Recently a great deal of improvement has been achieved in reducing the inherent conservativeness of the direct method of Lyapunov in its application to the transient stability analysis of multimachine power systems. One major discovery is the recognition of the fault location as a critical factor for the determination of the boundary of the stability region. The controlling UEP method takes into consideration the relevant unstable equilibrium points to construct Lyapunov surfaces, local approximations to the stability boundary, giving more accurate estimates. In this paper, three common Lyapunov functions are used in a comparative evaluation to determine their feasibility for the local Lyapunov surface approach. It is shown that the performance of the chosen Lyapunov functions varies considerably in transient stability analysis. The accuracy in the estimates provided by each function, on the other hand, is understood to be rather different in various cases of instability occurring in power systems.