Energy function methods have been studied for many years, and have bee
n applied to practical power system stability analysis problems of mul
ti-machine power systems. Recent developments in real-time power syste
m monitoring suggest that dynamic events can be monitored at the power
system control centers, and naturally the energy function methods wer
e tried as real-time stability prediction tools. However, a number of
instances were uncovered, where the energy function methods which use
the Potential Energy Boundary Surface as an approximation of the stabi
lity boundary produce unreliable results. In particular, during severa
l transient stability studies, the Boundary Controlling Unstable (BCU)
Equilibrium Point method seemed to predict stable swings, whereas in
reality the swings turned out to be unstable. This paper presents thes
e counter-examples, and suggests an explanation as to why these method
s produce a wrong result. It is hoped that this paper will lead to fur
ther researches and improvements in the theory of energy function base
d methods of stability analysis. In the mean time, alternative methods
for the real-time stability prediction problems are under investigati
on.