The U.S. chemical manufacturing and refining industries are two of the largest sources of energy demand and greenhouse gas (GHG) emissions in the country. They account for 15% of the country's energy consumption and nearly 20% of the U.S.'s greenhouse gas (GHG) emissions. Process heating creates most of these energy requirements and GHG emissions. Process heating is typically generated through direct fossil fuel combustion or steam, which also consumes fossil fuels. As the country moves toward carbon-neutrality and decarbonized electricity, chemical industries are seeking paths toward decarbonizing process heating. One pathway currently being considered is electrification. To truly reduce the industry's carbon footprint, it is necessary to integrate chemical plants with decarbonized energy systems and reduce emissions within the energy grid. However, integration efforts are currently challenged due to hesitance in directly sharing process data with Independent System Operators (ISOs) due to the private and sensitive nature of such data. In order to enable integration between electrified process heating systems and the power grid without direct data sharing, the present project develops decentralized algorithms for chemical plants and ISOs to use in operations planning while accommodating data privacy. Development began by establishing key chemical process heating applications with a high potential for electrification. One such process is steam cracking. Steam cracking is a highly endothermic petrochemical process that converts saturated hydrocarbons into smaller unsaturated hydrocarbons, such as converting natural gas into ethylene and propylene. This requires substantial process heating, but various electrification methods are possible, such as using hydrogen. The present study examines the plant-level microgrid for this process and formulates operational constraints related to its components for an optimization model. This presentation focuses on mathematically modeling proton-exchange membrane (PEM) electrolysers and fuel cells, two important operations within the microgrid. Various models and simulations of these operations were compiled from literature and used in creating constraints. Constraint formulation for other hydrogen technologies and infrastructure is also discussed. Future developments in this project are expected to include a larger, more integrated model and exploration into various pricing effects.