A Lyapunov approach to control of microgrids with a network-preserved differential-algebraic model

We provide sufficient conditions for asymptotic stability and optimal resource allocation for a network-preserved microgrid model with active and reactive power loads. The model considers explicitly the presence of constant-power loads as well as the coupling between the phase angle and voltage dynamics. The analysis of the resulting nonlinear differential algebraic equation (DAE) system is conducted by leveraging incremental Lyapunov functions, definiteness of the load flow Jacobian and the implicit function theorem.