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Deregulated energy markets, demand forecasting, and the continuously increasing share of renewable energy sources call---among others---for a structured consideration of uncertainties in optimal power flow problems. The main challenge is to…

Optimization and Control · Mathematics 2018-08-24 Tillmann Mühlpfordt , Timm Faulwasser , Veit Hagenmeyer

This paper proposes a graph computation based sequential power flow calculation method for Line Commutated Converter (LCC) based large-scale AC/DC systems to achieve a high computing performance. Based on the graph theory, the complex AC/DC…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-02-28 Wei Feng , Jingjin Wu , Chen Yuan , Guangyi Liu , Renchang Dai , Qingxin Shi , Fangxing Li

Force-based multiphysics coupling methods have become popular since they provide a simple and efficient coupling mechanism, avoiding the difficulties in formulating and implementing a consistent coupling energy. They are also the only known…

Numerical Analysis · Mathematics 2011-04-12 Mitchell Luskin , Christoph Ortner

The common linear optimal power flow (LOPF) formulation that underlies most transmission expansion planning (TEP) formulations uses bus voltage angles as auxiliary optimization variables to describe Kirchhoff's voltage law. As well as…

Systems and Control · Electrical Eng. & Systems 2020-09-25 Fabian Neumann , Tom Brown

Due to the energy transition, today's electrical networks include synchronous machines and inverter-based resources interfacing renewable energies such as wind turbines, solar panels, and Battery Energy Storage Systems to the grid. In such…

Systems and Control · Electrical Eng. & Systems 2024-02-08 Pamela Zoghby , Bogdan Marinescu , Antoine Rosse , Gregoire Prime

Chance-constrained optimization has emerged as a promising framework for managing uncertainties in power systems. This work advances its application to the DC Optimal Power Flow (DC-OPF) model, developing a novel approach to uncertainty…

Systems and Control · Electrical Eng. & Systems 2026-03-18 Tianyang Yi , D. Adrian Maldonado , Anirudh Subramanyam

The method of flow tracing follows the power flow from net-generating sources through the network to the net-consuming sinks, which allows to assign the usage of the underlying transmission infrastructure to the system participants. This…

Physics and Society · Physics 2017-11-09 Jonas Hörsch , Mirko Schäfer , Sarah Becker , Stefan Schramm , Martin Greiner

Voltage deviations occur frequently in power systems. If the violation at some buses falls outside the prescribed range, it will be necessary to correct the problem by controlling reactive power resources. In this paper, an optimal…

Systems and Control · Computer Science 2017-08-28 Ali Dehghan Banadaki , Ali Feliachi

The increasing penetration of renewable energy along with the variations of the loads bring large uncertainties in the power system states that are threatening the security of power system planning and operation. Facing these challenges,…

Systems and Control · Electrical Eng. & Systems 2020-04-14 Yijun Xu , Kiran Karra , Lamine Mili , Mert Korkali , Xiao Chen , Zhixiong Hu

The Alternating Current Optimal Power Flow (ACOPF) problem is a core task in power system operations, aimed at determining cost-effective generation dispatch while satisfying physical and operational constraints. However, conventional ACOPF…

Optimization and Control · Mathematics 2026-05-15 Vincenzo Di Vito , Kaarthik Sundar , Ferdinando Fioretto , Deepjyoti Deka

The power flow equations model the steady-state relationship between the power injections and voltage phasors in an electric power system. By separating the real and imaginary components of the voltage phasors, the power flow equations can…

Optimization and Control · Mathematics 2016-03-21 Daniel K. Molzahn , Matthew Niemerg , Dhagash Mehta , Jonathan D. Hauenstein

Conventional AC Power Flow (ACPF) solvers like Newton-Raphson (NR) face significant computational and convergence challenges in modern, large-scale power systems. This paper proposes a novel, two-stage hybrid method that integrates a…

Systems and Control · Electrical Eng. & Systems 2025-11-03 Mohamed Shamseldein

With increasing smart grid direct current (DC) deployments in distribution feeders, microgrids, buildings, and high-voltage transmission, there is a need for better understanding the landscape of power flow (PF) solutions as well as for…

Optimization and Control · Mathematics 2019-07-11 Sina Taheri , Vassilis Kekatos

Generative models have emerged as a powerful paradigm for solving physics systems and modeling complex spatiotemporal dynamics. However, achieving high physical accuracy without incurring high computational cost remains a fundamental…

Machine Learning · Computer Science 2026-05-27 Jiahe Huang , Sihan Xu , Sharvaree Vadgama , Rose Yu

The security-constrained optimal power flow (SCOPF) is fundamental in power systems and connects the automatic primary response (APR) of synchronized generators with the short-term schedule. Every day, the SCOPF problem is repeatedly solved…

Optimization and Control · Mathematics 2020-07-15 Alexandre Velloso , Pascal Van Hentenryck

This note outlines the exact solution to the power flow problem in AC electrical networks under the assumption of 'flat' or uniform voltage profiles. This solution generalises the common 'DC power flow' approach to electrical network…

History and Overview · Mathematics 2022-07-26 Anthony B. Morton

Power systems are getting more complex than ever and are consequently operating close to their limit of stability. Moreover, with the increasing demand of renewable wind generation, and the requirement to maintain a secure power system, the…

Systems and Control · Electrical Eng. & Systems 2022-06-13 Umair Shahzad

The ever increasing penetration of plug-in hybrid electric vehicles in distribution systems has triggered the need for a more accurate and at the same time fast solution to probabilistic distribution power flow problem. In this paper a…

Signal Processing · Electrical Eng. & Systems 2017-10-31 Mohammadhadi Rouhani , Mohammad Mohammadi

The solution of potential-driven steady-state flow in large networks is a task which manifests in various engineering applications, such as transport of natural gas or water through pipeline networks. The resultant system of nonlinear…

Numerical Analysis · Mathematics 2025-01-23 Shriram Srinivasan , Kaarthik Sundar

The bus admittance matrix is central to many power system simulation algorithms, but the link between problem size and computation time (i.e., the time complexity) using modern sparse solvers is not fully understood. It has recently been…

Systems and Control · Electrical Eng. & Systems 2023-11-21 Matthew Deakin , Davis Montenegro