Naval ship power systems are evolving towards more electronics, more “vital” electronic systems, and a larger percentage of the overall energy load needed in the form of electricity. This is due to larger load demands from sensors, future weapons systems, and electrified propulsion. New technologies, such as All-Electric Ships, Integrated Propulsion Systems, and DC-Microgrids, the combination of which is referred to as MVDC, bring the promise of greater flexibility in design and operation, improved system resiliency, and increased energy efficiency. These advancements, however, depend on power electronic devices to control power flow and ensure voltage stability. At points in the power network, power electronic devices can behave as constant power loads (CPLs), which exhibit negative impedance, and at other times can demand large, instantaneous pulses of power. An improperly designed MVDC will become unstable amid large swings in power demand, and the voltage will collapse bringing the entire system down. Through a hierarchical control structure, where ensuring that system stability is maintained at a different level of control than the optimization of the power flow, these challenges can be understood and overcome separately. Different system goals are accomplished at each level in the control hierarchy, and each higher level of control is executed on a successively slower time scale. At the lowest level are current and voltage control for each of the above mentioned devices. The next level involves droop control on the current and voltage set points to ensure stability and up to the moment power balance, and ensures proper voltage regulation at each bus, and the third level focuses on optimization of resources. This paper focuses on the middle level, establishes stability criteria using non-linear techniques, and demonstrates the feasibility using numerical simulation.