Algebraic connectivity conditions for synchronization in low-inertia microgrids with adaptive droop-controlled inverters

Abstract It is shown that a network of inverters equipped with adaptive droop controllers can be cast as a nonuniform model of phase-coupled oscillators. Necessary and sufficient conditions are derived for the global asymptotic synchronization of these droop-controlled oscillators coupled through the parameters of a dynamic Kuramoto network. For an electrical network with general interconnections and line conditions, where the coupling weight of oscillators varies with the electrical parameters of the connection lines, it is shown that the gain can be scaled with an adaptive droop coefficient. The synchronization condition is found to depend on algebraic connectivity, which must be larger than a critical value. In contrast to grid-connected inverters, which assume a priori network operation in a quasi-stationary sinusoidal steady state, adaptive droop is a control strategy that globally stabilizes a desired sinusoidal steady state. Implementing this control law in model reference adaptive control numerically validates the analytical results and demonstrates system performance in primary and secondary frequency control.