Coupled memory sampled-data control for fractional stochastic wind energy conversion models

Abstract

This study aims to design a coupled memory sampled-data control (CMSDC) for fractional stochastic wind energy conversion systems (WECSs). Theoretically, this paper introduces a permanent magnet synchronous generator (PMSG)-based WECS, which is crucial in predicting and optimizing system behavior without physical implementation and also useful in analyzing the various operating conditions. Mathematically, the model comprises voltage equations, electromagnetic torque, mechanical dynamic equations, and wind turbine mechanical power (WTMP). Technically, WTMP has wind speed characteristics, which are random in nature, hence, this study analyzes the PMSG-based WECS model through stochastic differential equations (SDEs). Besides, this paper extends the SDEs into fractional SDEs (FSDEs) that help to capture the long-term memory patterns and dependencies by introducing Hurst parameters into the derivative of Brownian motion. Further, this study introduces the equivalent linear submodels for complex nonlinear stochastic PMSG-WECSs in the Takagi–Sugeno (T-S) sense. To monitor and ensure stable performance, the external controllers become necessary. In this regard, this study proposes a sampled-data control involving the coupling characteristics and memory effects. Furthermore, this study proposes sufficient stability conditions in the form of inequalities by utilizing the Lyapunov stability theory, which may act as a threshold property for the different sets of model parameters. Moreover, this study validates the performance of proposed control algorithms that outperform certain traditional control schemes, which include proportional integral (PI) and proportional–integral–derivative (PID) in terms of fractional stochastic PMSG-based WECSs.