This paper presents the analysis and optimization procedure of a two-stage bidirectional AC/DC power supply. The exemplary power supply consists of a silicon carbide based active front end and a dual active bridge DC/DC converter. It is designed to supply 600 V DC applications from universal low voltage AC grids with a power up to 6 kW. The paper includes the topology and design considerations, as well as an in-depth loss distribution analysis based on a validated loss model. The loss model is then utilized for an operation space optimization. A special focus is drawn to the loss model and the optimization: It is based on analytical equations optimized for a low calculation effort. This enables quick modeling of a large operation space. Those results can both be used to validate design considerations as well as to optimize operating parameters. The presented dynamic operating parameter optimization enables a loss reduction at full load by 14% and at half load by even 48%. By means of the optimization the operating area can be expanded, losses decreased, and thermal stress reduced.