Sample-Based Piecewise Linear Power Flow Approximations Using Second-Order Sensitivities

TL;DR

This paper introduces a method for creating conservative piecewise linear approximations of power flow equations by selectively applying second-order sensitivity analysis to improve accuracy and computational efficiency in large-scale optimization.

Contribution

The paper presents a novel approach that uses second-order sensitivities to target nonlinearities, enhancing piecewise linear approximations of power flow equations while reducing computational complexity.

Findings

Selective targeting of nonlinear dimensions improves approximation accuracy.

Second-order sensitivity analysis effectively identifies key directions for linearization.

Method enhances efficiency in mixed-integer power system optimization.

Abstract

The inherent nonlinearity of the power flow equations poses significant challenges in accurately modeling power systems, particularly when employing linearized approximations. Although power flow linearizations provide computational efficiency, they can fail to fully capture nonlinear behavior across diverse operating conditions. To improve approximation accuracy, we propose conservative piecewise linear approximations (CPLA) of the power flow equations, which are designed to consistently over- or under-estimate the quantity of interest, ensuring conservative behavior in optimization. The flexibility provided by piecewise linear functions can yield improved accuracy relative to standard linear approximations. However, applying CPLA across all dimensions of the power flow equations could introduce significant computational complexity, especially for large-scale optimization problems. In this paper, we propose a strategy that selectively targets dimensions exhibiting significant nonlinearities. Using a second-order sensitivity analysis, we identify the directions where the power flow equations exhibit the most significant curvature and tailor the CPLAs to improve accuracy in these specific directions. This approach reduces the computational burden while maintaining high accuracy, making it particularly well-suited for mixed-integer programming problems involving the power flow equations.