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The analysis of transient stability plays a vital role in providing secured operating configurations in power systems. In this paper, we present a critical evaluation of several methods for estimating the stability boundary of stable equilibrium points and for assessing transient stability. These methods include the time-domain approach, the controlling UEP method, the hyperplane method and a quadratic approximation approach. A technique for visualizing informative stability regions of stable equilibrium points in high-dimensional power systems is also proposed. The evaluation is illustrated by two study cases, the WSCC 9-bus system and the IEEE 145-bus system. It is numerically shown that the controlling UEP method is overall the most suitable method for transient stability assessment in power systems.