{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,4]],"date-time":"2026-09-04T11:43:35Z","timestamp":1788522215237,"version":"build-2803163510"},"reference-count":35,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,3,14]],"date-time":"2025-03-14T00:00:00Z","timestamp":1741910400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Yunnan Power Grid Research Project","award":["YNKJXM20222400"],"award-info":[{"award-number":["YNKJXM20222400"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>To address the electric vehicle (EV) charging scheduling problem in rural distribution networks, this study proposes a novel two-phase optimization strategy that combines particle swarm optimization (PSO) and Q-learning for global optimization and real-time adaptation. In the first stage, PSO is used to generate an initial charging plan that minimizes voltage deviations and line overloads while maximizing user satisfaction. In the second phase, a Q-learning approach dynamically adjusts the plan based on real-time grid conditions and feedback. The strategy reduces the system\u2019s entropy by minimizing the uncertainty and disorder in power distribution caused by variable EV charging loads. Experimental results on a 33-bus distribution system under baseline and high-load scenarios demonstrate significant improvements over conventional dispatch methods, with voltage deviation reduced from 5.8% to 1.9%, maximum load factor reduced from 95% to 82%, and average customer satisfaction increased from 75% to 88%. While the computation time increases compared to standalone PSO (66 min vs. 34 min), the enhanced grid stability and customer satisfaction justify the trade-off. By effectively minimizing system entropy and balancing grid reliability with user convenience, the proposed two-phase strategy offers a practical and robust solution for integrating EVs into rural power systems.<\/jats:p>","DOI":"10.3390\/e27030303","type":"journal-article","created":{"date-parts":[[2025,3,14]],"date-time":"2025-03-14T07:02:16Z","timestamp":1741935736000},"page":"303","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Minimizing System Entropy: A Dual-Phase Optimization Approach for EV Charging Scheduling"],"prefix":"10.3390","volume":"27","author":[{"given":"Wenpeng","family":"Yuan","sequence":"first","affiliation":[{"name":"School of Electric Power Engineering, South China University of Technology, Guangzhou 510640, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2625-707X","authenticated-orcid":false,"given":"Lin","family":"Guan","sequence":"additional","affiliation":[{"name":"School of Electric Power Engineering, South China University of Technology, Guangzhou 510640, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1007\/s12667-014-0122-8","article-title":"The importance of spatial distribution when analysing the impact of electric vehicles on voltage stability in distribution networks","volume":"6","author":"Muenzel","year":"2015","journal-title":"Energy Syst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1016\/j.rser.2016.08.002","article-title":"Smart grid technologies and applications","volume":"66","author":"Bayindir","year":"2016","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"5406","DOI":"10.1109\/TPWRS.2022.3221163","article-title":"An MILP method for optimal planning of electric vehicle charging stations in coordinated urban power and transportation networks","volume":"38","author":"Li","year":"2022","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Dukpa, A., and Butrylo, B. (2022). MILP-based profit maximization of electric vehicle charging station based on solar and EV arrival forecasts. Energies, 15.","DOI":"10.3390\/en15155760"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"852","DOI":"10.1016\/j.renene.2022.07.055","article-title":"A genetic algorithm optimization approach for smart energy management of microgrids","volume":"197","author":"Torkan","year":"2022","journal-title":"Renew. Energy"},{"key":"ref_6","first-page":"100710","article-title":"Improved genetic algorithm for optimal demand response in smart grid","volume":"35","author":"Jeyaranjani","year":"2022","journal-title":"Sustain. Comput. Inform. Syst."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Chifu, V.R., Cioara, T., Pop, C.B., Rusu, H.G., and Anghel, I. (2024). Deep Q-Learning-Based Smart Scheduling of EVs for Demand Response in Smart Grids. Appl. Sci., 14.","DOI":"10.3390\/app14041421"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"120111","DOI":"10.1016\/j.apenergy.2022.120111","article-title":"Multi-agent deep reinforcement learning approach for EV charging scheduling in a smart grid","volume":"328","author":"Park","year":"2022","journal-title":"Appl. Energy"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1722","DOI":"10.1109\/TSG.2015.2505298","article-title":"Optimal management for parking-lot electric vehicle charging by two-stage approximate dynamic programming","volume":"8","author":"Zhang","year":"2015","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"5564","DOI":"10.1016\/j.ijhydene.2021.11.188","article-title":"A hybrid optimization technique for proficient energy management in smart grid environment","volume":"47","author":"Kumar","year":"2022","journal-title":"Int. J. Hydrogen Energy"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Chen, Z. (2024). Graph Adaptive Attention Network with Cross-Entropy. Entropy, 26.","DOI":"10.20944\/preprints202406.0939.v1"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Chen, Z. (2024). (HTBNet) Arbitrary Shape Scene Text Detection with Binarization of Hyperbolic Tangent and Cross-Entropy. Entropy, 26.","DOI":"10.20944\/preprints202405.1040.v1"},{"key":"ref_13","first-page":"340","article-title":"Rolling multi-period optimization to control electric vehicle charging in distribution networks","volume":"29","author":"Flynn","year":"2013","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2666","DOI":"10.1109\/TSG.2014.2336623","article-title":"Adaptive electric vehicle charging coordination on distribution network","volume":"5","author":"Hua","year":"2014","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1367","DOI":"10.1109\/TSTE.2015.2438037","article-title":"Demand response for residential electric vehicles with random usage patterns in smart grids","volume":"6","author":"Rassaei","year":"2015","journal-title":"IEEE Trans. Sustain. Energy"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"543","DOI":"10.1109\/TSG.2011.2164949","article-title":"Grid integration of electric vehicles and demand response with customer choice","volume":"3","author":"Shao","year":"2012","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Fang, Z., Hu, S., Wang, J., Deng, Y., Chen, X., and Fang, Y. (2025). Prioritized Information Bottleneck Theoretic Framework with Distributed Online Learning for Edge Video Analytics. IEEE Trans. Netw., 1\u201317.","DOI":"10.1109\/TON.2025.3526148"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Huang, J., Wu, B., Duan, Q., Dong, L., and Yu, S. (IEEE Trans. Mob. Comput., 2025). A Fast UAV Trajectory Planning Framework in RIS-assisted Communication Systems with Accelerated Learning via Multithreading and Federating, IEEE Trans. Mob. Comput., early access.","DOI":"10.1109\/TMC.2025.3544903"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Gao, J., Chen, M., and Xu, C. (IEEE Trans. Pattern Anal. Mach. Intell., 2025). Learning Probabilistic Presence-Absence Evidence for Weakly-Supervised Audio-Visual Event Perception, IEEE Trans. Pattern Anal. Mach. Intell., early access.","DOI":"10.1109\/TPAMI.2025.3546312"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Chen, Z. (IEEE Trans. Intell. Transp. Syst., 2025). Arbitrary Shape Text Detection with Discrete Cosine Transform and CLIP for Urban Scene Perception in ITS, IEEE Trans. Intell. Transp. Syst., early access.","DOI":"10.1109\/TITS.2025.3534291"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1016\/j.ijepes.2013.04.025","article-title":"Strategic charging method for plugged in hybrid electric vehicles in smart grids; a game theoretic approach","volume":"53","author":"Sheikhi","year":"2013","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1073","DOI":"10.1109\/JSTSP.2014.2334275","article-title":"Electric Vehicle Charging in Smart Grid: Optimality and Valley-Filling Algorithms","volume":"8","author":"Chen","year":"2014","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"4339","DOI":"10.1109\/TSG.2021.3074437","article-title":"Adaptive Charging Networks: A Framework for Smart Electric Vehicle Charging","volume":"12","author":"Lee","year":"2020","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"730","DOI":"10.1016\/j.renene.2015.11.084","article-title":"Multi-objective energy storage power dispatching using plug-in vehicles in a smart-microgrid","volume":"89","author":"Coelho","year":"2016","journal-title":"Renew. Energy"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"117104","DOI":"10.1016\/j.apenergy.2021.117104","article-title":"A multi-objective energy optimization in smart grid with high penetration of renewable energy sources","volume":"299","author":"Ullah","year":"2021","journal-title":"Appl. Energy"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"100886","DOI":"10.1016\/j.segan.2022.100886","article-title":"Smart grid resiliency improvement using a multi-objective optimization approach","volume":"32","author":"Mallaki","year":"2022","journal-title":"Sustain. Energy Grids Netw."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Ali, A., David, R., and Mahmoud, K. (2016, January 27\u201329). Adaptive multi-objective optimization for power loss minimization and voltage regulation in distribution systems. Proceedings of the 2016 Eighteenth International Middle East Power Systems Conference (MEPCON), Cairo, Egypt.","DOI":"10.1109\/MEPCON.2016.7836949"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/j.enconman.2013.11.042","article-title":"Multi-objective scheduling of electric vehicles in smart distribution system","volume":"79","author":"Zakariazadeh","year":"2014","journal-title":"Energy Convers. Manag."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/j.apenergy.2016.07.110","article-title":"Multi-objective optimization control of plug-in electric vehicles in low voltage distribution networks","volume":"180","author":"Zamora","year":"2016","journal-title":"Appl. Energy"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"124235","DOI":"10.1109\/ACCESS.2021.3109136","article-title":"Intelligent optimization framework for efficient demand-side management in renewable energy integrated smart grid","volume":"9","author":"Khan","year":"2021","journal-title":"IEEE Access"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"6350647","DOI":"10.1155\/2023\/6350647","article-title":"Model-Free Cooperative Optimal Output Regulation for Linear Discrete-Time Multi-Agent Systems Using Reinforcement Learning","volume":"2023","author":"Wu","year":"2023","journal-title":"Math. Probl. Eng."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"81180","DOI":"10.1109\/ACCESS.2023.3299340","article-title":"AoI-aware resource management for smart health via deep reinforcement learning","volume":"11","author":"Wu","year":"2023","journal-title":"IEEE Access"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"77","DOI":"10.18034\/apjee.v8i2.762","article-title":"Real-Time Scheduling for Energy Optimization: Smart Grid Integration with Renewable Energy","volume":"8","author":"Deming","year":"2021","journal-title":"Asia Pac. J. Energy Environ."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Moreno Escobar, J.J., Morales Matamoros, O., Tejeida Padilla, R., Lina Reyes, I., and Quintana Espinosa, H. (2021). A comprehensive review on smart grids: Challenges and opportunities. Sensors, 21.","DOI":"10.3390\/s21216978"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1109\/TPWRS.2014.2329324","article-title":"Resistive Network Optimal Power Flow: Uniqueness and Algorithms","volume":"30","author":"Tan","year":"2015","journal-title":"IEEE Trans. Power Syst."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/3\/303\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:53:41Z","timestamp":1760028821000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/3\/303"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,14]]},"references-count":35,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2025,3]]}},"alternative-id":["e27030303"],"URL":"https:\/\/doi.org\/10.3390\/e27030303","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,3,14]]}}}