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DETERMINATION OF ADMITTANCE AND IMPEDANCE BUS MATRICES USING LINEAR ALGEBRA AND MATLAB TM IN ELECTRIC POWER SYSTEMS

Bruno Osorno

California Sate University Northridge 18111 Nordhoff St Northridge CA 91330 Email: bruno@ecs.csun.edu Phone: (818)677-3956

Abstract In electrical engineering, specifically in Electric Power Systems linear algebra is used widely throughout the curriculum. More specifically in electric power systems, short circuit analysis requires the determination of impedance bus matrices Zbus. Admittance bus matrices, Y bus, are used in load flow analysis amongst other applications. The classic manipulation of these matrices has been done using high-level programs such as FORTAN and C. With the introduction of mathematical packages such as MATLAB and MATHCAD we have reduced the time being consumed in the solution of such matrices and focus more in the techniques and analysis of the results. This paper will attempt to demonstrate the usage of MATLAB in the solution of linear algebra problems in the analysis of electric power systems specifically in the use of the “building algorithm” and Kron’s reduction.

Kron’s1 reduction (Node Elimination) The size of a real Ybus, admittance matrix, is very large. Computational time can be a problem, therefore, we needed to come up with algorithms to reduce the size of such matrix. The selection of the buses to be eliminated (in order to reduce the size of the matrix) is usually determined by the fact that there is no current being injected and /or the bus is of no importance to the analysis. As a rule if there is no external load and/or there are not generating sources connected then we can eliminate such bus.

When we want to eliminate a bus, we use the method of Kron’s reduction. We simply identify the buses that are not active, or do not have an effect on the system. In our example it would be buses 5 and 6. The size of our matrix is a 6 by 6 (nxn). Kron’s reduction method is given as:

Y jp Y pk Y jk ( new) = Y jk − Y pp

1 Named after Dr. Gabriel Kron. 1901-1968. General Electric “Proceedings of the 2003 American Society for Engineering Education Annual Conference & Exposition Copyright© 2003, American Society for Engineering Education”

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Osorno, B. (2003, June), Determination Of Admittance And Impedance Bus Matrices Using Linear Algebra And Matlab In Electric Power Systems Paper presented at 2003 Annual Conference, Nashville, Tennessee. 10.18260/1-2--12277