This two-part paper presents the development of a hierarchical control framework for the control of power flow throughout mobile systems. These vehicles are comprised of multiple interconnected systems each with multiple subsystems which exhibit dynamics over a wide range of timescales. These interconnections and the timescale separation pose a significant challenge when developing an effective control strategy. Part I presents the proposed graph-based modeling approach and the three-level hierarchical control framework developed to directly address these interconnections and timescale separation. The mobile system is represented as a directed graph with vertices corresponding to the states of the vehicle and edges capturing the power flow throughout the vehicle. The mobile system and the corresponding graph are partitioned spatially into systems and subsystems and temporally into vertices of slow, medium, and fast dynamics. The partitioning facilitates the development of models used by model predictive controllers at each level of the hierarchy. A simple example system is used to demonstrate the approach. Part II utilizes this framework to control the power flow in the electrical and thermal systems of an aircraft. Simulation results show the benefits of hierarchical control compared to centralized and decentralized control methods.