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In the transition to decarbonized energy systems, green ammonia will play a key role in reducing greenhouse gas emissions. However, its production remains an energy-intensive and economically demanding process. This study addresses these challenges by conducting a techno-economic optimization of a photovoltaic powered green ammonia production system, operating under grid curtailment conditions, with the aim of minimizing the levelized cost of ammonia. The system comprises a photovoltaic plant, a battery energy storage system, a proton exchange membrane water electrolyzer, a hydrogen storage unit, and a Haber-Bosch reactor for ammonia synthesis. A Mixed-Integer Linear Programming approach is employed to optimize component sizes and operation scheduling, with a target annual production of 1 kton of ammonia. Two curtailment scenarios are considered: one in which surplus electricity sold to the grid is valued at the Levelized Cost of Electricity, and an extreme scenario where surplus electricity has zero value. The analysis results in a levelized cost of ammonia of 1,038 €/ton, adjusted to 995 €/ton when considering electricity sales.