Currently, the energy transfer process to the grid of the PV system is based on the importance of less harmonics and high efficiency. The evaluation of harmonics distortion of current is based on the value of THDi (<<5%), this last becomes very high if the current leakage is high, which causes losses of the grid and safety problems. Therefore, our job is to improve the classic control method of PV inverters used to reduce grid loss and improve electricity prices. This study is a proposal toward the modelization and improvement of the three-phase two-level, and multi-level photovoltaic (PV) inverter command, using space vector, and sinusoidal control based on controlling the active and reactive current delivered into the grid indirectly with a resonant controller (PIR) for a nonlinear load (NLL). The results of the simulations obtained by the new control methodology, SPWM, and SVPWM show that its performance is better compared with the simple modulation (PWM); the total harmonic distortion (THD) of current in both methods (SVPWM) and (SPWM) is better than that obtained with conventional commands. Also, multilevel converters control produces better quality waveforms, reducing current harmonic distortion.

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<span lang="EN-US">In this paper, we have studied the topologies of single-phase transformerless inverters with different levels using a <a name="_Hlk115945664"></a>proportional-integral-resonant (PIR) AC controller, and the multi-level cascade inverter topology with sinusoidal pulse with modulation (SPWM) control in an open and closed loop. To ensure that these photovoltaic inverters can inject a defined amount of reactive power into the grid according to international regulations. Therefore, precise monitoring of the mains voltage vector by a phase-locked loop (PLL) system is applied to ensure the proper functioning of this system. For inverter topologies with less than three levels, the simulation results show that the highly efficient and reliable inverter concept (HERIC) topology performance is better than that of H5 and H6. On the other hand, the performance of the topology H6 ameliorate is superior to those of H4, H5, and HERIC in currents of leakage. On the other hand, for the control of cascaded multi-level closed-loop inverters, we notice that there is an improvement in the spectra and the elimination of all frequency harmonics, close to that of the fundamental, and a reduction in the rate of harmonic current distortion.</span>

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