The rapid expansion of renewable energy, particularly photovoltaic (PV) systems, has significantly increased the occurrence of DC series arc faults. However, existing technologies have focused on detecting fault conditions, while extinction has remained at an implementation level. Although extinction is performed through power modulation, conventional approaches do not consider system impedance, which can lead to re-ignition or cause transient overvoltage due to line inductance. This paper proposes a optimized slew rate design according to the system impedance for power modulation algorithm to detect and extinguish the arc fault condition. From small signal analysis, the current dynamics are analyzed according to system impedance. The designed slew rate for power modulation can minimize times for the arc fault extinguishing. Experimental validation on a PV system confirmed that arc fault extinguishing and operational recovery are achievable at the optimal slew rate for each system impedance, thereby demonstrating the effectiveness and practical applicability of the proposed method.