Adaptive economic wind turbine control

Abstract. Model predictive control (MPC) for wind turbines offers several interesting advantages over simpler techniques, as for example the direct optimization of a goal function, the inclusion of constraints, non-linear coupled dynamics, and wind preview (when available). To enable real-time execution, MPC uses a reduced order model (ROM) that approximates the dynamics of the controlled system using only a limited number of degrees of freedom. As a result, the accuracy of the ROM is often the main limit to the performance of MPC. To address this problem, an adaptive controller-internal model can reduce plant-model mismatches, potentially leading to improved performance.

This work proposes an adaptive economic nonlinear MPC (ENMPC) for wind turbines. The controller maximizes profit by optimally balancing fatigue damage cost with revenue due to power generation. The cyclic fatigue cost is formulated directly within the controller using the novel parametric online rainflow counting (PORFC) approach. PORFC provides a rigorous continuous expression of the discontinuous cyclic fatigue cost using time-varying parameters. Adaptivity is obtained by a controller-internal grey-box model that combines reduced order physical dynamics with data-driven correction terms. These are implemented via a neural network that is trained offline. Additionally, system state and disturbance estimators are included in the closed-loop controller.

The improvement in state predictions due to model adaptation is first assessed and compared with respect to the non-adapted baseline ROM in open loop. The performance of the adaptive ENMPC and the impact of a reduced plant-model mismatch is then assessed in closed loop for a reference multi-MW onshore wind turbine in a realistic simulation environment. Results show that the adaptive ENMPC yields higher economic profits at significantly lower pitch and torque travels, compared to the baseline non-adaptive ENMPC. While the enhanced closed-loop performance and economic gains of the proposed model adaptation are significant, they come at the cost of a slight increase in the computational burden of the controller.