The consistently growing usage of wind power resources and the replacement of conventional thermal power plants with large-scale wind farms has a considerable impact on power system reliability and its generation adequacy. This impact is due to the intermittent and variable nature of the wind speed which causes a very changing, transient and random power generation by the wind turbines.One of the most commonly used methods for modeling the reliability of power systems, including wind farms, is the Markov method. The main advantage of this method is its ability to model the repairable systems and to consider the failure and repair rates of the system components, but, with increasing number of system elements, the number of model states increases exponentially. So, it has a heavy computing burden such that the modeling of systems having more than a certain number of components is impossible. On the other hand, the use of the Universal Generating Function method has also been proposed in recent years to model the reliability of wind farms in large dimensions, but the model derived from this method is limited to the evaluation of probabilistic reliability indices such as loss of load probability, loss of load expectation and expected energy not supplied and so on, and it is not capable for evaluation of the frequency-based reliability indices. However, in the high penetration of wind power, evaluation of the frequency-based indices is of particular importance.In this study, in order to assess the generation adequacy of the power system, a new analytical method based on the development of the Universal Generating Function (UGF) is proposed to model the reliability of large-scale wind farms that addresses both the problem posed by the above methods and provides a comprehensive model for estimating the probability and frequency indices of generation adequacy in the presence of very large wind farms. This method is called Comprehensive Universal Generating Function (CUGF). In the proposed method, effective factors in modeling the reliability of wind farms such as wind speed variations, the correlation between wind speed and turbines output power, and forced outage rate (FOR) of turbines are separately modeled and then combined together. Thus, a comprehensive vector function for conducting different analyzes is obtained. In this way, if the number of turbines increases, the number of model states does not increase exponentially. In addition, the lower number of states in the proposed method reduces the computational burden, and subsequently increases the computational speed. By the proposed method, the states probability and transition rates between states are simultaneously modeled in the reliability vector function of the generation system and resolves the major drawback of the UGF method in evaluation of the system frequency indices. In order to demonstrate the performance and effectiveness of the proposed method, sample wind farms are modeled in a variety of sizes, from small to very large, by the proposed method and compared with the Markov model for the number of states, computational burden and efficiency. Then, by adding some of these sample wind farms to the RBTS and IEEE-RTS test systems, and using their constructed models by the CUGF, different probability and frequency based indices of these systems are evaluated, analyzed and compared with the existing reports. Keywords: 1- reliability modeling 2- generation system adequacy 3- very large-scale wind farms 4- Universal Generating Function (UGF) 5- Markov model.