voltage sags represent the greatest threat to the sensitive loads of industrial consumers, the microprocessor based-loads, and any electrical sensitive components. In this paper, a special topology is proposed to mitigate deep and long duration sags by using a modified AC to AC boost converter with a new control method. A boost converter is redesigned with a single switch to produces an output voltage that is linearly proportional to the duty cycle of the switch. On the other hand, the proposed control system is based on introducing a mathematical model that relates the missing voltage to the duty cycle of the boost converter switch. The simulation results along with the system analysis are presented to confirm the effectiveness and feasibility of the proposed circuit.