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This paper proposes the use of an auxiliary gradient system to calculate the low-voltage solutions (LVSs) of the load flow equations of an electrical power system. It shows that the equilibrium points of that associated auxiliary dynamical system are the solutions of the load flow equations. In such a manner, the paper proposes to find the LVSs by calculating the equilibrium points of the auxiliary dynamical gradient system. The proposed method improves the classical state-space search methods by calculating a new LVS every lime the tracked one bifurcates and vanishes. It was tested on Stagg 5-bus, IEEE 39-bus, and IEEE 118-bus systems. The results are at the end of the paper and show that the proposed method presents a great tendency to find the critical LVS for the current load increase direction, as the load is slowly increased. [ABSTRACT FROM AUTHOR]