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With the fast development of wind power, the reliability of power systems becomes more difficult to be evaluated. Grid operators are lacking tools for day-ahead decision making in presence of a high penetration of uncertain generation. Short-term power system reliability evaluation using Monte Carlo Simulation (MCS) is not feasible due to its high computation cost. This study proposes to use the First-Order Reliability Method (FORM), coupled with the law of total probability, for short-term reliability assessment of power systems with large amount of wind power. This method is much faster than the MCS and allows us to evaluate the probability of load shedding due to many causes: lack of production, voltage constraints, line congestion, etc. A reliability assessment is implemented on a medium-voltage regional network using day-ahead forecasts. Using the proposed method, the reliability assessment of the power system is done with the same accuracy and with a computing time greatly reduced. Test results of the proposed method are compared with those obtained from the MCS.