Abstract

A methodology for enlarging the region of attraction (ROA) of a DC microgrid with constant power loads (CPLs) is proposed. The enlargement is achieved through the optimal design of a polynomial droop controller. The design of this nonlinear controller is done by solving a sum of squares (SOS) program. The proposed SOS program allows finding a Lyapunov function that serves to estimate the ROA. Therefore, the coefficients of the polynomial droop controller are optimized to maximize that estimate. Using the SOS approach, the estimate of the ROA exceeds the performance previously attained with alternative methods. It is illustrated how this nonlinear droop control approach is able to enlarge the ROA compared with a linear droop technique. Numerical simulations confirm that the proposed polynomial controller makes the system more robust against large disturbances and so enhances the transient stability.