With the proliferation of distributed energy resources (DERs), voltage regulation in active distribution networks (ADNs) 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 power of DERs are considered. Different types of asynchrony due to imperfect communication or other practical limits, such as random time delays and non-identical sampling/computation rates, are fitted into a unified analytic framework. The proposed asynchronous algorithm is then converted into a fixed-point problem by leveraging the operator splitting method, which leads to the convergence proof. Moreover, an online implementation method is introduced to make the controller adjustable to time-varying environments. Finally, numerical experiments are carried out on a rudimentary 8-bus and the IEEE-123 bus system to verify the effectiveness of the proposed method.

随着分布式能源（DER）的激增，有源配电网（ADN）中的电压调节一直面临着巨大的挑战。本文基于局部原对偶梯度算法推导了异步分布式电压控制策略，其中考虑了DER的有功功率和无功功率。由于通信不完善或其他实际限制而导致的不同类型的异步（例如随机时间延迟和不相同的采样/计算速率）被纳入统一的分析框架。然后，利用算子拆分方法将提出的异步算法转换为定点问题，从而证明了收敛性。此外，介绍了一种在线实现方法，以使控制器可适应时变环境。最后，