Optimization-Based Exploration of the Feasible Power Flow Space for Rapid Data Collection

TL;DR

This paper systematically evaluates 40 nonlinear objective functions to explore the feasible power flow space efficiently, comparing their performance against an exhaustive sampling method using Hausdorff distance across multiple test cases.

Contribution

It introduces a comprehensive comparison of nonlinear objectives for power flow exploration and proposes a novel evaluation framework using Hausdorff distance.

Findings

Certain nonlinear objectives outperform others in exploring the power flow space.

The Hausdorff distance effectively measures the exploration quality of different objectives.

The methodology is validated on five standard power system test cases.

Abstract

This paper provides a systematic investigation into the various nonlinear objective functions which can be used to explore the feasible space associated with the optimal power flow problem. A total of 40 nonlinear objective functions are tested, and their results are compared to the data generated by a novel exhaustive rejection sampling routine. The Hausdorff distance, which is a min-max set dissimilarity metric, is then used to assess how well each nonlinear objective function performed (i.e., how well the tested objective functions were able to explore the non-convex power flow space). Exhaustive test results were collected from five PGLib test-cases and systematically analyzed.