The growing demand for green hydrogen highlights the potential of wind energy as a renewable energy source. However, water electrolyzers, crucial for green hydrogen production, suffer from frequent shutdowns that can degrade membranes and catalysts, thus reducing both efficiency and lifespan. The variability of wind power adds further challenges, necessitating advanced control strategies to maintain system stability. Traditional rule-based control (RBC) methods often fail to effectively manage real-time power fluctuations and the uncertainty of future wind conditions, which limits system adaptability. This study introduces a novel RBC method that incorporates a 'target battery level' to balance reliability and productivity. Utilizing a bi-level optimization framework, the design and target battery level are co-optimized, providing a more adaptable and efficient solution. Case studies in six regions reveal that the levelized cost of hydrogen is realistically 6-20% higher than in idealized scenarios that assume perfect wind foresight. Furthermore, the proposed RBC strategy, maintaining a target battery level above 90%, consistently outperforms conventional RBC approaches in terms of reliability and economic viability. This method presents a robust, economically feasible solution to support sustainable green hydrogen production under real-world conditions. Highlights  A bi-level optimization framework is developed to optimize design and operational policies under uncertainty.  A novel rule-based control strategy is introduced, featuring a tunable target battery level, which can be optimized to balance reliability and productivity for a specific case.  Realistic evaluations indicate the Levelized Costs of Hydrogen approximately 6-20% higher than those in ideal scenarios with complete foresight of future wind conditions.