{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T01:47:10Z","timestamp":1782265630354,"version":"3.54.5"},"reference-count":28,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2026,6,20]],"date-time":"2026-06-20T00:00:00Z","timestamp":1781913600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computers"],"abstract":"<jats:p>Power systems continuously generate large-scale load time series data for forecasting, consumption analysis, and equipment health monitoring. However, real-world load measurements are often contaminated by anomalies caused by sensor faults, communication errors, and abnormal consumption behaviors, which may degrade data quality and affect operational decision-making. To address this issue, this paper proposes an integrated anomaly detection framework named PEL, which combines Prophet-based seasonal-trend decomposition, ensemble empirical mode decomposition (EEMD), and a multilayer long short-term memory (LSTM) network. Prophet is first employed to decompose the original series into trend, seasonal, holiday, and residual components. Sample entropy analysis and white noise tests are then adopted to evaluate whether the residual component still contains complex structured information requiring secondary decomposition. Next, EEMD is applied to the residual component to extract multi-scale intrinsic mode functions. Finally, all decomposed components are normalized and fed into a multilayer LSTM model for anomaly detection. Experiments on a real-world power load dataset demonstrate that the proposed PEL framework achieves an accuracy of 99.92%, a precision of 97.33%, a recall of 100%, an F1-score of 98.65%, and an AUC of 0.9996, outperforming or matching several baseline and hybrid models.<\/jats:p>","DOI":"10.3390\/computers15060396","type":"journal-article","created":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T01:03:23Z","timestamp":1782263003000},"page":"396","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["PEL: An Integrated Algorithm for Power Time Series Anomaly Detection"],"prefix":"10.3390","volume":"15","author":[{"given":"Lei","family":"Wang","sequence":"first","affiliation":[{"name":"School of Management Science and Engineering, Beijing Information Science and Technology University, Beijing 102206, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-2353-9897","authenticated-orcid":false,"given":"Yu","family":"Gao","sequence":"additional","affiliation":[{"name":"School of Management Science and Engineering, Beijing Information Science and Technology University, Beijing 102206, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-1747-2096","authenticated-orcid":false,"given":"Xiaoyong","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Management Science and Engineering, Beijing Information Science and Technology University, Beijing 102206, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,6,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"109205","DOI":"10.1016\/j.compeleceng.2024.109205","article-title":"Research on long term power load grey combination forecasting based on fuzzy support vector machine","volume":"116","author":"Chen","year":"2024","journal-title":"Comput. Electr. Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"136656","DOI":"10.1109\/ACCESS.2025.3594024","article-title":"Short and Medium-Term Power Load Anomaly Detection Method Based on Convolutional Neural Network and EL-DCC","volume":"13","author":"Li","year":"2025","journal-title":"IEEE Access"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"113022","DOI":"10.1016\/j.enbuild.2023.113022","article-title":"Short-term electric load forecasting using an EMD-BI-LSTM approach for smart grid energy management system","volume":"288","author":"Mounir","year":"2023","journal-title":"Energy Build."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Lin, R., Chen, S., He, Z., Wu, B., Zou, H., Zhao, X., and Li, Q. (2024). Electricity Behavior Modeling and Anomaly Detection Services Based on a Deep Variational Autoencoder Network. Energies, 17.","DOI":"10.3390\/en17163904"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"759","DOI":"10.1016\/j.procs.2013.05.098","article-title":"Energy time series data analysis based on a novel integrated data characteristic testing approach","volume":"17","author":"Tang","year":"2013","journal-title":"Procedia Comput. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1016\/j.ijepes.2018.01.036","article-title":"Detection of illegal consumers using pattern classification approach combined with Levenberg-Marquardt method in smart grid","volume":"99","author":"Ghasemi","year":"2018","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_7","first-page":"1920","article-title":"Electricity theft detection and localization in grid-tied microgrids","volume":"9","author":"Tariq","year":"2016","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"101984","DOI":"10.1016\/j.jocs.2023.101984","article-title":"Effective RNN-based forecasting methodology design for improving short-term power load forecasts: Application to large-scale power-grid time series","volume":"68","author":"Aseeri","year":"2023","journal-title":"J. Comput. Sci."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Park, C.H., and Kim, T. (2020). Energy Theft Detection in Advanced Metering Infrastructure Based on Anomaly Pattern Detection. Energies, 13.","DOI":"10.3390\/en13153832"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Hasan, M.N., Toma, R.N., Nahid, A.A., Islam, M.M.M., and Kim, J.M. (2019). Electricity Theft Detection in Smart Grid Systems: A CNN-LSTM Based Approach. Energies, 12.","DOI":"10.3390\/en12173310"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1678","DOI":"10.1016\/j.egyr.2021.12.067","article-title":"Short term electricity load forecasting using hybrid prophet-LSTM model optimized by BPNN","volume":"8","author":"Bashir","year":"2022","journal-title":"Energy Rep."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1016\/j.apenergy.2019.01.076","article-title":"A Practical Feature-Engineering Framework for Electricity Theft Detection in Smart Grids","volume":"238","author":"Razavi","year":"2019","journal-title":"Appl. Energy"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"109840","DOI":"10.1016\/j.epsr.2023.109840","article-title":"LITE-FORT: Lightweight Three-Stage Energy Theft Detection Based on Time Series Forecasting of Consumption Patterns","volume":"225","author":"Aoufi","year":"2023","journal-title":"Electr. Power Syst. Res."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"120279","DOI":"10.1016\/j.apenergy.2022.120279","article-title":"A real-time electrical load forecasting and unsupervised anomaly detection framework","volume":"330","author":"Wang","year":"2023","journal-title":"Appl. Energy"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/j.inffus.2022.10.008","article-title":"Deep learning for anomaly detection in multivariate time series: Approaches, applications, and challenges","volume":"91","author":"Li","year":"2023","journal-title":"Inf. Fusion"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"101335","DOI":"10.1016\/j.segan.2024.101335","article-title":"Application of machine learning in determining and resolving state estimation anomalies in power systems","volume":"38","author":"Ganjkhani","year":"2024","journal-title":"Sustain. Energy Grids Netw."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"14518","DOI":"10.3934\/mbe.2023650","article-title":"Artificial intelligence techniques for ground fault line selection in power systems: State-of-the-art and research challenges","volume":"20","author":"Wang","year":"2023","journal-title":"Math. Biosci. Eng."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Sun, Y., Sun, X., Hu, T., and Zhu, L. (2023). Smart Grid Theft Detection Based on Hybrid Multi-Time Scale Neural Network. Appl. Sci., 13.","DOI":"10.3390\/app13095710"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"101639","DOI":"10.1016\/j.aei.2022.101639","article-title":"Anomalous load profile detection in power systems using wavelet transform and robust regression","volume":"53","author":"Karkhaneh","year":"2022","journal-title":"Adv. Eng. Inform."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"012021","DOI":"10.1088\/1742-6596\/2095\/1\/012021","article-title":"Research and application of power system data anomaly identification based on time series and deep learning","volume":"2095","author":"Li","year":"2021","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"108193","DOI":"10.1016\/j.compeleceng.2022.108193","article-title":"Time series analysis and anomaly detection for trustworthy smart homes","volume":"102","author":"Priyadarshini","year":"2022","journal-title":"Comput. Electr. Eng."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"524","DOI":"10.1016\/j.procs.2021.01.036","article-title":"Time series analysis and forecasting of coronavirus disease in Indonesia using ARIMA model and PROPHET","volume":"179","author":"Satrio","year":"2021","journal-title":"Procedia Comput. Sci."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"110487","DOI":"10.1016\/j.asoc.2023.110487","article-title":"A floating offshore platform motion forecasting approach based on EEMD hybrid ConvLSTM and chaotic quantum ALO","volume":"144","author":"Li","year":"2023","journal-title":"Appl. Soft Comput."},{"key":"ref_24","first-page":"1577","article-title":"Electricity demand time series forecasting based on empirical mode decomposition and long short-term memory","volume":"118","author":"Taheri","year":"2021","journal-title":"Energy Eng. J. Assoc. Energy Eng."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"131724","DOI":"10.1016\/j.jclepro.2022.131724","article-title":"Accurate prediction of water quality in urban drainage network with integrated EMD-LSTM model","volume":"354","author":"Zhang","year":"2022","journal-title":"J. Clean. Prod."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"314","DOI":"10.1016\/j.measurement.2019.02.062","article-title":"Empirical mode decomposition based hybrid ensemble model for electrical energy consumption forecasting of the cement grinding process","volume":"138","author":"Liu","year":"2019","journal-title":"Measurement"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"107720","DOI":"10.1016\/j.compeleceng.2022.107720","article-title":"A LSTM-FCNN based multi-class intrusion detection using scalable framework","volume":"99","author":"Sahu","year":"2022","journal-title":"Comput. Electr. Eng."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"216","DOI":"10.1109\/TSG.2015.2425222","article-title":"Electricity Theft Detection in AMI Using Customers\u2019 Consumption Patterns","volume":"7","author":"Jokar","year":"2016","journal-title":"IEEE Trans. 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