In this work, we represent a shunt active power filter (SAPF) based on a serial three-phase flying capacitor multilevel inverter (FCMI) controlled by a Petri Nets representation (PNs). This structure is chosen for its significant performances. In fact, the use of the FCMI within the SAPF makes it possible to increase the apparent switching frequency of the structure in order to reduce the value then the volume and weight of the inductance of the output filter. Besides, the FCMI allows the synthesis of a high-voltage signal using low-voltage semiconductor components. Therefore, improving the reliability of this structure leads to the improvement of the dynamics of the SAPF. This paper deals with a new control methodology based on PNs to regulate the flying capacitor voltages and the reference currents issued by the instantaneous active and reactive power theory. Compared to a conventional SAPF composed by a classical two-level inverter and controlled by a simple PWM control, simulation results demonstrate that our proposed control enhances the dynamic system and the power quality by reducing the total harmonic distortion (THD) satisfying the limits of IEEE standards.