Aerodynamic analysis of standard variable-speed torque control in complex terrain

Abstract. Wind energy projects in complex terrain are often associated with high uncertainties regarding the expected power performance. These uncertainties are mostly attributed to difficulties in obtaining reliable wind speed estimates. Two additional factors are that the physical limits of energy extraction vary in these cases and that the employed wind turbine might operate differently than expected in these conditions. This study addresses these two factors with the goals of identifying the dominant factor influencing power performance and improving understanding of how a turbine controller operates in flow conditions for which it was not calibrated. For this purpose, Reynolds-averaged Navier–Stokes (RANS) simulations of a wind turbine modeled as an actuator disk (AD) subject to a neutral atmospheric inflow are performed. The influence of the turbine position relative to a quasi-two-dimensional Gaussian hill with varying dimensions on the maximum power performance and on the response of a torque controller in region 2 of the power curve is investigated. For two cases analyzed in detail, it is found that when the turbine is located at the foot of the hill, the maximum power coefficient increases by 2.46 %, while it decreases by 18.25 % on top of the hill. As a consequence, when placing wind turbines on elevated locations, the power does not scale with the cube of the increase in wind speed. The controller maintains a constant local power coefficient, i.e., the power coefficient based on the disturbed rotor-plane velocity. This local power coefficient does not necessarily coincide with the optimal power coefficient defined using the undisturbed wind speed. As a result, the controller does not track optimal performance when the relationship between undisturbed and disturbed wind speed differs from the calibration conditions, such as when a controller tuned for flat terrain is applied in complex terrain. In the present study, this mismatch leads to a maximum power loss of 1.96 %. Overall, this study sheds light on the interpretation of wind turbine performance results in complex terrain and helps shape efforts to reduce prediction uncertainties for future onshore wind projects in complex terrain.