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In distribution systems, power injection variability due to growing penetrations of distributed energy resources (DERs) and dispatchable loads can lead to power quality issues such as severe voltage unbalance. To ensure the safe operation…

Optimization and Control · Mathematics 2019-12-05 Bowen Li , Bai Cui , Feng Qiu , Daniel K. Molzahn

Power grids vulnerability is a key issue in society. A component failure may trigger cascades of failures across the grid and lead to a large blackout. Complex network approaches have shown a direction to study some of the problems faced by…

Physics and Society · Physics 2013-04-22 Trivik Verma , Wendy Ellens , Robert E. Kooij

The rapid growth of large data center loads and inverter-based generation is increasing the stress on transmission networks, while expanding grid capacity at the required pace remains challenging. Power flow controllers (PFCs) that adjust…

Optimization and Control · Mathematics 2025-11-20 Eric Haag , Yuhao Chen , Giri Venkataramanan , Manish K. Singh

The large penetration of distributed generations impacts both the secondary low-voltage (LV) and the primary medium-voltage (MV) segments of the distribution network. Optimizing power flow calculations for the integrated MV/LV networks is…

Systems and Control · Electrical Eng. & Systems 2025-11-24 Abduljalil S. Aljadani , Firdous U. Nazir , Bikash C. Pal , Izudin Džafić , Rabih A. Jabr

This paper establishes a sufficient condition for guaranteeing power flow solvability in distribution grids with inverter-based resources (IBRs) operating under IEEE 1547 compliant Volt-Var control. While designed to improve voltage…

Systems and Control · Electrical Eng. & Systems 2026-04-21 Taha Saeed Khan , Hamidreza Nazaripouya

Load flow analysis is a fundamental technique used by electrical engineers to simulate and evaluate power system behavior under steady-state conditions. It enables efficient operation and control by determining how active and reactive power…

Systems and Control · Electrical Eng. & Systems 2025-07-15 Sampson E. Nwachukwu

This letter presents a novel non-iterative power flow solution for radial distribution systems. In the pursuit of a linear power flow solution that seamlessly integrates into other power system operations, an approximate solution via…

Systems and Control · Electrical Eng. & Systems 2024-10-28 Ibrahim Habiballah , Wasiu Sulaimon , Fahad Al-Ismail

This report serves as a technology description of a Julia-based re-implementation of the fixed-point current injection algorithm, available in PowerModelsDistribution.jl [1]. This report does not describe a novel method for solving…

Optimization and Control · Mathematics 2023-05-09 Frederik Geth , Sander Claeys , Rahmat Heidari

We propose an approach based on neural networks and the AC power flow equations to identify single- and double-line outages in a power grid using the information from phasor measurement unit sensors (PMUs) placed on only a subset of the…

Computational Engineering, Finance, and Science · Computer Science 2018-03-28 Ching-pei Lee , Stephen J. Wright

Achieving robust and scalable convergence for simulation of realistic power flow cases can be challenging. One specific issue relates to the disconnected solution space that is created by the use of piecewise-discontinuous models of power…

Signal Processing · Electrical Eng. & Systems 2018-11-07 Aayushya Agarwal , Amritanshu Pandey , Marko Jereminov , Larry Pileggi

We investigate the geometry of injection regions and its relationship to optimization of power flows in tree networks. The injection region is the set of all vectors of bus power injections that satisfy the network and operation…

Optimization and Control · Mathematics 2016-11-17 Javad Lavaei , David Tse , Baosen Zhang

Increasing shares of fluctuating renewable energy sources induce higher and higher power flow variability at the transmission level. The question arises as to what extent existing networks can absorb additional fluctuating power injection…

Systems and Control · Computer Science 2014-11-18 Markus Schläpfer , Pierluigi Mancarella

The load-flow equations are the main tool to operate and plan electrical networks. For transmission or distribution networks these equations can be simplified into a linear system involving the graph Laplacian and the power input vector. We…

Classical Physics · Physics 2019-05-15 J. G. Caputo , A. Knippel , N. Retiere

Recent development of techniques that improve the convergence properties of power flow simulation have been demonstrated to facilitate scaling to large system sizes (80k+ buses). However, the problem remains to reliably identify cases that…

Signal Processing · Electrical Eng. & Systems 2019-12-10 Marko Jereminov , David M. Bromberg , Amritanshu Pandey , Martin R. Wagner , Larry Pileggi

First we present an approach to formulate unbalanced three-phase power flow problems for general networks that explicitly separates device models and network models. A device model consists of (i) an internal model and (ii) a conversion…

Optimization and Control · Mathematics 2022-07-27 Steven H. Low

Understanding the feasible power flow region is of central importance to power system analysis. In this paper, we propose a geometric view of the power system loadability problem. By using rectangular coordinates for complex voltages, we…

Optimization and Control · Mathematics 2018-07-31 Y. Weng , R. Rajagopal , B. Zhang

The increasing penetration of renewables in distribution networks calls for faster and more advanced voltage regulation strategies. A promising approach is to formulate the problem as an optimization problem, where the optimal reactive…

Optimization and Control · Mathematics 2020-02-24 Yize Chen , Yuanyuan Shi , Baosen Zhang

In this paper, we propose a graph neural network architecture to solve the AC power flow problem under realistic constraints. To ensure a safe and resilient operation of distribution grids, AC power flow calculations are the means of choice…

Machine Learning · Computer Science 2023-08-31 Luis Böttcher , Hinrikus Wolf , Bastian Jung , Philipp Lutat , Marc Trageser , Oliver Pohl , Andreas Ulbig , Martin Grohe

In this paper, we develop a data-driven voltage regulation framework for distributed energy resources (DERs) in a balanced radial power distribution system. The objective is to determine optimal DER power injections that minimize the…

Optimization and Control · Mathematics 2020-06-09 Hanchen Xu , Alejandro D. Domínguez-García , Venugopal V. Veeravalli , Peter W. Sauer

This paper address the problem of voltage regulation in power distribution networks with deep penetration of distributed energy resources (DERs) without any explicit communication between the buses in the network. We cast the problem as an…

Optimization and Control · Mathematics 2013-08-02 Baosen Zhang , Alejandro D. Domiguez-Garcia , David Tse