Orthogonal sparse vector methods

Vempati, N.; Slutsker, I.W.; Tinney, W.F.

doi:10.1109/59.141806

Cited by 10 publications

(5 citation statements)

References 13 publications

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“…1. References [5,6] have extensively investigated the effect of sparse vector method and the enhanced version of Givens rotation in addition to row ordering schemes that speed up solutions of power network equations.…”

Section: Discussion With Alimentioning

confidence: 99%

“…When V1 and V2 are orthogonal, the error of the solution will become the minimum. During the past years, significant progress has been achieved on orthogonal transformation, whose numerical stability has been generally accepted compared with WLS, hybrid method, normal equations with constraints, and etc [1][2][3][4][5][6][7] . How to improve computational efficiency is the target of this paper.…”

Section: Introductionmentioning

confidence: 99%

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An Efficient Engine for Orthogonal SE

Wang¹,

Karimi²,

Xu³

2013

Proceedings of the Third International Conference on Control, Automation and Systems Engineering

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Orthogonal transformation has been used for State Estimation, since it is hard to solve by normal WLS method when weights of some measurements differ much from others. Though the numerical stability of orthogonal transformation has been generally accepted, it is reported that the efficiency might be another problem for Orthogonal SE. An efficient engine for orthogonal SE has been proposed in this paper, which is based upon fast Givens rotation and sparse matrix techniques. Further considerations including column & rows ordering, block matrix, and fixed factor table are also explained in order to further improve the performance of this engine especially on large-scale systems. Performance testing has been made on a desktop computer using multiple power systems of different sizes, and the feasibility and efficiency of this engine has been verified.

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Section: Discussion With Alimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An Efficient Engine for Orthogonal SE

Wang¹,

Karimi²,

Xu³

2013

Proceedings of the Third International Conference on Control, Automation and Systems Engineering

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“…Figure 1 shows the flowchart of the GERI-based method. Step 1-The WLS SE combined with the orthogonal transformation method is adopted to improve the numerical stability and computation efficiency [32]. With fast Givens rotations technique [33], H x T WH x , the most important factor in WLS SE and our identification can be computed faster.…”

Section: Flowchart Of the Geri-based Methodsmentioning

confidence: 99%

“…According to WLS SE in Step 1, H x T WH x , which is the key part of A, can be simplified using the orthogonal transformation method [32] and the fast Givens rotations technique [33] as follows:…”

Section: Simplified Calculation Of Variablesmentioning

confidence: 99%

A Practical GERI-Based Method for Identifying Multiple Erroneous Parameters and Measurements Simultaneously

Guo

Dong

et al. 2021

Energies

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Even with modern smart metering systems, erroneous measurements of the real and reactive power in the power system are unavoidable. Multiple erroneous parameters and measurements may occur simultaneously in the state estimation of a bulk power system. This paper proposes a gross error reduction index (GERI)-based method as an additional module for existing state estimators in order to identify multiple erroneous parameters and measurements simultaneously. The measurements are acquired from a supervisory control and data acquisition system and mainly include voltage amplitudes, branch current amplitudes, active power flow, and reactive power flow. This method uses a structure consisting of nested two loops. First, gross errors and the GERI indexes are calculated in the inner loop. Second, the GERI indexes are compared and the maximum GERI in each inner loop is associated with the most suspicious parameter or measurement. Third, when the maximum GERI is less than a given threshold in the outer loop, its corresponding erroneous parameter or measurement is identified. Multiple measurement scans are also adopted in order to increase the redundancy of measurements and the observability of parameters. It should be noted that the proposed algorithm can be directly integrated into the Weighted Least Square estimator. Furthermore, using a faster simplified calculation technique with Givens rotations reduces the required computer memory and increases the computation speed. This method has been demonstrated in the IEEE 14-bus test system and several matpower cases. Due to its outstanding practical performance, it is now used at six provincial power control centers in the Eastern Grid of China.

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“…Hence we take advantage of the fact that when Matlab annihilates an element of a sparse matrix, the operating system does not deallocate the memory locations previously allocated for that element of the sparse matrix. Thus, rather than overlaying a data structure on the triangular factor (as did Vempati, Slutsker & Tinney [38]), we mark with an special value (e.g., NaN in Matlab) the elements not used in the structure previously set up, and we convert them into zeros just before selecting the submatrix to operate with. This allow us to take advantage of the sparse numerical linear algebra primitives of the sparse toolbox, but we have to recover the structure after the algebraic operation involved, reinserting NaNs in those elements where fill-in did not occur yet; this overhead would be avoided with low-level programming.…”

Section: Initial Factorization and Sparse Issuesmentioning

confidence: 99%

Updating and downdating an upper trapezoidal sparse orthogonal factorization†

Santos-Palomo¹,

Guerrero-Garcı́a²

2006

IMA Journal of Numerical Analysis

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We describe how to update and downdate an upper trapezoidal sparse orthogonal factorization, namely the sparse QR factorization of A T k , where A k is a "tall and thin" full column rank matrix formed with a subset of the columns of a fixed matrix A. In order to do that, we have adapted to rectangular matrices (with fewer columns than rows) Saunders' techniques of early 70s for square matrices, by using the static data structure of George and Heath of early 80s but allowing row downdating on it. An implicitly determined column permutation allow us to dispense with computing a new ordering after each update/downdate; it fits well into the Linpack downdating algorithm and ensures that the updated trapezoidal factor will remain sparse. We give all the necessary formulae even if the orthogonal factor is not available, and we comment on our implementation using the sparse toolbox of Matlab 5. Aims, difficulties and related workIn certain non-simplex active-set methods (also currently known as basisdeficiency-allowing simplex variations) for linear programming we need to solve a sequence of sparse compatible systems of the form:where b and c are iteration-dependent vectors, and x, y, and d are unknown vectors. Furthermore, the matrix A k ∈ R n×m k is a "tall and thin" iterationdependent full column rank matrix with m k ≤ n and rank(A k ) = m k . Such

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Orthogonal sparse vector methods

Cited by 10 publications

References 13 publications

An Efficient Engine for Orthogonal SE

An Efficient Engine for Orthogonal SE

A Practical GERI-Based Method for Identifying Multiple Erroneous Parameters and Measurements Simultaneously

Updating and downdating an upper trapezoidal sparse orthogonal factorization†

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