[Paper Review] Blade Effective Wind Speed Estimation: A Subspace Predictive Repetitive Estimator Approach

Yichao Liu, Atindriyo Kusumo Pamososuryo+3 more|arXiv (Cornell University)|Apr 7, 2021

Wind Energy Research and Development17 references4 citations

TL;DR

This paper proposes a Subspace Predictive Repetitive Estimator (SPRE) to estimate Blade Effective Wind Speed (BEWS) using blade load measurements, leveraging an azimuth-dependent cone coefficient to model wind-speed-to-load dynamics. The method successfully captures periodic wind variations and identifies wind shear and wake interference, enabling accurate BEWS estimation under complex inflow conditions including sheared and wake-impinged flows.

ABSTRACT

Modern wind turbine control algorithms typically utilize rotor effective wind speed measured from an anemometer on the turbine's nacelle. Unfortunately, the measured wind speed from such a single measurement point does not give a good representation of the effective wind speed over the blades, as it does not take the varying wind condition within the entire rotor area into account. As such, Blade Effective Wind Speed (BEWS) estimation can be seen as a more accurate alternative. This paper introduces a novel Subspace Predictive Repetitive Estimator (SPRE) approach to estimate the BEWS using blade load measurements. In detail, the azimuth-dependent cone coefficient is firstly formulated to describe the mapping between the out-of-plane blade root bending moment and the wind speed over blades. Then, the SPRE scheme, which is inspired by Subspace Predictive Repetitive Control (SPRC), is proposed to estimate the BEWS. Case studies exhibit the proposed method's effectiveness at predicting BEWS and identifying wind shear in varying wind speed conditions. Moreover, this novel technique enables complicated wind inflow conditions, where a rotor is impinged and overlapped by wake shed from an upstream turbine, to be estimated.

Motivation & Objective

• To address the limitation of nacelle anemometers in capturing spatially varying wind speeds across the rotor disk.
• To improve wind turbine control performance by estimating Blade Effective Wind Speed (BEWS) instead of relying on single-point hub measurements.
• To develop a method capable of identifying time-varying wind conditions, including wind shear and wake-induced velocity deficits.
• To enable real-time estimation of BEWS using only blade load measurements, avoiding the need for additional sensors.

Proposed method

• An azimuth-dependent cone coefficient is formulated to map out-of-plane blade root bending moments to effective wind speed over each blade.
• The SPRE algorithm is derived from Subspace Predictive Repetitive Control (SPRC), exploiting the periodic nature of wind inflow over rotating rotors.
• The estimator uses a recursive, receding-horizon optimization to minimize the error between measured and predicted blade loads.
• The BEWS is estimated per blade by solving a subspace identification problem using load measurements and the cone coefficient model.
• The Rotor Effective Wind Speed (REWS) is computed as the average of the estimated BEWS across all three blades.
• The method is validated using the NREL 5MW reference wind turbine model in FAST-Simulink co-simulation.

Experimental results

Research questions

• RQ1 Can BEWS be accurately estimated from blade load measurements alone, without direct wind speed sensors?
• RQ2 How well can the SPRE estimator capture periodic wind speed variations due to wind shear across the rotor disk?
• RQ3 Can the SPRE method detect and estimate the effects of wake-rotor overlap, such as velocity deficits and their propagation?
• RQ4 How does the SPRE estimator perform during abrupt changes in wind speed, such as stepwise increases?
• RQ5 Can the SPRE method distinguish between different inflow patterns, such as uniform sheared flow and non-uniform wake-impinged flow?

Key findings

• The SPRE estimator accurately tracks BEWS during stepwise changes in hub wind speed from 8 m/s to 15 m/s, with predicted blade root bending moments closely matching FAST simulation results.
• In sheared uniform wind conditions, the BEWS exhibits clear periodic fluctuations corresponding to azimuthal variations, which are successfully captured by the SPRE estimator.
• During wake-rotor overlap, the SPRE method detects velocity deficits over specific rotor sectors (e.g., 100° and 290° azimuth), indicating successful wake interference identification.
• Estimation errors are observed at the onset of wake impingement (350–450 s), but the error converges over time due to receding horizon optimization.
• The estimated REWS closely matches the reference value in both sheared and wake-impinged scenarios, confirming the robustness of the BEWS estimation.
• The SPRE method enables detection of wake propagation direction by observing the temporal evolution of BEWS fluctuations across azimuth angles.