A comparative study of time aggregation techniques in relation to power capacity expansion modeling

In this paper, we studied the aggregation techniques for power capacity expansion problems. Combining a growing demand for green energy with a hard constraint on demand satisfaction causes system flexibility to be a major challenge in designing a stable energy system. To determine both the need for flexibility and which technologies that could satisfy these needs at minimum cost, the system should be analyzed on an hour-by-hour scale for a long period of time. This often leads to computationally intractable problems. One way of getting more tractable models is to aggregate the time domain. Many different aggregation techniques have been developed, all with a common goal of selecting representative time slices to be used instead of the full time scale, gaining a problem size reduction in the number of variables and/or constraints. The art of aggregation is to balance the computational difficulty against the solution quality, making validation of the techniques crucial. We propose new aggregation techniques and compare these to each other and to a selection of aggregation techniques from the literature. We validate the aggregated problems against the non-aggregated problems and look into the sensitivity of the performance of the aggregation techniques to different data sets and to the selection of different element types. Our analysis shows that aggregation techniques can be used to achieve very good solutions in a short amount of time, and that simple aggregation techniques achieve good performance similar to that of techniques with higher complexity. Even though the aggregation techniques in this paper are applied to power capacity expansion models, the methodology can be used for other problems with similar time dependence, and we believe that results in agreement with the results seen here, would be achieved.