Distributed Dynamic Event-Triggered Control for Voltage Recovery in Islanded Microgrids by Using Artificial Delays

This article tackles secondary voltage recovery problem in islanded microgrids with the aim of reducing communication frequency among distributed generation (DG) units, while maintaining desired performance and saving communication network workload. To pursue this objective, a distributed proportional-integral-derivative controller is first introduced, whose sampled-data implementation is enabled by leveraging the finite-difference approximation for the derivative action, which leads to a distributed proportional-integral-retarded (PIR) controller with a small enough sampling period $h>0$ . Then, the resulting fully distributed PIR control law is combined with a dynamic event-triggered mechanism (DETM), which embeds Zeno-freeness property and avoids the requirement of continuous transmission in triggering process. Thus, the communication burden is significantly mitigated and the waste of communication resources is avoided. By exploiting Lyapunov-Krasovkii method, we derive exponential stability conditions expressed as linear matrix inequalities (LMIs), whose solution allows evaluating the maximum sampling period and DETM parameters preserving the stability of the microgrid. A thorough numerical analysis, carried out on the standard IEEE 14-bus test system, confirms the theoretical derivation.