In view of the significant challenges for active distribution networks when addressing the instability of distributed power output and coordinating diverse reactive power compensation devices within the network as numerous distributed power sources are integrated into the grid, a novel voltage stability index has thus been introduced on the basis of the branch decomposition and saddle point voltage difference in the PV curve so as to address the issues of excessive voltage deviation and high network losses in the current distribution network. By improving the artificial hummingbird algorithm to solve the above-mentioned model, in order to enhance the performance of the algorithm, Tent chaotic mapping method is introduced to realize a more uniform population distribution, with mutation operation introduced to avoid the algorithm from getting trapped in local optima. With a simulation validation conducted in the IEEE-33 system, the results demonstrate that compared to traditional algorithms, an optimization of the model with the improved artificial hummingbird algorithm significantly reduces voltage deviation and active power losses, thereby ensuring stable operation of the power grid.