{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T07:51:47Z","timestamp":1781596307392,"version":"3.54.5"},"reference-count":46,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T00:00:00Z","timestamp":1788220800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T00:00:00Z","timestamp":1788220800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T00:00:00Z","timestamp":1788220800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T00:00:00Z","timestamp":1788220800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T00:00:00Z","timestamp":1788220800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T00:00:00Z","timestamp":1788220800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T00:00:00Z","timestamp":1788220800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100012580","name":"Natural Science Foundation of Tianjin Science and Technology Correspondent Project","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100012580","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Engineering Applications of Artificial Intelligence"],"published-print":{"date-parts":[[2026,9]]},"DOI":"10.1016\/j.engappai.2026.115123","type":"journal-article","created":{"date-parts":[[2026,5,22]],"date-time":"2026-05-22T02:26:16Z","timestamp":1779416776000},"page":"115123","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"P1","title":["Parameterized safe reinforcement learning for operational flexibility quantification of active distribution networks with low-observability"],"prefix":"10.1016","volume":"179","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0933-1896","authenticated-orcid":false,"given":"Xihai","family":"Zhang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shaoyun","family":"Ge","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6698-4714","authenticated-orcid":false,"given":"Yue","family":"Zhou","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hong","family":"Liu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shida","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.engappai.2026.115123_b1","series-title":"The Power of Transformation: Wind, Sun and the Economics of Flexible Power Systems","first-page":"238","author":"Agency","year":"2014"},{"issue":"4","key":"10.1016\/j.engappai.2026.115123_b2","doi-asserted-by":"crossref","first-page":"4061","DOI":"10.1109\/TPWRS.2017.2767632","article-title":"Distribution locational marginal pricing (DLMP) for congestion management and voltage support","volume":"33","author":"Bai","year":"2018","journal-title":"IEEE Trans. Power Syst."},{"key":"10.1016\/j.engappai.2026.115123_b3","doi-asserted-by":"crossref","DOI":"10.3389\/fenrg.2025.1632604","article-title":"An optimal reactive power pre-dispatch approach for minimizing active power losses","volume":"13","author":"Baltensperger","year":"2025","journal-title":"Front. Energy Res."},{"issue":"1","key":"10.1016\/j.engappai.2026.115123_b4","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1109\/TPWRS.2017.2703835","article-title":"Convergence of the Z-bus method for three-phase distribution load-flow with ZIP loads","volume":"33","author":"Bazrafshan","year":"2018","journal-title":"IEEE Trans. Power Syst."},{"key":"10.1016\/j.engappai.2026.115123_b5","series-title":"2023 IEEE Belgrade PowerTech","first-page":"1","article-title":"Exploring operational flexibility of active distribution networks with low observability","author":"Chrysostomou","year":"2023"},{"key":"10.1016\/j.engappai.2026.115123_b6","unstructured":"DKA Solar Centre, , (2022). https:\/\/dkasolarcentre.com.au\/."},{"issue":"2","key":"10.1016\/j.engappai.2026.115123_b7","doi-asserted-by":"crossref","first-page":"876","DOI":"10.1109\/TPWRS.2021.3103128","article-title":"Flexibility management in economic dispatch with dynamic automatic generation control","volume":"37","author":"Fan","year":"2022","journal-title":"IEEE Trans. Power Syst."},{"key":"10.1016\/j.engappai.2026.115123_b8","doi-asserted-by":"crossref","DOI":"10.1016\/j.engappai.2026.114009","article-title":"Data-driven model-free graph multi-agent deep reinforcement learning for voltage-voltage-ampere reactive control in active distribution networks","volume":"168","author":"Gao","year":"2026","journal-title":"Eng. Appl. Artif. Intell."},{"key":"10.1016\/j.engappai.2026.115123_b9","doi-asserted-by":"crossref","unstructured":"Gelagaev, Ratmir, Vermeyen, Pieter, Vandewalle, Joos, Driesen, Johan, 2010. Numerical observability analysis of distribution systems. In: Proceedings of 14th International Conference on Harmonics and Quality of Power - ICHQP 2010. pp. 1\u20136.","DOI":"10.1109\/ICHQP.2010.5625500"},{"key":"10.1016\/j.engappai.2026.115123_b10","unstructured":"Hausknecht, Matthew, Stone, Peter, 2016. Deep reinforcement learning in parameterized action space. In: International Conference on Learning Representations, ICLR."},{"issue":"4","key":"10.1016\/j.engappai.2026.115123_b11","doi-asserted-by":"crossref","first-page":"2353","DOI":"10.1109\/TSTE.2022.3197175","article-title":"DLMP-based quantification and analysis method of operational flexibility in flexible distribution networks","volume":"13","author":"Jian","year":"2022","journal-title":"IEEE Trans. Sustain. Energy"},{"key":"10.1016\/j.engappai.2026.115123_b12","doi-asserted-by":"crossref","DOI":"10.1016\/j.apenergy.2022.120419","article-title":"Feasible operation region of an electricity distribution network","volume":"331","author":"Jiang","year":"2023","journal-title":"Appl. Energy"},{"key":"10.1016\/j.engappai.2026.115123_b13","unstructured":"Jiechao, Xiong, Qing, Wang, Zhuoran, Yang, Peng, Sun, Lei, Han, Yang, Zheng, Haobo, Fu, Tong, Zhang, Ji, Liu, Han, Liu, 2018. Parametrized Deep Q-Networks Learning: Reinforcement Learning with Discrete-Continuous Hybrid Action Space. In: International Conference on Learning Representations, ICLR."},{"issue":"3","key":"10.1016\/j.engappai.2026.115123_b14","doi-asserted-by":"crossref","first-page":"890","DOI":"10.1109\/59.780900","article-title":"Cost analysis of reactive power support","volume":"14","author":"Lamont","year":"1999","journal-title":"IEEE Trans. Power Syst."},{"issue":"2","key":"10.1016\/j.engappai.2026.115123_b15","doi-asserted-by":"crossref","first-page":"4600","DOI":"10.1109\/TPWRS.2023.3302421","article-title":"Time-Varying Operating Regions of end-users and feeders in low-voltage distribution networks","volume":"39","author":"Lankeshwara","year":"2024","journal-title":"IEEE Trans. Power Syst."},{"issue":"2","key":"10.1016\/j.engappai.2026.115123_b16","doi-asserted-by":"crossref","first-page":"922","DOI":"10.1109\/TPWRS.2011.2177280","article-title":"Evaluation of power system flexibility","volume":"27","author":"Lannoye","year":"2012","journal-title":"IEEE Trans. Power Syst."},{"key":"10.1016\/j.engappai.2026.115123_b17","doi-asserted-by":"crossref","first-page":"92622","DOI":"10.1109\/ACCESS.2025.3572595","article-title":"A critical review on flexibility quantification and evaluation methods in medium and low voltage networks","volume":"13","author":"Lazaridou","year":"2025","journal-title":"IEEE Access"},{"issue":"3","key":"10.1016\/j.engappai.2026.115123_b18","doi-asserted-by":"crossref","first-page":"2553","DOI":"10.1109\/TSG.2023.3315147","article-title":"Risk-aware flexible resource utilization in an unbalanced three-phase distribution network using SDP-based distributionally robust optimal power flow","volume":"15","author":"Lu","year":"2024","journal-title":"IEEE Trans. Smart Grid"},{"issue":"2","key":"10.1016\/j.engappai.2026.115123_b19","doi-asserted-by":"crossref","first-page":"887","DOI":"10.1109\/TPWRS.2019.2941635","article-title":"Distributionally robust co-optimization of power dispatch and do-not-exceed limits","volume":"35","author":"Ma","year":"2020","journal-title":"IEEE Trans. Power Syst."},{"key":"10.1016\/j.engappai.2026.115123_b20","series-title":"2024 IEEE Power & Energy Society General Meeting","first-page":"1","article-title":"Feasible operating envelopes of distribution network buses considering utilisation of allocated operating range and power injection limits","author":"Marcel","year":"2024"},{"key":"10.1016\/j.engappai.2026.115123_b21","doi-asserted-by":"crossref","first-page":"114250","DOI":"10.1109\/ACCESS.2023.3322365","article-title":"Value of flexibility alternatives for real distribution networks in the context of the energy transition","volume":"11","author":"Mart\u00edn-Utrilla","year":"2023","journal-title":"IEEE Access"},{"key":"10.1016\/j.engappai.2026.115123_b22","doi-asserted-by":"crossref","unstructured":"Masson, Warwick, Ranchod, Pravesh, Konidaris, George, 2016. Reinforcement Learning with Parameterized Actions. In: Proceedings of the AAAI Conference on Artificial Intelligence.","DOI":"10.1609\/aaai.v30i1.10226"},{"issue":"6","key":"10.1016\/j.engappai.2026.115123_b23","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1109\/MPE.2021.3104075","article-title":"A future with inverter-based resources: Finding strength from traditional weakness","volume":"19","author":"Matevosyan","year":"2021","journal-title":"IEEE Power Energy Mag."},{"issue":"3","key":"10.1016\/j.engappai.2026.115123_b24","doi-asserted-by":"crossref","first-page":"1321","DOI":"10.1109\/TAC.2022.3152724","article-title":"Safe policies for reinforcement learning via primal-dual methods","volume":"68","author":"Paternain","year":"2023","journal-title":"IEEE Trans. Autom. Control"},{"key":"10.1016\/j.engappai.2026.115123_b25","unstructured":"Pennsylvania-New Jersey-Maryland Interconnection: markets & operations, , (2017). https:\/\/www.pjm.com\/markets-and-operations."},{"key":"10.1016\/j.engappai.2026.115123_b26","unstructured":"Qingkai, Liang, Fanyu, Que, Eytan, Modiano, 2017. Accelerated Primal-Dual Policy Optimization for Safe Reinforcement Learning. In: 31st Conference on Neural Information Processing System, NIPS."},{"key":"10.1016\/j.engappai.2026.115123_b27","unstructured":"Tesla Powerwall, , (2023). https:\/\/www.tesla.com\/en_gb\/powerwall."},{"issue":"3","key":"10.1016\/j.engappai.2026.115123_b28","doi-asserted-by":"crossref","first-page":"2663","DOI":"10.1109\/TSG.2020.3047863","article-title":"Capturing spatio-temporal dependencies in the probabilistic forecasting of distribution locational marginal prices","volume":"12","author":"Toubeau","year":"2021","journal-title":"IEEE Trans. Smart Grid"},{"key":"10.1016\/j.engappai.2026.115123_b29","series-title":"Centre for Sustainable Electricity and Distributed Generation","year":"2007"},{"key":"10.1016\/j.engappai.2026.115123_b30","series-title":"Choosing the Optimal Energy System for Buildings and Districts","author":"Virtanen","year":"2011"},{"key":"10.1016\/j.engappai.2026.115123_b31","doi-asserted-by":"crossref","DOI":"10.1016\/j.apenergy.2019.114425","article-title":"Model and observation of dispatchable region for flexible distribution network","volume":"261","author":"Xiao","year":"2020","journal-title":"Appl. Energy"},{"key":"10.1016\/j.engappai.2026.115123_b32","doi-asserted-by":"crossref","DOI":"10.1016\/j.engappai.2025.112499","article-title":"Hybrid reinforcement learning in parameterized action space via fluctuates constraint","volume":"162","author":"Yan","year":"2025","journal-title":"Eng. Appl. Artif. Intell."},{"issue":"6","key":"10.1016\/j.engappai.2026.115123_b33","doi-asserted-by":"crossref","first-page":"5685","DOI":"10.1109\/TSG.2025.3596779","article-title":"FFRLS-based data-driven voltage security assessment for active distribution networks","volume":"16","author":"Yang","year":"2025","journal-title":"IEEE Trans. Smart Grid"},{"key":"10.1016\/j.engappai.2026.115123_b34","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1007\/s00158-025-04085-w","article-title":"Quantum mapping algorithm for structural non-probabilistic reliability optimization","volume":"68","author":"Yusheng","year":"2025","journal-title":"Struct. Multidiscip. Optim."},{"key":"10.1016\/j.engappai.2026.115123_b35","doi-asserted-by":"crossref","DOI":"10.1016\/j.apenergy.2023.121312","article-title":"Model and observation of the feasible region for PV integration capacity considering wasserstein-distance-based distributionally robust chance constraints","volume":"347","author":"Zhang","year":"2023","journal-title":"Appl. Energy"},{"key":"10.1016\/j.engappai.2026.115123_b36","doi-asserted-by":"crossref","DOI":"10.1016\/j.apenergy.2023.122175","article-title":"Region-based flexibility quantification in distribution systems: An analytical approach considering spatio-temporal coupling","volume":"355","author":"Zhang","year":"2024","journal-title":"Appl. Energy"},{"key":"10.1016\/j.engappai.2026.115123_b37","doi-asserted-by":"crossref","DOI":"10.1016\/j.apenergy.2022.120436","article-title":"Distributionally robust optimization for peer-to-peer energy trading considering data-driven ambiguity sets","volume":"331","author":"Zhang","year":"2023","journal-title":"Appl. Energy"},{"issue":"11","key":"10.1016\/j.engappai.2026.115123_b38","doi-asserted-by":"crossref","first-page":"13273","DOI":"10.1109\/TII.2024.3435430","article-title":"Deep learning framework for low-observable distribution system state estimation with multitimescale measurements","volume":"20","author":"Zhang","year":"2024","journal-title":"IEEE Trans. Ind. Inform."},{"issue":"2","key":"10.1016\/j.engappai.2026.115123_b39","doi-asserted-by":"crossref","first-page":"1286","DOI":"10.1109\/TPWRS.2021.3106263","article-title":"Predicting real-time locational marginal prices: A GAN-based approach","volume":"37","author":"Zhang","year":"2022","journal-title":"IEEE Trans. Power Syst."},{"issue":"2","key":"10.1016\/j.engappai.2026.115123_b40","first-page":"609","article-title":"Automatic programming for the optimal power flow in distribution networks: An edge-side adaptive computing approach based on large language models","volume":"12","author":"Zhang","year":"2026","journal-title":"CSEE J. Power Energy Syst."},{"issue":"1","key":"10.1016\/j.engappai.2026.115123_b41","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1109\/TPWRS.2015.2390038","article-title":"A unified framework for defining and measuring flexibility in power system","volume":"31","author":"Zhao","year":"2016","journal-title":"IEEE Trans. Power Syst."},{"issue":"1","key":"10.1016\/j.engappai.2026.115123_b42","doi-asserted-by":"crossref","first-page":"68","DOI":"10.23919\/PCMP.2025.000183","article-title":"Low-carbon economic dispatch in integrated energy systems: A set-based interval optimization with decision support under uncertainties","volume":"11","author":"Zheng","year":"2026","journal-title":"Prot. Control. Mod. Power Syst."},{"issue":"12","key":"10.1016\/j.engappai.2026.115123_b43","doi-asserted-by":"crossref","first-page":"5700","DOI":"10.1109\/TCYB.2025.3594793","article-title":"Data\u2013driven model\u2013free adaptive dynamic programming resilient control for nonlinear networked control systems under DoS attacks","volume":"55","author":"Zhong","year":"2025","journal-title":"IEEE Trans. Cybern."},{"key":"10.1016\/j.engappai.2026.115123_b44","first-page":"1","article-title":"Aggregated feasible Active Power Region for distributed energy resources with a distributionally robust joint probabilistic guarantee","author":"Zhou","year":"2024","journal-title":"IEEE Trans. Power Syst."},{"issue":"4","key":"10.1016\/j.engappai.2026.115123_b45","doi-asserted-by":"crossref","first-page":"2299","DOI":"10.1109\/TSTE.2025.3551314","article-title":"A data-and-model-driven acceleration approach for large-scale network-constrained unit commitment problem with uncertainty","volume":"16","author":"Zhou","year":"2025","journal-title":"IEEE Trans. Sustain. Energy"},{"key":"10.1016\/j.engappai.2026.115123_b46","doi-asserted-by":"crossref","unstructured":"Zhou, Fan, Rui, Su, Weinan, Zhang, Yong, Yu, 2019. Hybrid Actor-Critic Reinforcement Learning in Parameterized Action Space. In: Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence, (IJCAI-19). pp. 2279\u20132285.","DOI":"10.24963\/ijcai.2019\/316"}],"container-title":["Engineering Applications of Artificial Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0952197626014065?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0952197626014065?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T06:54:36Z","timestamp":1781592876000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0952197626014065"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9]]},"references-count":46,"alternative-id":["S0952197626014065"],"URL":"https:\/\/doi.org\/10.1016\/j.engappai.2026.115123","relation":{},"ISSN":["0952-1976"],"issn-type":[{"value":"0952-1976","type":"print"}],"subject":[],"published":{"date-parts":[[2026,9]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Parameterized safe reinforcement learning for operational flexibility quantification of active distribution networks with low-observability","name":"articletitle","label":"Article Title"},{"value":"Engineering Applications of Artificial Intelligence","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.engappai.2026.115123","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"115123"}}