This paper presents a systematic approach to derive the dynamic model of a multi-machine power system installed with multiple FACTS devices, including SVCs, TCSCs, TCPSs, STATCOMs and UPFCs. The derivation of the model is demonstrated comprehensively for a general n-machine power system. Based on the approach to model the multi-machine power system with multiple FACTS devices installed, two study cases of applications are presented in the paper. They are: (1) the multi-agent co-ordination of the secondary voltage control of SVC and STATCOM and (2) the investigation into the dynamic interactions between STATCOM and UPFC control. Study results are demonstrated by example power systems.