Individual pitch control by convex economic model predictive control for wind turbine side-side tower load alleviation

Abstract

The wind turbine side-side tower motion is known to be lightly damped. One viable active damping solution is realized by deploying individual pitch control (IPC) such that counteracting blade forces are created to alleviate the tower fatigue loading caused by this motion. Existing IPC methods for side-side tower damping in the literature, such as linear quadratic regulator and lead-lag controller, cannot accommodate direct optimization and tradeoff tunings of the wind turbine economic performance. In this work, a novel side-side tower damping IPC strategy under a convex economic model predictive control (CEMPC) framework is therefore developed to address these challenges. The main idea of the framework lies in the variable transformation in power and energy terms to obtain linear dynamics and convex constraints, over which the economic performance of the wind turbine is maximized with a globally optimal solution in a receding horizon manner. The effectiveness of the proposed method is showcased in a high-fidelity simulation environment under both steady and turbulent wind cases. Lower fatigue damage on the side-side tower bending moment is attained with an acceptable level of pitch activities, negligible impact on the blade loads, and minor improvement on the power production.

Convex Economic Model Predictive Control for Blade Loads Mitigation on Wind Turbines

“…Nevertheless, it can also be thought of as the sum of multiple blade-effective quantities 6,27 T r,i , with i ∈ {1, 2, 3} for three-bladed wind turbines, which is especially beneficial for IPC formulations, as considered in this work. This accumulation of individual blade torques is expressed by the following relation…”

“…A possible solution to this challenge is by applying first-order Taylor expansion to the nonlinear quantities so as to obtain their Jacobian matrices, which are linear in their variables. One may also opt for variable transformation capable of rendering the dynamics and constraints suitable for convex optimization algorithms 24,27 . The latter approach is adopted in this study and discussed in the next section.…”

“…Accordingly, the change of the system's state from x to xt above necessitates the drivetrain dynamics (1) and the corresponding system constraints, namely (2), ( 3), (7), and ( 9), to be re-expressed in the new terms. Since such a dynamics reformulation has been treated in the previous CEMPC works 24,27 , only brief summary of its derivation is presented in Section 3.1. Moreover, despite being kept as outputs in (18), the rotor moments M tilt and Myaw are still functions of the nominal variables (17) such that their equivalence in power and energy variables is yet to be established.…”

“…Such a CEMPC concept was initially introduced with the goal of ensuring the smoothness of grid power delivery with an integrated local storage system 24 . Some research efforts followed afterward, extending the latter CEMPC framework to account for fore-aft 25,26 and side-side 27 tower fatigue loads mitigation. Of particular interest is the latter extension since an individual pitching strategy was favored over the more conventional approach by generator torque control in order to lessen the variation of the generated power as a by-product of the damping activities.…”

“…Yet, little to no attention is paid to the augmentation of a blade loads mitigation objective, exploiting further the IPC potential of the CEMPC framework. This paper thus aimed to fill the knowledge gap by incorporating an individual pitching mechanism for blade loads alleviation into the CEMPC framework by the authors 24,27 . In detail, this extension includes OoP blade root bending moments and rotor tilt and yaw moments as parts of the wind turbine model description.…”