Lyapunov Method-Based Coherent Aggregation of Grid-Forming Converters for Transient Stability Equivalents

Paralleled grid-forming converters (GFMs) system suffers from transient instability issues while accurate model is complicated and unsuitable to give stability analysis. Existing aggregation method requires either extensive computation or linearized model assumption to realize coherent identification, which might not distinguish unstable units from stable clusters. In this paper, a two-step algorithm is proposed to realize coherent recognition for multi-GFMs system based on Lyapunov energy function: 1) unstable GFMs are distinguished from stable clusters based on Lyapunov’s function, 2) stable GFMs are further divided into different clusters using stored potential energy as a criterion. First, large-signal model considering transient interactions and virtual impedance-based fault ride through (VI-FRT) control is derived in transient stability time-scale. Then, Lyapunov energy function (LEF) is constructed for multi-GFMs system taking virtual damping coefficients and voltage dynamics into account. Compared with existing methods, the constructed LEF presents higher stability prediction accuracy and lower computational burden. Moreover, it is found that the relative potential energy among different GFMs can be adopted to identify coherent clusters, which is proved to be mathematically equivalent to coherency recognition using power angle deviation as the indicator. Finally, parameters aggregation is realized using the concept of center of inertia (COI). Based on the proposed method, equivalent reduced model has good accuracy in transient stability prediction compared with full-order model. Both numerical simulations and hardware-in-the-loop (HIL) experiments are provided to validate the feasibility of the proposed method.