(635h) Optimal Scheduling of an Air Separation Unit for Demand Response Under Price and Demand Uncertainty

Deregulation and the influx of renewable electricity generation from wind and solar photovoltaics has transformed the U.S. electricity markets. The presence of these renewables has increased variability and uncertainty on the supply side of the grid; coupled with significant variability on the demand side, this has led to an increasingly challenging environment for balancing supply and demand. Managing demand rather than generation, referred to as demand response (DR), has emerged as an attractive approach for mitigating grid imbalance. Electricity-intensive processes are promising industrial DR candidates: production can be increased during off-peak hours, and excess product stored for use during peak demand when production rate is lowered. Grid-balancing benefits notwithstanding, DR participation has the potential to significantly lower operating cost of the industrial entities due to the inherent fluctuations in electricity prices generated by mismatch between power supply and demand [1].

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.

[1] 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), 4562–4584. https://doi.org/10.1021/acs.iecr.5b03499

[2] 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, 951–966. https://doi.org/10.1016/j.apenergy.2017.12.127