The modern power system has its unique characteristics of long distance， heavily loaded and regional connected transmission framework. Owing to the above and the gradual deregulation of the power system， it is becoming increasingly necessary for the system to operate much closer to its loading limits. In this state， power flow equations are apt to have no real solution. By analyzing unsolvable cases in power systems， the reason for unsolvability is pointed out in this paper， that is， the transmission limit of a certain path or several weak paths has been violated. Based on this， an algorithm is proposed to regulate the parameters so as to return to the solvable region. First， find the weakest transmission path by reducing generators and loads. Then， enhance the power factors of loads to ensure the balance of the reactive power. Finally， based on the sensitivities， reschedule the active power of generators while shedding loads to get the convergent resolution of the power flow. The feasibility and veracity of the algorithm is demonstrated in the power grid of Central China.