A Unified Approach to Enforce Non-Negativity Constraint in Neural Network Approximation for Optimal Voltage Regulation

TL;DR

The paper tackles enforcing non-negativity constraints in ICNN-based voltage regulation for distribution grids with unknown PF models. It first shows that the common mirroring (duplication) strategy does not enhance representation power and can hinder training efficiency. The authors then propose a unified approach that embeds the non-negativity constraints directly into back-propagation via a weight-gating mechanism, ensuring convexity while maintaining gradient flow. Empirical results across multiple feeder configurations demonstrate improved training stability, faster convergence, and better voltage prediction compared to post-processing approaches. This work provides a robust, model-free pathway for data-driven voltage regulation under incomplete system information.

Abstract

Power system voltage regulation is crucial to maintain power quality while integrating intermittent renewable resources in distribution grids. However, the system model on the grid edge is often unknown, making it difficult to model physical equations for optimal control. Therefore, previous work proposes structured data-driven methods like input convex neural networks (ICNN) for "optimal" control without relying on a physical model. While ICNNs offer theoretical guarantees based on restrictive assumptions of non-negative neural network parameters, can one improve the approximation power with an extra step on negative duplication of inputs? We show that such added mirroring step fails to improve accuracy, as a linear combination of the original input and duplicated input is equivalent to a linear operation of ICNN's input without duplication. While this design can not improve performance, we propose a unified approach to embed the non-negativity constraint as a regularized optimization of the neural network, contrary to the existing methods, which added a loosely integrated second step for post-processing on parameter negation. Our integration directly ties back-propagation to simultaneously minimizing the approximation error while enforcing the convexity constraints. Numerical experiments validate the issues of the mirroring method and show that our integrated objective can avoid problems such as unstable training and non-convergence existing in other methods for optimal control. (preprint)

Figures (10)

• Figure 1: Overview of proposed smooth training in the training of convexified data-driven voltage regulation.
• Figure 2: The ICNN is convex from the input to the output because of the non-negative weights and the convex and non-decreasing activation functions.
• Figure 3: Convex functions can be represented as maximizing a group of affine functions for piecewise linear approximation.
• Figure 4: The smooth training via the weight gating design includes the gradient calculation of the non-negativity constraint in the training.
• Figure 5: With a similar number of parameters in the models, the basic ICNN and the ICNN with the duplication trick achieve similar training losses.

Theorems & Definitions (1)

• Proposition 1