The increasing market penetration of wind power in many countries leads to increased challenges for the power system operator in balancing production and consumption in real time. Imbalance between scheduled and realized wind power generation leads to reduced income (balancing costs) for the wind power producer. However the interest in using renewable electricity for hydrogen production could help offset the power deviations due to the operational flexibility of electrolysers and the storage capability of hydrogen. The grid can also be used as backup when there is little or no wind, substantially reducing the required hydrogen storage capacity while maintaining security of supply. In addition, connection to the power grid opens up for a diversified location of wind power and hydrogen production, thus reducing or eliminating the need for costly hydrogen distribution. In this study we present a method to optimize the scheduling and the real-time operation of a wind-hydrogen plant operating in a day-ahead electricity market. The plant model could represent a single plant or an aggregation of multiple wind power plants and electrolysis plants. The problems are formulated as stochastic linear optimization problems, taking into account probabilistic wind power forecasts, electricity prices and imbalance costs in addition to main component specifications. The objective is to maximize the total revenue while serving a required daily hydrogen load. Results include optimal day-ahead scheduling of power exchange, a real-time operational strategy for the electrolyser based on wind power production, estimations on reduced power imbalance and an overall cost-benefit analysis.