Steady-state stability analysis of regular circulant grids

Matter et al. derive a real-valued master stability function which determines whether and to what degree a given power grid is asymptotically stable. They base their work on an abstract grid having synchronous generators in presumed steady state equilibrium. They make some assumptions about the electrical and mechanical properties of these generators, then derive their stability function from the grid's admittance matrix. This stability function is thus a function not only of several electrical and mechanical parameters but also of the particular links joining the grid's generators and/or loads. Different choices of links can profoundly affect the stability of the grid. Building on Motter's work, we demonstrate that grids having only inductive admittances are stable (and conversely for grids with only capacitive admittances). We also present a family of regular circulant grids which can be easily analyzed to illustrate the influence of certain graph theoretic properties on grid stability.