Resumen: This article proposes a low-complexity model-free control method for grid-connected converters. It controls the grid current vector under normal and abnormal grid conditions through hysteresis controllers with a novel dynamic switching logic without any current/voltage reference frame transformation and sequence extraction. In addition, the proposed method has overcurrent protection, including under fault conditions due to a direct current magnitude regulation. Compared to the existing combined control method, it is model-free, enjoys current limiting and stable operation under fault conditions and power factor control mode, and lacks any estimation procedure. Compared to the predictive control method, it encounters a lower computation burden and is robust to the system model parameters. The performance effectiveness and superiority of the system under the proposed control and existing methods in terms of stability and robustness are shown by extensive analytical, simulation, and experimental studies.