Linear Programming Contractor for Interval Distribution State Estimation Using RDM Arithmetic

State estimation (SE) of distribution networks heavily relies on pseudo measurements that introduce significant errors, since real-time measurements are insufficient. Interval SE models are regularly used, where true values of system states are supposed to be within the estimated intervals. However,...

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Vydáno v:IEEE transactions on power systems Ročník 36; číslo 3; s. 2114 - 2126
Hlavní autoři: Ngo, VietCuong, Wu, Wenchuan
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York IEEE 01.05.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Algorithms
Arithmetic
Constraints
Correlation
Differential calculus
Distance measurement
Distribution network
Distribution networks
Electronic equipment tests
interval state estimation
Linear equations
Linear programming
Lower bounds
Mathematical model
mean value theorem
Measurement uncertainty
Optimization
Phase distribution
relative-distance-measurement
State estimation
State variable
Voltage measurement
ISSN:0885-8950, 1558-0679
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Abstract State estimation (SE) of distribution networks heavily relies on pseudo measurements that introduce significant errors, since real-time measurements are insufficient. Interval SE models are regularly used, where true values of system states are supposed to be within the estimated intervals. However, conventional interval SE algorithms cannot consider the correlations of same interval variables in different terms of constraints, which results in overly conservative estimation results. In this paper, we propose a new interval SE model that is based on the relative distance measure (RDM) arithmetic. In the proposed model, measurement errors are assumed to be bounded in given sets and the state variables are described as RDM variables. Since the SE model is a non-convex, the solution's credibility cannot be guaranteed. Therefore, each nonlinear measurement equation in the model is transformed into dual inequality linear equations using the mean value theorem. The SE model is finally reformulated as a linear programming contractor that iteratively narrows the upper and lower bounds of the estimated state variables. Numerical tests on IEEE three-phase distribution networks show that the proposed method outperforms the conventional interval-constrained propagation, modified Krawczyk-operator and optimization based interval SE methods.
AbstractList State estimation (SE) of distribution networks heavily relies on pseudo measurements that introduce significant errors, since real-time measurements are insufficient. Interval SE models are regularly used, where true values of system states are supposed to be within the estimated intervals. However, conventional interval SE algorithms cannot consider the correlations of same interval variables in different terms of constraints, which results in overly conservative estimation results. In this paper, we propose a new interval SE model that is based on the relative distance measure (RDM) arithmetic. In the proposed model, measurement errors are assumed to be bounded in given sets and the state variables are described as RDM variables. Since the SE model is a non-convex, the solution's credibility cannot be guaranteed. Therefore, each nonlinear measurement equation in the model is transformed into dual inequality linear equations using the mean value theorem. The SE model is finally reformulated as a linear programming contractor that iteratively narrows the upper and lower bounds of the estimated state variables. Numerical tests on IEEE three-phase distribution networks show that the proposed method outperforms the conventional interval-constrained propagation, modified Krawczyk-operator and optimization based interval SE methods.
Author Wu, Wenchuan
Ngo, VietCuong
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Cites_doi 10.1109/TPWRS.2012.2187804
10.1515/amcs-2017-0041
10.1109/TPWRS.2019.2926445
10.1109/TIE.2018.2890492
10.1109/TIM.2017.2728398
10.1109/TPAS.1970.292680
10.1016/S0005-1098(00)00068-6
10.1109/TIM.2018.2877549
10.1016/S0142-0615(01)00092-8
10.1016/j.measurement.2008.10.007
10.1109/TPWRS.2013.2264917
10.1007/978-94-017-1247-7_7
10.1109/ACCESS.2018.2856823
10.1007/978-1-4757-6484-0_16
10.1049/iet-gtd.2019.1679
10.1109/TII.2018.2804669
10.1007/BF01099647
10.1007/s40565-019-0522-9
10.1109/TPWRS.2011.2162859
10.1016/j.epsr.2005.12.016
10.1002/tee.22816
10.1109/TPWRS.2005.846163
10.1109/TIM.2014.2308352
10.1049/ip-gtd:20041167
10.1049/iet-gtd.2009.0167
10.1007/978-1-4471-0249-6
10.1049/iet-gtd.2012.0333
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References ref13
ref15
ref14
ref30
ref33
ref11
ref10
neumaier (ref12) 1990; 37
ref2
ref1
araya (ref32) 2011
ref17
ref16
ref19
ref18
piegat (ref25) 2013
ngo (ref31) 0
ref24
ref23
ref20
ref22
ref21
paolo (ref6) 2017; 66
piegat (ref26) 2013; 15
ref28
ref27
ref29
ref7
ref9
ref4
ref3
qi (ref8) 2012
ref5
References_xml – volume: 15
  start-page: 486
  year: 2013
  ident: ref26
  article-title: Two interpretations of multidimensional RDM interval arithmetic: Multiplication and division
  publication-title: Int J Fuzzy Syst
– ident: ref3
  doi: 10.1109/TPWRS.2012.2187804
– ident: ref27
  doi: 10.1515/amcs-2017-0041
– ident: ref16
  doi: 10.1109/TPWRS.2019.2926445
– ident: ref19
  doi: 10.1109/TIE.2018.2890492
– volume: 66
  start-page: 2957
  year: 2017
  ident: ref6
  article-title: Bayesian approach for distribution system state estimation with non-Gaussian uncertainty models
  publication-title: IEEE Trans Instrum Meas
  doi: 10.1109/TIM.2017.2728398
– ident: ref1
  doi: 10.1109/TPAS.1970.292680
– ident: ref21
  doi: 10.1016/S0005-1098(00)00068-6
– ident: ref20
  doi: 10.1109/TIM.2018.2877549
– year: 0
  ident: ref31
  article-title: Test data of modified IEEE 33-bus and 123-bus system
– volume: 37
  year: 1990
  ident: ref12
  publication-title: Interval Methods for Systems of Equations
– ident: ref29
  doi: 10.1016/S0142-0615(01)00092-8
– ident: ref7
  doi: 10.1016/j.measurement.2008.10.007
– ident: ref18
  doi: 10.1109/TPWRS.2013.2264917
– ident: ref30
  doi: 10.1007/978-94-017-1247-7_7
– ident: ref15
  doi: 10.1109/ACCESS.2018.2856823
– ident: ref22
  doi: 10.1007/978-1-4757-6484-0_16
– ident: ref24
  doi: 10.1049/iet-gtd.2019.1679
– ident: ref17
  doi: 10.1109/TII.2018.2804669
– ident: ref28
  doi: 10.1007/BF01099647
– ident: ref4
  doi: 10.1007/s40565-019-0522-9
– ident: ref11
  doi: 10.1109/TPWRS.2011.2162859
– start-page: 137
  year: 2013
  ident: ref25
  article-title: Multidimensional approach to interval-uncertainty calculations
  publication-title: New Developments in Fuzzy Sets Intuitionistic Fuzzy Sets Generalized Nets and Related Topics
– ident: ref14
  doi: 10.1016/j.epsr.2005.12.016
– start-page: 9
  year: 2011
  ident: ref32
  article-title: Exploiting monotonicity in interval constraint propagation
  publication-title: Proc 24th AAAI Conf Artif Intell
– ident: ref33
  doi: 10.1002/tee.22816
– ident: ref9
  doi: 10.1109/TPWRS.2005.846163
– ident: ref5
  doi: 10.1109/TIM.2014.2308352
– ident: ref10
  doi: 10.1049/ip-gtd:20041167
– start-page: 1
  year: 2012
  ident: ref8
  article-title: Power system set membership state estimation
  publication-title: Proc IEEE Power Energy Soc Gen Meeting
– ident: ref2
  doi: 10.1049/iet-gtd.2009.0167
– ident: ref13
  doi: 10.1007/978-1-4471-0249-6
– ident: ref23
  doi: 10.1049/iet-gtd.2012.0333
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SubjectTerms Algorithms
Arithmetic
Constraints
Correlation
Differential calculus
Distance measurement
Distribution network
Distribution networks
Electronic equipment tests
interval state estimation
Linear equations
Linear programming
Lower bounds
Mathematical model
mean value theorem
Measurement uncertainty
Optimization
Phase distribution
relative-distance-measurement
State estimation
State variable
Voltage measurement
Title Linear Programming Contractor for Interval Distribution State Estimation Using RDM Arithmetic
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Volume 36
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