A Decomposition Scheme for Integration of Production Scheduling and Control: Demand Response to Varying Electricity Prices

Abstract

One views demand response in industrial processes as the management of operating policies to accommodate variations in the availability and pricing of electricity from the grid. To find the optimal operating regimes and to facilitate the transitions in between such regimes in a costeffective manner, a mixed-integer nonlinear programming problem is often formulated. A full solution to this problem involves not only finding the optimal operating regimes but also determining the optimal control policies to ensure minimal transition costs; such solutions are often mathematically intractable. In this paper, a decomposition strategy is proposed to arrive at a feasible, albeit suboptimal, solution. The scheduling problem is first solved using a prefixed transition time to minimize the total operating cost; only the first scheduled transition of the obtained solution is implemented in the process, and optimization of controller parameters is then carried out to economically shape the transient profiles. When the first scheduled transition with the optimized controller parameters is completed, the scheduling and control problems are reformulated and resolved again in a receding-horizon optimization manner. A conceptual case study of a continuous stirred tank reactor demonstrates the key contributions and effectiveness of the strategy.

Integrated scheduling and control in discrete-time with dynamic parameters and constraints

“…Xu and Wang [61] investigate a feedback control approach to address energy consumption in a job-shop scheduling problem. Tong et al [52,62] incorporates chemical process dynamics in formulations accounting for DR in chemical process scheduling and control. Tong et al account for process dynamics during transition periods and incorporate DR in their objective; however, the process is considered at steady-state during production periods, not allowing the optimization to alter operation during production periods to respond to dynamic constraints and dynamic energy price.…”

“…Tong et al account for process dynamics during transition periods and incorporate DR in their objective; however, the process is considered at steady-state during production periods, not allowing the optimization to alter operation during production periods to respond to dynamic constraints and dynamic energy price. Additionally, Tong et al consider parameter tuning for linear controllers rather than utilizing nonlinear model predictive control in the SC formulation [62]. The SC problem is decomposed into a scheduling problem with constant transitions and a control problem (optimal parameter tuning).…”

A flexible design framework for process systems under demand‐side management

“…Later studies focused on the integration of the scheduling problem with process dynamics. Tong et al 16 introduced a decomposition scheme to perform process scheduling while optimizing the controller parameters that can manage the scheduling sequence under time‐varying electricity prices. Kelley et al 6 proposed an MILP scheduling model to account for the process dynamics using a low‐order model.…”