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NASA is pursuing research to advance Electrified Aircraft Propulsion (EAP) technologies that address fuel burn and emission reduction goals. EAP brings the potential for improved performance over the state of the art. However, for these systems to be practical and certifiable, they need to possess adequate robustness to adverse conditions including a variety of system failures that are not applicable to conventional turbofans today. Numerous EAP concepts interface gas turbine engines with an electrical power system that includes electric machines and sometimes electrical energy storage. The expansion of the powertrain increases the probability of encountering a failure and introduces new failure modes. Failures within the electrical power system may also impact the gas turbine engine(s) to which the electrical powertrain is coupled. This effort investigates failures originating in the electrical power system and their impact on the parallel hybrid propulsion system. Reversionary control strategies are also demonstrated to reduce the impact of the failures. Failure mitigation strategies were devised and employed in simulation. Various failure scenarios were simulated including those occurring during steady state operation, transients, and takeoff and landing scenarios. The timing of the failure and delay in failure identification and activation of mitigation strategies are noteworthy variables in the study. While the system remained stable throughout all failure scenarios, delays in failure identification could result in undesirable conditions such as increased operating temperatures and reduced stall margin. The results demonstrate successful mitigation of failures through reversionary control modes and help to generate confidence in the robustness of the conceptual parallel hybrid propulsion system.