Lyapunov-based Small Signal Analysis for Power Systems of Russia

A new mathematical general approach has been suggested to carry out small signals analysis of power systems by computing gramians spectral expansion in time and frequency domains. The gramians expansions are bilinear and quadratic forms for sequences of Faddeev matrices, generated by resolvents of the original matrices in the Lyapunov equation. A new tool for assessment of power system stability degree in small signals has been suggested. It is shown, that Frobenius norm of the system gramian may be considered as an index of the power system vicinity to stability boundary in small signals.