Cyclic Regularization of Input Convex Neural Networks for Robust Voltage Regulation

Traditional centralized voltage regulation in distribution grids is typically formulated using the DistFlow model, which requires complete system knowledge, including topology and line parameters. However, due to limited observability, complete system information is often unavailable or unreliable at the grid edge. Previous works introduce data-driven approaches to overcome this problem, and input convex neural networks (ICNNs) have been applied to preserve convexity, enabling tractable optimization. However, discriminative learning models like ICNNs often overfit historical data, leading to poor generalization to unseen operating conditions. Overfitting may lead to biased control, particularly under shifting operating conditions caused by high penetrations of distributed energy resources (DERs). Challenges to regularizing such data-driven surrogates lie in the absence of a generative mapping from voltage states to control variables like power injections. To address these limitations, we propose a Regularized ICNN (RegICNN) incorporating a cyclic neural architecture for physics-based regularization. In RegICNN, we 1) enable a form of generative regularization to capture bidirectional mappings between voltage and power for unseen operation points; 2) further introduce a quadratic regularization term tailored to power flow physics; and 3) theoretically analyze the injection-voltage mapping under the DistFlow model, showing its convexity conditions and justifying the use of ICNNs as optimum data-driven surrogates for voltage control. Specifically, RegICNN learns a convex neural surrogate that approximates the injection-voltage mapping while preserving feasibility and global optimality for gradient-based control. Experiments on 3-, 12-, 116-, and 123-bus distribution feeders demonstrate that the RegICNN-based surrogate significantly improves modeling accuracy and control robustness when facing changes in operating points, making it a promising approach for data-driven voltage control in modern, dynamic distribution grids.