The complex coupling between water and energy systems plays a critical role in sustainable development. As a primary source of both water consumption and carbon dioxide emissions

the energy system’s operation directly affects the environmental performance of integrated infrastructures. However

existing studies often fail to accurately represent the bidirectional interactions between systems and to model key energy conversion processes

limiting the potential for carbon reduction and water savings. To address these challenges

a coordinated water-energy-carbon optimization model is proposed for an integrated energy system incorporating seawater desalination for hydrogen production. A bidirectional coupling model is first developed to capture water consumption in the energy system and electricity consumption in the water system

thereby reflecting mutual feedback. An analytical model is then formulated to describe the relationship between electrolyzer efficiency and input power

allowing dynamic behavior to be represented through algebraic constraints within the optimization framework. The carbon emission flow of the water-energy nexus is subsequently calculated to allocate emissions across subsystems. Finally

an enhanced distributed optimization algorithm is applied to solve the low-carbon multi-system scheduling problem. Case studies confirm that the proposed approach effectively reduces carbon emissions and water consumption while maintaining economic efficiency.