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The aim of this article is the application of a new Metaheuristic algorithm (Firefly Algorithm) for solving a nonlinear algebraic system where the resolution is needed to study the Selective Harmonic Eliminated PWM strategy (SHEPWM); this strategy is applied to multilevel inverters. The Firefly Algorithm (FA), proposed by Xin-She Yang at the University of Cambridge, is a new Metaheuristic algorithm, which is inspired by the behavior of fireflies is one of the latest Metaheuristics inspired from nature. The principle of the SHEPWM strategy is to impose the voltage pulses and calculate the switching angles to eliminate the selected harmonic orders by solving a nonlinear equations by applying Firefly Algorithm by using a software calculation and plot the shape of the angles calculated based modulation rate where the spectre of voltage shows that the amplitudes of the selected harmonics are zero.

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The development of energies from renewable sources and the increase in electricity consumption will require new solutions to maintain the levels of service, quality of voltage and availability of electricity networks. A tailor made role for power electronics. The objective of this work on this paper is the remediation of the problem caused by the injection of harmonics discharged by the non-linear load (i.e. by the rectifier in our case). This remediation consists in reducing as much as possible the impurities diffused in the electrical network. For this we used a Shunt Active Power Filter (SAPF) as a perfect solution by eliminating all harmonics one by one. In this article, we have proposed a control technique on the voltage inverter, it is the technique "Synchronous Reference Frame -SRF" and an MPPT regulator on the photovoltaic generator which is used as a continuous source of the SAPF, it is the “Sliding Mode Control- SMC” technique. The simulation results obtained under MATLAB / Simulink clearly showed us that the system sizing choices, as well as the control techniques are efficient and according to the international standard recommendations IEEE519-92 (The total Harmonic Distortion is less than 5 percent).