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

## TL;DR

This paper investigates the empirical phenomenon that most line flow constraints in power system optimization are inactive at optimality, and introduces a two-step constraint screening method to identify and remove implied constraints, significantly reducing problem complexity.

## Contribution

It formalizes the concept of implied constraints in power system optimization and develops a novel two-step screening approach applicable over large load variation ranges.

## Key findings

- Significant reduction in constraints even with +/- 100% load variation.
- Improved computational efficiency in unit commitment problems.
- Validation on standard test cases demonstrating effectiveness.

## Abstract

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.