The climatic circumstances of the world have altered due to the world warming up, and this issue has increased high-impact and low-probability (HILP) events more than before. Supplying energy requirements has turned into one of the main challenges of utilities especially electrical distribution companies considering the frequency and intensity of HILP events. On the other hand, developments in storing electricity have varied expectations and will change the solutions leading to resilient electrical distribution networks (EDNs). Some researchers have studied and analyzed numerous aspects of resilient EDNs but hybridization of different types of energy storage systems (ESSs) has not evaluated before. This paper considers energy management of emergency-operated EDNs equipped with two different types of energy storage systems which are batteries and flywheels. Convex equations in all parts of the problem, including different types of energy storage systems are proposed and modeled as an MIQCP to optimize the resilient networks considering all limitations. The proposed framework is developed in GAMS software and the results are provided in the form of Pareto optimal solutions. Applicability of the conducted model is evaluated by the IEEE 33-bus test system aiming at outstanding the effects of flywheels in improving the resiliency of electrical distribution networks. The proposed model analyzed by various energy storing scenarios based on technical and economical limitations. Results showed that among the considered case studies, the 50 % of the cases included with flywheel while batteries participated in 30 % that were the most expensive ones. On the other hand, the lowest amount of objective function belongs to the case that is only included with flywheels. Accordingly, by considering flywheels as a newly born energy storage system in the emergency-operated EDNs, the flexibility of energy management is facilitated and can be developed economically.