Analytical stability investigations for grid-forming inverters by Hamilton functions

Stability is an essential property of a dynamic system. While it is highly desirable to prove stability analytically, this is a challenging task, especially for non-linear systems. Although Lyapunov’s stability theory provides a comprehensive basis for systems with non-linearities, the actual application of the theory is unclear. This is due to the difficulty of finding a Lyapunov function with the required properties. This work presents an approach to deduce a candidate Lyapunov function from a Hamilton representation of the system, which is a special structure of the systems’s differential equations. The methodology is applied to two connected grid-forming inverters with droop controls and is successful for a simplified version of the system. Then, efforts are being made to extend the procedure by including the transmission line losses. However, this step increases the complexity of the investigation and poses challenges that prevent clear results.