In this paper, we consider an active distribution network (ADN) that performs primary voltage control using real-time demand response via a broadcast low-rate communication signal. The ADN also owns distributed electrical energy storage. We show that it is possible to use the same broadcast signal deployed for controlling loads to manage the distributed storage. To this end, we propose an appropriate control law to be embedded into the distributed electrical storage controllers that reacts to the defined broadcast signal in order to control both active and reactive power injections. We analyze, in particular, the case where electrical storage systems consist of supercapacitor arrays and where the ADN uses the grid explicit congestion notification (GECN) for real-time demand response that the authors have developed in a previous contribution. We estimate the energy reserve required for successfully performing voltage control depending on the characteristics of the network. The performance of the scheme is numerically evaluated on the IEEE 34-node test feeder. We further evaluate the effect, depending on the line characteristics, of reactive versus active power controlled injections. We find that without altering the demand-response signal, a suitably designed controller implemented in the storage devices enables them to successfully contribute to primary voltage control.