# Implied Constraint Satisfaction in Power System Optimization: The Impacts of Load Variations

arXiv: https://arxiv.org/abs/1904.01757 · HTML: https://mlsanity.com/paper/1904.01757/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Apr 2019.

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

- [Leveraging power grid topology in machine learning assisted optimal power flow](https://mlsanity.com/paper/2110.00306/) (2021)
- [Confidence-Aware Graph Neural Networks for Learning Reliability Assessment Commitments](https://mlsanity.com/paper/2211.15755/) (2022)
- [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)
- [Enabling Fast Unit Commitment Constraint Screening via Learning Cost Model](https://mlsanity.com/paper/2212.00483/) (2022)
- [Unit Commitment Predictor With a Performance Guarantee: A Support Vector Machine Classifier](https://mlsanity.com/paper/2310.08601/) (2023)

## Abstract (arXiv)

In many power system optimization problems, we observe that only a small fraction of the line flow constraints ever become active at the optimal solution, despite variations in the load profile and generation costs. This observation has far-reaching implications not only for power system optimization, but also for the practical long-term planning, operation, and control of the system. We formalize this empirical observation for problems involving the DC power flow equations. We use a two-step constraint screening approach to identify constraints whose satisfaction is implied by other constraints in the problem, and can therefore be removed from the problem. For the first screening step, we derive analytical bounds that quickly identify redundancies in the flow limits on parallel lines. The second screening step uses optimization-based constraint screening, where we solve a (relaxed) optimization problem for each constraint to identify redundancies. Different from existing methods, we specifically focus our approach on large ranges of load variation such that the results are valid for long periods of time, thus justifying the computational overhead required for the screening method. Numerical results for a wide variety of standard test cases show that even with load variations up to +/- 100% of nominal loading, we are able to eliminate a significant fraction of the flow constraints. This large reduction in constraints may enable a range of possible applications. As one illustrative example, we demonstrate the computational improvements for the unit commitment problem obtained as a result of the reduced number of constraints.