  The voltage received by each customer connected to a power distribution line
with local controllers (inverters) is regulated to be within a desired margin
through a class of slope-restricted controllers, known conventionally as
\emph{droop} controllers. We adapt the design of the droop controllers
according to the known bounds of the net power consumption of each customer in
each observation time window. A sufficient condition for voltage regulation is
provided for each time window, which guides the design of the droop
controllers, depending on the properties of the distribution line (line
impedances) and the upper bound of all the customers' power consumption during
each time window. The resulting adaptive scheme is verified on a benchmark
model of a European low-voltage network by the CIGRE task force.
