure, reduces the overall reliability of the structure. Many active filter solutions for the depollution of electrical grids have been already proposed in the literature. In this paper, a PNs-based controller is applied to a multicell inverter for an active filter operation based on the principle of current reference. In fact, our SAPF structure based on an FCMI associated with a first-order output filter is not discussed in the literature; it has much fewer constraints, and the results presented here show the efficiency of the chosen algorithm in terms of robustness and stability. The remainder of this paper is structured as follows. First, the general model of our system is established. Then, SAPF is explained and the five-level FCMI is briefly described. Then, the control design based on PNs representation for an FCMI is presented along with Lyaponov analysis proofs. Afterwards, we give some simulation results to illustrate the validity of our proposed algorithm. Finally, some concluding remarks are given.