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One of the most important features of a unified power flow controller (UPFC) is its multiple control function that may be implemented by multiple controllers. However, simulation study has demonstrated the existence of the dynamic interactions among different UPFC controllers, i.e. power flow controller, AC voltage controller and DC voltage controller. In this paper a novel analytical approach based on normal form theory is proposed for the analysis of nonlinear interactions among the multi-controller channels of UPFC installed in a simple power system. Then, nonlinear participation factor is developed as an index to indicate the interaction extent among these UPFC controllers, which cause the negative interaction responsible for the closed-loop instability. The proposed approach is general and easy to be extended to include other FACTS devices. A single machine infinite bus system is used to validate the effect of these control channel interactions by simulation.