HIL Implementation of Proposed Fractional-Order Linear-Quadratic-Integral Controller for PV-Module Voltage Regulation to Enhance the Classical Perturb and Observe Algorithm

This paper addresses the limitations of conventional single-stage direct-control maximum power point tracking (MPPT) methods, such as the Perturb and Observe (P&O) algorithm. Fixed-step-size duty-cycle perturbations cause a trade-off between slow tracking with small oscillations and fast tracking with large oscillations, along with poor responsiveness to rapid weather variations and output voltage fluctuations. Two main contributions are presented. First, a fractional-order DC–DC boost converter (FOBC) is introduced, incorporating fractional-order dynamics to enhance system performance beyond improvements in control algorithms alone. Second, a novel indirect-control MPPT strategy based on a two-stage architecture is developed, where the P&O algorithm generates the optimal voltage reference and a fractional-order linear-quadratic-integral (FOLQI) controller—designed using a fractional-order small-signal model—regulates the PV module voltage to generate the FOBC duty cycle. Hardware-in-the-loop simulations confirm substantial performance improvements. The proposed FOLQI-based indirect-control approach with FOBC achieves a maximum MPPT efficiency of 99.26%. An alternative indirect method using a classical linear-quadratic-integral (LQI) controller with an integer-order boost converter reaches 98.38%, while the conventional direct-control P&O method achieves only 94.21%, demonstrating the superiority of the proposed fractional-order framework.