Dual active bridge (DAB) DC-DC converters have several advantages, such as bidirectional power flow, high power density, easy implementation of zero-voltage switching, convenient access to cascading and parallelism. As a result, these converters are widely used in the distributed generation systems [1–۳], DC-micro-grid systems [4], electric vehicle charging systems [5–۸], energy storage systems [9, 10], and power electronic transformers in railway locomotive applications [11, 12]. In applications mentioned above, it is significant to achieve robust dynamic performances of DAB DC-DC converters under challenging circumstances, such as input voltage fluctuation, output load disturbance, and etc. Various advanced control schemes have been proposed to enhance the dynamic response. Firstly, dynamic characteristics of DAB DC-DC converters were analyzed by the small-signal modeling and the discrete-time average modeling methods [13–۱۵]. A feed-forward compensation strategy [16], which feedbacks the load current to the control system, was used to improve transient response of DAB DC-DC converters in the load disturbance conditions. However, a table lookup is essential for the feed-forward strategy, which makes it less applicable in complex operation conditions. Besides, a model-based phase-shift (MPS) control was also developed to improve dynamic response under load disturbance [17, 18]. Meanwhile, high efficiency is another critical requirement for DAB DC-DC converters. Switching strategies utilizing off-line computation have capability in minimizing power losses [19, 20]. However, consecutive optimal control cannot be realized by these strategies. Reducing current stress and power reflow in a DAB DC-DC converter can increase efficiency as well [21]. Extended phase shift (EPS) control, which is able to largely improve efficiency by reducing current stress, was introduced in [4]. However, when EPS control was adopted to DAB DC-DC converters, there usually exists slow dynamic response issues. Direct power control (DPC) scheme is a popular active solution to enhance dynamic performance of AC-DC or DC-AC converters [22, 23]. It is well known for its strong abilities to improve dynamic and static performances of power converters. However, there are few reports about the DPC scheme applied in DAB DC-DC converters so far. By combing EPS control with DPC control, a hybrid scheme EPS-DPC is proposed in this paper. The EPS-DPC scheme unites high efficiency of EPS and great dynamic performance of DPC. As a result, the DAB DC-DC converter using EPS-DPC has advantages in both high efficiency and outstanding dynamic performance. The paper is organized as follows. SPS and EPS control schemes are introduced and compared in detail in Section 2. In Section 3, EPS-DPC control is proposed, and its derivation from combination of EPS and DPC is included as well. Theoretical comparison of dynamic response performance in EPS and SPS was demonstrated in Section 4.