Optimizing Parameters of the DC Power Flow

TL;DR

This paper introduces an optimization algorithm inspired by machine learning techniques to fine-tune parameters of the DC power flow model, significantly enhancing its accuracy for power system analysis.

Contribution

It proposes a gradient-based optimization method to determine the best coefficients and biases for the DC power flow approximation, improving accuracy over traditional methods.

Findings

Achieves several orders of magnitude accuracy improvement.

Effective for large power system models.

Applicable in real-time operational scenarios.

Abstract

Many power system operation and planning problems use the DC power flow approximation to address computational challenges from the nonlinearity of the AC power flow equations. The DC power flow simplifies the AC power flow equations to a linear form that relates active power flows to phase angle differences across branches, parameterized by coefficients based on the branches' susceptances. Inspired by techniques for training machine learning models, this paper proposes an algorithm that seeks optimal coefficient and bias parameters to improve the DC power flow approximation's accuracy. Specifically, the proposed algorithm selects the coefficient and bias parameter values that minimize the discrepancy, across a specified set of operational scenarios, between the power flows given by the DC approximation and the power flows from the AC equations. Gradient-based optimization methods like Broyden-Fletcher-Goldfarb-Shanno (BFGS), Limited-Memory BFGS (L-BFGS), and Truncated Newton Conjugate-Gradient (TNC) enable solution of the proposed algorithm for large systems. After an off-line training phase, the optimized parameters are used to improve the accuracy of the DC power flow during on-line computations. Numerical results show several orders of magnitude improvements in accuracy relative to a hot-start DC power flow approximation across a range of test cases.