Nonlinear Dynamics Analysis of GFL and GFM Converters Based on Hamiltonian Theory

Converter dynamics for both grid-following (GFL) and grid-forming (GFM) strategies play a key role in the operation of modern power system with the increasing penetration of renewable generation. The stability behavior of both GFL and GFM converters are difficult to be understood by circuit modeling because of the high-order nonlinearity. Therefore, by establishing the Hamilton model of the converters, it is a feasible scheme to analyze the transient synchronous stability from the energy function of classical mechanics. In this paper, the physical interpretation of Hamiltonian theory is introduced first, and the mapping relationship from the Lagrange equation to the Hamiltonian equation is deduced based on Legendre transformation. Then, the Hamilton equations of GFL and GFM converters are derived respectively. The mapping relationship between the electrical variables and the generalized mechanics with the generalized coordinate system is analyzed. Then, combined with Hamiltonian theory, the static and dynamic characteristics of the two types of converters are revealed from the perspective of classical mechanics and energy function. Finally, the effect of system parameters on converter dynamic characteristics is illustrated by simulation cases.