[Paper Review] Prediction of wind turbines power with physics-informed neural networks and evidential uncertainty quantification

Alfonso Gijón, Ainhoa Pujana-Goitia+3 more|arXiv (Cornell University)|Jul 27, 2023

Energy Load and Power Forecasting4 citations

TL;DR

This paper proposes physics-informed neural networks (PINNs) with evidential uncertainty quantification to predict wind turbine power with high accuracy while respecting physical laws. The model integrates torque-power relationships and achieves a MAPE below 4% and MAE under 16 kW, with uncertainty estimates that align with actual errors and enable confidence intervals on the power curve.

ABSTRACT

The ever-growing use of wind energy makes necessary the optimization of turbine operations through pitch angle controllers and their maintenance with early fault detection. It is crucial to have accurate and robust models imitating the behavior of wind turbines, especially to predict the generated power as a function of the wind speed. Existing empirical and physics-based models have limitations in capturing the complex relations between the input variables and the power, aggravated by wind variability. Data-driven methods offer new opportunities to enhance wind turbine modeling of large datasets by improving accuracy and efficiency. In this study, we used physics-informed neural networks to reproduce historical data coming from 4 turbines in a wind farm, while imposing certain physical constraints to the model. The developed models for regression of the power, torque, and power coefficient as output variables showed great accuracy for both real data and physical equations governing the system. Lastly, introducing an efficient evidential layer provided uncertainty estimations of the predictions, proved to be consistent with the absolute error, and made possible the definition of a confidence interval in the power curve.

Motivation & Objective

• To develop accurate, robust models for wind turbine power prediction using real historical data from four turbines at La Haute Borne wind farm.
• To integrate physical constraints—specifically the torque-power relationship P = gTω—into neural network architectures to improve model fidelity and generalization.
• To quantify predictive uncertainty using an evidential layer, enabling confidence intervals and anomaly detection in turbine performance.
• To enable application of the model in real-time control and maintenance by ensuring differentiability and physical consistency.

Proposed method

• Employed physics-informed neural networks (PINNs) that jointly minimize data loss and physical law loss, enforcing the equation P = gTω through dedicated layers.
• Used a two-hidden-layer neural network to regress power from inputs (wind speed v, pitch angle β, rotor speed ω), with torque T as an additional input.
• Applied lambda layers for unit standardization and conversion, ensuring physical consistency between torque, angular velocity, and power in original units.
• Incorporated an evidential output layer to estimate epistemic uncertainty, modeling prediction confidence as a Dirichlet distribution.
• Trained the model on 70% of the data after discarding 30% of anomalous points identified during preprocessing.
• Validated the model using test sets and compared predictions against real data, manufacturer curves, and theoretical equations.

(a)

Experimental results

Research questions

• RQ1 Can physics-informed neural networks improve the accuracy of wind turbine power prediction while respecting fundamental physical laws?
• RQ2 How well can a data-driven model capture the nonlinear relationship between wind speed, pitch angle, and power output when empirical formulas fail?
• RQ3 Can evidential uncertainty quantification provide reliable confidence intervals that correlate with actual prediction errors?
• RQ4 To what extent does incorporating physical constraints enhance model robustness and generalization across turbine operating conditions?

Key findings

• The PINN model achieved a mean absolute percentage error (MAPE) of less than 4% and a mean absolute error (MAE) below 16 kW for power prediction across the test set.
• The predicted uncertainty from the evidential layer was consistent with the absolute error, enabling reliable confidence intervals on the power curve.
• The model accurately reproduced both real data and the physical equation P = gTω, demonstrating strong compliance with the underlying physics.
• The power curve predicted by the model closely matched the manufacturer’s specifications, especially in the range of 5–15 m/s wind speed.
• The model’s differentiability supports integration into optimal pitch angle control systems for maximizing power generation.
• Anomalous data points were effectively filtered during preprocessing, improving model reliability and performance.

(b)