Abstract: The limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm(LBFGS) is one of the efficient and classical algorithms for fitting multi-terminal electrical quantity fault localization models for power cables. Nevertheless, the development and increasing scale of cables has resulted in a significant increase multi-terminal electrical quantity feature. This has rendered the current LBFGS algorithm difficult to meet practical needs and necessitates the urgent improvement of its efficiency. An exponential factor search operation mechanism is proposed, which is based on the classical LBFGS algorithm. As the model steadily progresses towards the optimal direction, the elements of the gradient matrix execute an exponential factor search operation mechanism. During the process of updating the gradient matrix element, the solution space search step-size is intelligently scaled by analysing previous steps-size updates data, causing the model function being fitted to converge quickly. Simulation experimental results show that the improved algorithm can make the model function fitting convergence process get rid of invalid step size, increase the number of valuable step size, and significantly improve the efficiency of model fitting. The analysis of the preceding step-size update data during the fitting process engenders a high degree of stability in the model fitting process. The efficacy of the algorithm is confirmed by simulation experiments.