{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T20:15:44Z","timestamp":1782936944037,"version":"3.54.5"},"reference-count":61,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,10,10]],"date-time":"2022-10-10T00:00:00Z","timestamp":1665360000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["52171317 and 51779262"],"award-info":[{"award-number":["52171317 and 51779262"]}]},{"name":"National Natural Science Foundation of China","award":["CX2021050"],"award-info":[{"award-number":["CX2021050"]}]},{"name":"Graduate Innovative Fund of Wuhan Institute of Technology","award":["52171317 and 51779262"],"award-info":[{"award-number":["52171317 and 51779262"]}]},{"name":"Graduate Innovative Fund of Wuhan Institute of Technology","award":["CX2021050"],"award-info":[{"award-number":["CX2021050"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Two-stage thermoelectric generators have been widely used in the aerospace, military, industrial and daily life fields. Based on the established two-stage thermoelectric generator model, this paper further studies its performance. Applying the theory of finite-time thermodynamics, the efficient power expression of the two-stage thermoelectric generator is deduced firstly. The maximum efficient power is obtained secondly by optimizing the distribution of the heat exchanger area, distribution of thermoelectric elements and working current. Using the NSGA-II algorithm, multi-objective optimizations of the two-stage thermoelectric generator are performed thirdly by taking the dimensionless output power, thermal efficiency and dimensionless efficient power as objective functions, and taking the distribution of the heat exchanger area, distribution of thermoelectric elements and output current as optimization variables. The Pareto frontiers with the optimal solution set are obtained. The results show that when the total number of thermoelectric elements is increased from 40 to 100, the maximum efficient power is decreased from 0.308W to 0.2381W. When the total heat exchanger area is increased from 0.03m2 to 0.09m2, the maximum efficient power is increased from 0.0603W to 0.3777W. The deviation indexes are 0.1866, 0.1866 and 0.1815 with LINMAP, TOPSIS and Shannon entropy decision-making approaches, respectively, when multi-objective optimization is performed on three-objective optimization. The deviation indexes are 0.2140, 0.9429 and 0.1815 for three single-objective optimizations of maximum dimensionless output power, thermal efficiency and dimensionless efficient power, respectively.<\/jats:p>","DOI":"10.3390\/e24101443","type":"journal-article","created":{"date-parts":[[2022,10,10]],"date-time":"2022-10-10T21:07:11Z","timestamp":1665436031000},"page":"1443","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Maximum Efficient Power Performance Analysis and Multi-Objective Optimization of Two-Stage Thermoelectric Generators"],"prefix":"10.3390","volume":"24","author":[{"given":"Lei","family":"Tian","sequence":"first","affiliation":[{"name":"Institute of Thermal Science and Power Engineering, Wuhan Institute of Technology, Wuhan 430205, China"},{"name":"Hubei Provincial Engineering Technology Research Center of Green Chemical Equipment, Wuhan 430205, China"},{"name":"School of Mechanical & Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9012-6736","authenticated-orcid":false,"given":"Lingen","family":"Chen","sequence":"additional","affiliation":[{"name":"Institute of Thermal Science and Power Engineering, Wuhan Institute of Technology, Wuhan 430205, China"},{"name":"Hubei Provincial Engineering Technology Research Center of Green Chemical Equipment, Wuhan 430205, China"},{"name":"School of Mechanical & Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yanlin","family":"Ge","sequence":"additional","affiliation":[{"name":"Institute of Thermal Science and Power Engineering, Wuhan Institute of Technology, Wuhan 430205, China"},{"name":"Hubei Provincial Engineering Technology Research Center of Green Chemical Equipment, Wuhan 430205, China"},{"name":"School of Mechanical & Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shuangshuang","family":"Shi","sequence":"additional","affiliation":[{"name":"Institute of Thermal Science and Power Engineering, Wuhan Institute of Technology, Wuhan 430205, China"},{"name":"Hubei Provincial Engineering Technology Research Center of Green Chemical Equipment, Wuhan 430205, China"},{"name":"School of Mechanical & Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"703","DOI":"10.1126\/science.285.5428.703","article-title":"Thermoelectric cooling and power generation","volume":"285","author":"DiSalvo","year":"1999","journal-title":"Science"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Zoui, M.A., Bentou-ba, S., Stocholm, J.G., and Bourouis, M. 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