Visualizing voltage relationships using the unity row summation and real valued properties of the FLG matrix

By manipulating the bus admittance matrix of a power system, a useful submatrix, FLG, can be derived. This matrix identifies, for every load bus, the set of generators that establish its no-load voltage, and the varying degree of their influence. The first contribution of the present work is to rigorously prove two observed properties of the FLG matrix; that it is substantially real-valued, and that its rows sum close to one. Six test systems are used in this work to validate these properties. With this proof in hand, this work also introduces a new conception of voltage profile monitoring in power systems, by explicitly mapping the relationships between load and generator voltages. This new visualization makes it easier to identify how influential each generator is in establishing the network's voltage profile. Poorly supported load buses, which may be vulnerable to voltage deviations, are clearly identified. This new visualization framework is suitable for pedagogy, research, and control room applications.