Ultimate boundedness of voltage droop control with distributed secondary control loops

Conditions are derived for ultimate boundedness of voltage stabilization and reactive power balancing in electrical microgrids with voltage (E-Q) droop control and distributed secondary control loops. This paper shows that under a bound on the load reactive power demand, an ultimate bound set and its associated region of attraction can be computed for the deviation of the microgrid voltages with respect to their nominal values. The proposed approach employs a nonlinear model of the microgrid, departing from prevailing analyses of stability in microgrids with secondary controllers, typically based on linearization around equilibrium points. The obtained ultimate bounds serve as a performance measure guaranteeing tight voltage regulation under large variations of the load reactive power demand. We illustrate the results with examples of microgrids having different complexity, including a subnetwork of the CIGRE benchmark representing a medium-voltage rural distribution network.