Interval-aware optimal control of PMSG-based wind energy conversion systems via piecewise Chebyshev inclusion

Due to the ever-increasing demand for wind energy, control strategies must be developed that can efficiently extract energy while ensuring system stability. Nevertheless, with significant excursion uncertainties like parametric variation, unmodeled dynamics, and environmental variations jeopardizing control performance and system reliability, the Wind Energy Conversion System (WECS) is subject to significant interval uncertainties. In this paper, a new Piecewise Chebyshev Inclusion Method (PCIM) is proposed for optimal control of Permanent Magnet Synchronous Generator (PMSG)-based WECS with uncertainty awareness under bounded parameter uncertainties. The method reformulates the finite-horizon Linear Quadratic Regulator (LQR) optimal control problem with interval-valued system matrices into Linear Matrix Inequality (LMI), thus enabling robust closed-loop control design. The proposed approach significantly reduces overestimation in propagating intervals with 98.5% accuracy in state bounding while consuming 60% less computational time than the Monte Carlo Method (MCM) by harnessing piecewise Chebyshev polynomial approximations. The simulation results show that the PCIM controller exhibits a 15% faster settling time and 32% lower Integral Absolute Error (IAE) under ± 15% parameter uncertainties as compared to conventional interval methods, namely, Natural Interval Method (NIM), Centered Interval Method (CIM), Taylor Interval Method (TIM), and Monte Carlo Method (MCM). The LMI-based formulation is also found to be real-time feasible with 10.2 s of solution time for a 10-second horizon, hence scalable for high-order WECS models. The results demonstrate the efficiency and robustness of the proposed method and highlight the practical possibility for application in modern wind energy systems.