An efficient algebraic approach to observability analysis in state estimation

Pruneda, Rosa Eva; Solares, Cristina; Conejo, Antonio J.; Castillo, Enrique

doi:10.1016/j.epsr.2009.09.010

Cited by 22 publications

(35 citation statements)

References 28 publications

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“…Observability analysis methods can be classified into 3 categories: topological, 8-10 numerical, [11][12][13][14][15][16][17][18] and hybrid ones. 19,20 The graph theory-based topological methods do not need floating point arithmetic but are known to be combinatorial and rather complicated for implementation.…”

Section: Literature Reviewmentioning

confidence: 99%

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PQ decoupled 3-phase numerical observability analysis and critical data identification for distribution systems

Wang

Liang

et al. 2016

Int. Trans. Electr. Energ. Syst.

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Summary Emerging active distribution systems are operated under more complicated and uncertain conditions. Because of frequent topology changes or temporary malfunctions of data acquisition, the network may lose observability and in turn may lead to the failure of distribution system state estimation. Without distribution system state estimation, the distribution system operator may not be able to make secure decisions, and the system may face with risk of serious damages. In this paper, a new real/reactive (PQ) decoupled 3‐phase numerical observability analysis method and a new critical data identification method for distribution systems are proposed. The methods can efficiently identify all unobservable branches and critical data in a non‐iterative manner. In addition to the 3‐phase decoupling, the normal equation is also PQ decoupled, and the computation burden is greatly reduced. Furthermore, all entries in the Jacobian matrix are non‐negative integers and the proposed methods present good numerical performance. Strict theoretical proofs on the performance of the proposed methods are provided and numerical results on different scales of test systems illustrate their validities.

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Section: Literature Reviewmentioning

confidence: 99%

“…Besides, H PI entries remain the same as that in (5), which means that H PI and G PI are constant matrices. In the second iteration, according to the measurement equations and Equations (12,13), the nonlinear measurement functions can be calculated as follows:…”

Section: Proof Of Decoupling and Non-iterationmentioning

confidence: 99%

PQ decoupled 3-phase numerical observability analysis and critical data identification for distribution systems

Wang

Liang

et al. 2016

Int. Trans. Electr. Energ. Syst.

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“…The corresponding reduced Jacobian matrix (19 4) × c W is given below. After forming the 22 Based on power and current flows, ten ( 10) r = flow islands are formed, as shown in Fig. 4.…”

Section: I I I I Imentioning

confidence: 99%

“…The non-iterative numerical algorithm [19], [20] relies on the factors of Gram matrix related with the measurement Jacobian. An algebraic technique, based on the calculus of the null space, is proposed in [21] and [22]. An observability checking algorithm, based on Gaussian elimination and binary arithmetic, is presented in [23].…”

Section: Introductionmentioning

confidence: 99%

Observability analysis and restoration for state estimation using SCADA and PMU data

Korres

Manousakis

2012

2012 IEEE Power and Energy Society General Meeting

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This paper presents a hybrid topological/numerical method for power system observability analysis, using conventional measurements, provided by SCADA, as well as synchronized phasor measurements, provided by phasor measurement units (PMUs). A PMU placed at a bus can measure the voltage phasor at that bus, as well as the current phasors in some or all the lines connected to that bus. Branch power flow and current phasor measurements are used to build topologically flow islands that, in turn, are used to construct a reduced network. A gain matrix associated with this reduced network is built, considering boundary injections at flow islands and all bus voltage phasors. Observability checking is carried out analyzing the pivots in the triangular factors of this gain matrix and observable islands are identified in a noniterative manner, by performing back substitutions. Additional measurements for observability restoration are provided by a direct method, using the triangular factors of a reduced Gram matrix associated with existing and candidate injections as well as PMUs at boundary buses of the observable islands. The IEEE 14 and 30 bus systems illustrate the steps of the proposed method.Index Terms--Conventional measurements, flow islands, Gram matrix, observability analysis, observability restoration, phasor measurement units.

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“…Observability algorithms for power system state estimation can be classified as topological, [1][2][3][4][5][6], numerical, [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21], and hybrids, [22][23][24]. The topological algorithm [1] is based on building a spanning tree of full rank.…”

Section: Introductionmentioning

confidence: 99%

Observability analysis and restoration for systems with conventional and phasor measurements

Korres

Manousakis

2012

Int. Trans. Electr. Energ. Syst.

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SUMMARY This paper presents an efficient and fast method, using topological and numerical procedures, for observability analysis in state estimation with phasor measurement units as well as conventional (SCADA) measurements. Power and current flow measurements are used to build topologically flow islands that, in turn, are used to construct a reduced network and an associated gain matrix. To build this reduced order gain matrix, boundary power injections, and voltage phasors at flow islands are considered. Observability checking is carried out analyzing the pivots encountered during the triangular factorization of the gain matrix, and the observable islands are identified in a noniterative manner, by performing back substitutions with its triangular factors. Additional measurements that will render the system barely observable are directly provided, using the triangular factors of a reduced Gram matrix associated with existing and candidate power injections and candidate phasor measurements at boundary buses of observable islands. The dimension of the gain and Gram matrix is equal to the number of flow islands and boundary measurements, respectively, which is relatively low even for very large systems, and that makes the proposed algorithms fast and computationally efficient. The IEEE 14 and 30‐bus systems are used to illustrate the steps of the proposed algorithms. Copyright © 2012 John Wiley & Sons, Ltd.

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An efficient algebraic approach to observability analysis in state estimation

Cited by 22 publications

References 28 publications

PQ decoupled 3-phase numerical observability analysis and critical data identification for distribution systems

PQ decoupled 3-phase numerical observability analysis and critical data identification for distribution systems

Observability analysis and restoration for state estimation using SCADA and PMU data

Observability analysis and restoration for systems with conventional and phasor measurements

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