Using clustering algorithms to characterise uncertain long-term decarbonisation pathways

Abstract

Long-term decarbonisation pathways to achieve ambitious low-carbon targets involve a range of uncertainties. Different energy system modelling approaches can be used to systematically evaluate the influence of the uncertainties, but this often leads to an unmanageable number of pathways. Summarising the large ensemble through a more limited number of representative pathways, to inform stakeholders, can be challenging. This study thus explores how to identify representative decarbonisation pathways using clustering algorithms, which can assist in grouping similar data points in uncategorised datasets, such as pathway ensembles. However, the suitability of clustering algorithms for pathway characterisation has not been investigated to date. Hence, k-means, hierarchical clustering, Gaussian mixture model, spectral clustering, and density-based clustering are adopted for comparisons. An illustrative pathway ensemble for the United Kingdom is applied to evaluate their performance based on cluster validity indices. Three metric transformations, including power, standardisation and sectoral standardisation, are also applied to create three additional sets of pathways for testing. The k-means algorithm is found to outperform others consistently, although hierarchical clustering might also be applicable if the distribution of pathway proximity is uneven. The results also highlight the utility of the approach in revealing distinctive trade-offs between technologies among the identified representative pathways. For instance, the electrification of heating can be replaced by district heating in the residential sector. The described, novel approach can be applied to characterise other sets of pathways, with greater technological details generated by any energy system models, to reveal insights for long-term decarbonisation.

Electric vehicle charging current scenario generation based on generative adversarial network combined with clustering algorithm

“…We assume that the number of clusters is four. Silhouette coefficient is used to verify the assumption given data 26 . What's more, It is defined as the ratio between the mean distance between a sample and other points in the same class and the mean distance between a sample and all the other points of the nearest cluster 27 .…”

A Novel Convex Clustering Method for High-Dimensional Data Using Semiproximal ADMM

“…In this section, we study the finite sample error bound and feature screening consistency of sparse group lasso convex clustering (2). We start with the following conditions that facilitate the technical proofs.…”

“…Suppose that condition A1 is satisfied. Let X be the solution of model (2) with q � 2. If c 1 ≥ 2δ ������������� (p log(p|Θ|)/n), then there exists positive constants b 1 and b 2 such that…”

“…It assigns samples into different clusters by minimizing the differences in the same cluster and maximizing the differences between different clusters. As an exploratory data analysis technique, it has been applied in many fields, such as image processing, energy engineering, and social networks [1][2][3]. To date, a wide variety of clustering methods have been introduced, including classical clustering methods such as K-means clustering [4,5] and hierarchical clustering [6,7].…”

“…We study the finite sample error bound and feature screening consistency of our proposed method in Section 3. In Section 4, we introduce an efficient optimization algorithm for solving (2). After that, in Section 5, we conduct numerical experiments to verify the effectiveness of the proposed method in synthetic datasets and four microarray datasets.…”