{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,3]],"date-time":"2026-04-03T14:50:12Z","timestamp":1775227812249,"version":"3.50.1"},"reference-count":38,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,1,26]],"date-time":"2025-01-26T00:00:00Z","timestamp":1737849600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100011011","name":"Andalusian Government","doi-asserted-by":"publisher","award":["PROYEXCEL_00588"],"award-info":[{"award-number":["PROYEXCEL_00588"]}],"id":[{"id":"10.13039\/501100011011","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Industry 4.0 (I4.0) represents a transformative approach, integrating technology, production methods, and information and communication technology to enhance industrial value creation. A central I4.0 goal in the energy domain is improving energy efficiency to boost industrial competitiveness and profitability. Given that induction motors account for nearly two-thirds of industrial electrical energy consumption, optimizing their efficiency is crucial. Energy management systems (EMSs) need real-time data to assess motor efficiency, enabling prompt identification and replacement of inefficient motors with alternatives that have optimal efficiency class and rated power for specific applications. This paper introduces a novel non-intrusive method for estimating the load and efficiency of induction motors without disrupting their operation. To reach that goal, the proposed method optimizes the parameters of a set of relationships between output power, input power, and losses with the motor speed, minimizing the error in the estimates. It requires only input electrical power and motor speed measurements to set the model parameters and estimates the load and efficiency using either speed or input power measurements. The experimental results demonstrate that the proposed method, with a mean overall error of less than 3.5% in estimating output power and efficiency, outperforms conventional methods.<\/jats:p>","DOI":"10.3390\/s25030754","type":"journal-article","created":{"date-parts":[[2025,1,28]],"date-time":"2025-01-28T07:54:08Z","timestamp":1738050848000},"page":"754","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Estimation of Power Output and Efficiency of Induction Motors: A New Non-Intrusive Approach"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9979-6568","authenticated-orcid":false,"given":"Paula","family":"Paramo-Balsa","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, Universidad de Sevilla, 41092 Sevilla, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3811-1078","authenticated-orcid":false,"given":"Juan Manuel","family":"Roldan-Fernandez","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Universidad de Sevilla, 41092 Sevilla, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7667-7910","authenticated-orcid":false,"given":"Jorge","family":"Semi\u00e3o","sequence":"additional","affiliation":[{"name":"Departamento de Engenharia Electrot\u00e9cnica, Instituto Superior de Engenharia, Universidade do Algarve, 8005-139 Faro, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8072-1593","authenticated-orcid":false,"given":"Manuel","family":"Burgos-Payan","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Universidad de Sevilla, 41092 Sevilla, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,26]]},"reference":[{"key":"ref_1","unstructured":"Van Werkhoven, M., and Kulterer, K. (2019, January 17\u201319). Digitalization in Electric Motor-Driven Systems. Proceedings of the 11th International Conference EEMODS\u201919, Tokyo, Japan."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Dinolova, P., Ruseva, V., and Dinolov, O. (2023). Energy Efficiency of Induction Motor Drives: State of the Art, Analysis and Recommendations. Energies, 16.","DOI":"10.3390\/en16207136"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Beleiu, H.G., Maier, V., Pavel, S.G., Birou, I., Pica, C.S., and Darab, P.C. (2020). Harmonics consequences on drive systems with induction motor. Appl. Sci., 10.","DOI":"10.3390\/app10041528"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1271","DOI":"10.1109\/TEC.2020.3019934","article-title":"Rotor Design Optimization of Squirrel Cage Induction Motor\u2014Part I: Problem Statement","volume":"36","author":"Marfoli","year":"2021","journal-title":"IEEE Trans. Energy Convers."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1280","DOI":"10.1109\/TEC.2020.3019934","article-title":"Rotor Design Optimization of Squirrel Cage Induction Motor\u2014Part II: Results Discussion","volume":"36","author":"Marfoli","year":"2021","journal-title":"IEEE Trans. Energy Convers."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"924","DOI":"10.1109\/TIA.2006.876065","article-title":"A Survey of Efficiency-Estimation Methods for In-Service Induction Motors","volume":"42","author":"Lu","year":"2006","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2282","DOI":"10.1016\/j.enconman.2009.05.004","article-title":"Are my Motors Oversized?","volume":"50","author":"Bortoni","year":"2009","journal-title":"Energy Conv. Manag."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3170","DOI":"10.1109\/TIM.2017.2735718","article-title":"A New Field Test Method for Determining Energy Efficiency of Induction Motor","volume":"66","author":"Esen","year":"2017","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Tsybikov, B., Beyerleyn, E., and Tyuteva, P. (2016, January 10\u201314). Comparison of Energy Efficiency Determination Methods for the Induction Motors. Proceedings of the 4th International Youth Forum on Smart Grids, Tomsk, Russia.","DOI":"10.1051\/matecconf\/20179101034"},{"key":"ref_10","unstructured":"(2014). Rotating Electrical Machines\u2014Part 2-1: Standard Methods for Determining Losses and Efficiency from Tests (Excluding Machines for Traction Vehicles) (Standard No. IEC 60034-2-1:2014)."},{"key":"ref_11","unstructured":"(2017). Standard Test Procedure for Polyphase Induction Motors and Generators (Standard No. IEEE Std 112-2017)."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1464","DOI":"10.1016\/j.enconman.2005.08.018","article-title":"Design and Analysis of Sensorless Torque Optimization for Single Phase Induction Motors","volume":"47","author":"Payman","year":"2006","journal-title":"Energy Conv. Manag."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/j.measurement.2018.12.080","article-title":"Assessment of the Energy Efficiency Estimation Methods on Induction Motors Considering Real-Time Monitoring","volume":"136","year":"2019","journal-title":"Measurement"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Geravandi, M., and CheshmehBeigi, H.M. (2023, January 9\u201311). Efficiency Estimation Methods of In-Service Induction Motors-A Review. Proceedings of the 2023 31st International Conference on Electrical Engineering (ICEE), Tehran, Iran.","DOI":"10.1109\/ICEE59167.2023.10334652"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1109\/28.658732","article-title":"Comparison of Induction Motor Field Efficiency Evaluation Methods","volume":"34","author":"Hsu","year":"1998","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1070","DOI":"10.1080\/15325008.2018.1466939","article-title":"An Improved Non-Intrusive Induction Motor Efficiency Estimation Technique for Non-Ideal Supply Voltage Conditions","volume":"46","author":"Dlamini","year":"2018","journal-title":"Electr. Power Comp. Syst."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Stopa, M.M., Resende, M.R., Luiz, A.S.A., Justino, J.C.G., Rodrigues, G.G., and Cardoso-Filho, B.J. (2018, January 23\u201327). A Simple Torque Estimator for In-Service Efficiency Determination of Inverter-Fed Induction Motors. Proceedings of the 2018 IEEE Industry Applications Society Annual Meeting (IAS), Portland, OR, USA.","DOI":"10.1109\/IAS.2018.8544702"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Salomon, C.P., Sant\u2019Ana, W.C., Lambert-Torres, G., Borges Da Silva, L.E., Bonaldi, E.L., and De Oliveira, L.E. (2018). Comparison among methods for induction motor low-intrusive efficiency evaluation including a new AGT approach with a modified stator resistance. Energies, 11.","DOI":"10.3390\/en11040691"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"115315","DOI":"10.1016\/j.measurement.2024.115315","article-title":"A non-intrusive technique for estimating the efficiency of low voltage three-phase induction motors","volume":"238","author":"Geravandi","year":"2024","journal-title":"Measurement"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"7301","DOI":"10.1109\/TIE.2019.2945269","article-title":"A Simplified Equivalent Circuit Method for Induction Machine Nonintrusive Field Efficiency Estimation","volume":"67","author":"Aminu","year":"2020","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_21","unstructured":"(2013). Rotating Electrical Machines: Test Methods for Determining Quantities of Equivalent Circuit Diagrams for Three-Phase Low-Voltage Cage Induction Motors (Standard No. IEC 60034-28:2013)."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Lu, B., Habetler, T.G., and Harley, R.G. (2006, January 18\u201322). A Nonintrusive Efficiency Estimation Method for In-Service Motor Testing Using a Modified Induction Motor Equivalent Circuit. Proceedings of the 2006 37th IEEE Power Electronics Specialists Conference, Jeju, Republic of Korea.","DOI":"10.1109\/pesc.2006.1712010"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1205","DOI":"10.1109\/TIA.2003.813686","article-title":"An Accurate Low-Cost Method for Determining Electric Motors\u2019 Efficiency for the Purpose of Plant Energy Management","volume":"39","year":"2003","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"4541","DOI":"10.1109\/TIA.2015.2453257","article-title":"Analysis of a Nonintrusive Efficiency Estimation Technique for Induction Machines Compared to the IEEE 112B and IEC 34-2-1 Standards","volume":"51","author":"Gajjar","year":"2015","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1221","DOI":"10.1109\/TEC.2016.2539959","article-title":"A New Stray-Load Loss Formula for Small and Medium-Sized Induction Motors","volume":"31","author":"Pillay","year":"2016","journal-title":"IEEE Trans. Energy Convers."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"771","DOI":"10.1109\/TEC.2022.3219097","article-title":"Modified Efficiency Estimation Tool for Three-Phase Induction Motors","volume":"38","author":"Pillay","year":"2023","journal-title":"IEEE Trans. Energy Convers."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"4186","DOI":"10.1109\/TIA.2018.2836344","article-title":"Induction Machine Parameter Range Constraints in Genetic Algorithm Based Efficiency Estimation Techniques","volume":"54","author":"Pillay","year":"2018","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Srited, T., and Chayakulkheeree, K. (2022, January 9\u201311). Induction Motor Efficiency Estimation Using Particle Swarm Optimization with Multiple Operating Conditions. Proceedings of the 2022 International Electrical Engineering Congress (iEECON), Khon Kaen, Thailand.","DOI":"10.1109\/iEECON53204.2022.9741616"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1016\/j.measurement.2018.01.028","article-title":"Efficiency Determination of In-Service Induction Machines Using Gravitational Search Optimization","volume":"118","author":"Grewal","year":"2018","journal-title":"Measurement"},{"key":"ref_30","unstructured":"(2021). Rotating Electrical Machines\u2014Part 31: Selection of Energy-Efficient Motors Including Variable Speed Applications\u2014Application Guidelines (Standard No. IEC TS 60034-31:2021)."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1031","DOI":"10.1016\/j.apenergy.2019.02.016","article-title":"Techno-Economic Optimal Power Rating of Induction Motors","volume":"240","year":"2019","journal-title":"Appl. Energy"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Paramo-Balsa, P., Roldan-Fernandez, J.M., Burgos-Payan, M., and Riquelme-Santos, J.M. (2021). A Low-Cost Non-Intrusive Method for In-Field Motor Speed Measurement Based on a Smartphone. Sensors, 21.","DOI":"10.3390\/s21134317"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Paramo-Balsa, P., Roldan-Fernandez, J.M., Gonzalez-Longatt, F., and Burgos-Payan, M. (2022). Measurement of the Speed of Induction Motors Based on Vibration with a Smartphone. Appl. Sci., 12.","DOI":"10.3390\/app12073371"},{"key":"ref_34","unstructured":"(2011). Rotating Electrical Machines\u2014Part 1: Rating and Performance (Standard No. IEC 60034-1:2011)."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1109\/60.536998","article-title":"Field Assessment of Induction Motor Efficiency Through Air-Gap Torque","volume":"11","author":"Hsu","year":"1996","journal-title":"IEEE Trans. Energy Convers."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1109\/60.124561","article-title":"Possible Errors in Measurement of Air-Gap Torque Pulsations of Induction Motors","volume":"7","author":"Hsu","year":"1992","journal-title":"IEEE Trans. Energy Conver."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1109\/60.464871","article-title":"Field Test of Motor Efficiency and Load Changes Through Air-Gap Torque","volume":"10","author":"Hsu","year":"1995","journal-title":"IEEE Trans. Energy Convers."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1666","DOI":"10.1109\/TIA.2008.2006297","article-title":"A Nonintrusive and In-Service Motor-Efficiency Estimation Method Using Air-Gap Torque with Considerations of Condition Monitoring","volume":"44","author":"Lu","year":"2008","journal-title":"IEEE Trans. Ind. Appl."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/25\/3\/754\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T10:36:51Z","timestamp":1759919811000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/25\/3\/754"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,1,26]]},"references-count":38,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2025,2]]}},"alternative-id":["s25030754"],"URL":"https:\/\/doi.org\/10.3390\/s25030754","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,1,26]]}}}