Sample-Based Conservative Bias Linear Power Flow Approximations

The power flow equations are central to many problems in power system planning, analysis, and control. However, their inherent non-linearity and non-convexity present substantial challenges during problem-solving processes, especially for optimization problems. Accordingly, linear approximations are commonly employed to streamline computations, although this can often entail compromises in accuracy and feasibility. This paper proposes an approach termed Conservative Bias Linear Approximations (CBLA) for addressing these limitations. By minimizing approximation errors across a specified operating range while incorporating conservativeness (over- or under-estimating quantities of interest), CBLA strikes a balance between accuracy and tractability by maintaining linear constraints. By allowing users to design loss functions tailored to the specific approximated function, the bias approximation approach significantly enhances approximation accuracy. We illustrate the effectiveness of our proposed approach through several test cases.

I. Introduction

The power flow equations play a central role in the operation and analysis of electrical power systems. These equations are essential for evaluating the behavior of power networks, making them key to various optimization problems such as resilient infrastructure planning [1]–[3], AC unit commitment [4], [5], and bilevel problems [6], [7]. However, the nonlinearity of the power flow equations induces non-convexities in these problems that pose significant computational challenges.