Two-three (2/3)-level dual-active-bridge (DAB) DC-DC converter has high potential to become a promising solution for medium-voltage high-power applications. However, its switching characteristics, modeling, and optimal modulation schemes have not been comprehensively explored yet. In order to avoid voltage and current distortions, and ensure reliable operation, this paper analyzes the operating constraints for the neutral-point-clamped (NPC)-based DAB converters. Based on the obtained operating constraints, the transferred power and current stress models under a five-level control scheme, which is considered as one of the most advantageous control strategies for the NPC-based DAB converters, are obtained with an equivalentwave modeling method. Generic control strategies based on analytical solutions have not be fully explored for the multi-level DAB converters due to the increased number of control variables. With the above, this paper proposes a minimum-current-stress control strategy employing analytical solutions in the entire power range, which are obtained by combining the Karush-Kuhn-Tucker (KKT) conditions and numerical-solution analysis. With the proposed modulation scheme, the control variables can be automatically modified online, instead of relying on offline calculation of the numerical control variables. Therefore, the control complexity can be reduced significantly, especially when the operating parameters change in a wide range. Finally, experimental tests verify the effectiveness of the analysis.