  This paper proposes a mode-in-state contribution factor for a class of
nonlinear dynamical systems by utilizing spectral properties of the Koopman
operator and sensitivity analysis. Using eigenfunctions of the Koopman operator
for a target nonlinear system, we show that the relative contribution between
modes and state variables can be quantified beyond a linear regime, where the
nonlinearity of the system is taken into consideration. The proposed
contribution factor is applied to the numerical analysis of large-signal
simulations for an interconnected AC/multi-terminal DC power system.
