Abstract
The ideal distributed network composed of distributed generations (DGs) has unweighted and undirected interactions which omit the impact of the power grid structure and actual demand. Apparently, the coupling relationship between DGs, which is determined by line impedance, node voltage, and droop coefficient, is generally non-homogeneous. Motivated by this, this paper investigates the phase synchronization of an islanded network with large-scale DGs in a non-homogeneous condition. Furthermore, we explicitly deduce the critical coupling strength formula for different weighting cases via the synchronization condition. On this basis, three cases of Gaussian distribution, power-law distribution, and frequency-weighted distribution are analyzed. A synthetical analysis is also presented, which helps to identify the order parameter. Finally, this paper employs the numerical simulation methods to test the effectiveness of the critical coupling strength formula and the superiority over the power-law distribution.