A fast assessment algorithm of power system security is proposed to handle the interval uncertainty of loads existing in high-voltage transmission network. Firstly， the proposed algorithm makes an enhancement to conventional branch and bound method， proves the load boundary characteristics of minimum load cutting problem in power systems， which means load of each bus is fixed at its maximum value or minimum value in the most dangerous load conditions. Based on these characteristics， a bi-level linear programming model is obtained and solved by solving a few linear programming models. This novel model is expressed as a DC power flow model， and the enhanced branch and bound algorithm can solve this model quickly and precisely to get the maximum value of the minimum load cutting amount of different schemes， with generators' regulatory abilities considered. Comparing with Monte-Carlo method and the conventional branch-and-bound method， the enhanced algorithm shows great advantages in speed and precision. The testing results on 6-bus and 46-bus power systems validate the efficiency of the proposed algorithm.