  This paper investigates the performance of a microgrid with droop-controlled
inverters in terms of the total power losses incurred in maintaining synchrony
under persistent small disturbances. The inverters are modeled with variable
frequencies and voltages under droop control. For small fluctuations from a
steady state, these transient power losses can be quantified by an input-output
H2 norm of a linear system subject to distributed disturbances. We evaluate
this H2 norm under the assumption of a dominantly inductive network with
identical inverters. The results indicate that while phase synchronization, in
accordance with previous findings, produces losses that scale with a network's
size but only weakly depend on its connectivity, the losses associated with the
voltage control will be larger in a highly connected network than in a loosely
connected one. The typically higher rate of convergence in a highly
interconnected network thus comes at a cost of higher losses associated with
the power flows used to reach the steady state.
