Abstract: To some extent, power grid with increasingly complex structure can maintain long-term stable operation due to inherent system characteristics. As a qualitative characteristic of dynamic system, mixed monotonicity is derived from monotonicity, which can account for the inherent growth and decay mechanisms in the system structure. Jacobian matrices of dynamic electromechanical transient mathematical models of power grid generally exhibit constant sign patterns during different periods, which are consistent with the characteristics of the monotone system. Combined with the mixed monotone decomposition technique, the system parts with positive and negative effects on the key system state variables are decomposed. The growth and decay mechanisms among various state variables are studied and the dynamic response characteristics of the system in electromechanical transient scale are analyzed to explain some operation experiences of power grids. Finally, based on the result of the mixed monotone decomposition,a monotonic augmented system with bilateral comparison performance is constructed. Its vertex response gives a quick estimation of the interval response of the original system, which provides quantitative analysis results for uncertainty problems.