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140 Results Found

  • Article
  • Open Access
5 Citations
6,304 Views
17 Pages

26 April 2017

This paper proposes a probabilistic power flow (PPF) method considering continuous and discrete variables (continuous and discrete power flow, CDPF) for power systems. The proposed method—based on the cumulant method (CM) and multiple deterministic p...

(This article belongs to the Section F: Electrical Engineering)
  • Article
  • Open Access
13 Citations
4,791 Views
12 Pages

1 October 2018

In this paper, we propose a new scheme for probabilistic power flow in networks with renewable power generation by making use of a data clustering technique. The proposed clustering technique is based on the combination of Principal Component Analysi...

(This article belongs to the Section F: Electrical Engineering)
  • Article
  • Open Access
153 Views
18 Pages

Distribution-Matching Likelihood-Free Sampling for Probabilistic Power Flow

  • Carlos D. Zuluaga-Ríos,
  • Paola M. Ortiz-Grisales and
  • Eduardo Duque-Grisales

The increasing penetration of renewable generation and electrified loads introduces non-Gaussian and strongly nonlinear uncertainty in power system operation. While Monte Carlo-based probabilistic power flow (PPF) methods provide accurate uncertainty...

(This article belongs to the Special Issue Recent Advances in Power System and Smart Grid Technologies)
  • Article
  • Open Access
12 Citations
7,393 Views
21 Pages

31 October 2013

This paper presents a novel probabilistic optimization algorithm for simultaneous active and reactive power dispatch in power systems with significant wind power integration. Two types of load and wind-speed uncertainties have been assumed that follo...

  • Article
  • Open Access
3 Citations
940 Views
23 Pages

Data-Driven Probabilistic Power Flow for Energy-Storage Planning Considering Interconnected Grids

  • Tingting Cheng,
  • Xirui Jiang,
  • Zheng Fan,
  • Yanan Wu and ,
  • Ying Mu,
  • Dashun Guan,
  • Dongliang Zhang and
  • Ying Bai
  • + 3 authors+ 0 author

18 December 2025

As renewable energy penetration increases, the volatility and uncertainty of photovoltaic generation and load demand pose significant challenges to power-system stability. This paper proposes a data-driven probabilistic load-flow method that employs...

(This article belongs to the Section A: Sustainable Energy)
  • Article
  • Open Access
2 Citations
1,167 Views
15 Pages

Three-Phase Probabilistic Power Flow Calculation Method Based on Improved Semi-Invariant Method for Low-Voltage Network

  • Ke Liu,
  • Xuebin Wang,
  • Han Guo,
  • Wenqian Zhang and ,
  • Yutong Liu,
  • Cong Zhou and
  • Hongbo Zou
  • + 2 authors+ 0 author

25 August 2025

Power flow analysis of low-voltage network (LVN) is one of the most crucial methods for achieving refined management of such networks. To accurately calculate the three-phase (TP) probabilistic power flow (PPF) distribution in LVN, this paper first d...

(This article belongs to the Special Issue Smart Optimization Techniques for Microgrid Management)
  • Article
  • Open Access
45 Citations
3,627 Views
23 Pages

Probabilistic Optimal Power Flow Solution Using a Novel Hybrid Metaheuristic and Machine Learning Algorithm

  • Mohamed A. M. Shaheen,
  • Hany M. Hasanien,
  • Said F. Mekhamer,
  • Mohammed H. Qais and ,
  • Saad Alghuwainem,
  • Zia Ullah,
  • Marcos Tostado-Véliz,
  • Rania A. Turky,
  • Francisco Jurado and
  • Mohamed R. Elkadeem
  • + 5 authors+ 0 author

23 August 2022

This paper proposes a novel hybrid optimization technique based on a machine learning (ML) approach and transient search optimization (TSO) to solve the optimal power flow problem. First, the study aims at developing and evaluating the proposed hybri...

  • Article
  • Open Access
3 Citations
898 Views
22 Pages

7 January 2026

To address active power fluctuations in power grids induced by high renewable energy penetration and overcome the limitations of existing probabilistic power flow (PPF) methods that ignore generator frequency regulation constraints, this paper propos...

  • Review
  • Open Access
1,587 Views
23 Pages

2 June 2026

This paper presents a comprehensive and systematic review of probabilistic power flow (PPF) methods applied to power systems with high penetration of renewable energy sources (RES). The study covers developments from the 1970s to recent advances (201...

(This article belongs to the Section F1: Electrical Power System)
  • Article
  • Open Access
7 Citations
2,423 Views
19 Pages

8 March 2023

For a new power system using high-penetration renewable energy, the traditional deterministic power flow analysis method cannot accurately represent the stochastic characteristics of each state variable. The aggregation of renewable energy with diffe...

(This article belongs to the Section F2: Distributed Energy System)
  • Article
  • Open Access
20 Citations
2,501 Views
27 Pages

5 September 2023

In this study, the Giant Trevally Optimizer (GTO) is employed to solve the probabilistic optimum power flow (P-OPF) issue, considering Renewable Energy Source (RES) uncertainties, achieving notable cost reduction. The objective function is establishe...

  • Article
  • Open Access
23 Citations
5,013 Views
21 Pages

17 October 2017

The traditional cumulant method (CM) for probabilistic optimal power flow (P-OPF) needs to perform linearization on the Karush–Kuhn–Tucker (KKT) first-order conditions, therefore requiring input variables (wind power or loads) varying within small ra...

(This article belongs to the Section F: Electrical Engineering)
  • Article
  • Open Access
7 Citations
1,334 Views
15 Pages

21 February 2025

The uncertainty caused by renewable energy (RES) and diverse load demands may cause power flow fluctuations in modern power systems, where the probabilistic power flow (PPF) is a reliable method for quantifying and analyzing such power flow fluctuati...

(This article belongs to the Section A: Sustainable Energy)
  • Article
  • Open Access
1 Citations
548 Views
22 Pages

9 June 2026

High renewable penetration introduces stochastic variability in distribution-network operation, requiring probabilistic AC power-flow tools that remain accurate in the tails while avoiding the computational burden of large Monte Carlo simulation. Thi...

  • Article
  • Open Access
66 Citations
9,671 Views
25 Pages

Monte Carlo Simulation and a Clustering Technique for Solving the Probabilistic Optimal Power Flow Problem for Hybrid Renewable Energy Systems

  • Mohamed S. Hashish,
  • Hany M. Hasanien,
  • Haoran Ji,
  • Abdulaziz Alkuhayli and ,
  • Mohammed Alharbi,
  • Tlenshiyeva Akmaral,
  • Rania A. Turky,
  • Francisco Jurado and
  • Ahmed O. Badr
  • + 4 authors+ 0 author

1 January 2023

This paper proposes a new, metaheuristic optimization technique, Artificial Gorilla Troops Optimization (GTO), for a hybrid power system with photovoltaic (PV) and wind energy (WE) sources, solving the probabilistic optimum power flow (POPF) issue. F...

(This article belongs to the Special Issue Sustainable Development in the Built Environment: Renewable Energy and Thermal Energy Storage)
  • Article
  • Open Access
8 Citations
3,884 Views
21 Pages

Probabilistic Power Flow for Hybrid AC/DC Grids with Ninth-Order Polynomial Normal Transformation and Inherited Latin Hypercube Sampling

  • Sui Peng,
  • Huixiang Chen,
  • Yong Lin,
  • Tong Shu and ,
  • Xingyu Lin,
  • Junjie Tang,
  • Wenyuan Li and
  • Weijie Wu
  • + 3 authors+ 0 author

10 August 2019

This paper proposes a new probabilistic power flow method for the hybrid AC/VSC-MTDC (Voltage Source Control-Multiple Terminal Direct Current) grids, which is based on the combination of ninth-order polynomial normal transformation (NPNT) and inherit...

(This article belongs to the Special Issue Modern Power System Dynamics, Stability and Control)
  • Article
  • Open Access
385 Views
29 Pages

6 September 2026

Probabilistic power flow quantifies voltage and phase angle uncertainty under variable photovoltaic generation, but repeated AC Monte Carlo simulation is costly. A local topology change also modifies the electrical operator and state dimension when o...

(This article belongs to the Special Issue Advances in Smart Grid Architectures: Sensor Technologies and Intelligent Monitoring Systems)
  • Article
  • Open Access
12 Citations
3,148 Views
19 Pages

Probabilistic Optimal Power Flow for Day-Ahead Dispatching of Power Systems with High-Proportion Renewable Power Sources

  • Yue Chen,
  • Zhizhong Guo,
  • Hongbo Li,
  • Yi Yang and ,
  • Abebe Tilahun Tadie,
  • Guizhong Wang and
  • Yingwei Hou
  • + 2 authors+ 0 author

9 January 2020

With the increasing proportion of uncertain power sources in the power grid; such as wind and solar power sources; the probabilistic optimal power flow (POPF) is more suitable for the steady state analysis (SSA) of power systems with high proportions...

(This article belongs to the Section Energy Sustainability)
  • Article
  • Open Access
11 Citations
4,025 Views
13 Pages

8 May 2020

The traditional security-constrained optimal power flow (SCOPF) model under the classical N-1 criterion is implemented in the power industry to ensure the secure operation of a power system. However, with increasing uncertainties from renewable energ...

(This article belongs to the Special Issue Power System Simulation, Control and Optimization)
  • Article
  • Open Access
11 Citations
2,692 Views
22 Pages

The Effect of Power Flow Entropy on Available Load Supply Capacity under Stochastic Scenarios with Different Control Coefficients of UPFC

  • Zhongxi Ou,
  • Yuanyuan Lou,
  • Junzhou Wang,
  • Yixin Li and ,
  • Kun Yang,
  • Sui Peng and
  • Junjie Tang
  • + 2 authors+ 0 author

21 April 2023

With the sharp increase in fluctuant sources in power systems, the deterministic power flow (DPF) calculation has been unable to meet the demands of practical applications; thus, the probabilistic method becomes indispensable for the reliable and sta...

(This article belongs to the Collection Power System and Sustainability)
  • Article
  • Open Access
1 Citations
865 Views
21 Pages

9 December 2025

Extreme disasters such as typhoons pose severe frequency stability challenges to modern power systems with a high penetration of new energy sources. Traditional probabilistic power flow (PPF) methods, which assume constant frequency, are insufficient...

(This article belongs to the Special Issue Digital Modeling, Operation and Control of Sustainable Energy Systems)
  • Feature Paper
  • Article
  • Open Access
51 Citations
3,876 Views
19 Pages

Solution of Probabilistic Optimal Power Flow Incorporating Renewable Energy Uncertainty Using a Novel Circle Search Algorithm

  • Mohamed A. M. Shaheen,
  • Zia Ullah,
  • Mohammed H. Qais,
  • Hany M. Hasanien and ,
  • Kian J. Chua,
  • Marcos Tostado-Véliz,
  • Rania A. Turky,
  • Francisco Jurado and
  • Mohamed R. Elkadeem
  • + 4 authors+ 0 author

7 November 2022

Integrating renewable energy sources (RESs) into modern electric power systems offers various techno-economic benefits. However, the inconsistent power profile of RES influences the power flow of the entire distribution network, so it is crucial to o...

  • Article
  • Open Access
18 Citations
5,554 Views
20 Pages

10 March 2022

Renewable resources integration through distributed generation (DG) affects conventional consideration of power system performance and confronts deterministic load flow (DLF) analysis with serious challenges. The DLF gives a snapshot of the system st...

(This article belongs to the Special Issue Recent Advances in Smart Power Electronics)
  • Article
  • Open Access
5 Citations
2,760 Views
21 Pages

30 December 2020

Power systems can be analyzed using either a deterministic or a probabilistic approach. The deterministic analysis centers on studying the quantities and indicators that characterize the operating states of the power system under strictly defined con...

(This article belongs to the Special Issue Uncertainty Analysis and Risk Management in Power Systems and Electricity Markets)
  • Article
  • Open Access
3 Citations
1,493 Views
21 Pages

Efficient Probabilistic Evaluation and Sensitivity Analysis of Load Supply Capability for Renewable-Energy-Based Power Systems

  • Jie Zhang,
  • Kaixiang Fu,
  • Weizhi Huang,
  • Yilin Zhang and ,
  • Qing Sun,
  • Yuan Chi and
  • Junjie Tang
  • + 2 authors+ 0 author

6 May 2025

In renewable energy generation, uncertainties mainly refer to power output fluctuations caused by the intermittency, variability, and forecasting errors of wind and photovoltaic power. These uncertainties have adverse effects on the secure operation...

(This article belongs to the Special Issue Advances and Challenges in Power Systems with High Penetration of Renewable Energies)
  • Article
  • Open Access
4 Citations
1,050 Views
19 Pages

Safety Assessment of Loop Closing in Active Distribution Networks Based on Probabilistic Power Flow

  • Wenchao Cai,
  • Yuan Gao,
  • Xiping Zhang,
  • Qin Si and ,
  • Jiaoxin Jia and
  • Bingzhen Li
  • + 1 author+ 0 author

22 May 2025

To investigate the security issues of loop-closing operations in medium–low-voltage distribution networks under the influence of stochastic fluctuations from distributed generators (DGs) and loads, probabilistic power flow is introduced for ana...

(This article belongs to the Special Issue Trends and Challenges in Power System Stability and Control)
  • Feature Paper
  • Article
  • Open Access
4 Citations
1,719 Views
38 Pages

11 September 2025

As electric grids decarbonize and distributed energy resources (DERs) become increasingly prevalent, interconnection assessments must evolve to reflect operational variability and control flexibility. This paper highlights key modeling limitations ob...

(This article belongs to the Special Issue Optimization and Machine Learning Approaches for Power Systems)
  • Article
  • Open Access
9 Citations
2,631 Views
14 Pages

8 July 2020

Because the penetration level of renewable energy sources has increased rapidly in recent years, uncertainty in power system operation is gradually increasing. As an efficient tool for power system analysis under uncertainty, probabilistic power flow...

(This article belongs to the Special Issue Electric Power Systems Research 2020)
  • Article
  • Open Access
7 Citations
2,827 Views
31 Pages

Probabilistic Forecasting of Available Load Supply Capacity for Renewable-Energy-Based Power Systems

  • Qizhuan Shao,
  • Shuangquan Liu,
  • Yigong Xie,
  • Xinchun Zhu and ,
  • Yilin Zhang,
  • Junzhou Wang and
  • Junjie Tang
  • + 2 authors+ 0 author

31 July 2023

In order to accurately analyze the load supply capability of power systems with high penetration of renewable energy generation, this paper proposes a probabilistic available load supply capability (ALSC) forecasting method. Firstly, the optimal inpu...

(This article belongs to the Special Issue Advances and Challenges in Power Systems with High Penetration of Renewable Energies)
  • Article
  • Open Access
4 Citations
2,221 Views
15 Pages

28 June 2022

This paper aims at presenting a novel effective approach to probabilistic analysis of distribution power grid with high penetration of PV sources. The novel method adopts a Gaussian Mixture Model for reproducing the uncertainty of correlated PV sourc...

(This article belongs to the Section A2: Solar Energy and Photovoltaic Systems)
  • Article
  • Open Access
10 Citations
5,922 Views
19 Pages

2 June 2017

This paper proposes voltage-stability based on congestion management (CM) for electricity market environments and considers the incorporation of wind farms into systems as well. A probabilistic voltage-stability constrained optimal power flow (P-VSCO...

(This article belongs to the Special Issue Advances in Integrated Energy Systems Design, Control and Optimization)
  • Article
  • Open Access
8 Citations
3,754 Views
21 Pages

A Vine-Copula Based Voltage State Assessment with Wind Power Integration

  • Xiaolu Chen,
  • Ji Han,
  • Tingting Zheng,
  • Ping Zhang and ,
  • Simo Duan and
  • Shihong Miao
  • + 1 author+ 0 author

27 May 2019

With the increasing rate of wind power installed capacity, voltage state assessment with large-scale wind power integration is of great significance. In this paper, a vine-copula based voltage state assessment method with large-scale wind power integ...

  • Article
  • Open Access
2 Citations
1,574 Views
13 Pages

A Practical Security Assessment Methodology for Power System Operations Considering Uncertainty

  • Nhi Thi Ai Nguyen,
  • Dinh Duong Le,
  • Van Duong Ngo,
  • Van Kien Pham and
  • Van Ky Huynh

Today, renewable energy sources (RESs) are increasingly being integrated into power systems. This means adding more sources of uncertainty to the power system. To deal with the uncertainty of input random variables (RVs) in power system calculation a...

(This article belongs to the Section Systems & Control Engineering)
  • Article
  • Open Access
3 Citations
2,367 Views
22 Pages

4 November 2022

The large-scale, nonlinear and uncertain factors of hybrid power systems (HPS) have always been difficult problems in dynamic stability control. This research mainly focuses on the dynamic and transient stability performance of large HPS under variou...

(This article belongs to the Special Issue Advanced Control Technology of Integrated Wind and Wave Energy Conversion System)
  • Review
  • Open Access
833 Views
54 Pages

19 August 2026

Power Flow (PF) analysis is a fundamental tool in distribution systems since it determines the steady-state operating point for specified input conditions. Modern distribution networks face high distributed energy resource (DER) penetration and varia...

(This article belongs to the Section F1: Electrical Power System)
  • Editorial
  • Open Access
5 Citations
2,482 Views
4 Pages

26 November 2021

This editorial document provides the main motivations and a brief description of each paper published in the “Rethinking the Distribution Power Network Planning and Operation for a Sustainable Smart Grid and Smooth Interaction with Electrified...

(This article belongs to the Special Issue Rethinking the Distribution Power Network Planning and Operation for a Sustainable Smart Grid and Smooth Interaction with Electrified Transportation)
  • Article
  • Open Access
419 Views
34 Pages

13 August 2026

With the large-scale integration of distributed photovoltaic generation (PV) into modern distribution networks, the inherent stochasticity and volatility of renewable energy outputs have imposed non-negligible impacts on the secure and economic opera...

(This article belongs to the Special Issue Advanced Control Systems for Power Electronics, Smart Grids, and Renewable Energy Integration)
  • Article
  • Open Access
3 Citations
820 Views
27 Pages

Hybrid Metaheuristic-Based Probabilistic Planning of Weak Power Grids with Renewable Generation and Hydrogen Energy Storage

  • Ayman Hussein Badawi,
  • Mohamed M. Zakaria Moustafa,
  • Mostafa S. Hamad,
  • Ayman Samy Abdel-Khalik and
  • Ragi A. R. Hamdy

4 March 2026

The large-scale integration of wind turbine generators (WTGs) and photovoltaic (PV) generation increases operational uncertainty and can exacerbate stability limitations in weak transmission networks, motivating the use of green hydrogen energy stora...

(This article belongs to the Topic AI and Computational Methods for Modelling, Simulations and Optimizing of Advanced Systems: Innovations in Complexity, 2nd Edition)
  • Article
  • Open Access
3 Citations
1,795 Views
28 Pages

14 July 2025

This paper proposes a novel integer-mixed probabilistic optimal power flow (IM-POPF) strategy for frequency regulation in islanded microgrids under uncertain operating conditions. Existing load-shedding approaches face critical limitations: continuou...

(This article belongs to the Section F: Engineering and Materials)
  • Article
  • Open Access
264 Views
19 Pages

Voltage-Increment-Based Low-Rank Representation with Polynomial Chaos Expansions for Probabilistic Voltage Assessment Under Multiple Contingencies

  • Yuzhi Wang,
  • Xingyu Lin,
  • Junzhou Wang,
  • Liu Zhu and ,
  • Chen Liang and
  • Junjie Tang
  • + 1 author+ 0 author

2 October 2026

Probabilistic voltage assessment under multiple contingencies involves numerous network topologies and uncertain operating conditions, resulting in substantial surrogate modeling and computational costs. To address this problem, this paper proposes a...

(This article belongs to the Special Issue Mathematical Methods Applied in Power Systems, 2nd Edition)
  • Article
  • Open Access
1 Citations
1,996 Views
41 Pages

10 April 2026

This paper develops a probabilistic Available Transfer Capability (ATC) framework that quantifies export headroom for renewables across transmission-distribution interfaces under time-varying uncertainty. Static transmission reliability margins can u...

(This article belongs to the Special Issue Renewable Energy Development in Distribution Networks: Optimization, Assessment and Design of Renewable Plants)
  • Article
  • Open Access
833 Views
31 Pages

Probabilistic Voltage Stability Screening Under Stochastic Load Allocation at Weak Buses Using Stability Index

  • Manuel Jaramillo,
  • Diego Carrión,
  • Alexander Aguila Téllez and
  • Edwin Garcia

17 February 2026

Voltage security assessment is increasingly challenged by stochastic demand growth and localized stress patterns that are not well represented by deterministic, single-snapshot analyses. This paper proposes a fully steady-state probabilistic stress-t...

(This article belongs to the Section A1: Smart Grids and Microgrids)
  • Feature Paper
  • Review
  • Open Access
10 Citations
4,059 Views
49 Pages

Power System Decision Making in the Age of Deep Learning: A Comprehensive Review

  • Yeji Lim,
  • Minjae Son,
  • Kyungnam Park,
  • Minsoo Kim and ,
  • Keunju Song,
  • Haejoong Lee and
  • Hongseok Kim
  • + 2 authors+ 0 author

12 September 2025

Modern power systems are facing growing complexity and uncertainty due to electrification, large-scale renewable integration, and evolving consumption behaviors. These changes have pushed traditional numerical optimization methods to their practical...

  • Article
  • Open Access
4 Citations
3,295 Views
18 Pages

21 September 2018

Along with the emerging development of demand side management applications, it is still a challenge to exploit flexibility realistically to resolve or prevent specific geographical network issues due to limited situational awareness of the (unbalance...

(This article belongs to the Special Issue Intelligent Control in Energy Systems)
  • Article
  • Open Access
9 Citations
3,019 Views
20 Pages

A Nonlinear Analytical Algorithm for Predicting the Probabilistic Mass Flow of a Radial District Heating Network

  • Guoqiang Sun,
  • Wenxue Wang,
  • Yi Wu,
  • Wei Hu and ,
  • Zijun Yang,
  • Zhinong Wei,
  • Haixiang Zang and
  • Sheng Chen
  • + 3 authors+ 0 author

28 March 2019

This paper develops a nonlinear analytical algorithm for predicting the probabilistic mass flow of radial district heating networks based on the principle of heat transfer and basic pipe network theory. The use of a nonlinear mass flow model provides...

  • Article
  • Open Access
7 Citations
2,894 Views
13 Pages

4 November 2020

As the importance of renewable generating resources has grown around the world, South Korea is also trying to expand the proportion of renewable generating resources in the power generation sector. Among the various renewable energy sources, wind gen...

(This article belongs to the Section A: Sustainable Energy)
  • Article
  • Open Access
11 Citations
3,919 Views
13 Pages

Probabilistic Load Flow Analysis Using Nonparametric Distribution

  • Li Bin,
  • Rashana Abbas,
  • Muhammad Shahzad and
  • Nouman Safdar

27 December 2023

In the pursuit of sustainable energy solutions, this research addresses the critical need for accurate probabilistic load flow (PLF) analysis in power systems. PLF analysis is an essential tool for estimating the statistical behavior of power systems...

(This article belongs to the Special Issue Critical Issues in Power Engineering and Renewable Energy Technologies)
  • Article
  • Open Access
1 Citations
599 Views
21 Pages

Risk Assessment of Distribution Network Based on Dirichlet Process Mixture Model and the Cumulant Method

  • Yuxuan Huang,
  • Yuwei Chen,
  • Zhenguo Shao,
  • Feixiong Chen and ,
  • Yunting Shao,
  • Yifan Zhang and
  • Changming Chen
  • + 2 authors+ 0 author

To address the increased operational risk in distribution network caused by the grid integration of distributed wind power, a distribution network risk assessment method that combines a Dirichlet process mixture model (DPMM) with the cumulant method...

(This article belongs to the Special Issue Recent Advances and Challenges in Emerging Power Systems: 3rd Edition)
  • Article
  • Open Access
596 Views
15 Pages

3 February 2026

The variability of renewable energy sources, coupled with the decentralised configuration of distributed generation (DG), significantly complicates grid management, necessitating sophisticated visual analytics to enhance power system performance and...

(This article belongs to the Special Issue Smart Grid and Energy Storage)
  • Article
  • Open Access
8 Citations
1,798 Views
18 Pages

Transient Stability Constraints for Optimal Power Flow Considering Wind Power Uncertainty

  • Songkai Liu,
  • Biqing Ye,
  • Pan Hu,
  • Ming Wan and ,
  • Jun Cao and
  • Yitong Liu
  • + 1 author+ 0 author

4 September 2025

To address the issue of uncertainty in renewable energy and its impact on the safe and stable operation of power systems, this paper proposes a transient stability constrained optimal power flow (TSCOPF) calculation method that takes into account the...

(This article belongs to the Section F1: Electrical Power System)

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