An Iteration-free Approach for Stability Analysis of DC Microgrids based on Lyapunov Functions

The stability of a DC microgrid is at the risk of being challenged by constant power loads (CPLs). As a key index of stability, the region of attraction (ROA) provides intuitive information on the degree of stability. In this paper, the adaptive Lyapunov function (ALF) method is proposed, which enables systematic estimation of the ROA without using iterative algorithms. After modeling the microgrid as a Lur’e system, the adaptive sector condition is derived. Then, based on the Lyapunov stability condition, the ROA estimation is formulated as an optimization problem and is further converted into a semi-definite programming (SDP) problem. Hence, the candidate Lyapunov function and the adaptive parameters are co-optimized to achieve the optimal estimation of ROA. Fast estimation of the ROA is achieved without iteratively solving the corresponding SDP. Moreover, the scalability of the ALF approach is ensured since the scale of the SDP increases linearly with the number of CPLs. Numerical validations of the proposed method are carried out on two DC microgrids with promising results.