The optimisation of high-power converters providing high-quality voltage levels and high-efficiency energy conversion leads to low-switching frequencies and second-order LC filters with high-resonant frequencies. Because of these narrow frequency ratios, classical control schemes comprising an inner current loop and an outer voltage loop are not feasible. The same applies to the single-loop dead-beat strategy or to the direct control technique, as their simple single-order predictive model does not offer the required level of accuracy. This article develops higher order prediction models and computes the prediction error for different frequency ratios and approximation orders. This analysis shows that in the case of an optimised industrial outage and sag compensator, a second-order prediction model provides the required accuracy; hence, the second-order predictive direct control is developed. This control drives both the inductor current and the capacitor voltage simultaneously, assures constant switching frequency and results in robust and stable behaviour. Simulation and experimental results show the validity of the approach.