The Super Turbine Wind Power Conversion Paradox: Using Machine Learning to Overcome Jensen’s Inequality

Wind power is a variable generation resource and therefore requires accurate forecasts for integration into the electric grid. Generally, the wind speed is forecast for a wind plant and the forecasted wind speed is converted to power to provide an estimate of the expected generating capacity of the plant. The average wind speed forecast for the plant is a function of the underlying meteorological phenomena being predicted; however, the wind speed for each turbine at the farm is also a function of the local terrain and the array orientation. Conversion algorithms that assume an average wind speed for the plant, i.e. the super turbine power conversion, assume that the effects of the local terrain and array orientation are insignificant in producing variability in the wind speeds across the turbines at the farm. Here, we quantify the differences in converting wind speed to power at the turbine-level compared to a super turbine power conversion for a hypothetical wind farm of one hundred two megawatt turbines as well as from empirical data. The simulations show a maximum difference of approximately 3% at 11 m/s with 1 m/s standard deviation of wind speeds and 8% at 11 m/s with 2 m/s standard deviation of wind speeds as a consequence of Jensen’s Inequality. These significant differences can lead to wind power forecasters over-estimating the wind generation when utilizing a super turbine power conversion for high wind speeds and indicates that power conversion is more accurately done at the turbine level if no other compensatory mechanism is used to account for Jensen’s Inequality. However, we show that machine learning algorithms can be trained to over-come the power conversion differences caused by Jensen’s Inequality to accurately convert wind speed to wind power for the total power generated at the plant.