Now showing 1 - 3 of 3
  • Publication
    Analytic Loss Minimization: A Proof
    Loss minimizing generator dispatch profiles for power systems are usually derived using optimization techniques. However, some authors have noted that a system’s KGL matrix can be used to analytically determine a loss minimizing dispatch. This letter draws on recent research on the characterization of transmission system losses to demonstrate how the KGL matrix achieves this. A new proof of the observed zero row summation property of the YGGM matrix is provided to this end.
    Scopus© Citations 11  592
  • Publication
    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.
    Scopus© Citations 18  469
  • Publication
    Calculating Nodal Voltages Using the Admittance Matrix Spectrum of an Electrical Network
    Calculating nodal voltages and branch current flows in a meshed network is fundamental to electrical engineering. This work demonstrates how such calculations can be performed using the eigenvalues and eigenvectors of the Laplacian matrix which describes the connectivity of the electrical network. These insights should permit the functioning of electrical networks to be understood in the context of spectral analysis.
      348Scopus© Citations 10