A Physics-Informed Graph Neural Network Surrogate for Operational Estimation of Wake-Induced Power Losses in Wind Farms

Abstract

Limited land packs wind turbines a few rotor diameters apart as electricity demand continues to rise. Wind already supplies about 10% of U.S. electricity and 23% of Texas ERCOT generation. Each rotor leaves a wake of slower, more turbulent air. Power scales with the cube of wind speed, so a 15% speed drop is about a 39% power drop, and dense farms often lose 10–20% of isolated-rotor energy. This study asks how to estimate that wake-affected energy on an operating farm from quantities the farm already records. The questions are whether a one-to-one upstream-to-downstream map can represent overlapping wakes, and whether a farm graph can score those wakes in one iteration. The variables are upstream generation, wind-alignment angle, spacing, and downstream energy. The layout is fixed (Sweetwater, Texas, 2013, ten-minute records). The study is limited to neural estimators. The purpose was to build a reusable surrogate that estimates wake-affected energy for the turbines in a farm graph in one pass. The project was undertaken because the historian already logs every meter over 2 months; what is missing is an estimator that sees the neighborhood that produced the reading. The hypothesis was that pairwise neural networks would fit a hub meter but could not scan overlapping wakes in one pass; that using Jensen’s wake equation only as a soft constraint in the loss would improve the close-pair estimate; and that a physics-induced graph neural network would then estimate many links with one set of weights in one iteration. Filtered 2013 ten-minute generation records (negatives set to zero; values above 1600 kilowatt-hours removed) were aligned with wind direction on turbine coordinates. One hundred eight validated directed wake links formed the farm graph. Networks were trained in a 1000-epoch window and evaluated on a chronological 80%/20% split. Hub T118 was estimated from T117 (0.54 km) and T145 (2.61 km). Errors were reported in three isolated stages: pairwise feed-forward, long short-term memory, and temporal-convolutional networks; then a physics-induced pairwise feed-forward network; then the physics-induced graph neural network. The feed-forward network reached 292.13 kilowatt-hours (R² = 0.724) on T117 to T118 and 242.02 (0.811) on T145 to T118. The 24-hour memory and convolutional networks were worse (336.79 and 322.21; 303.42 and 262.66). Adding two pairwise guesses would count the same meter twice. The physics-induced pairwise network reached 270.45 (0.764) and 240.29 (0.813), supporting the close-pair hypothesis. The graph network on the same single edge reached 276.14 and 254.41. A shared-weight scan of 28 links reached mean error 198.86 kilowatt-hours and mean R² 0.866, supporting the graph hypothesis.