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A special issue of Energies (ISSN 1996-1073). This special issue belongs to the section "F1: Electrical Power System".

Deadline for manuscript submissions: 30 June 2025 | Viewed by 13950

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Special Issue Editors

Dr. Lin Zhu

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Guest Editor

School of Electric Power Engineering, South China University of Technology, Guangzhou 510640, China
Interests: power system stability and control; power system modeling and simulation; DC /FACTS technology; new energy generation and grid connection

Dr. Zhigang Wu

E-Mail Website
Guest Editor

School of Electric Power Engineering, South China University of Technology, Guangzhou 510640, China
Interests: power system modeling; numerical simulation technology and applications of complex network theory in power systems

Special Issue Information

Dear Colleagues,

Power systems are complex and interconnected networks that facilitate the generation, transmission, and distribution of electrical energy. Modeling, simulation, and optimization are crucial tools for understanding and managing the complex behavior of power systems, as well as for designing more efficient and reliable power systems.

This Special Issue seeks to bring together researchers and practitioners from academia to present the latest advances in the modeling, simulation, and optimization of power systems.

We invite original research papers, review articles, and case studies on topics that include, but are not limited to:

Power system modeling and simulation techniques.
Optimization methods for power system planning and operation.
Energy management systems and smart grid technologies.
Power system stability and control.
Power system protection and reliability.
Power electronics and renewable energy integration.
Power system dynamics and transient analysis.
Demand response and energy storage systems.
Cybersecurity in power systems.
Economic analysis of power system planning and operation.

Dr. Lin Zhu
Dr. Zhigang Wu
Guest Editors

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Energies is an international peer-reviewed open access semimonthly journal published by MDPI.

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Keywords

power system transient stability
model reduction
real-time simulator
nonlinear modeling
parameter identification
dynamic equivalent
data-driven

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Published Papers (11 papers)

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Research

15 pages, 3732 KiB

Open AccessArticle

The Impact of Post-Furnace Steel Processing Equipment on Reducing Voltage Fluctuations Caused by Arc Furnaces

by Zbigniew Olczykowski

Energies 2024, 17(21), 5360; https://doi.org/10.3390/en17215360 - 28 Oct 2024

Viewed by 669

Abstract

Arc devices are among the receivers with the highest power connected to power systems. Due to dynamic load changes, these receivers generate a number of disturbances that affect the quality of electric power. The most important disturbances include voltage fluctuations. It is also worth mentioning the asymmetry and deformation of the supply voltage curve. This article discusses the mutual interaction of receivers operating in parallel, operating stably, and devices with dynamic current consumption. Calculations based on model tests and the results of parameters characterizing the quality of energy, which were recorded in the line supplying the steelworks, are presented. The power supply conditions (power of the short-circuit network) were assessed to influence the degree of suppression of voltage fluctuations by loads with stable current consumption. Full article

(This article belongs to the Special Issue Modeling, Simulation and Optimization of Power System)

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25 pages, 5071 KiB

Open AccessArticle

Multi-Stage ANN Model for Optimizing the Configuration of External Lightning Protection and Grounding Systems

by Rohana Rohana, Surya Hardi, Nasaruddin Nasaruddin, Yuwaldi Away and Andri Novandri

Energies 2024, 17(18), 4673; https://doi.org/10.3390/en17184673 - 20 Sep 2024

Cited by 2 | Viewed by 997

Abstract

This paper proposes an Artificial Neural Network (ANN) model using a Multi-Stage method to optimize the configuration of an External Lightning Protection System (ELPS) and grounding system. ELPS is a system designed to protect an area from damage caused by lightning strikes. Meanwhile, the grounding system functions to direct excess electric current from lightning strikes into the ground. This study identifies the optimal protection system configuration, reducing the need for excessive components. The ELPS configuration includes the number of protection pole units and the height of the protection poles. In contrast, the grounding system configuration consists of the number of electrode units and the length of the electrodes. This study focuses on the protection system configuration at a Photovoltaic Power Station, where the area is highly vulnerable to lightning strikes. Several aspects need to be considered in determining the appropriate configuration, such as average thunderstorm days per year, ELPS efficiency, total area of photovoltaic module, area to be protected, soil resistivity, electrode spacing factor, and the total required electrode resistance. The proposed multi-stage ANN model consists of three processing stages, each responsible for handling a portion of the overall system tasks. The first stage is responsible for determining the protection pole configuration. In the second stage, the Lightning Protection Level (LPL) classification is performed. Then, in the third stage, the process of determining the grounding configuration is handled. The analysis results show that the Multi-Stage ANN model can effectively determine the configuration with a low error rate: MAE of 0.265, RMSE of 0.314, and MPE of 9.533%. This model can also explain data variation well, as indicated by the high

R^{2}

value of 0.961. The comparison results conducted with ATP/EMTP software show that the configuration produced by ANN results in fewer protection pole units but with greater height. Meanwhile, ANN produces a configuration with shorter electrode lengths but fewer units in the grounding system. Full article

(This article belongs to the Special Issue Modeling, Simulation and Optimization of Power System)

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28 pages, 563 KiB

Open AccessArticle

Exploring a Dynamic Homotopy Technique to Enhance the Convergence of Classical Power Flow Iterative Solvers in Ill-Conditioned Power System Models

by Alisson Lima-Silva and Francisco Damasceno Freitas

Energies 2024, 17(18), 4642; https://doi.org/10.3390/en17184642 - 17 Sep 2024

Viewed by 866

Abstract

This paper presents a dynamic homotopy technique that can be used to calculate a preliminary result for a power flow problem (PFP). This result can then be used as an initial estimate to efficiently solve the PFP using either the classical Newton-Raphson (NR) method or its fast decoupled version (FDXB) while still maintaining high accuracy. The preliminary stage for the dynamic homotopy problem is formulated and solved by employing integration techniques, where implicit and explicit schemes are studied. The dynamic problem assumes an initial condition that coincides with the initial estimate for a traditional iterative method such as NR. In this sense, the initial guess for the FPF is adequately set as a flat start, which is a starting for the case when this initialization is of difficult assignment for convergence. The static homotopy method requires a complete solution of a PFP per homotopy pathway point, while the dynamic homotopy is based on numerical integration methods. This approach can require only one LU factorization at each point of the pathway. Allocating these points properly helps avoid several PFP resolutions to build the pathway. The hybrid technique was evaluated for large-scale systems with poor conditioning, such as a 109,272-bus model and other test systems under stressed conditions. A scheme based on the implicit backward Euler scheme demonstrated the best performance among other numerical solvers studied. It provided reliable partial results for the dynamic homotopy problem, which proved to be suitable for achieving fast and highly accurate solutions using both the NR and FDXB solvers. Full article

(This article belongs to the Special Issue Modeling, Simulation and Optimization of Power System)

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20 pages, 1894 KiB

Open AccessArticle

A Grouping and Aggregation Modeling Method of Induction Motors for Transient Voltage Stability Analysis

by Zhaowen Liang, Yongqiang Liu, Lili Mo and Yan Zhang

Energies 2024, 17(17), 4388; https://doi.org/10.3390/en17174388 - 2 Sep 2024

Viewed by 737

Abstract

Induction motors are the most common type of motor in power systems, constituting approximately 70–90% of the dynamic loads, making them significant contributors to system dynamics. In transient voltage stability analysis, dynamic equivalent models are commonly used to simplify the representation of a group of induction motors. This paper presents a method for the grouping and aggregation of induction motors at a common bus. Firstly, grouping rules are provided for clustering induction motors into several subgroups based on the mechanical principles of rotor force and motion, and aggregation rules are provided for aggregating a motor subgroup into a single-unit model based on the relationship between voltage drop and power transmission in distribution networks. Secondly, guided by the grouping rules, high-speed remaining electromagnetic torque and low-speed remaining electromagnetic torque are defined as new clustering indicators, and an adaptive K-means clustering method using silhouette coefficient verification is introduced to obtain the optimal motor subgroups. Thirdly, guided by the aggregation rules, a dynamic equivalent method is further introduced to obtain the equivalent single-unit model from a motor subgroup. Lastly, a transient voltage stability simulation in a typical distribution network is presented to illustrate that the proposed clustering and equivalent methods are more reasonable, accurate, and effective than traditional methods, as the obtained model has better dynamic characteristics and can more accurately reproduce the process of voltage collapse. Full article

(This article belongs to the Special Issue Modeling, Simulation and Optimization of Power System)

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25 pages, 9713 KiB

Open AccessArticle

Ground Fault in Medium-Voltage Power Networks with an Isolated Neutral Point: Spectral and Wavelet Analysis of Selected Cases in an Example Industrial Network Modeled in the ATP-EMTP Package

by Krzysztof Kuliński and Adam Heyduk

Energies 2024, 17(7), 1532; https://doi.org/10.3390/en17071532 - 22 Mar 2024

Viewed by 1343

Abstract

The paper presents some case spectral analysis of zero-sequence voltages and currents in an example industrial power distribution network. The network layout is based on typical power delivery networks in underground coal mines. Ground fault simulations have been made using an ATP/EMTP program. Due to the high environmental risks, the reliability of the protection relay operation related to their selectivity plays an important role. This paper tries to find the reasons for nonselective operation and unnecessary tripping in extensive mine cable networks, particularly with large power sources of higher-order harmonics. It was found that in transient states—due to the decaying oscillations occurring in complex RLC circuits—the results of short time measurements of the criterion values for ground fault protective relays can be overestimated (particularly for small values of ground resistance) and lead to nonselective tripping of a healthy cable line. Therefore, it might be advisable to increase the integration time used for measuring rms values. Also, if there is a significant level of higher harmonics in the industrial network generated by high-power converters, it should be noted that the higher harmonics of the ground fault current and currents measured by ground fault protection relays assume much higher values, which may also cause nonselective tripping. In this case, it may be advisable to use higher harmonic filters in the measuring circuits and to select a sufficiently high sampling frequency in the digital protective relays. Full article

(This article belongs to the Special Issue Modeling, Simulation and Optimization of Power System)

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19 pages, 2945 KiB

Open AccessArticle

Optimization of Ampacity in High-Voltage Underground Cables with Thermal Backfill Using Dynamic PSO and Adaptive Strategies

by Brayan A. Atoccsa, David W. Puma, Daygord Mendoza, Estefany Urday, Cristhian Ronceros and Modesto T. Palma

Energies 2024, 17(5), 1023; https://doi.org/10.3390/en17051023 - 22 Feb 2024

Cited by 5 | Viewed by 2573

Abstract

This article addresses challenges in the design of underground high-voltage transmission lines, focusing on thermal management and cable ampacity determination. It introduces an innovative proposal that adjusts the dimensions of the backfill to enhance ampacity, contrasting with the conventional approach of increasing the core cable’s cross-sectional area. The methodology employs a particle swarm optimization (PSO) technique with adaptive penalization and restart strategies, implemented in MATLAB for parameter autoadaptation. The article emphasizes more efficient solutions than traditional PSO, showcasing improved convergence and precise results (success probability of 66.1%). While traditional PSO is 81% faster, the proposed PSO stands out for its accuracy. The inclusion of thermal backfill results in an 18.45% increase in cable ampacity, considering variations in soil thermal resistivity, backfill properties, and ambient temperature. Additionally, a sensitivity analysis was conducted, revealing conservative values that support the proposal’s robustness. This approach emerges as a crucial tool for underground installation, contributing to continuous ampacity improvement and highlighting its impact on decision making in energy systems. Full article

(This article belongs to the Special Issue Modeling, Simulation and Optimization of Power System)

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19 pages, 4628 KiB

Open AccessArticle

Evaluation of FACTS Contributions Using Branch Flow Model and Newton–Raphson Algorithm

by Marco Junior Ticllacuri Corpus and Jonatas B. Leite

Energies 2024, 17(4), 918; https://doi.org/10.3390/en17040918 - 16 Feb 2024

Viewed by 796

Abstract

Flexible alternating current transmission systems (FACTSs) have been widely incorporated in electric power systems in order to control system parameters. This paper proposes the modeling of four FACTS devices, using the Branch Flow Model (BF) as an optimization problem to reduce the complexity of the Newton–Raphson (NR) load flow code with FACTS devices. The devices are represented as variable impedances, as a function of a firing angle, and as voltage source converters (VSCs) located on the buses and transmission lines. This proposed model solves the problem associated with the selection of appropriate initial conditions of the parameters of each device that guarantee convergence. The model is validated by evaluating its percentage deviation with respect to the NR method, using the standard test systems, IEEE 5-bus, IEEE 14-bus, IEEE 30-bus, and IEEE 57-bus systems. Full article

(This article belongs to the Special Issue Modeling, Simulation and Optimization of Power System)

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21 pages, 4437 KiB

Open AccessArticle

A Dynamic Nonlinear VDCOL Control Strategy Based on the Taylor Expansion of DC Voltages for Suppressing the Subsequent Commutation Failure in HVDC Transmission

by Hongzheng Li, Kunlun Han, Shuhao Liu, Hailin Chen, Xiongfeng Zhang and Kangtai Zou

Energies 2023, 16(21), 7342; https://doi.org/10.3390/en16217342 - 30 Oct 2023

Viewed by 1368

Abstract

Subsequent commutation failure in high-voltage DC transmission systems seriously emphasizes the safe and stable operation of power systems. Via analyzing the mechanism of commutation failure and the principle of voltage-dependent current order limiter (VDCOL), this paper proposes a dynamic nonlinear VDCOL control strategy based on the Taylor expansion of DC voltage for suppressing subsequent commutation failure. To solve the problem of fluctuating DC current command value caused by a large drop in DC voltage, this paper constructs a nonlinear VDCOL control that can be dynamically adjusted according to the AC bus voltage level, and Taylor expansion of DC voltage is used to obtain its first-order and second-order differential components. Different scales of differential elements are chosen to predict the DC voltage compensation value while balancing sensitivity and accuracy. The compensated DC voltage, used as the starting voltage of VDCOL, is input to the VDCOL control constructed in this paper to suppress the subsequent commutation failure of the transmission system by reducing the fluctuation of the current command value. Finally, the standard test model of HVDC is established based on the actual parameters, and the simulation results show that the Method proposed in this paper has an effective suppressing effect in the case of single-phase or three-phase faults of different severity and is conducive to the restoration of the system power transmission. Full article

(This article belongs to the Special Issue Modeling, Simulation and Optimization of Power System)

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21 pages, 4373 KiB

Open AccessEditor’s ChoiceArticle

A Two-Terminal Directional Protection Method for HVDC Transmission Lines of Current Fault Component Based on Improved VMD-Hilbert Transform

by Shuhao Liu, Kunlun Han, Hongzheng Li, Tengyue Zhang and Fengyuan Chen

Energies 2023, 16(19), 6987; https://doi.org/10.3390/en16196987 - 7 Oct 2023

Cited by 1 | Viewed by 1236

Abstract

The traveling wave protection of high voltage direct current (HVDC) transmission lines is susceptible to the influence of transition resistance. As a backup protection, current differential protection has absolute selectivity, but usually requires an increase in delay to avoid misoperation caused by distributed capacitance on the line, resulting in a longer action time. Based on this, a two-terminal directional protection method for HVDC transmission lines is proposed based on Sparrow Search Algorithm (SSA)-Variational Mode Decomposition (VMD) and Hilbert phase difference. On the basis of analyzing the directional characteristics of the current fault component at both ends of the rectifier and inverter sides under different faults, SSA is first used to optimize the parameters of VMD. The residual components representing the direction of the current fault component at both ends are extracted through VMD, and then the Hilbert phase difference of the residual components at both ends is calculated to identify faults inside and outside the line area. In addition, fault pole selection can be achieved based on the ratio of the sum of multi-band Hilbert energy of single-terminal voltage fault components at the positive and negative poles. Simulation experiments have shown that the proposed protection scheme can quickly and effectively identify fault and has good tolerance to transition resistance and noise interference. Full article

(This article belongs to the Special Issue Modeling, Simulation and Optimization of Power System)

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20 pages, 6042 KiB

Open AccessArticle

Dynamic Equivalent Modeling of a Large Renewable Power Plant Using a Data-Driven Degree of Similarity Method

by Mengjun Liao, Lin Zhu, Yonghao Hu, Yang Liu, Yue Wu and Leke Chen

Energies 2023, 16(19), 6934; https://doi.org/10.3390/en16196934 - 3 Oct 2023

Cited by 2 | Viewed by 1225

Abstract

This paper aims to develop a novel method for the dynamic equivalence of a renewable power plant, ultimately contributing to power system modeling and enhancing the integration of renewable energy sources. In order to address the challenge posed by clusters of renewable generation units during the equivalence process, the paper introduces the degree of similarity to assess similarity features under data. After leveraging the degree of similarity in conjunction with data-driven techniques, the proposed method efficiently entails dividing numerous units in a large-scale plant into distinct clusters. Additionally, the paper adopts practical algorithms to determine the parameters for each aggregated cluster and streamline the intricate collector network within the renewable power plant. The equivalent model of a renewable power plant is thereby conclusively derived. Comprehensive case studies are conducted within a practical offshore wind plant setting. These case studies are accompanied by simulations, highlighting the advantages and effectiveness of the proposed method, offering an accurate representation of the renewable power plant under diverse operating conditions. Full article

(This article belongs to the Special Issue Modeling, Simulation and Optimization of Power System)

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21 pages, 2301 KiB

Open AccessArticle

A Collaborative Planning Method for the Source and Grid in a Distribution System That Considers Risk Measurement

by Jiahao Deng, Lingxue Lin, Yongjie Zhang and Yuxin Ma

Energies 2023, 16(15), 5648; https://doi.org/10.3390/en16155648 - 27 Jul 2023

Cited by 1 | Viewed by 955

Abstract

The existing distribution system planning methods do not fully consider improving power supply capacity and reliability through the coordination of multiple planning factors, and they are not comprehensive enough in quantifying planning risks. Therefore, this paper proposes a collaborative planning method for sources and networks that considers risk measurement. A multi-layer planning model is first constructed that includes a grid planning layer, a power planning layer, a switch planning layer, and an operation optimization layer. In the model, a risk measurement method combining opportunity constraints and conditional value-at-risk objectives is used to comprehensively assess the risk of the node voltage and branch current exceeding the limit caused by load uncertainty. Then, a solution strategy based on a genetic algorithm and a sparrow search algorithm is proposed to coordinate the contradiction between the solution time and the accuracy of the multi-layer model. Finally, taking a planned area to be expanded as an example, the results show that compared to the existing collaborative planning methods for sources and networks, the proposed method in this paper reduces the planning risks caused by load uncertainty by more than 50% and increases the annual net income of the power distribution company and the DG operators by RMB 1.5 million and RMB 1.1 million, respectively. Full article

(This article belongs to the Special Issue Modeling, Simulation and Optimization of Power System)

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