Fourier methods for estimating power system stability limits

This paper shows how the use of new-generation tools such as a generalized shell for dynamic security analysis can help improve the understanding of fundamental power systems behaviour. Using the ELISA prototype shell as a laboratory tool, it is shown that the signal energy of the network impulse response acts as a barometer to define the relative severity of a contingency with respect to some parameter, for instance power generation or power transfer. In addition, for a given contingency, as the parameter is varied and a network approaches instability, signal energy increases smoothly and predictably towards an asymptote which defines the network´s stability limit: this, in turn, permits a comparison of the severity of different contingencies. Using a Fourier transform approach, it is shown that this behaviour can be explained in terms of the effect of increasing power on the damping component of a power system´s dominant poles. A simple function is derived which estimates network stability limits with surprising accuracy from two or three simulations, provided that at least one of these is within 5% of the limit. These results hold notwithstanding the presence of many active, nonlinear voltage-support elements (i.e. generators, synchronous condensers, SVCs, static excitation systems, etc.) in the network