Sampled-Data-Based Secondary Frequency Control for Fractional-Order Islanded Microgrid Subject to External Disturbance

The motivation for this paper is that most of the works on secondary frequency control are focused on conventional synchronous communication approaches. To extend this research, this paper investigates the sampled-data-based H∞ load frequency control (LFC) problem for fractional-order islanded microgrids under a multi-region communication scheme. In contrast to conventional synchronous communication approaches, the proposed scheme allows each regional sensor to operate asynchronously based on its own sampling interval. To model this multi-region communication mechanism, a unified sampling sequence is constructed by collecting all sampling instants from regional sensors. Accordingly, a closed-loop system model is established through the introduction of virtual state variables. Furthermore, a novel class of looped functionals is developed to fully exploit the sampling interval characteristics of each regional sensor. By employing inequality techniques and stability analysis, sufficient conditions are derived to achieve multi-region sampled-data-based H∞ LFC for fractional-order islanded microgrids. In addition, a co-design method is proposed to simultaneously determine the control gain and the maximum allowable sampling period. The simulations are conducted in MATLAB/Simulink (R2024a) and the LMI conditions are solved by using the LMI Toolbox and YALMIP. Finally, comprehensive simulations in MATLAB/Simulink validate the proposed scheme. For the two-region system, the method achieves a maximum sampling period of ζmax=0.106 s with an H∞ performance ratio of 2.87 (below γ=5) and settling times of 8.5 s and 9.2 s. Compared to synchronous sampling, it reduces the communication bandwidth by 50% for slower regions while maintaining comparable performance. For the single-region multi-rate case (0.104 s and 0.140 s sampling periods), the H∞ ratio is 3.12, also satisfying γ=5. The relationship between γ and ζmax is quantified: ζmax increases from 0.050 s to 0.106 s as γ increases from 3 to 5, confirming that relaxed disturbance attenuation allows larger sampling intervals.