Renewable energies especially Run-Of the-River (ROR) power plants are increasingly used for the electricity generation in the power systems. The uncertain and intermittent nature of these plants arisen from variability of water flow, however, has led to some problems in their integration to power systems. Thus, the operating reserve requirement in a power system containing large ROR plants is a main challenge, which has to be addressed properly. In this way, this paper presents an analytical approach to determine the adequate spinning reserve based on the well-being approach during the system operation. The reliability model based on the components failures and uncertainty nature of water flow is introduced for ROR plants operation studies. This approach not only evaluates the interaction between these energies and conventional units, but also determines the contribution that ROR power plants can make in load carrying capability of a power generating system. Two reliability test systems, utilized from water flow data of Sheshpir River in Iran, are examined to demonstrate the effectiveness of the proposed model.