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# On the unity row summation and real valued nature of the F_{LG} matrix

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posted on 2022-10-07, 08:29 authored by Ioannis K. Dassios, Paul Cuffe, Andrew KeaneElectrical 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.

## Funding

### Study on Aerodynamic Characteristics Control of Slender Body Using Active Flow Control Technique

Japan Society for the Promotion of Science

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SFI, ERC## Language

English## Also affiliated with

- MACSI - Mathematics Application Consortium for Science & Industry

## Department or School

- Mathematics & Statistics

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