Switching loss and conduction loss are two main loss mechanisms in dual-active-bridge (DAB) converter and the degree to which they affect the efficiency of DAB converter depends on the chosen power modulation scheme. In general, no single modulation scheme will perform optimally under all operating conditions. In this article, a hybrid modulation scheme and a new DAB converter topology designed for its realization are presented. The DAB converter is designed to switch between two operation modes - dynamic frequency matching (DFM) for medium- to full-load condition and enhanced dual-phase-shift (EDPS) modulation for light-load condition. Under DFM modulation, a switch-controlled capacitor is used to tune the resonant frequency of an LCL immittance network such that minimum rms current is guaranteed by unity-power-factor operation under different load conditions, leading to zero backflow power, zero circulating current, and zero-voltage switching (ZVS) operation of all switches. Under EDPS modulation, zero backflow power, and ZVS operation of all switches are achieved. These advantageous features are critical to ensuring a high-efficiency operation of DAB converter. The proposed solution is experimentally verified using a 1.5-kW hardware prototype with efficiency exceeding 96% for all output power levels.