{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T00:01:09Z","timestamp":1780531269499,"version":"3.54.1"},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T00:00:00Z","timestamp":1779321600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T00:00:00Z","timestamp":1779321600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"Zhejiang Energy Group Scientific and Technological Development Program","award":["ZNKJ-2022-126"],"award-info":[{"award-number":["ZNKJ-2022-126"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["SIViP"],"published-print":{"date-parts":[[2026,6]]},"DOI":"10.1007\/s11760-026-05433-z","type":"journal-article","created":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T18:19:19Z","timestamp":1779387559000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Cost-effective power system operation with nonparametric Probabilistic optimal power flow and quantile regression forests method"],"prefix":"10.1007","volume":"20","author":[{"given":"Chengfu","family":"Sun","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chengyu","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,5,21]]},"reference":[{"key":"5433_CR1","doi-asserted-by":"publisher","first-page":"652","DOI":"10.1016\/j.renene.2018.02.087","volume":"123","author":"S Ali","year":"2018","unstructured":"Ali, S., Lee, S.-M., Jang, C.-M.: Statistical analysis of wind characteristics using Weibull and Rayleigh distributions in Deokjeok-do Island\u2013Incheon, South Korea. Renew. Energy 123, 652\u2013663 (2018)","journal-title":"Renew. Energy"},{"key":"5433_CR2","doi-asserted-by":"publisher","first-page":"42","DOI":"10.22034\/aeis.2022.355486.1036","volume":"001","author":"A Sohel","year":"2022","unstructured":"Sohel, A., Bin Ashab, M.F.: Determining appropriate strategy for managing the energy production system in the presence of renewable energy sources and improved intelligence method. Adv. Eng. Intell. Syst. 001, 42\u201353 (2022). https:\/\/doi.org\/10.22034\/aeis.2022.355486.1036","journal-title":"Adv. Eng. Intell. Syst."},{"key":"5433_CR3","doi-asserted-by":"publisher","first-page":"20160296","DOI":"10.1098\/rsta.2016.0296","volume":"375","author":"JV Milanovi\u0107","year":"2017","unstructured":"Milanovi\u0107, J.V.: Probabilistic stability analysis: the way forward for stability analysis of sustainable power systems. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. 375, 20160296 (2017)","journal-title":"Philos. Trans. R. Soc. A Math. Phys. Eng. Sci."},{"key":"5433_CR4","doi-asserted-by":"publisher","first-page":"107457","DOI":"10.1016\/j.epsr.2021.107457","volume":"199","author":"E Faraji","year":"2021","unstructured":"Faraji, E., Abbasi, A.R., Nejatian, S., Zadehbagheri, M., Parvin, H.: Probabilistic planning of the active and reactive power sources constrained to securable-reliable operation in reconfigurable smart distribution networks. Electr. Power Syst. Res. 199, 107457 (2021)","journal-title":"Electr. Power Syst. Res."},{"key":"5433_CR5","doi-asserted-by":"crossref","unstructured":"\u0130skendero\u011flu, A., G\u00fcl, \u00d6.: Probabilistic power flow analysis of power systems with PV and wind using Monte Carlo method. In: 2023 10th International Conference on Electrical and Electronics Engineering (ICEEE). pp. 480\u2013485. IEEE (2023)","DOI":"10.1109\/ICEEE59925.2023.00093"},{"key":"5433_CR6","doi-asserted-by":"publisher","first-page":"138","DOI":"10.18196\/jrc.v3i2.13118","volume":"3","author":"R Alayi","year":"2022","unstructured":"Alayi, R., Ma\u2019arif, A., Ebazadeh, Y., Gharadaghi, F., Jahanbin, F., Shafaghatian, N.: Optimization of renewable energy consumption in charging electric vehicles using intelligent algorithms. J. Robotics Control (JRC) 3, 138\u2013142 (2022)","journal-title":"J. Robotics Control (JRC)"},{"key":"5433_CR7","doi-asserted-by":"crossref","unstructured":"Gu, J., Zhao, L., Zhu, C.: Quasi-Monte Carlo method for probabilistic power flow considering uncertainty of heat loads. In: 2020 IEEE 3rd Student Conference on Electrical Machines and Systems (SCEMS). pp. 808\u2013812. IEEE (2020)","DOI":"10.1109\/SCEMS48876.2020.9352425"},{"key":"5433_CR8","doi-asserted-by":"crossref","unstructured":"Maharjan, M., Ekic, A., Wu, D.: Probabilistic grid strength assessment of power systems with uncertain renewable generation based on probabilistic collocation method. In: 2022 17th International Conference on Probabilistic Methods Applied to Power Systems (PMAPS). pp. 1\u20136. IEEE (2022)","DOI":"10.1109\/PMAPS53380.2022.9810616"},{"key":"5433_CR9","doi-asserted-by":"publisher","first-page":"4108","DOI":"10.3390\/en16104108","volume":"16","author":"F Zishan","year":"2023","unstructured":"Zishan, F., Tightiz, L., Yoo, J., Shafaghatian, N.: Sustainability of the permanent magnet synchronous generator wind turbine control strategy in on-grid operating modes. Energies 16, 4108 (2023)","journal-title":"Energies"},{"key":"5433_CR10","doi-asserted-by":"publisher","first-page":"2537","DOI":"10.1109\/TPWRS.2019.2959404","volume":"35","author":"C Lin","year":"2019","unstructured":"Lin, C., Bie, Z., Pan, C., Liu, S.: Fast cumulant method for probabilistic power flow considering the nonlinear relationship of wind power generation. IEEE Trans. Power Syst. 35, 2537\u20132548 (2019)","journal-title":"IEEE Trans. Power Syst."},{"key":"5433_CR11","doi-asserted-by":"publisher","first-page":"1042","DOI":"10.1007\/s40565-018-0384-6","volume":"6","author":"B Sui","year":"2018","unstructured":"Sui, B., Hou, K., Jia, H., Mu, Y., Yu, X.: Maximum entropy based probabilistic load flow calculation for power system integrated with wind power generation. J. Mod. Power Syst. Clean Energy 6, 1042\u20131054 (2018)","journal-title":"J. Mod. Power Syst. Clean Energy"},{"key":"5433_CR12","doi-asserted-by":"publisher","first-page":"1014","DOI":"10.1109\/TSG.2023.3272343","volume":"15","author":"T Zhang","year":"2023","unstructured":"Zhang, T., Zhang, W., Zhao, Q., Li, Z., Zhao, J.: Forecasting-aided joint topology\/state estimation for distribution systems via Bayesian non-parametric modeling. IEEE Trans. Smart Grid 15, 1014\u20131029 (2023)","journal-title":"IEEE Trans. Smart Grid"},{"key":"5433_CR13","doi-asserted-by":"crossref","unstructured":"Dubey, A., Verma, H.K.: Probabilistic approach for optimal power flow using Cornish Fisher and Gram Charlier series expansion. In: 2020 21st National Power Systems Conference (NPSC). pp. 1\u20136. IEEE (2020)","DOI":"10.1109\/NPSC49263.2020.9331870"},{"key":"5433_CR14","doi-asserted-by":"crossref","unstructured":"Li, B., Zhang, J., Hobbs, B.F.: A copula enhanced convolution for uncertainty aggregation. In: 2020 IEEE power & energy society innovative smart grid technologies conference (ISGT). pp. 1\u20135. IEEE (2020)","DOI":"10.1109\/ISGT45199.2020.9087644"},{"key":"5433_CR15","doi-asserted-by":"crossref","unstructured":"de Bruyn, J., Bekker, B., Dalton, A.: A review of load flow methodologies for constrained networks: A south african case study. In: 2022 International Conference on Electrical, Computer, Communications and Mechatronics Engineering (ICECCME). pp. 1\u20136. IEEE (2022)","DOI":"10.1109\/ICECCME55909.2022.9988460"},{"key":"5433_CR16","doi-asserted-by":"crossref","unstructured":"Chothani, N., Desai, I.: Fourier transform and probabilistic neural network based fault detection in distribution system containing DGs. In: 2021 Innovations in Power and Advanced Computing Technologies (i-PACT). pp. 1\u20135. IEEE (2021)","DOI":"10.1109\/i-PACT52855.2021.9696718"},{"key":"5433_CR17","doi-asserted-by":"crossref","unstructured":"Saito, S., Matsushima, T.: Cumulant generating function of codeword lengths in variable-length lossy compression allowing positive excess distortion probability. In: 2018 IEEE International Symposium on Information Theory (ISIT). pp. 881\u2013885. IEEE (2018)","DOI":"10.1109\/ISIT.2018.8437695"},{"key":"5433_CR18","first-page":"89","volume":"6","author":"F Zishan","year":"2023","unstructured":"Zishan, F., Akbari, E., Sheikholeslami, A.R., Shafaghatian, N.: Optimization and placement of DG resources in the network to reduce line loading. Int. J. Ind. Electron. Control Optim. 6, 89\u2013100 (2023)","journal-title":"Int. J. Ind. Electron. Control Optim."},{"key":"5433_CR19","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1109\/ICJECE.2021.3123091","volume":"45","author":"R Taghavi","year":"2021","unstructured":"Taghavi, R., Samet, H., Seifi, A.R., Ali, Z.M.: Stochastic optimal power flow in hybrid power system using reduced-discrete point estimation method and Latin hypercube sampling. IEEE Can. J. Electr. Comput. Eng. 45, 63\u201367 (2021)","journal-title":"IEEE Can. J. Electr. Comput. Eng."},{"key":"5433_CR20","doi-asserted-by":"crossref","unstructured":"Ban, G., Xu, Y., Yang, X., Zheng, H., Yuan, X., Zhao, Z., Ma, X.: Improved three-point estimation method for probabilistic power flow calculation. In: 2022 7th Asia Conference on Power and Electrical Engineering (ACPEE). pp. 1330\u20131334. IEEE (2022)","DOI":"10.1109\/ACPEE53904.2022.9784066"},{"key":"5433_CR21","unstructured":"Ordoudis, C., Pinson, P., Gonz\u00e1lez, J.M.M., Zugno, M.: An Updated Version of the IEEE RTS 24-Bus System for Electricity Market and Power System Operation Studies. (2016)"},{"key":"5433_CR22","doi-asserted-by":"publisher","first-page":"2758","DOI":"10.1109\/TPWRS.2021.3124579","volume":"37","author":"Y Li","year":"2021","unstructured":"Li, Y., Wan, C., Chen, D., Song, Y.: Nonparametric probabilistic optimal power flow. IEEE Trans. Power Syst. 37, 2758\u20132770 (2021)","journal-title":"IEEE Trans. Power Syst."}],"container-title":["Signal, Image and Video Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11760-026-05433-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11760-026-05433-z","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11760-026-05433-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T23:11:42Z","timestamp":1780528302000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11760-026-05433-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5,21]]},"references-count":22,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2026,6]]}},"alternative-id":["5433"],"URL":"https:\/\/doi.org\/10.1007\/s11760-026-05433-z","relation":{},"ISSN":["1863-1703","1863-1711"],"issn-type":[{"value":"1863-1703","type":"print"},{"value":"1863-1711","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,5,21]]},"assertion":[{"value":"11 May 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 April 2026","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 May 2026","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 May 2026","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"The research paper has received ethical approval from the institutional review board, ensuring the protection of participants\u2019 rights and compliance with the relevant ethical guidelines.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}}],"article-number":"354"}}