Hybrid-electric gas turbine generators are considered a promising technology for more efficient and sustainable air transportation. The Ohio State University is leading the NASA University Leadership Initiative (ULI) Electric Propulsion: Challenges and Opportunities, focused on the design and demonstration of advanced components and systems to enable high-efficiency hybrid turboelectric powertrains in regional aircraft to be deployed in 2030. Within this large effort, the team is optimizing the design of the battery energy storage system (ESS) and, concurrently, developing a supervisory energy management strategy for the hybrid system to reduce fuel burn while mitigating the impact on the ESS life. In this paper, an energy-based model was developed to predict the performance of a battery-hybrid turboelectric distributed-propulsion (BHTeDP) regional jet. A study was conducted to elucidate the effects of ESS sizing and cell selection on the optimal power split between the turbogenerators (TGs) and ESS. To this extent, the supervisory energy management strategy is formulated into a discrete time optimal control problem and solved via dynamic programming. The performance of BHTeDP was compared to a turboelectric distributed-propulsion (TeDP) next-gen aircraft that assumes improvements in weight, drag, and engine efficiency consistent with regional jet entering operation in 2035.