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The on-line assessment of transient stability of power systems could be only achieved by adopting direct methods such as that of Liapunov. The construction of serveral Liapunov functions was based on simplified models dictated by the different methods. The inclusion of transfer conductances effect was hitherto impossible. A method is proposed to include this effect and a new Liapunov function is presented. The application of this function to two power systems has shown its superiority to other available functions.