Comparison of Physical, Gaussian Process, and Physics-Informed Gaussian Process Models for Wind Turbine Power Curve Estimation

Accurate modelling of power production in wind power systems is essential for optimizing their real-time operation and meeting technical or economic objectives. However, the precise modelling of wind turbine power output remains challenging, particularly when relying on conventional parametric models, which often struggle to capture complex or non-linear behaviors. This paper compares three modelling approaches to estimate the power produced by a real wind turbine (a Senvion MM82/2050 located in France): one parametric, based on analytical expressions of the power coefficient C_P(λ, β); another nonparametric, which uses Gaussian processes (GP) to probabilistically model the relationship between operating variables and the power generated; and a third semiparametric approach, which uses a physics-informed GP that explicitly incorporates the wind conversion model based on the power coefficient C_P(λ, β) within the Gaussian process as a mean function. Parametric models are efficient, interpretable, and useful when the underlying system model is known; however, they exhibit less predictive power in the face of complex behavior. In contrast, GPs offer greater flexibility, quantify uncertainty, and adapt to complex patterns in the data; however, their extrapolation outside the training range is limited and can lead to erroneous or even physically impossible predictions. The physics-informed GP integrates physical knowledge about the conversion of wind speed to power, improving the estimations outside the training range. Four model estimation procedures were performed using real data obtained from the SCADA system: the first one, retrieves the parameters of the power coefficient C_p from the physical model; the second estimates the hyperparameters of the GP; the third simultaneously estimates both the Gaussian process hyperparameters and the power coefficient parameters of the physics-informed GP; and the fourth computes only the hyperparameters of the physics-informed GP, keeping the optimal power coefficient parameters obtained in the first procedure. The fitting results were analyzed using the Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) as metrics, as well as the time required for fitting/training. The results show that the parametric approach has a lower predictive capacity than the GP and physics-informed GP. The latter has an RMSE that is slightly lower than that of the standard GP and makes more accurate predictions in regions with limited or no data availability. The results also show a trade-off between accuracy and computational efficiency, the physics-informed GP has a training time considerably longer than that of the other two models, nevertheless, it is a valuable tool when prediction robustness is a priority. Finally, the results highlight the need to include additional explanatory variables to better capture the observed dispersion and the effect of the high short-term variability of the 1-min SCADA measurements on model fitting.