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This paper will consider the benefits of neural controllers over model-based current regulators to supervise the current generation of a shunt active power filter. The task consists in generating appropriate compensation currents with a system composed of a voltage source inverter and a low-pass filter. These currents cancel the harmonic terms introduced by nonlinear loads in a power distribution grid. The performances of conventional controllers such as a PI and resonant current regulators are confronted to neural controllers. If conventional regulators present some advantages in terms of engineering specifications, their tuning remains difficult and their design relies on a rough linearization of the system. Their performances are acceptable without perturbations. However, fast changes of nonlinear loads lead to different operating points of the system. Furthermore, the inverter's nonlinearities and low-pass filter parameters have to be considered for generating precise currents. Two neural approaches have therefore been proposed, one which estimates the input-output relationship of the system, and one which relies on a state-space representation of the system. These approaches combine learning capabilities with a priori knowledge of the system. The benefits of the neural approaches are discussed and illustrated by simulations and by experimental tests with real-time implementations on a digital signal processing board.