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The proton exchange membrane (PEM) electrolyzer is vital for converting surplus renewable energy (RE) into hydrogen, underpinning the efficient and stable operation of the electric–hydrogen system. However, frequent start–stop cycles and load variations accelerate the degradation of proton exchange membranes and catalyst layers, incurring significant lifetime costs that existing studies ignore. To explore how the PEM electrolyzer’s dynamic traits impact system performance, we introduce an optimized operation approach for the electricity–hydrogen integrated energy system (IES) that incorporates these dynamic features and the novel Loss of Life Cost (LLC) model. Initially, to rectify the inadequacy in modeling the PEM electrolyzer within the current electricity–hydrogen IES operational framework, we integrate its dynamic characteristics based on electrochemical properties and establish a quantitative relationship between operational cycles and degradation costs. This enhanced model accurately reflects how operational conditions affect the electrolyzer’s hydrogen production efficiency and lifetime consumption, enabling precise performance simulation and economic assessment. This, in turn, promotes high-quality renewable energy utilization via hydrogen production while ensuring asset longevity, meeting the rising demand for hydrogen energy applications. Building on this, we further factor in constraints related to diverse energy conversion and safe operation within the electricity–hydrogen IES, as well as the operational limits of hydrogen fuel cells, various energy storage (ES) options, cogeneration units, and other pertinent equipment, aiming to minimize the system’s total daily costs (operational plus degradation costs). Consequently, we develop an optimization operation model for the electricity–hydrogen IES that accounts for the PEM electrolyzer’s dynamic characteristics and degradation economics. Finally, through simulation examples validated against published experimental data, we comprehensively analyze how the PEM electrolyzer’s dynamic traits influence system operation, confirming the effectiveness of our proposed model and methodology. Simulation findings reveal that, under varying electrolyzer capacities, ignoring the PEM electrolyzer’s dynamic characteristics can result in a deviation in system operating. Compared with the proposed method, it can reduce the equipment degradation speed by a maximum of 5.78 times.