Simultaneous mixed-integer dynamic scheduling of processes and their energy systems

Increasingly volatile electricity prices make simultaneous scheduling optimization for production processes and their energy supply systems desirable. Simultaneous scheduling needs to account for both process dynamics and binary on/off-decisions in the energy system and thus leads to challenging mixed-integer dynamic optimization problems. In this contribution, we propose an efficient scheduling formulation that consists 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 are discretized by collocation yielding a mixed-integer linear programming (MILP) formulation. We apply the scheduling method to a single-product reactor, with 5.6% economic improvement compared to steady-state operation, and a multi-product reactor, with 5.2% improvement compared to sequential scheduling. While capturing 85% and 96% of the improvement realized by a nonlinear optimization, the MILP formulation achieves optimization runtimes sufficiently fast for real-time scheduling.