Author

# Gabriel Kron

Bio: Gabriel Kron is an academic researcher from General Electric. The author has contributed to research in topics: Equivalent circuit & Induction motor. The author has an hindex of 19, co-authored 58 publications receiving 1754 citations.

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TL;DR: In this article, a set of principles and a systematic procedure are presented to establish the exact solutions of very large and complicated physical systems, without solving a large number of simultaneous equations and without finding the inverse of large matrices.

Abstract: A set of principles and a systematic procedure are presented to establish the exact solutions of very large and complicated physical systems, without solving a large number of simultaneous equations and without finding the inverse of large matrices. The procedure consists of tearing the system apart into several smaller component systems. After establishing and solving the equations of the component systems, the component solutions themselves are interconnected to obtain outright, by a set of transformations, the exact solution of the original system. The only work remaining is the elimination or solution of the comparatively few superfluous constraints appearing at the points of interconnection.The component and resultant solutions may be either exact or approximate and may represent either linear or, with certain precautions, nonlinear physical systems. The component solutions may be expressed in numerical form or in terms of matrices having as their elements real or complex numbers, functions of time, ...

132 citations

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TL;DR: A review paper describing different types of faults and the signatures they generate and their diagnostics' schemes will not be entirely out of place to avoid repetition of past work and gives a bird's eye view to a new researcher in this area.

Abstract: Recently, research has picked up a fervent pace in the area of fault diagnosis of electrical machines. The manufacturers and users of these drives are now keen to include diagnostic features in the software to improve salability and reliability. Apart from locating specific harmonic components in the line current (popularly known as motor current signature analysis), other signals, such as speed, torque, noise, vibration etc., are also explored for their frequency contents. Sometimes, altogether different techniques, such as thermal measurements, chemical analysis, etc., are also employed to find out the nature and the degree of the fault. In addition, human involvement in the actual fault detection decision making is slowly being replaced by automated tools, such as expert systems, neural networks, fuzzy-logic-based systems; to name a few. It is indeed evident that this area is vast in scope. Hence, keeping in mind the need for future research, a review paper describing different types of faults and the signatures they generate and their diagnostics' schemes will not be entirely out of place. In particular, such a review helps to avoid repetition of past work and gives a bird's eye view to a new researcher in this area.

1,869 citations

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TL;DR: In this article, the authors derive global patterns of global relations from a detailed social network, within which classes of equivalently positioned individuals are delineated by a "functorial" mapping of the original pattern.

Abstract: The aim of this paper is to understand the interrelations among relations within concrete social groups. Social structure is sought, not ideal types, although the latter are relevant to interrelations among relations. From a detailed social network, patterns of global relations can be extracted, within which classes of equivalently positioned individuals are delineated. The global patterns are derived algebraically through a ‘functorial’ mapping of the original pattern. Such a mapping (essentially a generalized homomorphism) allows systematically for concatenation of effects through the network. The notion of functorial mapping is of central importance in the ‘theory of categories,’ a branch of modern algebra with numerous applications to algebra, topology, logic. The paper contains analyses of two social networks, exemplifying this approach.

1,488 citations

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31 Aug 2001TL;DR: In this paper, the authors present an approximate method of analysis Voltage Drop Line Impedance K Factors Uniformly Distributed Loads Lumping Loads in Geometric Configurations.

Abstract: Introduction to Distribution Systems The Distribution System Distribution Substations Radial Feeders Distribution Feeder Map Distribution Feeder Electrical Characteristics Summary The Nature of Loads Definitions Individual Customer Load Distribution Transformer Loading Feeder Load Summary Approximate Method of Analysis Voltage Drop Line Impedance K Factors Uniformly Distributed Loads Lumping Loads in Geometric Configurations Summary References Series Impedance of Overhead and Underground Lines Series Impedance of Overhead Lines Series Impedance of Underground Lines Series Impedances of Parallel Lines Summary References Shunt Admittance of Overhead and Underground Lines General Voltage Drop Equation Overhead Lines Concentric Neutral Cable Underground Lines Tape-Shielded Cable Underground Lines Sequence Admittance The Shunt Admittance of Parallel Underground Lines Summary References Distribution System Line Models Exact Line Segment Model The Modified Line Model The Approximate Line Segment Model The General Matrices for Parallel Lines Summary References Voltage Regulation Standard Voltage Ratings Two-Winding Transformer Theory Two-Winding Autotransformer Step-Voltage Regulators Summary References Three-Phase Transformer Models Introduction Generalized Matrices The Delta-Grounded Wye Step-Down Connection The Ungrounded Wye-Delta Step-Down Connection The Grounded Wye--Grounded Wye Connection The Delta-Delta Connection Open Wye--Open Delta Thevenin Equivalent Circuit Summary Load Models Wye Connected Loads Delta Connected Loads Two-Phase and Single-Phase Loads Shunt Capacitors The Three-Phase Induction Machine Summary References Distribution Feeder Analysis Power-Flow Analysis Short-Circuit Studies Summary References Center-Tapped Transformers and Secondaries Center-Tapped Single-Phase Transformer Model Ungrounded Wye-Delta Transformer Bank Leading Open Wye--Open Delta Transformer Connection Lagging Open Wye--Open Delta Connection Four-Wire Secondary Putting It All Together Summary Reference Appendix A Appendix B Index

1,449 citations

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TL;DR: A novel domain decomposition approach for the parallel finite element solution of equilibrium equations is presented, which exhibits a degree of parallelism that is not limited by the bandwidth of the finite element system of equations.

Abstract: A novel domain decomposition approach for the parallel finite element solution of equilibrium equations is presented. The spatial domain is partitioned into a set of totally disconnected subdomains, each assigned to an individual processor. Lagrange multipliers are introduced to enforce compatibility at the interface nodes. In the static case, each floating subdomain induces a local singularity that is resolved in two phases. First, the rigid body modes are eliminated in parallel from each local problem and a direct scheme is applied concurrently to all subdomains in order to recover each partial local solution. Next, the contributions of these modes are related to the Lagrange multipliers through an orthogonality condition. A parallel conjugate projected gradient algorithm is developed for the solution of the coupled system of local rigid modes components and Lagrange multipliers, which completes the solution of the problem. When implemented on local memory multiprocessors, this proposed method of tearing and interconnecting requires less interprocessor communications than the classical method of substructuring. It is also suitable for parallel/vector computers with shared memory. Moreover, unlike parallel direct solvers, it exhibits a degree of parallelism that is not limited by the bandwidth of the finite element system of equations.

1,302 citations

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TL;DR: The history of these fomulas is presented and various applications to statistics, networks, structural analysis, asymptotic analysis, optimization, and partial differential equations are discussed.

Abstract: The Sherman–Morrison–Woodbury formulas relate the inverse of a matrix after a small-rank perturbation to the inverse of the original matrix. The history of these fomulas is presented and various applications to statistics, networks, structural analysis, asymptotic analysis, optimization, and partial differential equations are discussed. The Sherman-Morrison-Woodbury formulas express the inverse of a matrix after a small rank perturbation in terms of the inverse of the original matrix. This paper surveys the history of these formulas and we examine some applications where these formulas are helpful

1,026 citations