Frequency stability is a crucial consideration in power system operation and planning, particularly as a consequence of recent increase in load demand. There is an urgent need in each power system to consider load-generation balance to prevent system from breaking up into islands. In this paper, a system frequency response model has been presented and a new method has been offered to analytically calculate the border of frequency stability of power system. It can be realized, whether system is stable from frequency viewpoint or not. Moreover, the threshold of UFLS (under frequency load shedding) relays can more effectively be determined, compared to the previous works in the area. The proposed method is examined on a four unit test system. Obtained results confirm the validity of the developed approach. (C) 2010 Elsevier Ltd. All rights reserved.