The increasing share of volatile renewable electricity production motivates demand response. Substantial potential for demand response is offered by flexible processes and their local multi-energy supply systems. Simultaneous optimization of their schedules can exploit the demand response potential, but leads to numerically challenging problems for nonlinear dynamic processes. In this paper, we propose to capture process dynamics using dynamic ramping constraints. In contrast to traditional static ramping constraints, dynamic ramping constraints are a function of the process state and can capture high-order dynamics. We derive dynamic ramping constraints rigorously for the case of single-input single-output processes that are exactly input-state linearizable. The resulting scheduling problem can be efficiently solved as a mixed-integer linear program. In a case study, we study two flexible reactors and a multi-energy system. The proper representation of process dynamics by dynamic ramping allows for faster transitions compared to static ramping constraints and thus higher economic benefits of demand response. The proposed dynamic ramping approach is sufficiently fast for application in online optimization.
Increasingly volatile electricity prices make simultaneous scheduling optimization desirable for production processes and their energy systems. Simultaneous scheduling needs to account for both process dynamics and binary on/off‐decisions in the energy system leading to challenging mixed‐integer dynamic optimization problems. We propose an efficient scheduling formulation consisting of three parts: a linear scale‐bridging model for the closed‐loop process output dynamics, a data‐driven model for the process energy demand, and a mixed‐integer linear model for the energy system. Process dynamics is discretized by collocation yielding a mixed‐integer linear programming (MILP) formulation. We apply the scheduling method to three case studies: a multiproduct reactor, a single‐product reactor, and a single‐product distillation column, demonstrating the applicability to multiple input multiple output processes. For the first two case studies, we can compare our approach to nonlinear optimization and capture 82% and 95% of the improvement. The MILP formulation achieves optimization runtimes sufficiently fast for real‐time scheduling.
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