The super-turbine wind power conversion paradox: using machine learning to reduce errors caused by Jensen's inequality

Abstract

Abstract. Wind power is a variable generation resource and therefore requires accurate forecasts to enable 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 with a super-turbine power conversion for a hypothetical wind farm of 100 2 MW turbines as well as from empirical data. The simulations with simulated turbines show a maximum difference of approximately 3 % at 11 m s−1 with a 1 m s−1 standard deviation of wind speeds and 8 % at 11 m s−1 with a 2 m s−1 standard deviation of wind speeds as a consequence of Jensen's inequality. The empirical analysis shows similar results with mean differences between converted wind speed to power and measured power of approximately 68 kW per 2 MW turbine. However, using a random forest machine learning method to convert to power reduces the error in the wind speed to power conversion when given the predictors that quantify the differences due to Jensen's inequality. These significant differences can lead to wind power forecasters overestimating the wind generation when utilizing a super-turbine power conversion for high wind speeds, and indicate that power conversion is more accurately done at the turbine level if no other compensatory mechanism is used to account for Jensen's inequality.