Stability of a Distributed Generation Network Using the Kuramoto Models

We derive a Kuramoto-like equation from the Cardell-Ilic distributed electrical generation network and use the resulting model to simulate the phase stability and the synchronization of a small electrical grid. It is well-known that a major problem for distributed generation is the frequency stability. This is a non linear problem and proper models for analysis are sorely lacking. In our model nodes are arranged in a regular lattice, the strength of their couplings are randomly chosen and allowed to vary as square waves. Although the system undergoes several synchronization losses, nevertheless it is able to quickly resynchronize. Moreover, we show that the synchronization rising-time follows a power-law.