Natural Minimal Set of State Equations of Linear Power Grids

Abstract

For linear RLC power grids, a minimal set of state equations is derived that is suited to impressed voltage sources and contains only physically existing quantities (currents and node voltages) as state variables. In principle, other kinds of sources are also possible, e.g. impressed currents or mixtures of impressed voltages and currents. The described algorithm needs the eigenvalues of the system – in particular their number. Such methods of calculating the eigenvalues have already been developed; the stability of the results has been proved for grids with more than 500 nodes. Three-phase modeled grids are briefly treated too.