SOS programming-based large-signal stability analysis and controller synthesis for DC microgrid using invariant sets

Nowadays, DC microgrids are prevalent around the world, whose stability analysis is crucial for their stable operations. The small-signal stability analysis of DC microgrids now is reasonably mature. In contrast, there still exists a lot of difficulties in large-signal stability analysis. LaSalle's invariant set theorem, which is an extension of Lyapunov's theorem with less conservatism, provides a general method for dealing with this type of problem. However, the construction of a suitable invariant set function has few universal solutions, which restricts its further application. Besides, large-signal stability-oriented controller synthesis is strongly desired for enhancing the stability. In this paper, a sum-of-squares (SOS) programming method is proposed to find proper invariant set function for large-signal stability analysis of DC microgrid considering the control loop. Then the region of attraction (ROA) of system is estimated by level set of invariant set function. The parameters of control loop are also optimized to maximize the ROA estimation by using SOS programming. Superiority of SOS programming-based method is shown by comparison of the ROA estimated by the proposed method and those obtained by other methods. In addition, comparison with real ROA drawn by Monte Carlo method has validated the accuracy of estimated ROA and confirmed that the system with optimized control loop can tolerate larger disturbances, indicating the enhancement of large-signal stability.