{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,8]],"date-time":"2025-12-08T22:32:11Z","timestamp":1765233131253,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"14","license":[{"start":{"date-parts":[[2021,7,6]],"date-time":"2021-07-06T00:00:00Z","timestamp":1625529600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Distribution system state estimation (DSSE) plays a significant role for the system operation management and control. Due to the multiple uncertainties caused by the non-Gaussian measurement noise, inaccurate line parameters, stochastic power outputs of distributed generations (DG), and plug-in electric vehicles (EV) in distribution systems, the existing interval state estimation (ISE) approaches for DSSE provide fairly conservative estimation results. In this paper, a new ISE model is proposed for distribution systems where the multiple uncertainties mentioned above are well considered and accurately established. Moreover, a modified Krawczyk-operator (MKO) in conjunction with interval constraint-propagation (ICP) algorithm is proposed to solve the ISE problem and efficiently provides better estimation results with less conservativeness. Simulation results carried out on the IEEE 33-bus, 69-bus, and 123-bus distribution systems show that the our proposed algorithm can provide tighter upper and lower bounds of state estimation results than the existing approaches such as the ICP, Krawczyk-Moore ICP(KM-ICP), Hansen, and MKO.<\/jats:p>","DOI":"10.3390\/s21144644","type":"journal-article","created":{"date-parts":[[2021,7,6]],"date-time":"2021-07-06T11:36:44Z","timestamp":1625571404000},"page":"4644","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Interval State Estimation in Active Distribution Systems Considering Multiple Uncertainties"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0404-031X","authenticated-orcid":false,"given":"Tengpeng","family":"Chen","sequence":"first","affiliation":[{"name":"Department of Instrumental and Electrical Engineering, Xiamen University, Xiamen 361102, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"He","family":"Ren","sequence":"additional","affiliation":[{"name":"Department of Instrumental and Electrical Engineering, Xiamen University, Xiamen 361102, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8614-2864","authenticated-orcid":false,"given":"Gehan A. J.","family":"Amaratunga","sequence":"additional","affiliation":[{"name":"Department of Engineering, University of Cambridge, Cambridge CB3 0FA, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,7,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"106247","DOI":"10.1016\/j.epsr.2020.106247","article-title":"Active distribution system state estimation incorporating photovoltaic generation system model","volume":"182","author":"Fang","year":"2020","journal-title":"Electr. Power Syst. Res."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Abur, A., and G\u00f3mez-Exp\u00f3sito, A. (2004). Power System State Estimation: Theory and Implementation, CRC Press.","DOI":"10.1201\/9780203913673"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1808","DOI":"10.1109\/TSG.2014.2302213","article-title":"LAV Based Robust State Estimation for Systems Measured by PMUs","volume":"5","author":"Abur","year":"2014","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"(2018). Decentralized three-phase distribution system static state estimation based on phasor measurement units. Electr. Power Syst. Res., 160, 327\u2013336.","DOI":"10.1016\/j.epsr.2018.03.010"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"(2020). Robust pseudo-measurement modeling for three-phase distribution systems state estimation. Electr. Power Syst. Res., 180, 106138.","DOI":"10.1016\/j.epsr.2019.106138"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"3875","DOI":"10.1109\/TPWRS.2016.2632156","article-title":"A Review on Distribution System State Estimation","volume":"32","author":"Primadianto","year":"2017","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"9422","DOI":"10.1109\/JSEN.2019.2926089","article-title":"Probabilistic State Estimation Approach for AC\/MTDC Distribution System Using Deep Belief Network With Non-Gaussian Uncertainties","volume":"19","author":"Huang","year":"2019","journal-title":"IEEE Sens. J."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"762","DOI":"10.1109\/TPWRS.2019.2926445","article-title":"Interval State Estimation With Uncertainty of Distributed Generation and Line Parameters in Unbalanced Distribution Systems","volume":"35","author":"Zhang","year":"2020","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"106424","DOI":"10.1016\/j.epsr.2020.106424","article-title":"Analysis of bad data in power system state estimation under non-gaussian measurement noise","volume":"186","year":"2020","journal-title":"Electr. Power Syst. Res."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1066","DOI":"10.1109\/JSYST.2020.2987612","article-title":"A Distributed Robust Power System State Estimation Approach Using t-Distribution Noise Model","volume":"15","author":"Chen","year":"2020","journal-title":"IEEE Syst. J."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3301","DOI":"10.1109\/TSG.2018.2823398","article-title":"The Impact of Model and Measurement Uncertainties on a State Estimation in Three-Phase Distribution Networks","volume":"10","author":"Kuhar","year":"2019","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3090","DOI":"10.1109\/TIM.2018.2877549","article-title":"Interval State Estimation for Low-Voltage Distribution Systems Based on Smart Meter Data","volume":"68","author":"Huang","year":"2019","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"106703","DOI":"10.1016\/j.epsr.2020.106703","article-title":"Deriving power uncertainty intervals for low voltage grid state estimation using affine arithmetic","volume":"189","author":"Schmidt","year":"2020","journal-title":"Electr. Power Syst. Res."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1109\/TPWRS.2008.2009383","article-title":"Radial Power Flow Tolerance Analysis by Interval Constraint Propagation","volume":"24","author":"Vaccaro","year":"2009","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"988","DOI":"10.1109\/TIM.2015.2494619","article-title":"Uncertainty of Voltage Profile in PMU-Based Distribution System State Estimation","volume":"65","author":"Muscas","year":"2016","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"105974","DOI":"10.1016\/j.epsr.2019.105974","article-title":"Enhanced state estimation and bad data identification in active power distribution networks using photovoltaic power forecasting","volume":"177","author":"Cheng","year":"2019","journal-title":"Electr. Power Syst. Res."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"954","DOI":"10.1109\/TIM.2013.2243502","article-title":"Robustness-Oriented Meter Placement for Distribution System State Estimation in Presence of Network Parameter Uncertainty","volume":"62","author":"Pegoraro","year":"2013","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1077","DOI":"10.1109\/TPWRD.2014.2369500","article-title":"Parameter Estimation of Multiterminal Transmission Lines Using Joint PMU and SCADA Data","volume":"30","author":"Aminifar","year":"2015","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1002","DOI":"10.1109\/TIM.2018.2861058","article-title":"Line Impedance Estimation Based on Synchrophasor Measurements for Power Distribution Systems","volume":"68","author":"Pegoraro","year":"2019","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"8509","DOI":"10.1109\/TIE.2018.2890492","article-title":"An Interval Arithmetic-Based State Estimation Framework for Power Distribution Networks","volume":"66","author":"Xu","year":"2019","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2957","DOI":"10.1109\/TIM.2017.2728398","article-title":"Bayesian Approach for Distribution System State Estimation With Non-Gaussian Uncertainty Models","volume":"66","author":"Pegoraro","year":"2017","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"246","DOI":"10.1109\/TPWRS.2012.2201178","article-title":"Stochastic Monitoring of Distribution Networks Including Correlated Input Variables","volume":"28","author":"Valverde","year":"2013","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Moore, R.E., Kearfott, R.B., and Cloud, M.J. (2009). Introduction to Interval Analysis, Society for Industrial and Applied Mathematics.","DOI":"10.1137\/1.9780898717716"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"40826","DOI":"10.1109\/ACCESS.2018.2856823","article-title":"Interval State Estimation of Distribution Network With Power Flow Constraint","volume":"6","author":"Wu","year":"2018","journal-title":"IEEE Access"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1329","DOI":"10.1049\/iet-gtd.2019.1679","article-title":"Revised constraint-propagation method for distribution interval state estimation","volume":"14","author":"Ngo","year":"2020","journal-title":"IET Gener. Transm. Distrib."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"(2020). Sparse and numerically stable implementation of a distribution system state estimation based on Multifrontal QR factorization. Electr. Power Syst. Res., 189, 106734.","DOI":"10.1016\/j.epsr.2020.106734"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"A152","DOI":"10.12693\/APhysPolA.121.A-152","article-title":"Uncertainty Evaluation in Modelling of Acoustic Phenomena with Uncertain Parameters Using Interval Arithmetic","volume":"121","author":"Batko","year":"2012","journal-title":"Acta Phys. Pol."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1968435","DOI":"10.1155\/2018\/1968435","article-title":"The Multiobjective Based Large-Scale Electric Vehicle Charging Behaviours Analysis","volume":"2018","author":"Zhou","year":"2018","journal-title":"Complexity"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1096","DOI":"10.1109\/TIM.2013.2295657","article-title":"Optimal Meter Placement for Robust Measurement Systems in Active Distribution Grids","volume":"63","author":"Liu","year":"2014","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1109\/59.574922","article-title":"Distribution circuit state estimation using a probabilistic approach","volume":"12","author":"Ghosh","year":"1997","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1866","DOI":"10.1109\/TII.2017.2764800","article-title":"A Framework for Robust Hybrid State Estimation With Unknown Measurement Noise Statistics","volume":"14","author":"Zhao","year":"2018","journal-title":"IEEE Trans Ind. Inform."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"3233","DOI":"10.1109\/TPWRD.2017.2762927","article-title":"Assessing Gaussian Assumption of PMU Measurement Error Using Field Data","volume":"33","author":"Wang","year":"2018","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Kotz, S., and Nadarajah, S. (2004). Multivariate T-Distributions and Their Applications, Cambridge University Press.","DOI":"10.1017\/CBO9780511550683"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1104","DOI":"10.1109\/TPWRS.2017.2715561","article-title":"Sparse State Recovery Versus Generalized Maximum-Likelihood Estimator of a Power System","volume":"33","author":"Zhao","year":"2018","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1109\/TIM.2018.2838706","article-title":"A Joint Filter Approach for Reliable Power System State Estimation","volume":"68","author":"Yu","year":"2019","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1109\/MSP.2012.2187037","article-title":"State Estimation in Electric Power Grids: Meeting New Challenges Presented by the Requirements of the Future Grid","volume":"29","author":"Huang","year":"2012","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1511","DOI":"10.1109\/TPWRS.2014.2344012","article-title":"A Hybrid State Estimator For Systems With Limited Number of PMUs","volume":"30","author":"Abur","year":"2015","journal-title":"IEEE Trans. Power Syst."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/14\/4644\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:26:52Z","timestamp":1760164012000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/14\/4644"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,7,6]]},"references-count":37,"journal-issue":{"issue":"14","published-online":{"date-parts":[[2021,7]]}},"alternative-id":["s21144644"],"URL":"https:\/\/doi.org\/10.3390\/s21144644","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2021,7,6]]}}}