This paper investigates the application of an improved Modulated Model Predictive Control strategy to active power compensators. The proposed control is able to retain all the advantages of a Finite Control Set Model Predictive Control whilst improving the waveform harmonic spectrum. In fact a modulation algorithm, based on the cost function ratio for different output vectors, is inherently included in the predictive control algorithm. In particular the case of a Shunt Active Filter is investigated and the converter topology, its analytical modeling and its control implementation are described in details. The cost function-based modulator is introduced and its effectiveness on reducing the current ripple is demonstrated. The proposed approach provides a straightforward and effective single loop control solution, maintaining an excellent dynamic performance despite the modulated output and it is self-synchronizing with the grid. Significant results obtained by experimental testing are reported and commented.