{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:32:00Z","timestamp":1760232720462,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"22","license":[{"start":{"date-parts":[[2022,11,17]],"date-time":"2022-11-17T00:00:00Z","timestamp":1668643200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the National Key Research and Development Program of China","award":["2019YFE0104800"],"award-info":[{"award-number":["2019YFE0104800"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper focuses on how to identify normal, derated power and abnormal data in operation data, which is key to intelligent operation and maintenance applications such as wind turbine condition diagnosis and performance evaluation. Existing identification methods can distinguish normal data from the original data, but usually remove power curtailment data as outliers. A multi-Gaussian\u2013discrete probability distribution model was used to characterize the joint probability distribution of wind speed and power from wind turbine SCADA data, taking the derated power of the wind turbine as a hidden random variable. The maximum expectation algorithm (EM), an iterative algorithm derived from model parameters estimation, was applied to achieve the maximum likelihood estimation of the proposed probability model. According to the posterior probability of the wind-power scatter points, the normal, derated power and abnormal data in the wind turbine SCADA data were identified. The validity of the proposed method was verified by three wind turbine operational data sets with different distribution characteristics. The results are that the proposed method has a degree of universality with regard to derated power operational data with different distribution characteristics, and in particular, it is able to identify the operating data with clustered distribution effectively.<\/jats:p>","DOI":"10.3390\/s22228891","type":"journal-article","created":{"date-parts":[[2022,11,18]],"date-time":"2022-11-18T06:11:34Z","timestamp":1668751894000},"page":"8891","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Research on the Derated Power Data Identification Method of a Wind Turbine Based on a Multi-Gaussian\u2013Discrete Joint Probability Model"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7409-7077","authenticated-orcid":false,"given":"Yuanchi","family":"Ma","sequence":"first","affiliation":[{"name":"State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yongqian","family":"Liu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhiling","family":"Yang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jie","family":"Yan","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6392-1902","authenticated-orcid":false,"given":"Tao","family":"Tao","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"David","family":"Infield","sequence":"additional","affiliation":[{"name":"Wind Energy and Control Centre, Department of Electronic and Electrical Engineering, University of Strathclyde, Glasgow G1 1XQ, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"126905","DOI":"10.1016\/j.jclepro.2021.126905","article-title":"Optimal Site Selection for Distributed Wind Power Coupled Hydrogen Storage Project Using a Geographical Information System Based Multi-Criteria Decision-Making Approach: A Case in China","volume":"299","author":"Wu","year":"2021","journal-title":"J. Clean. Prod."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/j.renene.2017.03.097","article-title":"Ageing Assessment of a Wind Turbine over Time by Interpreting Wind Farm SCADA Data","volume":"116","author":"Dai","year":"2018","journal-title":"Renew. Energy"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"841","DOI":"10.1016\/j.renene.2018.07.068","article-title":"Using High-Frequency SCADA Data for Wind Turbine Performance Monitoring: A Sensitivity Study","volume":"131","author":"Gonzalez","year":"2019","journal-title":"Renew. Energy"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"185557","DOI":"10.1109\/ACCESS.2020.3029435","article-title":"Research on Fault Diagnosis of Wind Turbine Based on SCADA Data","volume":"8","author":"Liu","year":"2020","journal-title":"IEEE Access"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1016\/j.rser.2014.11.012","article-title":"Behavior of Chinese Enterprises in Evaluating Wind Power Projects: A Review Based on Survey","volume":"43","author":"Wu","year":"2015","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1849","DOI":"10.1016\/j.ymssp.2010.12.007","article-title":"Comparative Analysis of Neural Network and Regression Based Condition Monitoring Approaches for Wind Turbine Fault Detection","volume":"25","author":"Schlechtingen","year":"2011","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1016\/j.renene.2008.05.032","article-title":"Models for Monitoring Wind Farm Power","volume":"34","author":"Kusiak","year":"2009","journal-title":"Renew. Energy"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"75531","DOI":"10.1109\/ACCESS.2018.2883681","article-title":"A New Outlier Detection Model Using Random Walk on Local Information Graph","volume":"6","author":"Wang","year":"2018","journal-title":"IEEE Access"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"521","DOI":"10.3233\/IDA-2006-10604","article-title":"A Comprehensive Survey of Numeric and Symbolic Outlier Mining Techniques","volume":"10","author":"Agyemang","year":"2006","journal-title":"Intell. Data Anal."},{"key":"ref_10","first-page":"708","article-title":"Survey on Anomaly Detection Using Data Mining Techniques","volume":"Volume 60","author":"Ding","year":"2015","journal-title":"Proceedings of the Knowledge-Based and Intelligent Information & Engineering Systems 19th Annual Conference, Kes-2015"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1145\/1497577.1497581","article-title":"DOLPHIN: An Efficient Algorithm for Mining Distance-Based Outliers in Very Large Datasets","volume":"3","author":"Angiulli","year":"2009","journal-title":"ACM Trans. Knowl. Discov. Data"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Zemene, E., Tesfaye, Y.T., Prati, A., and Pelillo, M. (2016, January 4\u20138). Simultaneous Clustering and Outlier Detection Using Dominant Sets. Proceedings of the 2016 23rd International Conference on Pattern Recognition (icpr), Cancun, Mexico.","DOI":"10.1109\/ICPR.2016.7899983"},{"key":"ref_13","first-page":"38","article-title":"Methods for elimination and reconstruction of abnormal power data in wind farms","volume":"3","author":"Zhu","year":"2015","journal-title":"Power Syst. Prot. Control"},{"key":"ref_14","first-page":"14","article-title":"Reconstruction Method of Active Power Historical Operating Data for Wind Farm","volume":"5","author":"Zhang","year":"2021","journal-title":"Autom. Electr. Power Syst."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1677","DOI":"10.1002\/we.1661","article-title":"Copula-Based Model for Wind Turbine Power Curve Outlier Rejection: Copula-Based Model for Wind Turbine Power Curve Outlier Rejection","volume":"17","author":"Wang","year":"2014","journal-title":"Wind Energy"},{"key":"ref_16","first-page":"5001309","article-title":"A Fast Abnormal Data Cleaning Algorithm for Performance Evaluation of Wind Turbine","volume":"70","author":"Wang","year":"2021","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_17","first-page":"3353","article-title":"Characteristics of Outliers in Wind Speed-Power Operation Data of Wind Turbines and Its Cleaning Method","volume":"33","author":"Shen","year":"2020","journal-title":"Trans. China Electrotech. Soc."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1399","DOI":"10.1007\/s11424-015-3160-y","article-title":"Computing Halfspace Depth Contours Based on the Idea of a Circular Sequence","volume":"28","author":"Liu","year":"2015","journal-title":"J. Syst. Sci. Complex."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"923","DOI":"10.1080\/14786451.2021.1890736","article-title":"Condition Monitoring Systems: A Systematic Literature Review on Machine-Learning Methods Improving Offshore-Wind Turbine Operational Management","volume":"40","author":"Black","year":"2021","journal-title":"Int. J. Sustain. Energy"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"I43","DOI":"10.1190\/1.2976116","article-title":"2D Vector Gravity Potential and Line Integrals for the Gravity Anomaly Caused by a 2D Mass of Depth-Dependent Density Contrast","volume":"73","author":"Zhou","year":"2008","journal-title":"Geophysics"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"De, S., Dey, S., Bhattacharyya, S., and Bhatia, S. (2022). Chapter 1\u2014An Introduction to Data Mining in Social Networks. Advanced Data Mining Tools and Methods for Social Computing, Academic Press. Hybrid Computational Intelligence for Pattern Analysis.","DOI":"10.1016\/B978-0-32-385708-6.00008-4"},{"key":"ref_22","first-page":"58","article-title":"Data stream outlier detection algorithm based on K-means","volume":"3","author":"Han","year":"2017","journal-title":"Comput. Eng. Appl."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"109391","DOI":"10.1016\/j.knosys.2022.109391","article-title":"Twin Robust Matrix Machine for Intelligent Fault Identification of Outlier Samples in Roller Bearing","volume":"252","author":"Pan","year":"2022","journal-title":"Knowl.-Based Syst."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"901","DOI":"10.1016\/j.ins.2022.06.013","article-title":"Efficient Density and Cluster Based Incremental Outlier Detection in Data Streams","volume":"607","author":"Degirmenci","year":"2022","journal-title":"Inf. Sci."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"107079","DOI":"10.1016\/j.asoc.2021.107079","article-title":"CELOF: Effective and Fast Memory Efficient Local Outlier Detection in High-Dimensional Data Streams","volume":"102","author":"Chen","year":"2021","journal-title":"Appl. Soft Comput."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"117988","DOI":"10.1016\/j.eswa.2022.117988","article-title":"Robust Outlier Detection Based on the Changing Rate of Directed Density Ratio","volume":"207","author":"Li","year":"2022","journal-title":"Expert Syst. Appl."},{"key":"ref_27","first-page":"40","article-title":"Characteristic and Processing Method of Abnormal Data Clusters Caused by Wind Curtailments in Wind Farms","volume":"38","author":"Zhao","year":"2014","journal-title":"Autom. Electr. Power Syst."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1109\/TSTE.2017.2717021","article-title":"Data-Driven Correction Approach to Refine Power Curve of Wind Farm Under Wind Curtailment","volume":"9","author":"Zhao","year":"2018","journal-title":"IEEE Trans. Sustain. Energy"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/22\/8891\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:20:14Z","timestamp":1760145614000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/22\/8891"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,17]]},"references-count":28,"journal-issue":{"issue":"22","published-online":{"date-parts":[[2022,11]]}},"alternative-id":["s22228891"],"URL":"https:\/\/doi.org\/10.3390\/s22228891","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2022,11,17]]}}}