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This paper presents a real time power system transient stability assessment method using synchrophasor data and the catastrophe theory. It is designed to satisfy the requirement of real time stability assessment in the wide area power system. Different from conventional approaches the proposed method does not consider the process of system operation by certain parameter values but by the concept of continuity of system operation. The stability margin is defined by discontinuity boundary. This feature can greatly simplify the complicity of defining the stability margin for different cases. In this paper the discontinuity of the maximum swing angle has been studied for the power system TSA. The operation trajectory of the maximum swing angle is obtained via different fault clearing angles. Then the stability condition is determined by the continuity of maximum swing angle. The value of fault clearing angle, which correlated to the intersection of the operational trajectory and the discontinuity boundary, is equal to the critical clearing angle. The synchrophasor has been applied here to provide the initial condition of the disturbance and to obtain the center of inertia with the rotor angle as a reference.