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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

Variations of loading level and changes in system topological property may cause the operating point of an electric power systems to move gradually towards the verge of its transmission capability, which can lead to catastrophic outcomes…

Systems and Control · Computer Science 2019-04-19 Bai Cui , Xu Andy Sun

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

The growing integration of inverter-based resources (IBRs) into modern power systems poses significant challenges for maintaining reliable operation under dynamic and constrained conditions. This paper focuses on the power tracking problem…

Systems and Control · Electrical Eng. & Systems 2025-03-17 Zixiao Ma , Baosen Zhang

Inverter-based resources (IBRs) are becoming increasingly prevalent in power systems. Due to the inherently low inertia of inverters, there is a heightened risk of disruptive voltage oscillations. A particular challenge in the operation of…

Systems and Control · Electrical Eng. & Systems 2023-11-21 Zixiao Ma , Baosen Zhang

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

Certifying power flow solvability is important for reliable power system operations under volatile operating conditions, but solving power flow equations repeatedly can be costly and may encounter convergence issues. In this paper, we…

Optimization and Control · Mathematics 2026-05-26 Puskar Neupane , Bai Cui

In complex power systems, nonlinear load flow equations have multiple solutions. Under typical load conditions only one solution is stable and corresponds to a normal operating point, whereas the second solution is not stable and is never…

Chaotic Dynamics · Physics 2014-04-29 Hung D. Nguyen , Konstantin S. Turitsyn

This paper proposes a necessary condition for power flow insolvability in power distribution systems with distributed generators (DGs). We show that the proposed necessary condition indicates the impending singularity of the Jacobian matrix…

Optimization and Control · Mathematics 2020-12-16 Zhaoyu Wang , Bai Cui , Jianhui Wang

Time-varying renewable energy generation can result in serious under-/over-voltage conditions in future distribution grids. Augmenting conventional utility-owned voltage regulating equipment with the reactive power capabilities of…

Systems and Control · Computer Science 2015-08-27 Vassilis Kekatos , Liang Zhang , Georgios B. Giannakis , Ross Baldick

The IEEE 1547 Standard for the interconnection of distributed energy resources (DERs) to distribution grids provisions that smart inverters could be implementing Volt/VAR control rules among other options. Such rules enable DERs to respond…

Systems and Control · Electrical Eng. & Systems 2023-05-24 Ilgiz Murzakhanov , Sarthak Gupta , Spyros Chatzivasileiadis , Vassilis Kekatos

In this two-part paper we develop a unifying framework for the analysis of the feasibility of the power flow equations for DC power grids with constant-power loads. In Part I of this paper we present a detailed introduction to the problem…

Systems and Control · Electrical Eng. & Systems 2020-11-19 Mark Jeeninga , Claudio De Persis , Arjan van der Schaft

The AC power flow equations describe the steady-state behavior of the power grid. While many algorithms have been developed to compute solutions to the power flow equations, few theoretical results are available characterizing when such…

Optimization and Control · Mathematics 2017-06-19 Krishnamurthy Dvijotham , Enrique Mallada , John W Simpson-Porco

Modern power systems face a grand challenge in grid management due to increased electricity demand, imminent disturbances, and uncertainties associated with renewable generation, which can compromise grid security. The security assessment…

Numerical Analysis · Mathematics 2021-03-02 Mazhar Ali , Elena Gryazina , Anatoly Dymarsky , Petr Vorobev

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

Volt-VAR and Volt-Watt functionality in photovoltaic (PV) smart inverters provide mechanisms to ensure system voltage magnitudes and power factors remain within acceptable limits. However, these control functions can become unstable,…

Systems and Control · Electrical Eng. & Systems 2023-01-02 Daniel Arnold , Shammya Saha , Sy-Toan Ngo , Ciaran Roberts , Anna Scaglione , Nathan Johnson , Sean Peisert , David Pinney

The fault characteristics of inverter-based resources (IBRs) are different from conventional synchronous generators. The fault response of IBRs is non-linear due to saturation states and mainly determined by fault ride through (FRT)…

Systems and Control · Electrical Eng. & Systems 2025-04-15 Zahid Javid , Firdous Ul Nazir , Wentao Zhu , Diptargha Chakravorty , Ahmed Aboushady , Mohamed Galeela

High levels of penetration of distributed generation and aggressive reactive power compensation with modern power electronics may result in the reversal of active and reactive power flows in future distribution grids. The voltage stability…

Chaotic Dynamics · Physics 2014-07-09 Hung D. Nguyen , Konstantin Turitsyn

This paper considers the problem of voltage regulation in distribution networks. The primary motivation is to keep voltages within preassigned operating limits by commanding the reactive power output of distributed energy resources (DERs)…

Systems and Control · Electrical Eng. & Systems 2022-08-22 Guido Cavraro , Zhenyi Yuan , Manish K. Singh , Jorge Cortés

The intent of the study detailed in this paper is to demonstrate the benefits of inverter var control on a fast timescale to mitigate rapid and large voltage fluctuations due to the high penetration of photovoltaic generation and the…

Emerging Technologies · Computer Science 2011-12-26 Masoud Farivar , Russell Neal , Christopher Clarke , Steven Low
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