On using trasformation matrices and constraint equations for analy-sis of non-symmetric faults

Authors

  • P. L. Voronov I.N. Ulyanov Chuvash State University, Cheboksary

DOI:

https://doi.org/10.14529/power180104

Keywords:

non-symmetric faults, transformation matrices, symmetric components, sequence equivalent circuits, coupling equations

Abstract

Kron’s tensor-topological method being advanced by many Russian and foreign researchers opens wide opportunities for solving applied problems in complex electric power systems by means of tensor analysis and diakoptics. Its application to the analysis and calculation of asymmetric and complex types of faults occurring in power supply systems has its own peculiarities which are due to the need for transformations of variables (coordinate systems). In addition to the problems of defining transformation matrices and constraint equations, there are problems of combining individual parts of the system represented in different coordinates. Difficulties arise from the need to transform these matrices when constructing equivalent circuits.

The paper discusses simplest examples to show some features of how coordinate transformation matrices, coupling matrices and constraint equations can be jointly applied, as well as how they can be differentiated when modeling and analyzing non-symmetric faults in power supply systems.

Author Biography

P. L. Voronov, I.N. Ulyanov Chuvash State University, Cheboksary

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References

Kron G. Tenzornyy analiz setey [Tensor Analysis of Networks]. Moscow, Sov. Radio Publ., 1978. 720 p.

Happ H.H. Foundations of Tensor Network Theory. Journal of the Franklin Institute, 1968, vol. 286, no. 6, pp. 561–564. DOI: 10.1016/0016-0032(68)90392-X

Petrov A.E. Tenzornyy metod dvoystvennykh setey [Tensor Method of Dual Networks]. Moscow, TsITiP Publ., 2007. 602 p.

Sohor Ju.N. Tenzornyy analiz setey i diakoptika v inzhenernykh raschetakh [Tensor Analysis of Net-works and Diakoptics in Engineering Calculations]. Moscow, Lambert Academic Publishing, 2012. 200 p.

Amari S. Topological Foundations of Kron’s Tearing of Electrical Networks. RAAG Memoirs, 1962, vol. 3, pp. 322–350.

Park R.H. Two-Reaction Theory of Synchronous Machines. Part II. Trans. AIEE, 1933, vol. 52, pp. 352–354. DOI: 10.1109/T-AIEE.1933.5056309

Clarke E., Wiley J. Circuit Analysis of A-C Power Systems. New York, 1943, vol. 1. 540 p.

Ky Y.H. Transient Analysis of Rotating Machines and Stationary Networks by Means of Rotating Ref-e¬rence Frames. Part I. Trans. AIEE, 1951, vol. 70, pp. 943–957. DOI: 10.1109/T-AIEE.1951.5060505

Voronov P.L., Shchedrin V.A. [Application of the Coordinate Transformation Method to the Analysis of Electrical Networks with Distributed Sources of Energy]. Regional'naya energetika i elektrotekhnika: prob-lemy i resheniya: sb. nauch. tr. [Regional Power Engineering and Electrical Engineering: Problems and Solu-tions: a Collection of Sci. Papers], 2015, iss. XI, pp. 42–65. (in Russ.)

Ul'yanov S.A. Elektromagnitnye perekhodnye protsessy v elektricheskikh sistemakh [Electromagnetic Transients in Electrical Systems]. Moscow, Energiya Publ., 1964. 704 p.

Han Z.X. Generalized Method of Analysis of Simultaneous Faults in Electric Power Systems. IEEE Transactions on Power Apparatus and Systems, vol. 101, no. 10, pp. 3933–3942. DOI: 10.1109/TPAS.1982.317045

Losev S.B., Chernin A.B. Vychislenie elektricheskikh velichin v nesimmetrichnykh rezhimakh elektri-cheskikh sistem [Calculation of Electrical Values in Nonsymmetric States of Electrical Systems]. Moscow, Energoatomizdat Publ., 1983. 528 p.

Averbuh A.M. Primery raschetov nepolnofaznykh rezhimov i korotkikh zamykaniy [Examples of Cal-culating Incomplete Phase States and Short Circuits]. Leningrad, Energiya Publ., 1979. 184 p.

Lyamets, Yu.Ya., Eremeev D.G., Nudel'man G.S. [Equivalence of Multi-Wire Systems in the Case of Short-Circuits and Partial Wire Breakage]. Elektrichestvo [Electricity], 2003, no. 11, pp. 17–27. (in Russ.)

Anderson P.M. Analysis of Faulted Power Systems. Ames, Iowa: The Iowa State University Press, 1973. 513 p.

Anderson P.M. Analysis of Simultaneous Faults by Two-Port Network Theory. IEEE Transactions on Power Apparatus and Systems, 1971, vol. 90, no. 5, pp. 2199–2205. DOI: 10.1109/TPAS.1971.293041

Lewis W.E., Banks J.H. Matrix Methods for the Evaluation of Simultaneous Faults in Three-Phase Systems. Institution Monograph, 1955. pp. 231–243.

Voronov P.L. [Piecewise Calculation of Three-Phase Networks with Asymmetric and Complex Types of Damage]. Bulletin of the Chuvash University, 2017, iss. 1, pp. 76–87. (in Russ.)

Kron G. Diacoptics: The Piecewise Solution of Large-Scale Systems. London, MacDonald, 1965. 166 p.

White D., Woodson G. Elektromekhanicheskoe preobrazovanie energii [Electromechanical Energy Conversion]. Moscow, Energiya Publ., 1964. 537 p.

Ionkina P.A. Teoreticheskie osnovy elektrotekhniki [Theoretical Foundations of Electrical Engineer-ing]. Moscow, Vysshaya Shkola Publ., 1976, vol. 1. 544 p.

Published

2018-07-30

Issue

Section

Electric power engineering