  Voltage collapse is a type of blackout-inducing dynamic instability that
occurs when power demand exceeds the maximum power that can be transferred
through a network. The traditional (preventive) approach to avoid voltage
collapse is based on ensuring that the network never reaches its maximum
capacity. However, such an approach leads to inefficient use of network
resources and does not account for unforeseen events. To overcome this
limitation, this paper seeks to initiate the study of voltage collapse
stabilization, i.e., the design of load controllers aimed at stabilizing the
point of voltage collapse. We formulate the problem of voltage stability for a
star direct current network as a dynamic problem where each load seeks to
achieve a constant power consumption by updating its conductance as the voltage
changes. We introduce a voltage collapse stabilization controller and show that
the high-voltage equilibrium is stabilized. More importantly, we are able to
achieve proportional load shedding under extreme loading conditions. We further
highlight the key features of our controller using numerical illustrations.
