A method of assessing dynamic stability of largescale power system by Rayleigh's quotient is proposed. One-machine infinite-bus systems show damping torque characteristics similar to diagonal components of operational transfer matrices for original multimachine systems, which means that design of PSS with one-machine systems controls those components. An expression for damping constants of oscillation modes is derived based on an energy function and its time derivative for a simplified system representation. This expression demonstrates that oscillations do not necessarily become unstable even if there are some generators with negative damping; and the effect of damping torque is determined by eigenvectors. The expression is generalized with Rayleigh's quotient, and a method of estimating eigenvalues of large-scale power systems is proposed. With this method, approximate eigenvalues are refined to accurate eigenvalues. Only a specified number of eigenvalue analyses are required irrespective of the number of generators, hence much calculation is saved. Finally, this method is applied to a 107-machine system to verify its effectiveness.