Stochastic Model Predictive Control Based on Polynomial Chaos Expansion With Application to Wind Energy Conversion Systems

The wind energy conversion system (WECS) has a complex structure, and its state space model is highly nonlinear. Due to the random uncertainty of wind speed, it poses a huge challenge to achieve optimal control tasks and ensure the safe and stable operation of the system. Therefore, this article proposes a stochastic model predictive control strategy based on Polynomial Chaotic Expansion (PCE), which achieves the control tasks of MPPT and constant power regions in wind energy conversion systems. Firstly, a simple algorithm is proposed to obtain a set of basis functions that are suitable for the stochastic variable wind speed. Then, the obtained basis functions are used to propagate the uncertainty of the original uncertain differential equation of the wind energy conversion system through polynomial chaotic expansion. Combining the operating region and constraint conditions of the wind energy conversion system, the original stochastic uncertainty problem is transformed into a deterministic convex optimization problem. Using NREL 5MW wind turbine as the research object for simulation, the task of capturing maximum wind energy in MPPT area and tracking rated power points in constant power area was achieved. The experimental results show that the proposed control method can effectively improve the wind energy capture capability and achieve accurate tracking of output power to rated power.