[Objective] To address the limitation that local optimization search methods for alternating-current optimal power flow （AC-OPF） generally converge only to local optima and struggle to obtain higher-quality feasible solutions， this paper investigates a method that can deterministically escape from an obtained local optimum and continue searching for better solutions. [Methods] An augmented quotient gradient system （AQGS） bifurcation-based superior solution search method （ABS） was proposed based on the bifurcation behavior of the AQGS. By analyzing the bifurcation-induced disappearance mechanism of stable equilibrium points corresponding to suboptimal solutions in AC-OPF， this study revealed the influence of penalty-parameter adjustment on the equilibrium-point structure of the AQGS. Furthermore， the saddle-node bifurcation between a stable equilibrium point and a type-1 unstable equilibrium point was exploited to eliminate the stable equilibrium point corresponding to the current local optimum， thereby guiding the system trajectory to converge to a new optimal solution. [Results] The proposed method was validated on multi-solution test systems with 2， 3， 9， and 300 buses. Numerical results show that ABS successfully obtains feasible local optima with lower objective function values from given local optima in all tested cases， achieving maximum objective-function improvements of 2.92%， 0.21%， 27.60%， and 2.46%， respectively. [Conclusions] The proposed ABS method uses the bifurcation behavior of the AQGS to achieve deterministic escape from local optima and improve solution quality. It provides a new analytical perspective and computational method for multi-solution search and local optimum improvement in AC-OPF， verifying its effectiveness in complex multi-solution power flow optimization problems.