Conservative Bias Linear Power Flow Approximations: Application to Unit Commitment

Abstract

Accurate modeling of power flow behavior is essential for a wide range of power system applications, yet the nonlinear and nonconvex structure of the underlying equations often limits their direct use in large-scale optimization problems. As a result, linear models are frequently adopted to improve computational tractability, though these simplifications can introduce excessive approximation error or lead to constraint violations. This paper presents a linear approximation framework, referred to as Conservative Bias Linear Approximations (CBLA), that systematically incorporates conservativeness into the approximation process. Rather than solely minimizing local linearization error, CBLA constructs linear constraints that bound the nonlinear functions of interest over a defined operating region while reducing overall approximation bias. The proposed approach maintains the simplicity of linear formulations and allows the approximation to be shaped through user-defined loss functions tailored to specific system quantities. Numerical studies demonstrate that CBLA provides more reliable and accurate approximations than conventional linearization techniques, and its integration into a unit commitment formulation results in improved feasibility and reduced operating costs.