# Hull Clustering with Blended Representative Periods for Energy System Optimization Models

## TL;DR

This paper introduces hull clustering with blended representative periods, a novel method that improves the accuracy and efficiency of energy system planning models by better capturing demand and renewable variability.

## Contribution

It proposes a new clustering approach using extreme points and blended RPs to enhance traditional representative period methods in energy system optimization.

## Key findings

- Outperforms traditional RP techniques in accuracy and computational efficiency.
- Reduces the number of RPs needed for accurate modeling.
- Demonstrated effectiveness on European energy data.

## 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.