(751c) Top-Down Approach for Scheduling and Control Under Time-Varying Electricity Prices

As the pressure for making processes more competitive, efficient and cost-effective increases, production optimization emerges as an essential task to meet these goals. Traditionally, scheduling and control have been addressed separately as independent problems in different levels of the enterprise decision hierarchy. However, this strategy overlooks the interaction between the two tasks, which in general leads to a suboptimal solution and underestimates the effects of disturbances and uncertainty in the overall operation. The integrated problem, on the other hand, presents a substantial challenge in terms of formulation and efficient solution. Some of the difficulties are related to the presence of integer variables in scheduling decisions, nonlinear dynamic equations for control, and the inherent multiple time-scales present. In addition, accounting for parameter uncertainty and multi-period decisions considerably increases problem size and complexity. This last issue is particularly relevant when analyzing Demand Response scenarios, in which electricity prices may vary hourly, daily or seasonally, or when dealing with intermittent renewable energy generation. In this work, the problem of integrating scheduling and control under time-varying electricity prices is investigated.

Following the classification proposed by Baldea and Harjunkoski (2014), there are mainly two approaches for integrating scheduling and control: (i) top-down approach, which incorporates control elements into the scheduling framework and includes the sub-categories of control-defined transition times, dynamic optimization-based scheduling and bridging models; and (ii) bottom-up approach, which incorporates economic considerations into the control framework, e.g. Economic MPC. For the top-down approach, more specifically using control-defined transition times, recent studies have shown the benefits of integration. Mahadevan et al. (2002) presented a first study on how the control layer affects the scheduling of grade transitions in polymerization reactors, in which the authors screen the more difficult transitions before solving a simplified scheduling problem. Chu and You (2012) simplified the optimal control task by generating a set of candidate PI controller parameter values offline and selecting the optimal candidate in the integrated problem online. Subsequently, the same authors made several contributions extending the methodology for batch processes and different formulation and solution strategies (Chu and You, 2015). In these studies, the problem is originally cast as a mixed-integer dynamic optimization (MIDO), which requires a decomposition approach to be implemented online.

More recently, Tong et al. (2017) analyzed the integration with varying electricity prices and proposed a decomposition solution method and online implementation based on a receding horizon approach which address both optimal controller tuning and scheduling decisions. In the present work, the model proposed by Tong et al. (2017) is expanded to include important features such as start and end times for the scheduling task, and different criteria for the optimal tuning of the regulatory control parameters. A comparison is made between different solution strategies for the scheduling task, and the benefits and drawbacks of using the mathematical optimization formulation are highlighted. The impact of parameter uncertainty in the problem size and the choice of the solution method is also evaluated. Finally, the decomposition-based solution strategy originally proposed is adjusted to accommodate the more flexible scheduling model, and the results are evaluated from a Demand Response viewpoint. The methodology is applied to a simple case-study employing an energy intensive process unit.

References

Baldea M, Harjunkoski I. Integrated production scheduling and process control: a systematic review. Comput Chem Eng 2014; 71:377–90.

Chu Y, You F. Integration of scheduling and control with online closed-loop implementation: fast computational strategy and large-scale global optimization algorithm. Comput Chem Eng 2012; 47:248–68.

Chu Y, You F. Model-based integration of control and operations: overview, challenges, advances, and opportunities. Comput. Chem. Eng. 2015; 83, 2.

Mahadevan R, Doyle F J, Allcock A C. Control-relevant scheduling of polymer grade transitions. AIChE J 2002; 48:1754–64.

Tong C, Palazoglu A, El-Farra N H. A Decomposition Scheme for Integration of Production Scheduling and Control: Demand Response to Varying Electricity Prices. Ind. Eng. Chem. Res. 2017; 56, 8917−8926.