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

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.