A new approach to determine the local boundary of voltage stability region in a cut-set power space（CVSR） is presented. Power flow tracing is first used to determine the generator-load pair most sensitive to each branch in the interface. The generator-load pairs are then used to realize accurate small disturbances by controlling the branch power flow in increasing and decreasing directions to obtain new equilibrium points around the initial equilibrium point. And， continuous power flow is used starting from such new points to get the corresponding critical points around the initial critical point on the CVSR boundary. Then a hyperplane cross the initial critical point can be calculated by solving a set of linear algebraic equations. Finally， the presented method is validated by some systems， including New England 39-bus system， IEEE 118-bus system， and EPRI-1000 bus system. It can be revealed that the method is computationally more efficient and has less approximation error. It provides a useful approach for power system online voltage stability monitoring and assessment.