To enhance the utilization efficiency of by-product hydrogen and decrease the power supply expenses of industrial parks, local utilization of by-product hydrogen plays a crucial role. However, the methods of utilizing by-product hydrogen in industrial parks are relatively limited. In response to this issue, an optimization method for a multi-energy system with by-product hydrogen considering the production process of chlor-alkali plants was proposed in this paper. Firstly, on the source side, models were established for hydrogen production using the ion exchange membrane electrolyzer and for the energy consumption during the caustic soda solution evaporation process. Secondly, on the load side, this paper explored the potential for local utilization of by-product hydrogen, including its participation in the production of downstream chemical products, combustion when mixed with natural gas, and utilization in hydrogen fuel cells. Next, this paper considered the influence of correlations among various loads within the factory and wind power generation, proposing a method for generating scenarios that takes into account the spatiotemporal correlation of source-load variables. Then, aiming to minimize the system operation cost and carbon trading cost, an operation strategy for a multi-energy system in a low-carbon industrial park, considering local utilization of by-product hydrogen, was proposed. Finally, the effectiveness of the scenario generation method proposed in this paper, considering spatiotemporal correlation, and the economic and environmental benefits of the proposed operation model utilizing the by-product hydrogen are verified through arithmetic simulation, based on the operation data of a chlor-alkali chemical park.