# Controlling Smart Inverters using Proxies: A Chance-Constrained DNN-based Approach

arXiv: https://arxiv.org/abs/2105.00429 · HTML: https://mlsanity.com/paper/2105.00429/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 32 references that are in the map.
- First posted on arXiv 2 May 2021.

## Builds on (most cited first, 19 of 19)

- [Learning Optimal Solutions for Extremely Fast AC Optimal Power Flow](https://mlsanity.com/paper/1910.01213/) (2019)
- [Optimal Power Flow Using Graph Neural Networks](https://mlsanity.com/paper/1910.09658/) (2019)
- [Learning Optimal Resource Allocations in Wireless Systems](https://mlsanity.com/paper/1807.08088/) (2018)
- [DeepOPF: Deep Neural Network for DC Optimal Power Flow](https://mlsanity.com/paper/1905.04479/) (2019)
- [Learning to Solve the AC-OPF using Sensitivity-Informed Deep Neural Networks](https://mlsanity.com/paper/2103.14779/) (2021)
- [Machine Learning for AC Optimal Power Flow](https://mlsanity.com/paper/1910.08842/) (2019)
- [Data-driven Optimal Power Flow: A Physics-Informed Machine Learning Approach](https://mlsanity.com/paper/2006.00544/) (2020)
- [Fast Calculation of Probabilistic Power Flow: A Model-based Deep Learning Approach](https://mlsanity.com/paper/1906.06017/) (2019)
- [Convex Relaxation of Optimal Power Flow, Part II: Exactness](https://mlsanity.com/paper/1405.0814/) (2014)
- [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)
- [PSSE Redux: Convex Relaxation, Decentralized, Robust, and Dynamic Approaches](https://mlsanity.com/paper/1708.03981/) (2017)
- [Data-driven Local Control Design using Optimization and Machine Learning Techniques](https://mlsanity.com/paper/1808.01009/) (2018)
- [Stochastic Reactive Power Management in Microgrids with Renewables](https://mlsanity.com/paper/1409.6758/) (2014)
- [Network-Cognizant Voltage Droop Control for Distribution Grids](https://mlsanity.com/paper/1702.02969/) (2017)
- [Two-Timescale Stochastic Dispatch of Smart Distribution Grids](https://mlsanity.com/paper/1608.05269/) (2016)
- [Ergodic Energy Management Leveraging Resource Variability in Distribution Grids](https://mlsanity.com/paper/1508.00654/) (2015)
- [Decentralized Stochastic Control of Distributed Energy Resources](https://mlsanity.com/paper/1611.00093/) (2016)
- [Optimal Real-Time Coordination of Energy Storage Units as a Voltage-Constrained Game](https://mlsanity.com/paper/1712.08554/) (2017)

## Built on by (most cited first, 5 of 5)

- [DNN-based Policies for Stochastic AC OPF](https://mlsanity.com/paper/2112.02441/) (2021)
- [Risk-Aware Learning for Scalable Voltage Optimization in Distribution Grids](https://mlsanity.com/paper/2110.01490/) (2021)
- [Optimal Design of Volt/VAR Control Rules of Inverters using Deep Learning](https://mlsanity.com/paper/2211.09557/) (2022)
- [Variational Quantum Eigensolver with Constraints (VQEC): Solving Constrained Optimization Problems via VQE](https://mlsanity.com/paper/2311.08502/) (2023)
- [A Data-Driven Real-Time Optimal Power Flow Algorithm Using Local Feedback](https://mlsanity.com/paper/2502.15306/) (2025)

## Abstract (arXiv)

Coordinating inverters at scale under uncertainty is the desideratum for integrating renewables in distribution grids. Unless load demands and solar generation are telemetered frequently, controlling inverters given approximate grid conditions or proxies thereof becomes a key specification. Although deep neural networks (DNNs) can learn optimal inverter schedules, guaranteeing feasibility is largely elusive. Rather than training DNNs to imitate already computed optimal power flow (OPF) solutions, this work integrates DNN-based inverter policies into the OPF. The proposed DNNs are trained through two OPF alternatives that confine voltage deviations on the average and as a convex restriction of chance constraints. The trained DNNs can be driven by partial, noisy, or proxy descriptors of the current grid conditions. This is important when OPF has to be solved for an unobservable feeder. DNN weights are trained via back-propagation and upon differentiating the AC power flow equations assuming the network model is known. Otherwise, a gradient-free variant is put forth. The latter is relevant when inverters are controlled by an aggregator having access only to a power flow solver or a digital twin of the feeder. Numerical tests compare the DNN-based inverter control schemes with the optimal inverter setpoints in terms of optimality and feasibility.