Stability Analysis of DC-Microgrids: A Gradient Formulation

This paper presents a nonlinear stability analysis for DC-microgrids in both, interconnected and island operation with primary control. The proposed analysis is based on the fact that the dynamical model of the grid is a gradient system generated by a strongly convex function. The stability analysis is thus reduced to a series of convex optimization problems. The proposed method allows to: (i) demonstrate the existence and uniqueness of the equilibrium, (ii) calculate this equilibrium, (iii) give conditions for global stability using a Lyapunov function and (iv) estimate the region of attraction. Previous works only address one of these aspects. Numeric calculations performed in CVX and simulation results in MATLAB complement the analysis and demonstrate how to use this theoretical results in practical problems.