# Joint Chance Constraints in AC Optimal Power Flow: Improving Bounds through Learning

arXiv: https://arxiv.org/abs/1809.04153 · HTML: https://mlsanity.com/paper/1809.04153/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Sep 2018.

## Built on by (most cited first, 3 of 3)

- [Ensuring DNN Solution Feasibility for Optimization Problems with Convex Constraints and Its Application to DC Optimal Power Flow Problems](https://mlsanity.com/paper/2112.08091/) (2021)
- [Machine Learning for Fairness-Aware Load Shedding: A Real-Time Solution via Identifying Binding Constraints](https://mlsanity.com/paper/2407.18989/) (2024)
- [Calibrated uncertainty quantification for prosumer flexibility aggregation in ancillary service markets](https://mlsanity.com/paper/2601.14663/) (2026)

## Abstract (arXiv)

This paper considers distribution systems with a high penetration of distributed, renewable generation and addresses the problem of incorporating the associated uncertainty into the optimal operation of these networks. Joint chance constraints, which satisfy multiple constraints simultaneously with a prescribed probability, are one way to incorporate uncertainty across sets of constraints, leading to a chance-constrained optimal power flow problem. Departing from the computationally-heavy scenario-based approaches or approximations that transform the joint constraint into conservative deterministic constraints, this paper develops a scalable, data-driven approach which learns operational trends in a power network, eliminates zero-probability events (e.g., inactive constraints), and accurately and efficiently approximates bounds on the joint chance constraint iteratively. In particular, the proposed framework improves upon the classic methods based on the union bound (or Boole's inequality) by generating a much less conservative set of single chance constraints that also guarantees the satisfaction of the original joint constraint. The proposed framework is evaluated numerically using the IEEE 37-node test feeder, focusing on the problem of voltage regulation in distribution grids.