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One of the main challenges and essentials of the power system is the flexibility of generation scheduling. The flexibility of a system can be enhanced by using a smart grid comprising demand response, hybrid/diesel generation units and energy storage system. In this paper, an improved flexibility index is defined with the concept of fast reserve supply. The uncertainties of wind/solar power plants and required reserve of thermal units are considered using Latin Hypercube Sampling (LHS). The smart grid supplies a part of load profile of commercial consumers and a part of charge profile of plug-in hybrid electric vehicles (PHEVs) through wind and solar virtual power plants (VPPs), responsive loads, distributed generators (DGs) and the energy storage system. Moreover, the PHEVs considered in this paper provide a system with more flexibility. This paper has solved the unit commitment problem in a single-node system that has no transmission constraints. The mixed integer linear programming (MILP) and the mixed integer non-linear programming (MINLP) methods have been used in order to solve the unit commitment problem and the smart grid scheduling, respectively. The results show that the presented model can optimize the costs of the system and causes the system to become more flexible. • A flexibility index is defined with the concept of fast reserve supply. • A smart grid containing fast-power generation resources are designed. • The plug-in hybrid electric vehicles provide a system with improved flexibility. • The LHS method is used to make the uncertainties of required reserve. [ABSTRACT FROM AUTHOR]