{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T21:42:00Z","timestamp":1772055720363,"version":"3.50.1"},"reference-count":28,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2022,12,5]],"date-time":"2022-12-05T00:00:00Z","timestamp":1670198400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100010880","name":"State Grid Corporation of China","doi-asserted-by":"publisher","award":["5500-202158417A-0-0-00"],"award-info":[{"award-number":["5500-202158417A-0-0-00"]}],"id":[{"id":"10.13039\/501100010880","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Piezoelectric vibration energy harvester (PVEH) is a promising device for sustainable power supply of wireless sensor nodes (WSNs). PVEH is resonant and generates power under constant frequency vibration excitation of mechanical equipment. However, it cannot output high power through off-resonance if it has frequency offset in manufacturing, assembly and use. To address this issue, this paper designs and optimizes a PVEH to harvest power specifically from grid transformer vibration at 100 Hz with high power density of 5.28 \u03bcWmm\u22123g\u22122. Some resonant frequency modulation methods of PVEH are discussed by theoretical analysis and experiment, such as load impedance, additional mass, glue filling, axial and transverse magnetic force frequency modulation. Finally, efficient energy harvesting of 6.1 V output in 0.0226 g acceleration is tested in grid transformer reactor field application. This research has practical value for the design and optimization process of tunable PVEH for a specific vibration source.<\/jats:p>","DOI":"10.3390\/s22239493","type":"journal-article","created":{"date-parts":[[2022,12,5]],"date-time":"2022-12-05T08:10:57Z","timestamp":1670227857000},"page":"9493","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Frequency Modulation Approach for High Power Density 100 Hz Piezoelectric Vibration Energy Harvester"],"prefix":"10.3390","volume":"22","author":[{"given":"Dengfeng","family":"Ju","sequence":"first","affiliation":[{"name":"State Grid Smart Grid Research Institute Co., Ltd., Beijing 102209, China"},{"name":"Electric Power Intelligent Sensing Technology and Application State Grid Corporation Joint Laboratory, Beijing 102209, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4171-5873","authenticated-orcid":false,"given":"Lu","family":"Wang","sequence":"additional","affiliation":[{"name":"State Key Laboratory for Manufacturing Systems Engineering, International Joint Laboratory for Micro\/Nano Manufacturing and Measurement Technologies, Xi\u2019an Jiaotong University (Yantai) Research Institute for Intelligent Sensing Technology and System, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"},{"name":"School of Mechanical Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"},{"name":"Shandong Laboratory of Yantai Advanced Materials and Green Manufacturing, Yantai 265503, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chunlong","family":"Li","sequence":"additional","affiliation":[{"name":"State Grid Smart Grid Research Institute Co., Ltd., Beijing 102209, China"},{"name":"Electric Power Intelligent Sensing Technology and Application State Grid Corporation Joint Laboratory, Beijing 102209, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-7557-8130","authenticated-orcid":false,"given":"Hui","family":"Huang","sequence":"additional","affiliation":[{"name":"State Grid Smart Grid Research Institute Co., Ltd., Beijing 102209, China"},{"name":"Electric Power Intelligent Sensing Technology and Application State Grid Corporation Joint Laboratory, Beijing 102209, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hongjing","family":"Liu","sequence":"additional","affiliation":[{"name":"State Grid Beijing Electric Power Research Institute, Beijing 100075, China"},{"name":"Standard Verification Laboratory for On-Site Testing Technology, Beijing 102209, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kewen","family":"Liu","sequence":"additional","affiliation":[{"name":"State Grid Beijing Electric Power Research Institute, Beijing 100075, China"},{"name":"Standard Verification Laboratory for On-Site Testing Technology, Beijing 102209, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qian","family":"Wang","sequence":"additional","affiliation":[{"name":"State Key Laboratory for Manufacturing Systems Engineering, International Joint Laboratory for Micro\/Nano Manufacturing and Measurement Technologies, Xi\u2019an Jiaotong University (Yantai) Research Institute for Intelligent Sensing Technology and System, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"},{"name":"School of Mechanical Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiangguang","family":"Han","sequence":"additional","affiliation":[{"name":"State Key Laboratory for Manufacturing Systems Engineering, International Joint Laboratory for Micro\/Nano Manufacturing and Measurement Technologies, Xi\u2019an Jiaotong University (Yantai) Research Institute for Intelligent Sensing Technology and System, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"},{"name":"School of Mechanical Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"},{"name":"Shandong Laboratory of Yantai Advanced Materials and Green Manufacturing, Yantai 265503, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Libo","family":"Zhao","sequence":"additional","affiliation":[{"name":"State Key Laboratory for Manufacturing Systems Engineering, International Joint Laboratory for Micro\/Nano Manufacturing and Measurement Technologies, Xi\u2019an Jiaotong University (Yantai) Research Institute for Intelligent Sensing Technology and System, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"},{"name":"School of Mechanical Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"},{"name":"Shandong Laboratory of Yantai Advanced Materials and Green Manufacturing, Yantai 265503, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ryutaro","family":"Maeda","sequence":"additional","affiliation":[{"name":"State Key Laboratory for Manufacturing Systems Engineering, International Joint Laboratory for Micro\/Nano Manufacturing and Measurement Technologies, Xi\u2019an Jiaotong University (Yantai) Research Institute for Intelligent Sensing Technology and System, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"},{"name":"School of Mechanical Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,5]]},"reference":[{"key":"ref_1","first-page":"27","article-title":"Power Sensor-oriented Development and Challenges of Environmental Energy Harvesting Technologies","volume":"54","author":"Li","year":"2021","journal-title":"Electr. Power"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"10308","DOI":"10.1109\/TPEL.2017.2775961","article-title":"Design Optimization of an Energy Harvesting Platform for Self-Powered Wireless Devices in Monitoring of AC Power Lines","volume":"33","author":"Abasian","year":"2018","journal-title":"IEEE Trans. Power Electron."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"4447","DOI":"10.1109\/TIE.2018.2860557","article-title":"Vacuum-Packaged Piezoelectric Energy Harvester for Powering Smart Grid Monitoring Devices","volume":"66","author":"Abasian","year":"2019","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Yu, Z., Li, D., and Chen, L. (2018, January 20\u201324). Statistical analysis of vibration characteristics of power transformers with different voltage levels. Proceedings of the 12th IEEE International Conference on the Properties and Applications of Dielectric Materials, Xi\u2019an, China.","DOI":"10.1109\/ICPADM.2018.8401146"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"112039","DOI":"10.1016\/j.sna.2020.112039","article-title":"System level design of wireless sensor node powered by piezoelectric vibration energy harvesting","volume":"310","author":"Wang","year":"2020","journal-title":"Sens. Actuators A Phys."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Tian, W., Ling, Z., Yu, W., and Shi, J. (2018). A Review of MEMS Scale Piezoelectric Energy Harvester. Appl. Sci., 8.","DOI":"10.3390\/app8040645"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"093002","DOI":"10.1088\/1361-6439\/ac168e","article-title":"Technology evolution from micro-scale energy harvesters to nanogenerators","volume":"31","author":"Guo","year":"2021","journal-title":"J. Micromech. Microeng."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"105555","DOI":"10.1016\/j.nanoen.2020.105555","article-title":"Self-sustained autonomous wireless sensing based on a hybridized TENG and PEG vibration mechanism","volume":"80","author":"Wang","year":"2020","journal-title":"Nano Energy"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"294","DOI":"10.1016\/j.energy.2018.11.085","article-title":"High power density energy harvester with non-uniform cantilever structure due to high average strain distribution","volume":"169","author":"Hu","year":"2019","journal-title":"Energy"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1016\/j.sna.2019.06.034","article-title":"A packaged piezoelectric vibration energy harvester with high power and broadband characteristics","volume":"295","author":"Wang","year":"2019","journal-title":"Sens. Actuators A Phys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"075001","DOI":"10.1088\/1361-665X\/ab859f","article-title":"Study on cantilever piezoelectric energy harvester with tunable function","volume":"29","author":"Lihua","year":"2020","journal-title":"Smart Mater. Struct."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Elvira-Hernandez, E.A., Uscanga-Gonzalez, L.A., de Leon, A., Lopez-Huerta, F., and Herrera-May, A.L. (2019). Electromechanical Modeling of a Piezoelectric Vibration Energy Harvesting Microdevice Based on Multilayer Resonator for Air Conditioning Vents at Office Buildings. Micromachines, 10.","DOI":"10.3390\/mi10030211"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"109169","DOI":"10.1016\/j.ymssp.2022.109169","article-title":"Modeling and analysis of a three-degree-of-freedom piezoelectric vibration energy harvester for broadening bandwidth","volume":"176","author":"Zhang","year":"2022","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"104001","DOI":"10.1088\/0960-1317\/20\/10\/104001","article-title":"Vacuum-packaged piezoelectric vibration energy harvesters: Damping contributions and autonomy for a wireless sensor system","volume":"20","author":"Elfrink","year":"2010","journal-title":"J. Micromech. Microeng."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"095067","DOI":"10.1063\/1.5119328","article-title":"High accuracy comsol simulation method of bimorph cantilever for piezoelectric vibration energy harvesting","volume":"9","author":"Wang","year":"2019","journal-title":"AIP Adv."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1413","DOI":"10.1088\/0964-1726\/15\/5\/030","article-title":"Resonance tuning of piezoelectric vibration energy scavenging generators using compressive axial preload","volume":"15","author":"Leland","year":"2006","journal-title":"Smart Mater. Struct."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"035013","DOI":"10.1088\/0964-1726\/25\/3\/035013","article-title":"A self-adaptive energy harvesting system","volume":"25","author":"Hoffmann","year":"2016","journal-title":"Smart Mater. Struct."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"025009","DOI":"10.1088\/1361-665X\/aaf0ea","article-title":"Frequency tuning of piezoelectric energy harvesters thanks to a short-circuit synchronous electric charge extraction","volume":"28","author":"Morel","year":"2019","journal-title":"Smart Mater. Struct."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"033001","DOI":"10.1088\/1361-665X\/ab6484","article-title":"Maximum power point of piezoelectric energy harvesters: A review of optimality condition for electrical tuning","volume":"29","author":"Brenes","year":"2020","journal-title":"Smart Mater. Struct."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"116886","DOI":"10.1016\/j.jsv.2022.116886","article-title":"Multistable vibration energy harvesters: Principle, progress, and perspectives","volume":"528","author":"Zhou","year":"2022","journal-title":"J. Sound Vib."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"107672","DOI":"10.1016\/j.ymssp.2021.107672","article-title":"Achieve frequency-self-tracking energy harvesting using a passively adaptive cantilever beam","volume":"156","author":"Lan","year":"2021","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"125012","DOI":"10.1088\/1361-665X\/ac9d74","article-title":"High performance piezoelectric vibration energy harvesting by electrical resonant frequency tuning","volume":"31","author":"Gibus","year":"2022","journal-title":"Smart Mater. Struct."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"075057","DOI":"10.1088\/1361-665X\/aabf4a","article-title":"Optimal power, power limit and damping of vibration based piezoelectric power harvesters","volume":"27","author":"Liao","year":"2018","journal-title":"Smart Mater. Struct."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2225","DOI":"10.1109\/TIE.2020.2975457","article-title":"A Sensorless Self-Tuning Resonance System for Piezoelectric Broadband Vibration Energy Harvesting","volume":"68","author":"Shi","year":"2021","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"045023","DOI":"10.1088\/0964-1726\/19\/4\/045023","article-title":"Modeling and experimental verification of proof mass effects on vibration energy harvester performance","volume":"19","author":"Kim","year":"2010","journal-title":"Smart Mater. Struct."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.sna.2014.01.032","article-title":"Vibrational piezoelectric energy harvesters based on thinned bulk PZT sheets fabricated at the wafer level","volume":"210","author":"Janphuang","year":"2014","journal-title":"Sens. Actuators A: Phys."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"38798","DOI":"10.1038\/srep38798","article-title":"A piezoelectric micro generator worked at low frequency and high acceleration based on PZT and phosphor bronze bonding","volume":"6","author":"Tang","year":"2016","journal-title":"Sci. Rep."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"45041","DOI":"10.1088\/0964-1726\/23\/4\/045041","article-title":"Design optimization of vibration energy harvesters fabricated by lamination of thinned bulk-PZT on polymeric substrates","volume":"23","author":"Quintero","year":"2014","journal-title":"Smart Mater. Struct."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/23\/9493\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:34:04Z","timestamp":1760146444000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/23\/9493"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,5]]},"references-count":28,"journal-issue":{"issue":"23","published-online":{"date-parts":[[2022,12]]}},"alternative-id":["s22239493"],"URL":"https:\/\/doi.org\/10.3390\/s22239493","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,12,5]]}}}