Optimal Process Operations in Fast-Changing Electricity Markets: Framework for Scheduling with Low-Order Dynamic Models and an Air Separation Application

Today’s fast-changing markets often require the granularity of production schedules to be refined to time scales comparable to the time constants of a chemical process. Consequently, the process dynamics must be considered explicitly in production scheduling. High dimensionality, nonlinearity, and the associated computational complexity make incorporating dynamic models in scheduling calculations challenging. We propose a novel scheduling approach based on scheduling-oriented low-order dynamic models identified from historical process operating data. We introduce a methodology for selecting scheduling-relevant variables and identify empirical models that capture their dynamic response to production target changes imposed at the scheduling level. The optimal scheduling calculation is then formulated as a dynamic optimization aimed at minimizing operating cost. We apply these concepts to an industrial-size model of an air separation unit operating under time-sensitive electricity prices. Our approach reduces computational effort considerably while preserving essential information required for the optimal schedule to be feasible from a dynamic point of view. Extensive simulations show that significant savings can be derived from operating in a transient regime, where the production rate is increased when energy prices are low, and reduced during peak price periods, while taking advantage of available storage capacity.