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A method based on a Lure Lyapunov function is developed to analyse subsynchronous resonance (SSR) phenomena in power systems. An improved Lure Lyapunov function used to analyse the stability of a power system including the turbine-generator (T-G) shaft is presented first. Then, a standard Lure control model for a power system with a T-G shaft is obtained. The stability of such nonlinear systems at the equilibrium points is discussed in detail. The stable operation region of the system is discussed with the proposed method. The effectiveness of the proposed method is verified by a case study. This study has shown potential benefits and the validity of the Lyapunov direct method in the subsynchronous resonance analysis. Compared with the conventional analysis method, such as eigenvalue and frequency scanning techniques, the proposed method is based on the original nonlinear system. Error, that may be introduced by linearisation, is avoided completely. Moreover, the stable operation region of power systems can be obtained by the proposed method.