Wind and solar as two renewable energy resources are largely used to generate clean and sustainable energy in the power
systems. To integrate these renewable energies in the power system, different aspects of the power system such as reliability and operation are affected that must be investigated. It is due to the variation in the generated power of these resources that are arisen from the variation in the wind speed and solar radiation. To model the uncertainty nature of large-scale wind and photovoltaic farms in the operation studies of the power system, an appropriate multistate reliability model is developed for the wind and photovoltaic farms considering both failure of main components and variation in the wind speed and solar radiation. To determine the optimum number of states in the reliability model of wind and photovoltaic farms, XB index is calculated and based on the fuzzy c-means clustering technique the transition rates among different states are obtained. To calculate the transition rates among different states, the fuzzy numbers are used that results in the accurate and reduced reliability model for wind and photovoltaic farms. To determine the probability of different states in the reliability model of wind and photovoltaic farms in the operation studies, matrix multiplication technique is utilized to determine important indices of the power system such as the unit commitment risk. In this paper, the amount of required spinning reserve of a power system containing wind and solar generation units can be determined based on the reliability criterion. The proposed technique is applied to the two reliability test systems including RBTS and IEEE-RTS and the reliability-based operation indices of these systems are calculated to present the effectiveness of the proposed analytical method.