[Paper Review] A parametric model for wind turbine power curves incorporating environmental conditions

Yves‐Marie Saint‐Drenan, Romain Besseau+8 more|arXiv (Cornell University)|Sep 26, 2019

Wind Energy Research and Development46 references170 citations

TL;DR

The paper introduces an open-source parametric model to generate wind turbine power curves for any turbine under site-specific environmental conditions, and validates it against 91 manufacturer curves using Python, R, and MATLAB implementations.

ABSTRACT

A wind turbine's power curve relates its power production to the wind speed it experiences. The typical shape of a power curve is well known and has been studied extensively; however, the power curves of individual turbine models can vary widely from one another. This is due to both the technical features of the turbine (power density, cut-in and cut-out speeds, limits on rotational speed and aerodynamic efficiency), and environmental factors (turbulence intensity, air density, wind shear and wind veer). Data on individual power curves are often proprietary and only available through commercial databases. We therefore develop an open-source model which can generate the power curve of any turbine, adapted to the specific conditions of any site. This can employ one of six parametric models advanced in the literature, and accounts for the eleven variables mentioned above. The model is described, the impact of each technical and environmental feature is examined, and it is then validated against the manufacturer power curves of 91 turbine models. Versions of the model are made available in MATLAB, R and Python code for the community.

Motivation & Objective

• Provide an open-source, physically-based method to generate turbine power curves for any turbine using site-specific environmental inputs.
• Quantify the impact of environmental factors (turbulence intensity, air density, wind shear, wind veer) on power curves.
• Validate the model against manufacturer power curves and assess sensitivity of inputs to the resulting curves.
• Offer implementations in Python, R, and MATLAB to enable community use and reproducibility.

Proposed method

• Model power production in four operating regions and focus on the region II (between cut-in and rated wind speeds).
• Compute P_WT as P = 0.5 * rho * A_rotor * V_WS^3 * Cp(lambda, beta) with Cp modeled by empirical parametric forms from six literature sources.
• Determine tip-speed ratio lambda_opt that maximizes Cp(lambda, beta) with beta set to zero in region II; enforce rotor speed bounds (omega_min, omega_max) via lambda-based relation.
• Incorporate environmental effects by: (i) convolving the power curve with a Gaussian kernel to reflect turbulence intensity; (ii) explicitly varying air density; (iii) adjusting wind speed across rotor using rotor-equivalent wind speed U_eq to account for wind shear and wind veer.
• Summarize workflow in a seven-step process and provide open-source code in Python, R, and MATLAB for power-curve generation.

Experimental results

Research questions

• RQ1 How can a physically-based parametric model generate wind turbine power curves for any turbine given its design and operating limits?
• RQ2 What is the impact of environmental conditions (TI, air density, wind shear, veer) on the shape and magnitude of the power curve?
• RQ3 How well does the parametric model reproduce manufacturer power curves across a wide set of turbine models?
• RQ4 Which input parameters most influence the accuracy and uncertainty of the generated power curves?

Key findings

• The model can reproduce turbine power curves and was validated against 91 turbine models from manufacturer data.
• Turbulence intensity has a significant effect on the power curve, especially near the nominal wind speed.
• Air density effects are present across Region II but generally smaller than TI effects.
• Wind shear and wind veer have relatively modest impacts on the power curve, with veer having a somewhat larger effect than shear.
• The cut-off wind speed has the largest impact on the power curve, more than cut-in, and nominal power and rotor area are the most sensitive design parameters.
• The maximum Cp value (Cp,max) and its parameterisation significantly influence the resulting power curve, more so than the chosen Cp(lambda, beta) form.