The CCEBC/EEAC method is an effective method in the quantitative analysis of power system transient stability. This paper provides a qualitative analysis of the CCEBC/EEAC method and shows that from a geometrical point of view, the CCCOI-RM transformation used in the CCEBC/EEAC method can be regarded as a projection of the variables of the system model on a weighted vector space, from which a generalized(-P)-(-δ) trajectory is obtained. Since a transient process of power systems can be approximately regarded as a time-piecewise simple Hamiltonian system, in order to qualitatively analyse the CCEBC/EEAC method, this paper compares the potential energy of a two-machine infinite bus system with its CCEBC/EEAC energy. Numerical result indicates their similarity. Clarifying the qualitative relation between these two kinds of energies is significant in verifying mathematically the CCEBC/EEAC method for judging the criterion of power system transient stability. Moreover, the qualitative analysis of the CCEBC/EEAC method enables us to better understand some important phenomena revealed by quantitative analysis, such as multi-swing loss of stability and isolated stable domain.