Optimal α-Variable Model-Free Adaptive Barrier Function Fractional Order Nonlinear Sliding Mode Control for Four Area Interconnected Hybrid Power System With Nonlinearities

Abstract

This paper proposes an optimal α-variable model-free adaptive barrier-function fractional-order nonlinear sliding mode control (α(t)-MF-ABFFONSMC) for the load frequency control (LFC) problem of a four-area interconnected hybrid power system with boiler dynamics and physical constraints. The proposed α(t)-MF-ABFFONSMC is comprised of the ultra-local model (ULM)-based sliding mode disturbance observer (SMDO), proportional-differential (PD) controller, and adaptive barrier-function fractional-order nonlinear sliding mode control (ABFFONSMC). The ULM mechanism is utilized to re-formulate the complex four-area interconnected hybrid power system so as to reduce the controller’s design complexity, wherein SMDO is utilized to observe and eliminate the uncertain dynamics or lumped disturbance. Then, the SMDO based-iPD controller is designed. However, there always exists non-null estimation error under the SMDO method and the control performance cannot be ensured. Therefore, the ABFFONSMC is proposed and inserted into the SMDO-iPD controller to avoid the impact of estimation error and improve the control performance. In addition, an adaptive gain based on barrier function is formulated to approximate the upper bound of SMDO’s estimation error and thus decrease the undesired chattering on the sliding surface. Correspondingly, the α(t)-MF-ABFFONSMC is established. Moreover, the parameter optimizer based on the Marine Predator Algorithm (MPA) is proposed to tune the parameters of the proposed α(t)-MF-ABFFONSMC controller. Furthermore, using the Lyapunov theorem, the stability of α(t)-MF-ABFFONSMC via a closed-loop system is verified. To validate the performance of the proposed controller, the numerical simulation on a four-area interconnected hybrid power system is carried out in a Matlab/Simulink environment. The corresponding simulation results are presented to show the superiority and effectiveness of the proposed technique.