Connecting Representative Periods in Energy System Optimization Models using Markov Transition Matrices

Abstract

Time series aggregation reduces the computational complexity of large-scale energy system optimization models, but maintaining chronological continuity between the resulting representative periods (RPs) remains a key challenge, as transitions between RPs are typically lost. This causes inaccuracies in storage behavior, unit commitment, and other time-linked aspects of the model. We propose a novel method that uses the Transition Matrix between RPs to link them via probabilistic transitions and expected values. In contrast to existing Transition Matrix approaches that add variables and constraints to reconstruct inter-period chronology (e.g., for seasonal storage), our method reformulates the existing intra-RP constraints at the period boundaries without introducing any additional variables or constraints. It also handles constraints that connect multiple time steps and can be adapted to binary variables. We demonstrate the benefits on an illustrative case study and validate them on the updated IEEE Reliability Test System (RTS-GMLC). The improvement over the state of the art depends on the structure of the Transition Matrix, which can be inspected a priori at no additional data cost. When it is near-diagonal, the established cyclic connection already performs well, whereas for less diagonal matrices the Markov Transition reduces the median operational deviation by up to 80% (from about 32% to 6%). These gains come at practically no extra cost, as the mean computational effort stays below 2% of the full-model runtime, at most 0.9 percentage points more than the cyclic connection.