Affected by the nonlinear time-varying factors due to fault scenarios, protection relaying, and control measures, the dynamic behaviors of a power system may be significantly different from the results of previous methods. In order to analyze the oscillation characteristics of complex power systems more accurately and suppress the low frequency oscillation more effectively, this paper improves the trajectory section eigenvalue method. Firstly, the time response of a system is obtained by numerical simulation in a given fault scenario. Secondly, the algebraic variables are substituted to the differential equations along the trajectory. Thus, the original time-varying differential-algebraic equations are approximated by a set of linear ordinary differential equations, which can be updated along the trajectory. On this basis, this paper proposes a method to extract instantaneous features of the oscillation from the micro perspective. The non-equilibrium points with strong nonlinearity or critical eigenmodes are identified by the proposed method. The simulation test results of the IEEE 3-machine 9-bus system and the New England system illustrate the validity of the proposed method.