Analysis of Fractional Resonant Controllers for Voltage-Controlled Applications

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Abstract
This paper investigates the application of fractional proportional–resonant controllers within the voltage control loop of grid-forming inverters. The use of such controllers introduces an additional degree of freedom, enabling greater flexibility in manipulating frequency trajectories. This flexibility can be harnessed to improve tracking error and enhance disturbance rejection, particularly in applications requiring precise voltage regulation. The paper conducts a conceptual stability analysis of ideal fractional proportional–resonant controllers using the Nyquist criterion. A tuning procedure based on robustness criteria for the proposed controller is also addressed. This tuning strategy is used to compare different controllers under the same conditions. In addition, a sensitivity analysis is provided, comparing the performance of fractional proportional–resonant controllers with traditional proportional–resonant controllers equipped with harmonic compensation. The controller’s formulation and performance are validated through simulations and tested with a 20 kVA inverter under high non-linear loads. Compared to classical control approaches, the fractional tuning parameter enhances tracking performance, reduces phase delay, and improves disturbance rejection. These improvements are achieved with a controller designed to minimise computational demands in terms of memory usage and execution time.

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