Convergence Analysis of the Kuramoto Model via Mean-Field Coupling for Micro-Generation Networks

Abstract

This work presents a convergence analysis focused on the decentralized synchronization of dynamical networks composed of Permanent Magnet Synchronous Generators (PMSGs). To achieve autonomous islanded operation, a mathematical control architecture based on the mean-field coupling of the Kuramoto model of coupled oscillators is implemented. Under this scalable approach, the phase and frequency dynamics of each micro-generator are governed strictly by their deviation from a global centroid, computed from the vector average of the active units, rather than relying on pairwise interactions. The system's stability and convergence under initial frequency mismatches are analytically examined and validated through a continuous digital twin developed in Simulink, comprising a four-node PMSG network. The integration of a Synchronous Reference Frame Phase-Locked Loop (SRF-dqPLL) allows each node to estimate its state exclusively from local voltage measurements. The simulation results demonstrate that the proposed adaptive-gain scheme guarantees cooperative convergence toward a global frequency consensus. It successfully minimizes the relative steady-state phase error through a smooth exponential decay without underdamped oscillations. This method not only ensures network resilience to node disconnection but also drastically reduces the computational complexity from quadratic  to linear, thereby validating its feasibility for real-time embedded systems.