Droop control by means of virtual resistance (VR) control loops can be applied to paralleled dc-dc converters for achieving autonomous equal power sharing. However, equal power sharing does not guarantee an efficient operation of the whole system. In order to achieve higher efficiency and lower energy losses, this paper proposes a tertiary control level including an optimization method for achieving efficient operation. As the efficiency of each converter changes with the output power, VR values are set as decision variables for modifying the power sharing ratio among converters. A genetic algorithm is used in searching for a global efficiency optimum. In addition, a secondary control level is added to regulate the output voltage drooped by the VRs. However, system dynamics is affected when shifting up/down the VR references. Therefore, a secondary control for system damping is proposed and applied for maintaining system stability. Hardware-in-the-loop simulations are conducted to validate the effectiveness of this method. The results show that the system efficiency is improved by using tertiary optimization control and the desired transient response is ensured with system damping secondary control.Index Terms-DC-DC converters, droop method, efficiency optimization, hierarchical control, secondary control, system damping, tertiary control.1949-3053 c 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.Lexuan Meng (S'13) received the B.S. degree in electrical engineering, and the M.S. degree in electric machines and electric apparatus from the