Prosumer Clustering for Optimized Control and Peer-to-Peer Energy Trading in Solar-PV and Electric Vehicle Integrated Community Microgrids: A Comparative Analysis of K-Means and Spectral Methods ^†

Abstract

This study presents a comprehensive clustering analysis of residential prosumer profiles for optimizing control and peer-to-peer (P2P) energy trading in community renewable energy systems (CRES). Using data from 25 prosumer households equipped with rooftop solar photovoltaic (PV) systems and electric vehicle (EV) charging capabilities, this study implements and compares k-means and spectral clustering algorithms to identify optimal segmentation strategies for prosumer energy management. K-means clustering identifies seven practical prosumer categories with a silhouette coefficient of 0.17, while spectral clustering achieves superior mathematical separation with a silhouette coefficient of 0.275 in ten clusters, though producing six singleton outliers. The k-means solution demonstrates three primary prosumer categories: net producers, net consumers, and balanced profiles. Cluster size variation requires adaptive optimization, while singleton outliers need custom strategies. EV ownership impact consumption, so future proliferation demands dynamic clustering, and these findings will guide metaheuristic algorithms for energy trading and pricing.

1. Introduction

The increasing availability of high-resolution data and analytical methods has made the investigation of residential electricity consumption dynamics at finely resolved timescales progressively more feasible. Distributed generation and load profile clustering constitutes a prevalent methodological approach to exploring production and consumption dynamics. Notwithstanding the abundance of available algorithmic techniques, clustering load profiles poses challenges, as clustering methods do not invariably capture the temporal aspects of electricity production or consumption, and clusters are difficult to explicate without supplementary descriptive household data. These challenges circumscribe the utility of cluster analysis in elucidating behavioral and other drivers of electricity usage patterns [1]. The proliferation of smart meters, decentralized energy resources, and sensors has driven the importance of data analysis, leading to increased complexity in processing and leveraging data [2]. Clustering techniques, such as k-means and spectral clustering, can extract underlying patterns from energy consumption data, but determining the most appropriate clusters of consumers with similar behaviours remains a challenge [3,4].

This paper presents an unsupervised machine learning framework for optimal load and prosumer generation profiling, utilizing real consumption data from 25 households. Various clustering algorithms are reviewed and compared, with empirical analysis and evaluation metrics assessing their performance.

2. Literature Review

The integration of solar generation into power systems, particularly at low-voltage and medium-voltage levels, poses significant operational challenges for distribution systems. Centralized voltage control schemes have been proposed to mitigate voltage violations, but their efficacy relies on accurate forecasted data and a reliable communication infrastructure [5]. Research on clustering algorithms has focused on load consumption, with limited attention paid to embedded generation production or surplus energy sharing. Studies have applied clustering approaches to group households by energy consumption and production patterns, enhancing efficiency through dimensionality reduction and feature extraction [6]. However, these approaches often neglect the dynamic nature of surplus energy in communities with rooftop systems. Existing research has also explored clustering algorithms for electricity customer segmentation, aiming to identify groups with similar consumption patterns [7,8]. Techniques such as k-means, fuzzy k-means, and hybrid approaches have been applied, but researchers often overlook fairness and equity issues in community surplus energy sharing. Comparative analyses of clustering algorithms, including spectral, genetic, and adaptive algorithms, have been conducted using real datasets [9]. However, these studies often prioritize market efficiency over community resiliency, misaligning with distributed energy sharing objectives.

Other approaches, such as Gaussian Mixture Models (GMMs) and Self-Organizing Maps (SOMs), have been applied to analyze prosumer and consumer patterns [10,11]. However, these methods can create ambiguity in P2P trading and may not adapt to varying patterns of variability in electrical demand profiles.

Table 1. Models for clustering residential loads and embedded generation.

Algorithm	Load Clustering	Generation Clustering
K-means	[7,8,9,12,13,14,15,16,17]	[10]
Hierarchical clustering	[10,11]	[10]
DBSCAN	[9]	[9]
Genetic algorithms	[9]	[9]
Spectral clustering	[9]	[9]
Gaussian Mixture Model	[10,18]	[10]
Fuzzy K-means	[8]	Lack of clustering in distributed home energy production
Fuzzy C-means	[11,15]
Self-Organizing Maps	[11,13]
Artificial Neural Networks	[12]
Probabilistic Neural Networks	[8]

shows the selection of research completed on several load consumption and surplus generation clustering algorithms.

Static clustering methods in microgrid energy management have limitations, as they cannot adapt to dynamic changes in load profiles and generation patterns, leading to inefficiencies. Renewable energy variability makes real-time forecasting and demand response optimization complex. Key gaps include uncertainty around ideal cluster size, limited understanding of effective configurations, and a lack of comprehensive clustering studies. No established methods exist for the simultaneous allocation of distributed generators, EV charging stations, and protection equipment, which are crucial for smart grid reliability. Addressing these gaps can enhance microgrid efficiency, reliability, and adaptability, supporting renewable energy integration and smart grid development.

3. Methodology

This study tackles the challenge of characterizing prosumer energy profiles in community renewable energy management systems, focusing on peer-to-peer energy trading frameworks. A comprehensive clustering analysis was conducted on 25 residential prosumer profiles, incorporating solar photovoltaic generation, household consumption patterns, and electric vehicle charging behaviors. K-means and spectral clustering algorithms were employed to identify optimal prosumer segmentation strategies, using the elbow method and silhouette coefficient as validation metrics. The clustering framework aims to establish homogeneous prosumer groups that facilitate efficient energy trading mechanisms while maintaining computational tractability for real-time optimization algorithms.

The data used for this research, presented in Figure 1, comprise measurements from 25 houses with varying characteristics, including solar rooftop PV embedded generation with storage, electric vehicles, and general household loads [19]. The figure provides insight into similarity analysis. Notably, a total of six days exhibit surplus generation below approximately 3.11 kW. The performances of k-means and spectral clustering algorithms are compared, with descriptions of each method provided in Section 4. This study’s findings will enable efficient energy trading mechanisms and inform real-time optimization algorithms.

4. Clustering Algorithms

Clustering algorithms partition data into meaningful groups based on similarity measures, with applications spanning machine learning, data mining, and pattern recognition [20]. Each algorithm addresses specific challenges, from handling different data types, discovering arbitrary cluster shapes and scaling, to massive datasets or adapting to evolving data streams.

4.1. Partitioning Methods: Optimizing Cluster Assignments Through Iterative Refinement—K-Means Clustering

K-means clustering aims to partition n data points into k clusters by minimizing the within-cluster sum of squares distances [21,22]. The algorithm rests on the principle that each data point should belong to the cluster whose centroid (mean) is nearest to it. The theoretical foundation involves minimizing an objective function representing total within-cluster variance, making it suitable for discovering compact, spherical clusters in numerical data.

Objective Function:

The k-means algorithm seeks to minimize:

$$Z\left(C_1,C_2\dots ,C_k\right)={\displaystyle \sum _{\mathcal{l}=1}^k}\sum _{i\in C_{\mathcal{l}}}{‖x_i-{\mu }_{\mathcal{l}}‖}_2^2$$

(1)

$${\mu }_{\mathcal{l}}={\displaystyle \frac{1}{\left|C_{\mathcal{l}}\right|}}\sum _{i\in C_{\mathcal{l}}}{x}_i$$

(2)

where $C_1 to C_k$ is the set of points in a cluster $\mathcal{l}$, ${\mu }_{\mathcal{l}}$ is the centroid of points in the cluster $\mathcal{l}$, $x_i$ is the $i^{th}$ object of the dataset, and ${‖x_i-{\mu }_{\mathcal{l}}‖}_2$ denotes the Euclidean norm or distance between the vectors $x_i \mathrm{a}\mathrm{n}\mathrm{d} {\mu }_{\mathcal{l}}$. $k$ is the cluster number and $C_{\mathcal{l}}$ is the ${\mathcal{l}}^{th}$ cluster.

4.2. Spectral Clustering: Graph Partitioning Through Eigenvalue Decomposition

Spectral clustering approaches data clustering from a graph partitioning perspective, representing data points as vertices in a weighted similarity graph. This method partitions the graph to group similar points together, leveraging the spectral properties of graph Laplacian matrices to identify arbitrarily shaped clusters. The graph Laplacian encodes connectivity structure, with eigenvectors revealing underlying cluster structure. Spectral clustering relates to random walks on graphs, where good clusters correspond to regions with extended walk durations. The normalized cut (Ncut) criterion balances between-cluster similarity minimization and within-cluster similarity maximization, finding partitions with rare transitions between clusters. While computing exact minimum Ncut is NP-hard, spectral methods provide efficient relaxations via eigenvector solutions [23,24].

4.2.1. Similarity Graph Construction

Given data points $x_1,\dots ,x_{\mathrm{n}}$, construct weighted adjacency matrix $W$ where:

$${\mathcal{w}}_{ij}=s\left(x_i, x_j\right)={\mathcal{e}}^{\left(-{\displaystyle \frac{{‖x_i-x_j‖}^2}{2{\mathcal{o}}^2}}\right)}$$

(3)

Degree matrix $D$ is diagonal with:

$$d_i=\sum _j{\mathcal{w}}_{ij}$$

(4)

where ${\mathcal{w}}_{ij}$ is the similarity weight between datapoints $i$ and $j$, and $s\left(x_i, x_j\right)$ is the similarity function between points $x_i$ and $x_j$. Datapoints $i$ and $j$ in the original d-dimensional feature space are denoted by $x_i$ and $x_j$, ${‖x_i-x_j‖}^2$ is the squared Euclidean norm or distance between $x_i$ and $x_j$, and the bandwidth parameter of the Gaussian kernel controlling the decay rate of similarities with distance is ${\mathcal{o}}^2$. The exponential function creates the Gaussian kernel.

4.2.2. Graph Laplacian Matrices

• Unnormalized Laplacian: $L=D-W$.
• Normalized Random Walk Laplacian: $L_{rw}=D^{-1}L=I-D^{-1}W$.
• Symmetric Normalized Laplacian:

$$L_{sym}=D^{-{\displaystyle \frac{1}{2}}}{LD}^{-{\displaystyle \frac{1}{2}}}=I-D^{-{\displaystyle \frac{1}{2}}}{WD}^{-{\displaystyle \frac{1}{2}}}$$

(5)

where $I$ is the identity matrix of an appropriate dimension.

4.2.3. Normalized Cut Objective

$$Ncut\left(A_1,\dots ,A_k\right)={\displaystyle \frac{1}{2}}\sum _j\left[{\displaystyle \frac{W\left(A_i,\overline{A_i}\right)}{vol\left(A_i\right)}}\right]$$

(6)

where:

$$cut\left(A,B\right)=\sum _{i\in A,j\in B}W\left(i,j\right)$$

(7)

and,

$$vol\left(A\right)=\sum _{i\in A}{d}_i$$

(8)

where $A_1,\dots ,A_k$ are the k clusters, $W\left(A_i,\overline{A_i}\right)$ is the total weight of edges between cluster $A_i$ and its complement, and $vol\left(A_i\right)$ is the volume of the cluster $A_i$.

5. Simulation Results

The comparative analysis of clustering methodologies reveals distinct segmentation characteristics that significantly impact the design of community energy management strategies. K-means clustering identified an optimal configuration of seven clusters (silhouette coefficient = 0.17), demonstrating a 47% reduction in within-cluster sum of squares from k = 1 to k = 7, with cluster sizes ranging from 1 to 7 profiles. Figure 2 and Figure 3 show the graphical representation of the solutions.

The distribution exhibits a reasonable balance with two dominant clusters containing 5 and 7 profiles, respectively, representing 48% of the total prosumer population. Conversely, spectral clustering yielded a 10-cluster solution with a superior silhouette coefficient (0.275), indicating enhanced cluster separation through the algorithm’s capacity to capture non-convex patterns in the high-dimensional energy consumption space. However, this improved separation manifests as six singleton clusters, suggesting the presence of unique prosumer behaviours that resist conventional categorization.

Table 2. Comparison summary for k-means and spectral clustering by metrics.

Optimization Metrics	K-Means	Spectral
Optimal k	7	10
Silhouette coefficient	0.17	0.275
WCSS reduction	47%	50%

shows a summary of the comparison.

6. Analysis of Results

The comparative analysis of clustering methodologies reveals distinct segmentation characteristics impacting community energy management strategies. K-means clustering identified seven clusters with a silhouette coefficient of 0.17, showing a 47% reduction in within-cluster sum of squares. The clusters are reasonably balanced, with two dominant clusters containing 48% of prosumers. Spectral clustering yielded 10 clusters with a superior silhouette coefficient (0.275), capturing non-convex patterns, but resulting in six singleton clusters indicating unique prosumer behaviours.

K-means identifies three prosumer categories: net producers, net consumers, and balanced clusters. EV charging patterns differentiate clusters, with concentrations in 02:00–08:00 and 16:00–23:00 periods. Spectral clustering amplifies distinctions, showing potential for sub-clustering. These findings enable complementary trading pairs for peer-to-peer energy transactions and demand response optimization opportunities through alignment with solar generation peaks. Sub-clustering can refine trading strategies within larger groups.

7. Conclusions

The clustering results reveal the complexity of prosumer behavior in distributed energy systems, highlighting trade-offs between cluster quality and practical implementation. Spectral clustering shows superior mathematical separation over k-means, but its singleton clusters limit applicability for group-based energy trading. In contrast, k-means provides actionable prosumer segments suitable for differentiated tariffs and peer-to-peer trading. Complementary consumption-generation patterns enable temporal arbitrage strategies, with morning surplus in Clusters 1 and 5 potentially offsetting evening deficits in Clusters 6 and 7. The significant variation in cluster sizes and characteristics necessitates adaptive optimization approaches, while singleton clusters indicate outlier prosumers requiring customized strategies. The correlation between EV ownership and net consumption patterns suggests that future EV proliferation will alter community energy balance, requiring dynamic clustering approaches. These findings inform the development of metaheuristic optimization algorithms for energy trading and pricing.

Future work will incorporate a comparison of additional clustering algorithms to inform about the most optimal and dynamic solution, considering homes with solar rooftop PVs and electric vehicle charging stations.