Tailored Time Grids for Nonlinear Scheduling Subject to Time-variable Electricity Prices by Wavelet-based Analysis

Typically, the consideration of nonlinear process models in discrete-time scheduling is limited to short planning horizons and/or coarse discretizations due to a linear scaling of the problem size with the number of considered scheduling intervals. To overcome this limitation, we recently proposed a wavelet-based algorithm focusing on scheduling problems with time-variable electricity prices, which iteratively adapts the time grid (Schaferet int., Mitsos, doi:10.1016/j.compchemeng.2019.106598). In this work, we extend our approach by presenting a systematic method for the identification of promising initial aggregated time grids based on the analysis of the wavelet representation of the time series of electricity prices. We apply the procedure to a literature example addressing the scheduling of a seawater reverse osmosis (Ghobeity and Mitsos, doi: 10.1016/j.desal.2010.06.041). We demonstrate that substantial reductions in the number of optimization variables in a reduced-space formulation are possible, while furnishing feasible schedules that lead to insignificant deviations below0. 05 % in the objective value compared to the global optimum using the full time grid.