(635h) Optimal Scheduling of an Air Separation Unit for Demand Response Under Price and Demand Uncertainty
The industry-side benefits of DR increase when multi-day scheduling horizons are considered. Longer time horizons allow the plant to optimize the use of its storage capacity, and deploy stored products at times of peak electricity demand. However, considering a longer time horizon presents some disadvantages, notably, the inaccuracies present in the forecasts of electricity prices and product demand over an extended period of time.
To account for this uncertainty and generate a robust DR operating schedule, we implement a chance-constrained optimization framework. Chance constraints effectively restrict the feasibility region, thereby increasing the confidence level of the solution. The robustness of the solution can be adjusted by specifying the desired probability of meeting the uncertain constraint(s). We represent the applicability of chance constraints to solving DR scheduling problems under uncertainty by applying them to an air separation unit (ASU) capable of producing 50 tons of nitrogen per day. Owing to recent developments in representing the (nonlinear) dynamics of chemical processes via (exact) linearizations [1,2], the problem is formulated as a MILP. We retain the MILP formulation by implementing chance constraints using big-M indicator constraints, resulting in a large-scale MILP scheduling problem which accounts for price and demand uncertainty without adding significant computation time.
 Pattison, R. C., Touretzky, C. R., Johansson, T., Harjunkoski, I., & Baldea, M. (2016). Optimal Process Operations in Fast-Changing Electricity Markets: Framework for Scheduling with Low-Order Dynamic Models and an Air Separation Application. Industrial & Engineering Chemistry Research, 55(16), 4562â4584. https://doi.org/10.1021/acs.iecr.5b03499
 Kelley, M. T., Pattison, R. C., Baldick, R., & Baldea, M. (2018). An MILP framework for optimizing demand response operation of air separation units. Applied Energy, 222, 951â966. https://doi.org/10.1016/j.apenergy.2017.12.127