We consider the problem of voltage regulation for a power distribution network where each inverter-equipped customer is connected sequentially with the sub-station at the head of the line. The substation dictates the desired voltage and transmits the reference voltage to each inverter in the distribution line. The inverter generates reactive power using our modified droop control law, which regulates the voltage level by influencing the power flow in the line, described by the DistFlow model. This paper provides conditions on the distribution line (the line impedances), the droop control law employed, and the nominal voltage level at the substation such that the each customer's voltage level are within a desired margin, when only the bound on the customers' overall power consumption is known. Thereby preserving the privacy of each customer's net power usage. We have also widened the choice of droop functions by only requiring them to be sector bounded. Simulation studies are provided to illustrate our results.