Piecewise Linearization of Quadratic Branch Flow Limits by Irregular Polygon

TL;DR

This paper introduces a geometrical, irregular polygon-based linearization method for quadratic thermal limits in transmission lines, avoiding optimization problems and improving linear OPF formulations.

Contribution

It proposes a novel geometrical linearization approach using irregular polygons, reducing complexity without optimization-based methods.

Findings

Fewer constraints needed for similar accuracy

Validated with test cases showing accurate results

Reduced computational time compared to existing methods

Abstract

This letter addresses the issue of linearization of quadratic thermal limits of transmission lines for linear OPF formulation. A new irregular polygon based linearization is proposed. The approach is purely based on geometrical concepts and does not introduce any optimization problem. Comparison of the number of constraints is given with different errors for different branch capabilities and systems. Test case analysis is also presented to validate the irregular polygon linearization strategy with optimal value and computational time results.