Direct wind power forecasting using a polynomial decomposition of the general differential equation

Abstract

The wind power is primarily induced by the local wind speed, whose accurate daily forecasts are important for planning and utilization of the unstable power generation and its integration into the electrical grid. The main problem of the wind speed or direct output power forecasting is its intermittent nature due to the high correlation with chaotic large-scale pattern atmospheric circulation processes, which together with local characteristics and anomalies largely influence its temporal flow. Numerical global weather systems solve sets of differential equations to describe the time change of each three-dimensional grid cell in several atmospheric layers. They can provide as a rule only rough short-term surface wind speed prognoses, which are not entirely adequate to specific local conditions, e.g., the wind farm siting, surrounding terrain, and ground level (hub height). Statistical methods using historical observations can particularize the daily forecasts or provide independent predictions in several hours. Extended polynomial networks can produce fraction substitution sum terms in all the nodes, in consideration of data samples, to decompose and substitute for the general linear partial differential equation, being able to describe the local atmospheric dynamics. The designed method using the inverse Laplace transformation aims at the formation of stand-alone spatial derivative models, which can represent current local weather conditions for a trained input-output time shift to predict the daily wind power up to 12 h ahead. The proposed intraday multistep predictions are more precise than those based on middle-term numerical forecasts or adaptive intelligence techniques using local time series, which are worthless beyond a few hours.