<p>With the continuous integration of advanced information and communication technologies into smart grids, the distribution network is undergoing a digital transformation, making the power distribution system increasingly complex. Edge computing shifts computation from the central control station to the distribution substations, thus enabling true distributed autonomy in power system operations. Taking an edge-computing-based digital substation as an example, this paper proposes a deep neural networks-based voltage regulation strategy for PV-rich distribution networks. However, executing tasks on resource-constrained edge devices faces several challenges, including data flow congestion, the inapplicability of conventional modelling and algorithm, and low computational efficiency. Therefore, we employ a unified weights neural network for Volt-Var control to achieve compression of the network parameters while still achieving differentiated action output. Furthermore, a carefully designed pipeline parallel computing structure is employed to simultaneously perform computations at different levels, further improving computational efficiency. The tested results show that, compared with existing methods, the proposed approach effectively mitigates voltage violations, improves storage efficiency and computational speed, and maintains robust performance under communication failures with partial observation, highlighting its resilience and potential for edge deployment.</p>