Green hydrogen is a promising solution for decarbonizing hard-to-abate sectors; however, its production is challenged by the mismatch between intermittent renewable generation and fixed hydrogen demand. This paper proposes an integrated optimization framework for the capacity planning and operational scheduling of a grid-connected green hydrogen system under variable electricity tariffs. The system consists of photovoltaic generation, a proton exchange membrane electrolyzer, and a hydrogen storage tank supplying a fixed hydrogen demand. A bi-level optimization approach is adopted, where Particle Swarm Optimization determines optimal system sizing, while a linear programming-based Energy Management System optimizes hourly operation. The objective is to minimize the levelized cost of hydrogen by jointly optimizing design and dispatch decisions. The framework is evaluated under three representative solar irradiance scenarios (high, average, and low) to capture resource variability. Results show that solar availability significantly impacts both system sizing and operational strategy. The lowest levelized cost of hydrogen of 6.36 USD/kg is achieved under favorable solar conditions, while limited solar availability leads to increased reliance on grid electricity and higher costs. The findings highlight the importance of integrating storage and flexible operation to shift production toward low-tariff periods.