Wind Power Intra-day Multi-step Predictions Using PDE Sum Models of Polynomial Networks Based on the PDE Conversion and Substitution with the L-Transformation

Abstract

Precise forecasts of wind power are required as they allow full integration of wind farms into the electrical grid and their active operation. Their daily base poses a challenge due to the chaotic nature of global atmospheric dynamical processes resulting in local wind fluctuations and waves. Surface wind forecasts of NWP models are not fully adapted to local anomalies which can influence significantly in addition its temporal-flow. AI methods using historical observations can convert or refine forecasts in consideration of wind farm location, topography and hub positions. Their independent intra-day wind-power predictions are more precise then those based on NWP data as these are usually produced every 6 h with a delay. The designed AI method combines structures of polynomial networks with some mathematic techniques to decompose and substitute for the n-variable linear Partial Differential Equation, which allow complex representation of unknown dynamic systems. Particular 2-variable PDEs, produced in network nodes, are converted using the Laplace transformed derivatives. The inverse L-transformation is applied to the resulting pure rational terms to obtain the originals of unknown node functions, whose sum is the composite PDE model. Statistical models are developed with data samples from estimated periods of the last days which optimally represent spatial patterns in the current weather. They process the latest available data to predict wind power in the next 1–12 h according to the trained data inputs → output time-shift.