Detailed studies of modern large-scale wind turbines represent a significant challenge. The immense length scales characteristic of these machines, in combination with rotational effects, render numerical simulations and conventional wind tunnel tests unfeasible. Field experiments can give us important insight into the aerodynamics and operation, but they are always accompanied by large amounts of uncertainty, due to the changing nature of the inflow and the lack of accurate control of the test conditions. Here, a series of experiments is presented, using an alternative method that enables us to represent and study much of the physics governing the large-scale wind turbines in small-scale models. A specialized, compressed-air wind tunnel is used to achieve dynamic similarity with the field-scale, but under accurately controlled conditions of the laboratory. Power and thrust coefficients are investigated as a function of the Reynolds number up to ReD=14×106, at tip speed ratios representative of those typical in the field. A strong Reynolds number dependence is observed in the power coefficient, even at very high Reynolds numbers (well exceeding those occurring in most laboratory studies). We show that for an untripped rotor, the performance reaches a Reynolds number invariant state at Rec≥3.5×106, regardless of the tip speed ratio. The same model was also tested with scaled tripping devices, with a height of only 9μm, to study the effect of transition on the rotor performance. In the tripped case, the Reynolds number dependence was eliminated for all tested cases, suggesting that the state of the boundary layer is critical for correct predictions of rotor performance.