Under the combined pressures from the global ecological degradation and the gradual depletion of fossil fuel resources, the exploration of renewable sources has emerged as a prominent global priority. Among all renewable sources, wind energy is expected to become the major power generation owing to its mature technology and abundant energy resources. Wind Energy Conversion Systems (WECS), as the core technology of wind power generation, directly determine the efficiency and economic viability of wind power facilities [1]-[2]. However, the randomness and uncertainty of wind speed pose significant challenges to the stable operation and power control of WECS.
The inherent uncertainties in WECS lead to inevitable fluctuations in output power, hampering the achievement of stable and reliable power control in practical applications. These uncertainties can be categorized into two distinct additive bounded disturbance sources [3]: the non-random mismatch between nonlinear WECS and its linearized model, and the random fluctuations caused by external wind speed disturbances. Traditional control strategies often struggle to effectively address these challenges, even when they can handle uncertainties, they are typically designed for a single operating point. Nevertheless, due to frequent fluctuations in wind speed, operating points in WECS often change, making it even more challenging for traditional control methods to maintain feasibility and stability.
To overcome these challenges, this study proposes a stable stochastic model predictive control (SMPC) strategy tailored for uncertain WECS systems. The aim of this strategy is to ensure stable and reliable power control for WECS across the whole operating region while maintaining the feasibility and stability of WECS even when operating points change. The implementation of the proposed SMPC strategy involves four key components. Firstly, a Luenberger observer is utilized to address the model-plant mismatch between the nonlinear WECS and its linearized model. Through real-time monitoring and feedback correction, this mismatch is compensated, ensuring that the control strategy remains aligned with the actual system state and enhancing its rapid response to wind speed variations. Secondly, a tube-based SMPC strategy is employed to handle random wind speed disturbances [4]. By setting reasonable output probability constraints, we enable the WECS system to maintain safe and stable operation even under the influence of random wind speed disturbances, achieving an effective balance between maximizing power output and minimizing turbine fatigue loads [5]. Additionally, the feasibility at any operating point is ensured by incorporating artificial steady targets as optimization variables, which allows for the scenarios where the optimized steady target deviates from the desired value. Moreover, the stability of WECS is guaranteed under changing operating points by extending the terminal constraint to include the optimized artificial steady target. Through penalizing the deviation between the artificial and the desired steady target, the output of WECS is urged to converge towards the desired value.
In summary, a stable SMPC strategy tailored for uncertain WECS systems is proposed in this study, achieving stable and reliable power control across the whole operating region while maintaining feasibility and stability even during changes in operating points. This strategy combines the advantages of the Luenberger observer and the tube-based control framework to effectively address uncertainties in WECS systems. By parameterizing the steady target and modifying the cost function and the terminal constraint, the feasibility and stability for WECS are ensured even under varying operating points. The findings of this study not only provide a new solution for the stable operation and power control of WECS but also lay a solid foundation for the further development and widespread application of wind energy technology. In the future, we expect that this stable SMPC strategy will be implemented in more wind farms, contributing significantly to the global efforts to address climate change and promote renewable energy development.

Wind energy conversion system,stochastic model predictive control,wind speed disturbance,changing operating points