Hull Clustering with Blended Representative Periods for Energy System Optimization Models

TL;DR

The paper tackles the computational burden of high-resolution temporal modeling in ESOMs by reducing time dimensions with representative periods. It introduces hull clustering with blended RPs, using extreme points and conic blends to better capture constraints with fewer periods. A greedy hull clustering algorithm and weight-fitting procedures for Dirac, convex, sub-unit conic, and conic weights are developed and integrated into ESOMs. Case studies on GEP and P2X with European data show improved solution quality (lower regret) and reduced runtimes compared with traditional RP methods, demonstrating practical scalability.

Abstract

The growing integration of renewable energy sources into power systems requires planning models to account for not only demand variability but also fluctuations in renewable availability during operational periods. Capturing this temporal detail over long planning horizons can be computationally demanding or even intractable. A common approach to address this challenge is to approximate the problem using a reduced set of selected time periods, known as representative periods (RPs). However, using too few RPs can significantly degrade solution quality. In this paper, we propose the method of hull clustering with blended RPs to enhance traditional clustering-based RP approaches in two key ways. First, instead of selecting typical cluster centers (e.g., centroids or medoids) as RPs, our method is based on extreme points, which are more likely to be constraint-binding. Second, it represents base periods as weighted combinations of RPs (e.g., convex or conic blends), approximating the full time horizon more accurately and with fewer RPs. Through two case studies based on data from the European network operators, we demonstrate that hull clustering with blended RPs outperforms traditional RP techniques in both regret and computational efficiency.

Figures (8)

• Figure 1: Projection errors when approximating base period data using different weight types. Orange areas show the spaces of all points which can be represented without introducing a projection error. Errors decrease from left to right as we move from a discrete Dirac to more general weight types.
• Figure 2: Geometric interpretation of different hull types. A set of base period data (dots) is shown, and the shaded region indicates the span of each hull. Even when blended weights are used, this choice of RPs introduces projection errors. The more general the hull type is, the fewer RPs cover the dataset.
• Figure 3: Relative regret per clustering method in the GEP case study for four types of weights. Hull clustering outperforms $k$-means and $k$-medoids.
• Figure 4: Relative regret in the GEP case study for best-performing methods. The dashed line shows the relative regret of 7.4% with just 5 RPs, which is only achieved for non-hull methods for 80+ RPs.
• Figure 5: Relative regret versus (logarithmic) total time for GEP. When relative regret is under 100%, the Pareto front (thick black line) consists exclusively of hull methods. The coordinates of break points in the Pareto front are used as labeled tick marks on the axes. The dashed line shows mean time to solve the full problem.