Related papers: Sample-Based Piecewise Linear Power Flow Approxima…
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.…
The power flow equations are fundamental to power system planning, analysis, and control. However, the inherent non-linearity and non-convexity of these equations present formidable obstacles in problem-solving processes. To mitigate these…
We study the problem of deriving compressibility measures for Piecewise Linear Approximations (PLAs), i.e., error-bounded approximations of a set of two-dimensional increasing data points using a sequence of segments. Such approximations…
Linear approximations of the AC power flow equations are of great significance for the computational efficiency of large-scale optimal power flow (OPF) problems. Put differently, the feasibility of the obtained solution is essential for…
Effective power flow modeling critically affects the ability to efficiently solve large-scale grid optimization problems, especially those with topology-related decision variables. In this work, we put forth a generative modeling approach…
This paper presents novel methods to approximate the nonlinear AC optimal power flow (OPF) into tractable linear/quadratic programming (LP/QP) based OPF problems that can be used for power system planning and operation. We derive a linear…
Nonlinear power flow constraints render a variety of power system optimization problems computationally intractable. Emerging research shows, however, that the nonlinear AC power flow equations can be successfully modeled using Neural…
Linear active-power-only DC power flow approximations are pervasive in the planning and control of power systems. However, these approximations fail to capture reactive power and voltage magnitudes, both of which are necessary in many…
Mixed integer linear programming (MILP) has seen a sharp rise in use for engineering optimization applications in recent years. Even for initially non-linear problems, it is often the method of choice. Then, the non-linear functions have to…
This paper proposes a novel and simple linear model to capture line losses for use in linearized DC models, such as optimal power flow (DC-OPF) and security-constrained economic dispatch (SCED). The \textit{Line Loss Outer Approximation}…
To address computational challenges associated with power flow nonconvexities, significant research efforts over the last decade have developed convex relaxations and approximations of optimal power flow (OPF) problems. However, benefits…
A growing trend in the database and system communities is to augment conventional index structures, such as B+-trees, with machine learning (ML) models. Among these, error-bounded Piecewise Linear Approximation ($\epsilon$-PLA) has emerged…
Despite strong connections through shared application areas, research efforts on power market optimization (e.g., unit commitment) and power network optimization (e.g., optimal power flow) remain largely independent. A notable illustration…
Optimization problems that involve topology optimization in scenarios with large scale outages, such as post-disaster restoration or public safety power shutoff planning, are very challenging to solve. Using simple power flow…
Deep neural networks (DNNs) often produce overconfident out-of-distribution predictions, motivating Bayesian uncertainty quantification. The Linearized Laplace Approximation (LLA) achieves this by linearizing the DNN and applying Laplace…
DC power flow approximations are ubiquitous in the electricity industry. However, these linear approximations fail to capture important physical aspects of power flow, such as the reactive power and voltage magnitude, which are crucial in…
We allow for nonlinear effects in the likelihood analysis of peculiar velocities, and obtain ~35%-lower values for the cosmological density parameter and for the amplitude of mass-density fluctuations. The power spectrum in the linear…
This paper presents a quadratic approximation for the optimal power flow in power distributions systems. The proposed approach is based on a linearized load flow which is valid for power distribution systems including three-phase unbalanced…
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…
Research into cascading failures in power-transmission networks requires detailed data on the capacity of individual transmission lines. However, these data are often unavailable to researchers. As a result, line limits are often modelled…