The reduced Carleman linearization model is provided after introducing the Carleman embedding technology. The nonlinear modes and the time response of single state variables and corresponding nonlinear participation factors are given. The higher-order state variables are deduced and the concept of participation factors is developed to nonlinear participation factors of higher-order state variables. These results can be used to study the nonlinear dynamic performances and evaluate the interactions between each mode and variable. Finally, the proposed method is used to study a power system simulation case and compared with Prony analysis. Through analyzing time domain solutions of every order variable and corresponding participation factors, and comparing the changes of eigenvalues space when system’s operating condition changes, it verifies the validity of the method. This work is supported by National Natural Science Foundation of China (No. 51277022).