**1. Introduction**

Smart grid technologies and applications capable of adaptive, resilient, and sustainable self-healing, with foresight for prediction under different uncertainties, improve the reliability of the power system [1]. Furthermore, the smart grid allows bidirectional communication that supports the demand response (DR) programs [2]. Demand response technologies are widely applied and are constantly improving. The most common DR programs can be categorized into the following two classes: price-based programs and incentive-based programs. Price-based programs contain time of use (ToU), real time pricing (RTP) and critical peak pricing (CPP), which aim to motivate the end-user to change their consumption behavior [3]. On the other hand, incentive-based programs reach a consensus with consumers to reduce electricity consumption. Examples of these schemes are direct-load control (DLC), interruptible/curtailable service (I/C), demand bidding/buy (DB), etc. [4]. Considering various end-user consumption behaviors, it required the utility companies to design reasonable strategies. Therefore, it is necessary to analyze end-users' consumption data to acquire the load patterns.

Advanced metering infrastructure (AMI) and smart meters have been adopted to automatically collect energy consumption data at a fine granular interval, which is usually in intervals of 1 h, 30 min, or even 30 s [5]. Most countries have vigorously deployed smart meters because of the potential value of consumption data [6]. The massive amount of data sampled by smart meters could be used for research, typically load forecasting, customer segmentation, pricing/incentive mechanism, scheduling and control [7].

**Citation:** Cen, S.; Yoo, J.H.; Lim, C.G. Electricity Pattern Analysis by Clustering Domestic Load Profiles Using Discrete Wavelet Transform. *Energies* **2022**, *15*, 1350. https:// doi.org/10.3390/en15041350

Academic Editors: Sergio Nesmachnow and Islam Safak Bayram

Received: 10 December 2021 Accepted: 11 February 2022 Published: 13 February 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

However, the extracted load consumption data lack labels, hence, the need of clustering techniques to segment the electricity consumption data. In addition, with the high time resolution advanced smart meter implemented in the household, the massive data will increase the complexity of the clustering method, called the "curse of dimensionality" [8]. This is a problem for implementing clustering algorithms because most clustering algorithms become intractable to process high-dimensional data input. To deal with the issue of the curse of dimensionality, the load consumption data needs preprocessing i.e., dimensionality reduction.

This study proposed clustering for segment residential customer daily power data, using discrete wavelet transform to extract features and reduce dimension by statistical methods and principal component analysis (PCA). The dataset, named Multifamily Residential Electricity Dataset (MFRED), contains 10-s resolution daily power data for 26 apartment groups, collected over 365 days in Manhattan, New York, 2019 [9]. First, data cleansing and multi-level one-dimensional (1D) discrete wavelet transform were applied on 8640-value daily load curves. Second, we reduced extracted feature dimensions. Finally, clustering algorithms were implemented, and the evaluation of the methods was carried out. Our main contributions of this work include the following: (1) a proposed method to vastly reduce the daily load profile dimensionality, to accelerate the clustering, and (2) the three cluster validity indices (CVI) imply that our proposed method to extract features outperforms the clustering original data, especially on hierarchical clustering.

The paper is structured as follows: Section 2 briefly discusses the related works. Section 3 describes the MFRED data. Section 4 explains the methodology in the study. Analysis and results are presented in Section 5, with conclusions in Section 6.
