Error Analysis and Improvement Framework for Linear Power Flow Models Under Wide Operating Conditions

Abstract

Linear power flow models are typically derived through a Taylor expansion of specific state variable functions, serving as numerical approximations valid within a finite neighborhood of an initial operating point. With the large-scale integration of renewable energy sources (RES) into modern power systems, the volatility and operational range of physical quantities, such as bus power injections, have expanded significantly. Hence, the deviation between the system's actual operating point and the initial point is exacerbated, resulting in wide operating conditions. Under these conditions, the approximation errors of linear power flow models increase significantly. To address this challenge, this paper analyzes the accuracy limitations of linear power flow models under wide operating conditions and discusses a possible framework for improving the linearization accuracy in such scenarios. First, based on the derivation of linear power flow model with a unified state variable function of Taylor expansion, this paper analyzes the two major factors contributing to linearization errors under wide operating conditions. Next, the error performance of existing linear power flow models is evaluated across four representative dispatch applications, namely optimal power flow (OPF), unit commitment (UC), power flow calculations under extreme conditions, and chance-constrained OPF (CCOPF). Simulations are conducted on several IEEE standard test systems to explicitly quantify these linearization errors under wide operating conditions. Finally, an adaptive linear power flow modeling framework is proposed to improve linearization accuracy.