Modal representation of three-phase lines applying two transformation matrices: evaluation of its eigenvectors

2006 IEEE Power Engineering Society General Meeting Pub Date : 2006-10-16 DOI:10.1109/PES.2006.1709284

Sérgio Kurokawa, R. Daltin, A. J. Prado, J. Pissolato, L. F. Bovolato

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引用次数: 1

Abstract

The objective of this paper is to show an alternative representation in time domain of a non-transposed three-phase transmission line decomposed in its exact modes by using two transformation matrices. The first matrix is Clarke's matrix that is real, frequency independent, easily represented in computational transient programs (EMTP) and separates the line into quasi-modes alpha, beta and zero. After that, quasi-modes alpha and zero are decomposed into their exact modes by using a modal transformation matrix whose elements can be synthesized in time domain through standard curve-fitting techniques. The main advantage of this alternative representation is to reduce the processing time because a frequency dependent modal transformation matrix of a three-phase line has nine elements to be represented in time domain while a modal transformation matrix of a two-phase line has only four elements. This paper shows modal decomposition process and eigenvectors of a non-transposed three-phase line with a vertical symmetry plane whose nominal voltage is 440 kV and line length is 500 km

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应用两个变换矩阵的三相线的模态表示及其特征向量的求值

本文的目的是利用两个变换矩阵，给出非转置三相传输线精确模式分解的时域替代表示。第一个矩阵是Clarke's矩阵，它是实数的，频率无关的，易于在计算瞬态程序(EMTP)中表示，并将线划分为准模α， β和零。然后，利用模态变换矩阵将准模态α和准模态0分解为它们的精确模态，模态变换矩阵的元素可以通过标准曲线拟合技术在时域合成。这种替代表示的主要优点是减少了处理时间，因为三相线的频率相关模态变换矩阵在时域中有9个元素要表示，而两相线的模态变换矩阵只有4个元素。本文给出了标称电压为440 kV、线路长度为500 km的垂直对称面非转置三相线路的模态分解过程和特征向量

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2006 IEEE Power Engineering Society General Meeting

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