In this article we consider the spectral behaviour of turbulence-driven power fluctuations for a single horizontal-axis turbine. To this end, a small-scale instrumented axial-flow hydrokinetic turbine model (diameter = 0.724 m) is deployed in the long water flume situated in the laboratory facilities of IFREMER in Boulogne-sur-Mer, France, and synchronous measurements of the upstream velocity and the rotor are collected for different tip-speed ratios. The study confirms previous findings suggesting that the power spectra follow the velocity spectra behaviour in the large scales region and a steeper power law slope behaviour (-11/3) over the inertial frequency sub-range. However, we show that both the amplitude of the power spectra and low-pass filtering effect over the inertial sub-range also depend on the rotor aero/hydrodynamics (e.g. dC(L)/d alpha) and the approaching flow deceleration and not solely on the rotational effects. In addition, we present a novel semi-analytical model to predict the dominant blade-passing frequency harmonics in the high-frequency regime using the rotationally sampled spectra technique. For all calculations, the distortion of incoming turbulence is taken into account.