In view of the difficulty in accurately identifying the voltage sag domain of sensitive loads in large and complex power grids, a fast voltage sag domain identification method has thus been adopted based on golden section search. Firstly, an analytical formula can be obtained for the voltage temporary drop amplitude of sensitive load nodes in the network when various types of short circuit faults occur, with the node judgment vector, line correlation vector and corresponding judgment criteria to be introduced to realize a fast classification calculation of all line critical points. Then, a detailed elaboration has been made of the traditional interpolation methods, with an improved interpolation method proposed on the basis of golden section search, which helps to provide better initial values for secant iteration, thus improving the accuracy of critical point calculation. In view of the inevitable deviation of the fitted quadratic curves, the fault point method is adopted as a supplementary algorithm to calculate routes that are difficult to solve. Finally, taking the IEEE30-node standard testing system as an example, it is verified that the proposed method can simplify the solution process of voltage sag domain, and improve the convergence speed of the algorithm on the premise of ensuring calculation accuracy, which makes it widely applicable to large and complex power grids.