Admittance matrix computation and stability analysis of droop controlled DC micro-grids with CPL

In this paper, an analytical method of computing the admittance matrix is introduced that facilitates the stability analysis of DC micro-grid systems, in presence of constant power loads (CPLs). Due to their nonlinear behaviour, CPLs can yield instability in DC micro-grids; an effect referred to as ’negative impedance instability’. The proposed method is particularly useful when a typical controller (droop control, voltage regulation) is designed to control the DC bus voltage of the micro-grid, as it allows the factorisation of the impedance matrix separating singular matrices. In doing so, the closed-loop stability proof can be more easily approached by isolating the singularities and, then employing straightforward linear algebra tools to arrive at the stability conditions. In order to validate the proposed approach, compute the admittance matrix and test the stability conditions, a DC micro-grid with n DC/DC power converters connected to a CPL is considered. Simulation results are also displayed to demonstrate the desired operation of the DC micro-grid control and design framework.