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

Area of Science:

• Renewable Energy Systems
• Control Theory
• Robust Control

Background:

• Wind energy demand necessitates efficient control strategies for energy extraction and system stability.
• Wind Energy Conversion Systems (WECS) face significant interval uncertainties, impacting control performance and reliability.
• Existing methods struggle with accurate uncertainty propagation and computational efficiency.

Purpose of the Study:

• To propose a novel Piecewise Chebyshev Inclusion Method (PCIM) for robust optimal control of Permanent Magnet Synchronous Generator (PMSG)-based WECS.
• To address bounded parameter uncertainties in WECS control design.
• To enable uncertainty-aware control for enhanced system reliability and performance.

Main Methods:

• Reformulation of the finite-horizon Linear Quadratic Regulator (LQR) optimal control problem with interval-valued system matrices into Linear Matrix Inequality (LMI).
• Application of piecewise Chebyshev polynomial approximations to reduce interval overestimation.
• Development of a robust closed-loop control design framework.

Main Results:

• The PCIM achieved 98.5% accuracy in state bounding, significantly reducing overestimation.
• PCIM demonstrated a 60% reduction in computational time compared to the Monte Carlo Method (MCM).
• PCIM controller showed a 15% faster settling time and 32% lower Integral Absolute Error (IAE) under ±15% parameter uncertainties compared to conventional methods (NIM, CIM, TIM, MCM).
• The LMI-based formulation is real-time feasible (10.2s solution time for a 10s horizon), scalable for high-order WECS models.

Conclusions:

• The proposed PCIM offers an efficient and robust solution for optimal control of PMSG-based WECS under parameter uncertainties.
• PCIM significantly improves control performance, reducing settling time and error while enhancing computational efficiency.
• The method's real-time feasibility and scalability highlight its practical applicability in modern wind energy systems.