According to the theory and the applications of the Flexible AC Transmission System (FACTS) technology, the FACTS devices can improve the level of the power transmission and the power system stability. With the growing applications of FACTS devices, the interaction between the FACTS devices becomes increasingly an important issue. The normal form method provides a solution of the dynamic analysis of the power system embedded with the multiple FACTS devices. How to determine the critical operation mode of the power system, and the degree of the interaction of multiple FACTS devices in the critical operation mode become a key problem. The operating state of a power system has many modes. The interaction of the FACTS devices in different operating states is a key factor in increasing the computation speed and the computation efficiency. This paper, based on the high order normal form method, proposes an improved interaction index to analyze the degree of interaction between the FACTS devices. The improved interaction index also considers the determination of the critical operation mode of the power system. The electromagnetic transient simulation is used for the verification of the proposed method. Finally, taking the Static Var Compensator (SVC) and the Thyristor Controlled Series Compensation (TCSC) on the IEEE 9-bus power system as examples, the feasibility of the proposed improved interaction index is shown.