A Mathematical Framework for Simultaneous Voltage and Frequency Regulation in Distributed Generator (DG) Grid-Interfaced Systems

Abstract

Recent advancements in distributed generation (DG) systems interfaced with microgrids necessitate robust regulatory mechanisms to manage inherent power fluctuations, particularly from renewable sources like photovoltaics. These fluctuations can significantly impact the stability and efficiency of microgrids. This paper introduces a novel mathematical framework for simultaneous voltage and frequency regulation, aimed at addressing power quality and stability challenges in DG-grid interfaced systems. Utilizing a combination of algebraic topology and dynamical systems theory, we develop a model that incorporates an adaptive virtual frequency-impedance control loop. This mathematical approach allows for the analytical examination of the stability properties of the system and the design of control strategies that guarantee optimal operational thresholds. We extend the conventional droop control mechanisms with a rigorously defined Simultaneous Voltage and Frequency Correction Scheme (SVFCS), providing a theoretical underpinning that supports experimental observations. The efficacy of the proposed model is validated through numerical simulations that demonstrate adherence to the IEEE 519 standard, ensuring reduced harmonic distortion and enhanced system reliability. Our results highlight the potential for these mathematical methods to provide foundational insights into the control and optimization of microgrid operations.