Real-Time Iteration Nonlinear Model Predictive Control for Offshore Wind Turbines: Coordinated Power Tracking with Embedded Electrical Constraints

Abstract

Offshore wind turbines equipped with full-power converters (FPCs) require coordinated control of power tracking, electrical safety, and mechanical load mitigation. Nonlinear model predictive control (NMPC) provides a systematic framework for this multi-objective problem; however, standard implementations solve the nonlinear program to full convergence at every control step, incurring computational times incompatible with the 10–100 ms control periods of commercial turbines. Existing formulations also commonly omit electrical hard constraints and rely on expensive lidar for wind speed feedforward. To address these limitations, this paper proposes a real-time iteration NMPC (RTI-NMPC) framework in which each control step performs a truncated real-time iteration, i.e., a single inexact SQP step realized by at most five interior-point (IPOPT) Newton iterations on the parametric NLP, combined with warm-start initialization and a solution-shift strategy. Torque command amplitude bounds and a DC-link voltage deadband are embedded as hard bounds on the predicted trajectory within the OCP, while the torque rate limit is enforced through a dual mechanism consisting of a quadratic penalty in the cost function and a ±15 kN·m/s hard saturation at the solver output. A second-order autoregressive predictor supplies wind speed feedforward over a 2 s horizon, and the power-tracking weight is adaptively adjusted according to the prediction confidence. Ablation experiments confirm that the warm-start solution-shift mechanism is decisive for closed-loop performance: removing it degrades the power-tracking RMSE by up to 370% under grid load-drop transients, collapsing to the level of the higher-iteration-budget standard NMPC, while the adaptive weighting is shown to be intrinsically coupled to the predictor and remains inactive under persistence forecasting. Comparative simulations under four operating scenarios show that the proposed controller achieves an average per-step computation time of 3.796–4.313 ms, approximately one order of magnitude faster than standard NMPC, thereby satisfying the real-time requirement within the present simulation setting. Under a grid load-drop scenario, the root-mean-square power-tracking error is reduced by 78.1% and 78.5% relative to a PI controller and standard NMPC, respectively; under model mismatch, the corresponding reductions are 18.0% and 17.5%. This advantage is scenario- and model mismatch-dependent and partly arises from reduced commitment to an imperfect internal prediction model, rather than the general superiority of truncated optimization over a more fully solved NMPC. The torque rate remains within ±15 kN·m/s in all scenarios. It is noted that the DC-link hard bounds apply to the predicted trajectory within the OCP, while the actual plant voltage is subject to the simplified model dynamics. The results demonstrate the computational feasibility and engineering potential of the electrically constrained, lidar-free RTI-NMPC for coordinated power-tracking and electrical constraint management of offshore FPC wind turbines.