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Increasing demand for electricity has placed heavy stress on power system security. Therefore, this paper focuses on the problem of how to maximize power system static security in terms of branch loading and voltage level under normal operation and even the most critical single line contingency conditions. This paper proposes a hybrid approach to find out the optimal locations and settings of two classical types of flexible AC transmission system (FACTS) devices, namely thyristor-controlled series compensators (TCSCs) and static var compensators (SVCs) for solving this problem. Our proposed approach requires a two-step strategy. Firstly, the min cut algorithm (MCA) and tangent vector technique (TVT) are applied to determine the proper candidate locations of TCSC and SVC respectively so as to reduce the search scope for a solution to the problem, and then the cuckoo search algorithm (CSA) is employed to solve this problem by simultaneously optimizing the locations and settings for TCSC and SVC installation. The proposed hybrid approach has been verified on the IEEE 6-bus and modified IEEE 14-bus test systems. The results indicate that CSA outperforms particle swarm optimization (PSO), proving its effectiveness and potential, and they also show that our proposed hybrid approach can find the best locations and settings for TCSC and SVC devices as an effective way for enhancing power system static security by removing or alleviating the overloads and voltage violations under normal operation and even the most critical single line contingency conditions. Using this hybrid approach, the search space for solution to the problem becomes limited hence the computational burden will be decreased. [ABSTRACT FROM AUTHOR]