After positioning a 1:20 scaled model of a three-bladed horizontal-axis turbine in the wake of a wall-mounted cylinder, synchronized turbine performance and flow measurements are carried out to investigate the relationship between the incoming flow field and the turbine power fluctuations. The Linear Stochastic Estimation (LSE) is used to predict the turbine output fluctuations from the knowledge of the Large Scale flow Structures (LSS) embedded in the incoming turbulent flow. LSS extraction by Fourier analysis or Proper Orthogonal Decomposition shows that LSS are responsible for the main unsteady variations of the power fluctuations, especially their highest amplitudes. The RMS of turbine output fluctuations are entirely due to the LSS. It is also demonstrated that whatever the nature of the incoming turbulent flow is, the low frequency filtering process coupled with the LSE method allows the recovering of at least 90% of the turbine power RMS. Furthermore, the low-frequency spectral content of the turbine power fluctuations is very well predicted, especially the frequency peaks. A preliminary LSE application is performed in order to predict the instantaneous turbine output fluctuations at more than 85% confidence level, from only three velocity signals measured in front of the turbine.