Transient stability analysis plays an important role concerned with the ability of power systems to reach steady state following large disturbances. Today's power systems are operated in significantly stressed state close to their limits. Fast determination of the system response is a crucial issue which raises the need for online stability assessment. Direct methods appear to be key approach to this problem of the power system transient stability analysis. A new robust method for detecting Controlling Unstable Equilibrium Point (CUEP) is proposed in this paper. The solution is obtained on basis of a minimization problem. The critical trajectory method (CTrj), another our approach, is applied to the Boundary of stability region based Controlling UEP (BCU) method. The method is combined with new criterion characterized by the potential energy boundary surface (PEBS) property. Starting from an exit point the method computes simultaneously multiple points of a trajectory that reaches CUEP. The effectiveness of the method is demonstrated through six power system models.