A Novel Nonlinear Droop Function for Flexible Operation of Grid-Forming Inverters

This paper introduces the Exponent Droop Function (EDF), a nonlinear grid-forming (GFM) control paradigm that enhances the flexibility and performance of droop-based control in microgrids. Unlike conventional droop mechanisms, the EDF establishes a generalized framework that unifies multiple nonlinear droop relations, enabling adaptive shaping of droop characteristics through the adjustment of a single tuning parameter. This capability effectively mitigates the inherent limitations of traditional droop, particularly frequency degradation, while ensuring flexible power-sharing and improved dynamic performance. The proposed approach is rigorously validated through (i) detailed system modeling and small-signal stability analysis of EDF-controlled microgrids under variable load and droop conditions, (ii) dynamic assessments of distributed generators (DGs) supported by frequency-domain analysis, and (iii) extensive time-domain simulations encompassing seven representative operating scenarios. Comparative studies against state-of-the-art GFM controllers demonstrate that EDF achieves superior transient and steady-state performance with minimal control complexity, highlighting its potential as a practical and efficient next-generation GFM control strategy for microgrids.