On-line dynamic security assessment is becoming more and more important for the stable operation of power systems as load level increases. The necessity is getting apparent under Electricity Market environments, as operation of power system is exposed to more various operating conditions. For on-line dynamic security assessment, fast transient stability analysis tool is required for contingency selection. The TEF(Transient Energy Function) method is a good candidate for this purpose. The clustering of critical generators is crucial for the precise and fast calculation of energy margin. In this paper, we propose a new method for fast decision of mode of instability by using stability indices. Case study shows very promising results.