  With the explosion of distributed energy resources (DERs), voltage regulation
in distribution networks has been facing a great challenge. This paper derives
an asynchronous distributed voltage control strategy based on the partial
primal-dual gradient algorithm, where both active and reactive controllable
power of DERs are considered. Different types of asynchrony due to imperfect
communication or practical limits, such as random time delays and non-identical
sampling/control rates, are fitted into a unified analytic framework. The
asynchronous algorithm is then converted into a fixed-point problem by
employing the operator splitting method, which leads to a convergence proof
with mild conditions. Moreover, an online implementation method is provided to
make the controller adjustable to time-varying environments. Finally, numerical
experiments are carried out on a rudimentary 8-bus system and the IEEE-123
distribution network to verify the effectiveness of the proposed method.
