Enhancing Energy Consumption Time Series Clustering

with Variational Mode Decomposition

Resumen

The extensive use of Smart Metering Systems has revolutionized the monitoring and analysis of energy consumption data, enabling the derivation of representative demand profiles [1]. The profiles are essential for optimizing energy distribution, however, clustering energy usage profiles presents a significant challenge, particularly when data inconsistencies arise from unsynchronized timestamps in records.
Clustering algorithms need to separate noise from meaningful components while also managing the dimensionality of the data. This work proposes the use of Variational Mode Decomposition (VMD) [2], which isolates intrinsic mode functions (IMFs), providing a clearer representation of energy consumption patterns. By integrating VMD with K-means clustering, we aim to improve the accuracy of demand profile classification.
In this work we consider a real data sample from 2021 done by the National Electricity Administration of Paraguay (ANDE), encompassing data on energy use from 122 households in the Asunción metropolitan area [3]. First, the Lomb-Scargle Periodogram (LSP) is used to identify dominant periods in the real energy consumption data. Based on these periods, a synthetic energy demand profile is generated to aid in determining the optimal number of modes for VMD. The VMD algorithm is then applied to decompose the signals into IMFs, solving the following minimization problem:
min_{uk},{ωk} {Σ_k ||∂_t [(δ(t) + jπt) * u_k(t)] e^-jω_kt||₂²},
where u_k are the modes, ω_k are the center frequencies, and δ(t) is the Dirac delta function.
The mean squared error (MSE) was used to determine the optimal number of decomposition modes K. By comparing the results for 10 modes with an ideal curve based on the periods identified in the periodogram (24, 12, 8, and 6 hours), K=4 achieved the lowest MSE value of 3.3944, confirming it as the optimal number of modes. The signals are reconstructed using the optimal VMD decomposition, resulting in a denoised dataset, which is then aggregated into daily profiles by calculating the average hourly consumption for each user.
Then K-means Clustering (KMC) is applied, with the optimal number of clusters determined using the elbow method. These profiles are subsequently compared with those obtained from other clustering methods using validation indices such as the Silhouette score and the Calinski-Harabasz score to assess clustering quality. The clustering analysis of hourly energy consumption data identified six distinct user groups, as shown in Figure 1. Some clusters exhibit pronounced peaks in energy usage at specific hours, while others maintain a more stable consumption pattern throughout the day. These findings suggest that different user groups follow distinct energy usage routines. [...]