  This paper presents a non-linear stability analysis for dc-microgrids in
both, interconnected mode 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 numerically iii) give conditions for
global stability using a Lyapunov function iv) estimate the attraction region.
Previous works only address one of these aspects. Numeric calculations
performed in cvx and simulations results in Matlab complement the analysis and
demonstrate how to use this theoretical results in practical problems.
