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

Abstract

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.

Power‐to‐X: Between Electricity Storage, e‐Production, and Demand Side Management

“…The latter responses consider electricity spot prices to reduce electrical energy costs. In addition to the economic benefits, environmental impacts, especially carbon footprint, can be mitigated by exploiting electricity with a high share of RES [34,35] electricity-intensive industrial processes such as air separation units (ASU) [36][37][38][39], chlor-alkali (CA) electrolysis [32,40], seawater reverse osmosis [41], and aluminum production processes [42], DSM is particularly worthwhile.…”

Economic Benefit from Progressive Integration of Scheduling and Control for Continuous Chemical Processes

“…Potential for economic benefit from integrating process dynamics into design, scheduling, and control problems has also been demonstrated [41,44,52]. Computational reduction of incorporating process dynamics into scheduling has been investigated successfully, maintaining benefit from the incorporation of process dynamics into scheduling while reducing dynamic model order [10,15,16,33,42]. …”

“…Gutierrez-Limon et al demonstrated integrated planning, scheduling, and control responsive to fluctuations in market demand on a CSTR benchmark application [36,37]. Pattison et al investigated ISC with an air separation unit (ASU) in fast-changing electricity markets, responding optimally to price fluctuations [42]. Pattison et al also demonstrated theoretical developments with moving horizon closed-loop scheduling in volatile market conditions [10].…”

Reduced dynamic modeling approach for rectification columns based on compartmentalization and artificial neural networks

“…The vast majority of literature concerning the operation of ASUs subject to fluctuating electricity prices accounts for dynamic responses only indirectly by restricting the transitions between quasi‐stationary operating points . Recent work aims at directly accounting for dynamics when making scheduling decisions through the use of low‐order dynamic models, which is also extended to a closed‐loop scheduling formulation . This framework furthermore allows for explicit consideration of the tracking behavior of a subordinated model predictive controller (MPC) in scheduling of ASUs .…”