scholarly journals The Super-Turbine Wind Power Conversion Paradox: Using Machine Learning to Reduce Errors Caused by Jensen’s Inequality

2019 ◽  
Author(s):  
Anonymous
2019 ◽  
Vol 4 (2) ◽  
pp. 343-353 ◽  
Author(s):  
Tyler C. McCandless ◽  
Sue Ellen Haupt

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.


2019 ◽  
Author(s):  
Tyler C. McCandless ◽  
Sue Ellen Haupt

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 to 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 1 m s−1 standard deviation of wind speeds and 8 % at 11 m s−1 with 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 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.


2009 ◽  
Vol 50 ◽  
Author(s):  
Julije Jaksetic ◽  
Bogdan Gavrea ◽  
Josip Pecaric

Energies ◽  
2021 ◽  
Vol 14 (2) ◽  
pp. 338
Author(s):  
Lorenzo Donadio ◽  
Jiannong Fang ◽  
Fernando Porté-Agel

In the past two decades, wind energy has been under fast development worldwide. The dramatic increase of wind power penetration in electricity production has posed a big challenge to grid integration due to the high uncertainty of wind power. Accurate real-time forecasts of wind farm power outputs can help to mitigate the problem. Among the various techniques developed for wind power forecasting, the hybridization of numerical weather prediction (NWP) and machine learning (ML) techniques such as artificial neural networks (ANNs) are attracting many researchers world-wide nowadays, because it has the potential to yield more accurate forecasts. In this paper, two hybrid NWP and ANN models for wind power forecasting over a highly complex terrain are proposed. The developed models have a fine temporal resolution and a sufficiently large prediction horizon (>6 h ahead). Model 1 directly forecasts the energy production of each wind turbine. Model 2 forecasts first the wind speed, then converts it to the power using a fitted power curve. Effects of various modeling options (selection of inputs, network structures, etc.) on the model performance are investigated. Performances of different models are evaluated based on four normalized error measures. Statistical results of model predictions are presented with discussions. Python was utilized for task automation and machine learning. The end result is a fully working library for wind power predictions and a set of tools for running the models in forecast mode. It is shown that the proposed models are able to yield accurate wind farm power forecasts at a site with high terrain and flow complexities. Especially, for Model 2, the normalized Mean Absolute Error and Root Mean Squared Error are obtained as 8.76% and 13.03%, respectively, lower than the errors reported by other models in the same category.


2019 ◽  
Vol 94 (6) ◽  
pp. 1109-1121
Author(s):  
László Horváth

AbstractIn this paper some new refinements of the discrete Jensen’s inequality are obtained in real vector spaces. The idea comes from some former refinements determined by cyclic permutations. We essentially generalize and extend these results by using permutations of finite sets and bijections of the set of positive numbers. We get refinements of the discrete Jensen’s inequality for infinite convex combinations in Banach spaces. Similar results are rare. Finally, some applications are given on different topics.


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