A novel non-dimensional multiple operating conditions physics-informed neural networks for wind turbine wake and power prediction in complex terrains

Accurate prediction of turbine wakes in complex terrains is of great importance for the design and operational optimization of wind farms. Terrain effects not only cause significant deflection of the turbine wake but also substantially alter its recovery rate. These complex interactions go beyond the fundamental assumptions of traditional models, making it challenging for existing models to accurately predict wake velocity deficits and additional turbulence intensity. In this study, a physics-data hybrid non-dimensional multiple operating conditions physics-informed neural network (ND-MOC-PINN) wake model is proposed. The results demonstrate that inconsistencies between physical constraints and supervised data reduce the prediction accuracy of the model, whereas nondimensionalizing both the physical equations and the supervised data can significantly improve its predictive performance. The proposed ND-MOC-PINN model is employed to predict the three-dimensional turbine wake under different terrain heights. The maximum relative errors of the predicted wake velocity and turbulence intensity are within 5% and 2%, respectively. By combining the ND-MOC-PINN model with a wake superposition model, the power performance of wind farms in complex terrain is further evaluated. The results show that the proposed model achieves significantly higher accuracy than the analytical wake model, with a maximum relative error of only 5.91% in single turbine power prediction. This study can provide reliable technical support for power forecasting, layout optimization, and coordinated control in complex terrain wind farms.