Reliability of a system is the ability of that system to achieve intended goals and satisfactory performance degree under certain operational conditions in specified period of time. Frequency is a global quantity throughout the power grid whose stability lies on the balance between supply and consumption; any changes in demand or generated power in one point of the grid, results in frequency deviation to the entire grid; Meanwhile powerplants restrictions such as spinning reserve capacity and fixed generation rate capacity for eliminating power shortage are effective on frequency deviation and the time of reaching to steady state.All these factors are influence on the reliability of power system and should be considered and analyzed. In this article, power system reliability indexes has been evaluated with considering frequency deviation in process of primary frequency control on IEEE_RTS79 by MATLAB/Simulink Software. By evaluating reliability indices in the conditions where different amounts of spinning reserve, from 50 to 600 MW are available in power system, it has been tried to specify the role of reliability evaluation in power system expansion planning, finally the optimal amount of spinning reserve is suggested in terms of power system reliability.