A unified power quality conditioner (UPQC) is developed for the mitigation of grid-voltage and -current distortions under steady-state and dynamic conditions. The proposed configuration integrates series and shunt inverters through a common DC-link capacitor. The capacitor functions as an energy buffer by accommodating the power exchanged between the two inverters. Following an abrupt grid-voltage disturbance or load transition, the DC-link capacitor must instantaneously deliver or absorb power to maintain the power balance between the inverters while sustaining the required compensation. The resulting transient energy exchange can produce pronounced DC-link voltage excursions, with adverse consequences for system stability and compensation accuracy. Rapid and accurate regulation of the DC-link voltage is therefore essential for maintaining the dynamic compensation performance of the UPQC. To improve this regulation, a compensatory wavelet fuzzy neural network incorporating asymmetric membership functions (CWFNN-AMFs) is introduced in place of the conventional proportional–integral (PI) controller. The network architecture and its online learning algorithm are derived in detail. Finally, experimental results under steady-state and dynamic conditions demonstrate that the CWFNN-AMF-controlled UPQC improves both power quality compensation and DC-link voltage regulation, thereby verifying the feasibility and effectiveness of the proposed control framework.