# Optimal Design of Volt/VAR Control Rules of Inverters using Deep Learning

arXiv: https://arxiv.org/abs/2211.09557 · HTML: https://mlsanity.com/paper/2211.09557/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 41 references that are in the map.
- First posted on arXiv 17 Nov 2022.

## Builds on (most cited first, 14 of 14)

- [Stability Constrained Reinforcement Learning for Real-Time Voltage Control](https://mlsanity.com/paper/2109.14854/) (2021)
- [Reinforcement Learning for Optimal Primary Frequency Control: A Lyapunov Approach](https://mlsanity.com/paper/2009.05654/) (2020)
- [Learning to Optimize Power Distribution Grids using Sensitivity-Informed Deep Neural Networks](https://mlsanity.com/paper/2007.03728/) (2020)
- [Designing reactive power control rules for smart inverters using support vector machines](https://mlsanity.com/paper/1903.01016/) (2019)
- [Real-Time Local Volt/VAR Control Under External Disturbances with High PV Penetration](https://mlsanity.com/paper/1710.02551/) (2017)
- [Controlling Smart Inverters using Proxies: A Chance-Constrained DNN-based Approach](https://mlsanity.com/paper/2105.00429/) (2021)
- [Network-Cognizant Voltage Droop Control for Distribution Grids](https://mlsanity.com/paper/1702.02969/) (2017)
- [Voltage Regulation Algorithms for Multiphase Power Distribution Grids](https://mlsanity.com/paper/1508.06594/) (2015)
- [Reverse and Forward Engineering of Local Voltage Control in Distribution Networks](https://mlsanity.com/paper/1801.02015/) (2018)
- [Joint Grid Topology Reconfiguration and Design of Watt-VAR Curves for DERs](https://mlsanity.com/paper/1910.03020/) (2019)
- [Optimal Design of Volt/VAR Control Rules for Inverter-Interfaced Distributed Energy Resources](https://mlsanity.com/paper/2210.12805/) (2022)
- [Voltage Control Using Limited Communication](https://mlsanity.com/paper/1704.00749/) (2017)
- [Fast Inverter Control by Learning the OPF Mapping using Sensitivity-Informed Gaussian Processes](https://mlsanity.com/paper/2202.07500/) (2022)
- [Learning Local Volt/Var Controllers Towards Efficient Network Operation with Stability Guarantees](https://mlsanity.com/paper/2208.09117/) (2022)

## Built on by (most cited first, 2 of 2)

- [Scalable Optimal Design of Incremental Volt/VAR Control using Deep Neural Networks](https://mlsanity.com/paper/2301.01440/) (2023)
- [AC Power Flow Contingency Analysis Using a Single Deep Neural Network](https://mlsanity.com/paper/2609.30859/) (2026)

## Abstract (arXiv)

Distribution grids are challenged by rapid voltage fluctuations induced by variable power injections from distributed energy resources (DERs). To regulate voltage, the IEEE Standard 1547 recommends each DER inject reactive power according to piecewise-affine Volt/VAR control rules. Although the standard suggests a default shape, the rule can be customized per bus. This task of optimal rule design (ORD) is challenging as Volt/VAR rules introduce nonlinear dynamics, and lurk trade-offs between stability and steady-state voltage profiles. ORD is formulated as a mixed-integer nonlinear program (MINLP), but scales unfavorably with the problem size. Towards a more efficient solution, we reformulate ORD as a deep learning problem. The idea is to design a DNN that emulates Volt/VAR dynamics. The DNN takes grid scenarios as inputs, rule parameters as weights, and outputs equilibrium voltages. Optimal rule parameters can be found by training the DNN so its output approaches unity for various scenarios. The DNN is only used to optimize rules and is never employed in the field. While dealing with ORD, we also review and expand on stability conditions and convergence rates for Volt/VAR dynamics on single- and multi-phase feeders. Tests showcase the merit of DNN-based ORD by benchmarking it against its MINLP counterpart.