In this paper, a frequency-adaptive neural network-based virtual flux (FANN-VF) estimator is developed for sensorless control of a pulse-width modulation converter under unbalanced and distorted grid conditions. This method exploits two parallel FANNs configured as quadrature signal generators. The VF fundamental positive and negative sequence components (PNSCs) are inherently separated in the estimator without employing any cascaded filters. A frequency-locked loop is introduced to accurately track the frequency variations. The estimated VF PNSCs are directly exploited to compute the power references in VF-based predictive direct power control scheme. The developed strategy ensures constant active power and sinusoidal current waveforms under nonideal grid conditions. Simulation and experimental tests are performed to verify the effectiveness of the proposed method.