  Voltage control in power distribution networks has been greatly challenged by
the increasing penetration of volatile and intermittent devices. These devices
can also provide limited reactive power resources that can be used to regulate
the network-wide voltage. A decentralized voltage control strategy can be
designed by minimizing a quadratic voltage mismatch error objective using
gradient-projection (GP) updates. Coupled with the power network flow, the
local voltage can provide the instantaneous gradient information. This paper
aims to analyze the performance of this decentralized GP-based voltage control
design under two dynamic scenarios: i) the nodes perform the decentralized
update in an asynchronous fashion, and ii) the network operating condition is
time-varying. For the asynchronous voltage control, we improve the existing
convergence condition by recognizing that the voltage based gradient is always
up-to-date. By modeling the network dynamics using an autoregressive process
and considering time-varying resource constraints, we provide an error bound in
tracking the instantaneous optimal solution to the quadratic error objective.
This result can be extended to more general \textit{constrained dynamic
optimization} problems with smooth strongly convex objective functions under
stochastic processes that have bounded iterative changes. Extensive numerical
tests have been performed to demonstrate and validate our analytical results
for realistic power networks.
