Efficient solving of time-coupled energy system MILP models using a problem specific LP relaxation

Abstract

Energy system optimization models (ESOMs) often contain time coupling constraints, some of which couple short time frames as of daily storages or load changes of components, while other constraints couple longer periods like seasonal storages, peak load prices, or upper bounds to overall yearly CO2 consumption. Those ESOMs have binary constraints for minimal loads, efficiency curves, or discontinuous energy prices that are relevant for the short-term operation of the equipment. Calculation times for solving a whole year or longer as a coupled MILP problem are in many cases too high for practical applications that normally should not exceed one hour. Typical decomposition strategies to reduce calculation times are often designed for subclasses of energy system models and are not generally applicable. In order to have a generalized approach to solve these models efficiently, we investigate strategies that are based on a problem specific relaxation of integer constraints and downsampling of the input time series of the models. A rolling horizon strategy is proposed that relaxes and downsamples the time steps from the end of the rolling horizon to the end of the year to consider the operation during the rest of the year. In order to reduce the error of the relaxation, binary constraints are reformulated to get the best LP approximation of the original MILP model. Using this rolling horizon strategy, models that are almost unsolvable as coupled MILP can be solved efficiently and very robustly and deliver a result that is feasible for the original problem and very close to the optimum of the original problem.