Systems and methods for providing ride-through for interruptions in the power supplied to drives that are used to control equipment such as downhole submersible pumps. In one embodiment, a variable speed drive includes converter and inverter sections, a capacitor bank and a control system. The drive shuts down the converter section upon detecting a disruption in the AC input power and continues to generate output power by drawing on the energy stored in the capacitor bank. When the AC input power returns (or begins to return) to normal, the drive resumes operation of the converter section in a controlled manner (e.g., by presetting the firing angle of the SCR's in the converter to match the voltage across the capacitor bank.) The drive thereby limits the current that recharges the capacitor bank and prevents sudden inrushes of current that could damage the drive.