On the Unity Row Summation and Real Valued Nature of the $F_{LG}$ Matrix

Ioannis Dassios; Paul Cuffe; Andrew Keane

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arXiv · 1503.08652

On the Unity Row Summation and Real Valued Nature of the $F_{LG}$ Matrix

Ioannis Dassios·Paul Cuffe·Andrew Keane

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Abstract

Electrical power system calculations rely heavily on the $Y_{bus}$ matrix, which is the Laplacian matrix of the network under study, weighted by the complex-valued admittance of each branch. It is often useful to partition the $Y_{bus}$ into four submatrices, to separately quantify the connectivity between and among the load and generation nodes in the network. Simple manipulation of these submatrices gives the $F_{LG}$ matrix, which offers useful insights on how voltage deviations propagate through a power system and on how energy losses may be minimized. Various authors have observed that in practice the elements of $F_{LG}$ are real-valued and its rows sum close to one: the present paper explains and proves these properties.

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Ioannis Dassios, Paul Cuffe, Andrew Keane. 2015-03-30. On the Unity Row Summation and Real Valued Nature of the $F_{LG}$ Matrix. https://arxiv.org/abs/1503.08652

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