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The purpose of this paper is to provide a summary of an investigation of transient stability analysis using a combination of step-by-step integration and direct methods. The proposed method is based on extension of equal area criterion to transient stability analysis of multi-machine power systems. The proposed method first calculates the potential and kinetic energies of all machines in a power system before and after occurrence of faults. It then calculates two numbers based on energies of two groups of generators. It finally compares the largest group of kinetic energy to the smallest group of potential energy to determine the system's transient stability. A decision on stability of the system is made when the smallest group of potential energy is larger than the largest group of kinetic energy. The proposed method is used in analysis of the New England IEEE 39-bus system and the accuracy of the result is performed by comparison to the results obtained by pure numerical methods. Determination of stability using the proposed method is conservative and may be appropriate for power system operation as well as planning purposes.