Novel properties of heterogeneous delay in inverter-based cyber–physical microgrids under fully distributed control

Inverter-based microgrids will be vital components of future energy systems with large-scale integration of renewable energy resources. To cope with the low inertia problem induced by inverters, fully distributed control has been shown to effectively improve system stability owing to its fast response capability. Investigating the property of multiple delays in distributed control architecture is critical to guide its practical implementation in cyber–physical systems. Compared with power systems equipped with decentralized or centralized controllers, inverter-based cyber–physical microgrids under fully distributed control have a more complicated and heterogeneous delay environment. Existing, proven delay properties in centralized systems, such as the delay merge property that measurement and control delays of decentralized power system stabilizers can be merged for small-signal stability analysis, are not applicable to distributed systems To investigate the novel delay properties in distributed systems, we first propose a block-matrix-based cyber–physical model considering heterogeneous delays for inverter-based microgrids under fully distributed control. Then, we derive and prove the novel properties of heterogeneous delay in such systems. Finally, we perform numerical tests based on a real-world 7-bus islanded microgrid and a modified PG&E 69-bus microgrid under fully distributed frequency control. Our findings show that the impacts of measurement delay and control delay of one distributed controller on system stability are equivalent only if all distributed controllers are identical. Moreover, as the diversity of distributed controllers increases, the heterogeneous delay property becomes more significant.