Coherency Algorithm for Grid-Forming Converters in Microgrids Considering Line Resistance Effects

The high R/X ratio of feeders and grid-following inverters (GFLs) integration alter the dynamic power flow in microgrids, thereby affecting the virtual power angle variations of grid-forming inverters (GFMs) during disturbances. Conventional coherency identification methods exhibit limited clustering accuracy in microgrid applications due to their neglect of feeder resistance and GFL impacts on GFM dynamics. To enhance GFM clustering accuracy in microgrids, this work proposes a novel coherency identification algorithm that incorporates both feeder impedance characteristics (high feeder R/X ratio) and GFL interactions. Based on feeder impedance parameters, topological connections, and the dynamic characteristics of GFMs and GFLs, the active power output variation of GFMs post-disturbance is analyzed. Further, by incorporating GFM control parameters and power-frequency characteristics, the frequency deviation trend of GFMs during transients is evaluated, followed by the construction of a GFM power-angle similarity matrix. The DBSCAN method is applied to this matrix to obtain coherent GFMs clusters. Simulations on two modified 10-machine systems demonstrate that the proposed method achieves accurate identification of coherent GFMs in scenarios with high R/X ratios and GFL injections.