The computation of the Unstable Equilibrium Point (UEP) is a key step involved in the direct methods of power system transient stability analysis. This paper presents an idea for formulating generalized energy function for the stability detection of interconnected power systems and obtained the UEP in an easy way. The energy function is formulated based on Energy functions for individual machines. The technique is validated by computing the Stable Equilibrium Point (SEP), the controlling UEP, and The Critical Clearing Time (CCT). Then, a Conventional Time Domain Method (CTDM) is used to validate the novel technique's results.