A novel methodology is proposed for the customer security assessment with high penetration of wind power in modern distribution networks. The customer security is quantified through customer damage costs by operating wind farms without standing reserve, which causes an inadequate supply of power to meet loads at some operating conditions. Necessary reserve to mitigate intermittency of wind is quantified through shed load. The ability to estimate a network firm import capacity that can be replaced with a wind plant, which is operated with the necessary reserve, is an added advantage of the approach. Monte Carlo simulation is the prime tool of the assessment, which incorporates linear programming-based re-dispatching of generation and load shedding to eliminate constraint violations. Steady-state analysis is used for the assessment incorporating random contingencies, subsequent tripping, intermittency of wind power, and demand variations. A case study is presented considering a medium voltage island network that has a grid connection, and this is used to demonstrate the customer security assessment integrating uncertainty models and a formulation to extract the impact of intermittency.