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Most wind turbines are installed inside wind farms, where they often operate under wake-affected inflow conditions. New methods are required to evaluate the power performance of a wind turbine in wake, as the International Electrotechnical Commission (IEC) standard procedure is applicable only to wake-free turbines. In this work, we investigate the accuracy of a multivariate power curve acquired through a polynomial regression, whose input variables are wind speed and turbulence measurements retrieved upstream of the turbine's rotor. For this purpose, we use measurements from the SpinnerLidar, a continuous-wave, scanning Doppler lidar measuring the turbine inflow. The SpinnerLidar was mounted in the spinner of a Neg Micon 80 wind turbine located within an onshore wind farm in western Denmark. The input variables are selected among the available lidar measurements with a feature-selection algorithm, resulting in seven input variables, distributed in different locations along the rotor area: six wind speed and one turbulence measurements. The multivariate power curve is tested and compared with IEC-similar power curves under both wake-affected and wake-free conditions. Results show that the multivariate power curve estimates the turbine's power output more accurately than the IEC-similar power curves, with error reductions up to 66.5% and 34.2% under wake-affected and wake-free conditions, respectively. Furthermore, the multivariate power curve estimates have an accuracy of the same order under both wake-affected and wake-free conditions. Finally, we show that the multivariate model accurately predicts the power even when a simple measuring geometry is used, such as circular scanning pattern with a diameter equal to 90% of the rotor. • Measurements from a spinner-mounted lidar under wake conditions. • Wind speed and turbulence retrieved from lidar Doppler radial velocity spectra. • Wind turbine power curves modelled as multivariable polynomial regressions. • The multivariate power curves are more accurate than the IEC binning method. • The multivariate power curves are as accurate in wake as in wake-free conditions. [ABSTRACT FROM AUTHOR]