Partial Matrix Refactorization

Chan, Steve; Brandwajn, V.

doi:10.1109/tpwrs.1986.4334868

Cited by 147 publications

(34 citation statements)

References 5 publications

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“…Because (84) considers only one line limit at a time, determining the most restrictive case from a set of candidate lines requires repeated solutions, with different line parameters (s i , i ) for each case. The modifications required in (84) for each new case are minimal though, allowing efficient partial refactorization techniques [61] to be used to reduce the computational burden. Collecting the minima for all the candidate lines into the set P = {ρ 1 ,ρ 2 , .…”

Section: Quadratic Optimizationmentioning

confidence: 99%

Strategies for Voltage Control and Transient Stability Assessment

Hiskens¹

2013

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Section: Quadratic Optimizationmentioning

confidence: 99%

Strategies for Voltage Control and Transient Stability Assessment

Hiskens¹

2013

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“…They did not consider a static structure in spite of dispensing with the orthonormal factor [37, p. 56] by combining corrected seminormal equations as a previous stage for the Linpack downdate. Also in the m k ≥ n full rank case, Chan & Brandwajn [7] have been working with the static sparsity structure in the field of power system analysis.…”

Section: ] Claimedmentioning

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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“…The convergence rate of the simple steps is only linear, (6) and the estimated mismatch m steps ahead is (7) where is calculated using the previous two mismatches (8) The process starts with a Newton step followed by a simple step. After every simple step we compare the predicted mismatches obtained from equations (3) and (7).…”

Section: Solution Strategies 1) Full Newtonmentioning

confidence: 99%

“…For example, at some point may be more convenient to factorize the whole Jacobian than to keep it constant, while at some other stages a partial update (and corresponding partial refactorization) may be more convenient. Partial refactorizations are typically used in contingency analysis and have been used in the Newton power flow to deal with transformer taps and other automatic adjustments [6], but they have not been applied with a local identification strategy for the convergence trajectories.…”

Section: Introductionmentioning

confidence: 99%

Quasi-Newton Power Flow Using Partial Jacobian Updates

Semlyen

León

2001

IEEE Power Eng. Rev.

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Abstract-We present a quasi-Newton power flow methodology that incorporates several strategies to obtain substantial computing savings. Newton steps are combined with constant Jacobian (or "simple") steps and partial Jacobian updates to get an efficient quasi-Newton method. The methodology proposed includes the possibility of selecting the next best step by measuring the residuals. Partial Jacobian Updates (PJU) are included in the quasi-Newton power flow using LU factorization updates and/or the Matrix Modification Lemma. The method has been tested with systems ranging in size from 14 to 6372 buses. For large power systems we have obtained savings (in flops) in the order of 50% compared to Newton's method.

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Partial Matrix Refactorization

Cited by 147 publications

References 5 publications

Strategies for Voltage Control and Transient Stability Assessment

Strategies for Voltage Control and Transient Stability Assessment

Updating and downdating an upper trapezoidal sparse orthogonal factorization†

Quasi-Newton Power Flow Using Partial Jacobian Updates

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