Utility systems provide power and heat for chemical plants and drive production processes, while large amounts of greenhouse gases are emitted. The introduction of renewable energy sources can help reduce carbon emissions from traditional utility systems. A data-driven robust optimization for utility systems that introduce wind and solar energy is presented in this paper. The paper proposes a superstructure model for utility systems with renewable energy equipment, as well as physical models for wind turbines, photovoltaic power generation, and electrical energy storage. A robust optimization method is employed to solve the optimization problem in case of uncertainty in wind and solar energy. Then, an environmental and economic multi-objective optimization model was formulated to balance economic costs and carbon emissions. Finally, the feasibility of the proposed methods was demonstrated by a case study of a real industrial chemical plant. The optimization results indicate that a data-driven robust optimization approach overcomes the uncertainty within wind and solar energy by setting reasonable robust budget parameters, which reflects the ability to withstand system risk.