Economic nonlinear model predictive control of fatigue—Formulation and application to wind turbine control

Abstract

In this article, the estimation of fatigue is implemented in the cost function of a gradient‐based model predictive controller (MPC). This is a challenging problem, because calculating fatigue leads to a non‐standard and discontinuous cost function. Based on a brief previous publication, in the present work the method is derived, explained, and assessed in detail. The key enablers of the proposed method are a sequential implementation of MPC, the periodic substitution of discontinuous aspects of the cost function by linear functions, and the assumption of a sufficiently infrequent switching of this substitution. Fatigue cost gradients are obtained efficiently by automatic differentiation. The method is implemented in an economic nonlinear model predictive controller (ENMPC), which optimally balances revenue and fatigue cost. This novel formulation is applicable to a very wide range of domains, and it is demonstrated here on the control of a wind turbine. The proposed ENMPC is fully parameterized by physical and monetary variables, and outperforms a conventional ENMPC based on the literature. The method is assessed by considering various metrics, including frequency spectra, damage estimation, switching, and gradient dynamics, which together provide useful insight into its main characteristics and an initial assessment of its performance.

Economic nonlinear model predictive control of fatigue for a hybrid wind-battery generation system

“…This way, any possible increase/decrease in tower side-side stress oscillations due to control actions aimed for minimizing tower fore-aft stress is taken into account. The cost of cyclic fatigue damage for each of the projections for a given azimuth direction is obtained by first performing RFC analysis on the projected stress trajectory, then applying Goodman equation for mean stress correction, then obtaining damage cost of each stress cycle by the tower material S-N curve and the component cost, and then applying Miner-Palmgren algorithm to sum up the cost of individual cycles to finally obtain the total cost (refer [23] for detailed formulation). The cost of battery damage is obtained by first performing RFC analysis on SOC(t), then applying Woehler curve mapping to obtain equivalent damage per cycle, then summing up the damage over all the identified cycle, and finally multiplying it with w B to obtain the total cost (refer [10] for detailed formulation).…”