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All-electric ships (AES), enabled by integrated power systems (IPS), have been pursued for both commercial and military applications to meet the increasing ship-board power demand and environmental sustainability initiatives. They necessitate real-time power management (PM) for dynamic reconfiguration to support system critical operations in the event of dynamic load change or IPS component failures. The nonlinear, large scale trajectory optimization problem associated with IPS, along with the non-analytical nature of IPS model, makes many existing methods inadequate in meeting the real-time requirements. In this paper, we develop a methodology that exploits time scale separation, a characteristic associated with IPS dynamics, to achieve real-time optimization. In parallel, a dynamic model of the IPS with gas turbine and fuel cell as power plants is developed that captures the relevant dynamics but is simple enough for real-time optimization. The tradeoffs between the computational efficiency and optimization accuracy are analyzed. The optimization results for IPS PM on a real-time simulator are reported, which illustrate the real-time feasibility of the proposed optimization strategy.