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This two-part paper details a theory of solvability for the power flow equations in lossless power networks. In Part I, we derived a new formulation of the lossless power flow equations, which we term the fixed-point power flow. The model…

Optimization and Control · Mathematics 2017-09-21 John W. Simpson-Porco

Power flow in a low voltage direct current grid (LVDC) is a non-linear problem just as its counterpart ac. This paper demonstrates that, unlike in ac grids, convergence and uniqueness of the solution can be guaranteed in this type of grids.…

Optimization and Control · Mathematics 2017-02-06 Alejandro Garces

Different from the quasi-static network in the traditional power system, the dynamic network in the power-electronic-dominated power system should be considered due to rapid response of converters' controls. In this paper, a nonlinear…

Systems and Control · Electrical Eng. & Systems 2023-04-20 Rui Ma , Xiaowen Yang , Meng Zhan

In this study, electric power is processed using the logic operation method and the error correction algorithms to meet load demand. Electric power was treated as physically flow through the distribution network, which was governed by…

Systems and Control · Electrical Eng. & Systems 2021-08-25 Shota Inagaki , Shiu Mochiyama , Takashi Hikihara

We present Onsager formalism applied to random networks with arbitrary degree distribution. Using the well-known methods of non-equilibrium thermodynamics we identify thermodynamic forces and their conjugated flows induced in networks as a…

Disordered Systems and Neural Networks · Physics 2015-05-13 Agata Fronczak , Piotr Fronczak , Janusz A. Holyst

The degree distribution of many biological and technological networks has been described as a power-law distribution. While the degree distribution does not capture all aspects of a network, it has often been suggested that its functional…

Molecular Networks · Quantitative Biology 2007-05-23 Michael P. H. Stumpf , Piers J. Ingram

Optimal power flow problems (OPFs) are mathematical programs used to determine how to distribute power over networks subject to network operation constraints and the physics of power flows. In this work, we take the view of treating an OPF…

Optimization and Control · Mathematics 2020-03-06 Fengyu Zhou , James Anderson , Steven H. Low

This overview presents a collection of results from classical electrical network theory concerning properties of the network admittance matrix, and the relationship between electrical characteristics of the network and various mathematical…

History and Overview · Mathematics 2025-07-22 Anthony B. Morton

In this paper, a mathematical framework for the coupling of gas networks to electric grids is presented to describe in particular the transition from gas to power. The dynamics of the gas flow are given by the isentropic Euler equations,…

Numerical Analysis · Mathematics 2019-01-01 Eike Fokken , Simone Göttlich , Oliver Kolb

This paper discusses the modeling of inverters used in distributed energy resources in steady state. Modeling the interaction between distribution grids and inverter-based resources is crucial to understand the consequences for the…

Optimization and Control · Mathematics 2024-03-13 Rahmat Heidari , Frederik Geth

Understanding the interactions among nodes in a complex network is of great importance, since they disclose how these nodes are cooperatively supporting the functioning of the network. Scientists have developed numerous methods to uncover…

Physics and Society · Physics 2017-09-13 Chengwei Wang , Celso Grebogi , Murilo S. Baptista

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 two-part paper details a theory of solvability for the power flow equations in lossless power networks. In Part I, we derive a new formulation of the lossless power flow equations, which we term the fixed-point power flow. The model is…

Optimization and Control · Mathematics 2017-09-21 John W. Simpson-Porco

Synchronisation of parallel grid-forming inverters is crucial for stable operation of future power systems. This includes accurate and robust reactive power sharing under realistic operating conditions such as impedance mismatch and…

Systems and Control · Electrical Eng. & Systems 2026-03-25 E. D. Gomez Anccas , E. A. MacPherson , J. Tegeler , K. Röbert , M. Fischer , C. A. Hans , D. Schulz

Probabilistic power flow (PPF) analysis is critical to power system operation and planning. PPF aims at obtaining probabilistic descriptions of the state of the system with stochastic power injections (e.g., renewable power generation and…

Systems and Control · Electrical Eng. & Systems 2023-08-23 Kejun Chen , Yu Zhang

Increasing penetration of distributed energy resources complicate operations of electric power distribution systems by amplifying volatility of nodal power injections. On the other hand, these resources can provide additional control means…

Optimization and Control · Mathematics 2018-11-26 Robert Mieth , Yury Dvorkin

The knowledge of the topology of a wired network is often of fundamental importance. For instance, in the context of Power Line Communications (PLC) networks it is helpful to implement data routing strategies, while in power distribution…

Networking and Internet Architecture · Computer Science 2017-08-22 Federico Passerini , Andrea M. Tonello

Energy networks should strive for reliability. How can it be assessed, measured, and improved? What are the best trade-offs between investments and their worth? The flow-based framework for the reliability assessment of energy networks…

Systems and Control · Electrical Eng. & Systems 2021-08-03 Fabio Luiz Usberti , Celso Cavellucci , Christiano Lyra

The large-scale integration of Distributed Energy Resources (DERs) into the electric power system offers new opportunities to ensure stability. For example, Active Distribution Networks (ADNs) can be used in (sub-)transmission systems in…

Systems and Control · Electrical Eng. & Systems 2022-07-13 Jannik Zwartscholten , Christian Rehtanz

We consider the problem of exploiting the microgenerators dispersed in the power distribution network in order to provide distributed reactive power compensation for power losses minimization and voltage regulation. In the proposed…

Optimization and Control · Mathematics 2014-11-19 Saverio Bolognani , Guido Cavraro , Ruggero Carli , Sandro Zampieri