  This paper investigates transient performance of inverter-based microgrids in
terms of the resistive power losses incurred in regulating frequency under
persistent stochastic disturbances. We model the inverters as second-order
oscillators and compare two algorithms for frequency regulation: the standard
frequency droop controller and a distributed proportional-integral (PI)
controller. The transient power losses can be quantified using an input-output
H2 norm. We show that the distributed PI-controller, which has previously been
proposed for secondary frequency control (the elimination of static errors),
also has the potential to significantly improve performance by reducing
transient power losses. This loss reduction is shown to be larger in a loosely
interconnected network than in a highly interconnected one, whereas losses do
not depend on connectivity if standard droop control is employed. Moreover, our
results indicate that there is an optimal tuning of the distributed
PI-controller for loss reduction. Overall, our results provide an additional
argument in favor of distributed algorithms for secondary frequency control in
microgrids.
