Abstract：In order to intervale evaluate saddle node bifurcation points（SNB）in a power system during load

growth quickly and accurately，a quadratic approximation method to directly calculate the power system voltage

collapse point of was proposed. Based on the approximate quadratic PV-curve of output PQ nodes in the system，

load parameters were introduced into the node power balance equation，by using the complex function derivative

rules to differentiate power equation twice，the first and second derivatives of node voltage to load parameters were derived theoretically，and the expression of PV curve function was further determined，then vertex coordinates were used to determine the initial position of saddle junction bifurcation point in the power system and the voltage collapse point was approximated by multiple iterations of convergence. The proposed method avoids multiple power flow calculations using the continuous power flow method，significantly reducing computational complexity.Simulation results on IEEE 14 and IEEE 118 bus systems demonstrate the effectiveness of this method. Compared with the supplemented P’Q node method and Thevenin's equivalent method，the quadratic form iterative approximation method has higher computational efficiency and robustness.

      Key words：saddle node bifurcation poin（t SNB）；loading parameter；PV curve；quadratic approximation