We propose an algorithm for scheduling subject to time-variable electricity prices using nonlinear process models that enables long planning horizons with fine discretizations. The algorithm relies on a reduced-space formulation and enhances our previous work (Schäfer et al., Comput Chem Eng, 2020;132:106598) by a sensitivity-based refinement procedure. We therein expose the coefficients of the wavelet transform of the time series of independent process variables to the optimizer. The problem size is reduced by truncating the transform and iteratively adjusted using Lagrangian multipliers. We apply the algorithm to the scheduling of a multi-product air separation unit. The nonlinear power consumption characteristic is replaced by an artificial neural network trained on data from a rigorous model. We demonstrate that the proposed algorithm reduces the number of optimization variables by more than one order of magnitude, whilst furnishing feasible schedules with insignificant losses in objective values compared to solutions considering the full dimensionality.