Robust Data-Driven Linear Power Flow Model With Probability Constrained Worst-Case Errors

To limit the probability of unacceptable worst-case linearization errors that might yield risks for power system operations, this letter proposes a robust data-driven linear power flow (RD-LPF) model. It applies to both transmission and distribution systems and can achieve better robustness than the recent data-driven models. The key idea is to probabilistically constrain the worst-case errors through distributionally robust chance-constrained programming. It also allows guaranteeing the linearization accuracy for a chosen operating point. Comparison results with three recent LPF models demonstrate that the worst-case error of the RD-LPF model is significantly reduced over 2- to 70-fold while reducing the average error. A compromise between computational efficiency and accuracy can be achieved through different ambiguity sets and conversion methods.

I. Introduction

Constructing a linear power flow (LPF) model for a future system operating state is of great interest to system operators and useful for several system operation functions. LPF models can be generally categorized into two types whose main difference relies on whether the historical data are utilized. In the first type, AC power flow equations are linearized completely depending on mathematical tools [1] such as Taylor expansion [2]. In the second type, with the utilization of historical measurements, data-driven techniques such as partial least squares regression [1], [3], least squares regression [4], [5], support vector regression [6], Gaussian process regression [7], etc., are employed on top of or in place of the aforementioned linearization. These data-driven LPF (DD-LPF) models [1]–[7] have demonstrated improved average linearization accuracy as compared to the first-type model.