(212g) Optimal Load Scheduling for Efficient Operation of Air Separation Systems Under Uncertain Costs and Demands

Cryogenic air separation systems consume large amounts of electricity to provide significant quantities of high purity nitrogen, argon, and oxygen products. In many processes frequent load changes are required because of the variability of electricity pricing and uncertain product demands.

This work addresses the problem of determining optimal load scheduling to reduce energy costs while considering variability in the price of electricity and uncertainty in product demands. A rigorous mathematic model is built for three highly coupled cryogenic distillation columns with constraints on safe operating limits. Daily operation is separated into several periods, and different electrical prices are considered for each period. A linear relationship is assumed between the transition time and the absolute change in operating load, and a rigorous multi-period nonlinear programming formulation is developed to determine the optimal load scheduling. Because of uncertainty in product demands, a probabilistic fill rate relationship, formulated using standard loss function, is included in the objective function to calculate expected daily profit. In addition, various customer satisfaction levels are considered through a constraint on the expected fill rate.

In order to effectively solve this large-scale multi-period formulation, we make use of a recently developed Schur-complement decomposition approach, based on the existing primal-dual interior point nonlinear solver IPOPT. With this approach we identify the region where production is governed by the expected profits along with the region where production is governed by the customer satisfaction constraint. The optimal operating conditions under different customer satisfaction levels are provided to assist decision-making with respect to operations and contract negotiation.