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Keywords = VSC-HVDC

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18 pages, 7338 KiB  
Article
Droop Frequency Limit Control and Its Parameter Optimization in VSC-HVDC Interconnected Power Grids
by Han Jiang, Yichen Zhou, Yi Gao and Shilin Gao
Energies 2024, 17(15), 3851; https://doi.org/10.3390/en17153851 - 5 Aug 2024
Viewed by 321
Abstract
With the gradual emergence of trends such as the asynchronous interconnection of power grids and the increasing penetration of renewable energy, the issues of ultra-low-frequency oscillations and low-frequency stability in power grids have become more prominent, posing serious challenges to the safety and [...] Read more.
With the gradual emergence of trends such as the asynchronous interconnection of power grids and the increasing penetration of renewable energy, the issues of ultra-low-frequency oscillations and low-frequency stability in power grids have become more prominent, posing serious challenges to the safety and stability of systems. The voltage-source converter-based HVDC (VSC-HVDC) interconnection is an effective solution to the frequency stability problems faced by regional power grids. VSC-HVDC can participate in system frequency stability control through a frequency limit controller (FLC). This paper first analyses the basic principles of how VSC-HVDC participates in system frequency stability control. Then, in response to the frequency stability control requirements of the sending and receiving power systems, a droop FLC strategy is designed. Furthermore, a multi-objective optimization method for the parameters of the droop FLC is proposed. Finally, a large-scale electromagnetic transient simulation model of the VSC-HVDC interconnected power system is constructed to verify the effectiveness of the proposed droop FLC method. Full article
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<p>Double-ended VSC-HVDC System Structure.</p>
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<p>FLC Control Block Diagram.</p>
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<p>Slope characteristics of droop FLC of MMC-HVDC.</p>
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<p>Slope characteristics of the FLC controller with the limiter.</p>
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<p>Slope characteristics of the FLC controller after active and voltage limiting.</p>
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<p>Double-layer optimization framework for FLC of VSC-HVDC.</p>
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<p>Flowchart for solving the multi-objective optimization model of the initial layer of DC FLC.</p>
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<p>Flowchart for solving the multi-objective optimization model of the second layer of DC FLC.</p>
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<p>The topology of system S1.</p>
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<p>The topology of system S2.</p>
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<p>Frequency response of system S1.</p>
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<p>Frequency variation at bus 61.</p>
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<p>Topology of the interconnected system.</p>
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<p>The power curve of system S1.</p>
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<p>The power curve of system S2.</p>
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<p>Voltage profile of the system in steady state case.</p>
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<p>The frequency response curve of system S1 after parameter optimization.</p>
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<p>The active power curve of system S1.</p>
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<p>The active power curve of system S2.</p>
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<p>DC voltage profile of the system for low frequency problems.</p>
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<p>The frequency response curve of system S1 before parameter optimization.</p>
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<p>The frequency response curve of system S2 after parameter optimization.</p>
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<p>The frequency response curve of system S1 without parameter optimization.</p>
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<p>Voltage Curves of LCC2 sending and receiving ends.</p>
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<p>Active power curve for generator 3.</p>
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<p>Frequency response of system S1 for a power deficit of 600 MW.</p>
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<p>Voltage Curves of LCC5 sending and receiving ends.</p>
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<p>Voltage curves for substations 5 and 6.</p>
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15 pages, 1980 KiB  
Article
Optimal Multiple Wind Power Transmission Schemes Based on a Life Cycle Cost Analysis Model
by Xiaotong Ji, Dan Liu, Heng Luo, Ping Xiong, Daojun Tan, Pan Hu, Hengrui Ma and Bo Wang
Processes 2024, 12(8), 1594; https://doi.org/10.3390/pr12081594 - 30 Jul 2024
Viewed by 423
Abstract
Due to the high cost and complex challenges faced by offshore wind power transmission, economic research into offshore wind power transmission can provide a scientific basis for optimal decision-making on offshore wind power projects. Based on the analysis of the topology structure and [...] Read more.
Due to the high cost and complex challenges faced by offshore wind power transmission, economic research into offshore wind power transmission can provide a scientific basis for optimal decision-making on offshore wind power projects. Based on the analysis of the topology structure and characteristics of typical wind power transmission schemes, this paper compares the economic benefits of five different transmission schemes with a 3.6 GW sizeable onshore wind farm as the primary case. Research includes traditional high voltage alternating current (HVAC), voltage source converter high voltage direct current transmission (VSC-HVDC), a fractional frequency transmission system (FFTS), and two hybrid DC (MMC-LCC and DR-MMC) transmission scenarios. The entire life cycle cost analysis model (LCCA) is employed to thoroughly assess the cumulative impact of initial investment costs, operational expenses, and eventual scrap costs on top of the overall transmission scheme’s total cost. This comprehensive evaluation ensures a nuanced understanding of the financial implications across the project’s entire lifespan. In this example, HVAC has an economic advantage over VSC-HVDC in the transmission distance range of 78 km, and the financial range of a FFTS is 78–117 km. DR-MMC is better than the flexible DC delivery scheme in terms of transmission capacity, scalability, and offshore working platform construction costs in the DC delivery scheme. Therefore, the hybrid DC delivery scheme of offshore wind power composed of multi-type converters has excellent application prospects. Full article
(This article belongs to the Section Energy Systems)
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<p>Diagram of wind farm and connection point.</p>
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<p>Topology of kinds of wind grid integration scheme.</p>
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<p>Life cycle cost composition of wind power grid-connected scheme.</p>
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<p>LCCA investment cost change chart.</p>
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<p>Life cycle cost composition of wind power grid-connected scheme.</p>
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<p>Total cost composition of wind power grid-connected scheme LCCA.</p>
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<p>Total cost composition of wind power grid-connected scheme LCCA.</p>
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<p>Five types of offshore wind power are suitable for AC/DC transmission.</p>
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19 pages, 3260 KiB  
Article
Basic Circuit Model of Voltage Source Converters: Methodology and Modeling
by Christian Bipongo Ndeke, Marco Adonis and Ali Almaktoof
AppliedMath 2024, 4(3), 889-907; https://doi.org/10.3390/appliedmath4030048 - 29 Jul 2024
Viewed by 345
Abstract
Voltage source converters (VSCs) have emerged as the key components in modern power systems, facilitating efficient energy conversion and flexible power flow control. Understanding the fundamental circuit model of VSCs is essential for their accurate modeling and analysis in power system studies. A [...] Read more.
Voltage source converters (VSCs) have emerged as the key components in modern power systems, facilitating efficient energy conversion and flexible power flow control. Understanding the fundamental circuit model of VSCs is essential for their accurate modeling and analysis in power system studies. A basic voltage source converter circuit model connected to an LC filter is essential because it lowers the harmonic distortions and enhances the overall power quality of the micro-grid. This guarantees a clean and steady power supply, which is necessary for the integration of multiple renewable energy sources and sensitive loads. A comprehensive methodology for developing a basic circuit model of VSCs, focusing on the key components and principals involved, is presented in this paper. The methodology includes the modeling of space vector pulse-width modulation (SVPWM) as well as the direct quadrature zero synchronous reference frame. Different design controls, including the design of current control loop in the S-domain, the design of the direct current (DC) bus voltage control loop in the S-domain, and the design of the alternating current (AC) voltage control loop in the S-domain, are explored to capture the dynamic behavior and control strategies of VSCs accurately. The proposed methodology provides a systematic framework for modeling VSCs, enabling engineers and researchers to analyze their performance and assess their impact on power system stability and operation. Future studies can be conducted by using case studies and simulation scenarios to show the efficiency and applicability of the developed models in analyzing VSC-based power electronics applications, including high-voltage direct current (HVDC) transmission systems and flexible alternating current transmission systems (FACTS). The significance of this work lies in its potential to advance the understanding and application of VSCs, contributing to more resilient and efficient power systems. By providing a solid foundation for future research and development, this study supports the ongoing integration of renewable energy sources and the advancement of modern electrical infrastructure. Full article
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<p>Solid-state power converter groups based on their operating transformation [<a href="#B6-appliedmath-04-00048" class="html-bibr">6</a>].</p>
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<p>Voltage source converter with three phase-2 levels [<a href="#B7-appliedmath-04-00048" class="html-bibr">7</a>].</p>
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<p>A typical SVPWM diagram for a voltage source inverter with two levels.</p>
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<p>Output switching sequence at the first sector.</p>
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<p>Space phasor and <span class="html-italic">αβ</span>0 reference frame.</p>
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<p>Space phasor and DQ0 reference frame.</p>
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<p>A two-level VSC circuit diagram with an L filter included.</p>
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<p>An L filter in a simplified VSC per-phase circuit.</p>
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<p>Current-controlled VSC system block diagram in simplified form.</p>
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<p>Two-level VSC with an L filter and a DC link circuit bleed resistor.</p>
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<p>VSC <span class="html-italic">d</span>-axis component configuration with a bleed resistor and a L filter.</p>
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<p>Simplified DC link voltage loop model of the VSC system.</p>
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<p>Two level VSC with an LC filter.</p>
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<p>A VSC with an LC filter per-phase circuit in a simplified.</p>
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<p>A block diagram for the VSC system AC voltage loop in a simplified form.</p>
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16 pages, 7216 KiB  
Article
Humidity Diffusion Process Analysis and Life Prediction of a VSC-HVDC Control Protection Device Based on a Finite Element Simulation Method
by Changgeng Li, Yutao Cheng and Xiaochao Hou
Electronics 2024, 13(15), 2888; https://doi.org/10.3390/electronics13152888 - 23 Jul 2024
Viewed by 449
Abstract
Voltage Source Converter-based High-Voltage Direct Current Transmission (VSC-HVDC) is essential for integrating renewable energy sources and facilitating inter-regional power transmission. This study evaluates the reliability of control and protection devices within these systems, which are crucial for the stable operation of power grids. [...] Read more.
Voltage Source Converter-based High-Voltage Direct Current Transmission (VSC-HVDC) is essential for integrating renewable energy sources and facilitating inter-regional power transmission. This study evaluates the reliability of control and protection devices within these systems, which are crucial for the stable operation of power grids. Humidity significantly affects both the operational conditions and lifespan of these devices. Previous studies, reliant on extensive full-condition fatigue testing, have lacked effective test models and detailed analyses of mechanisms. To address this gap, a humidity diffusion model was developed to comprehensively investigate moisture diffusion mechanisms. Using the insights gained, the Hallberg–Peck model was applied to predict the lifespan of these devices, quantitatively assessing how changes in humidity affect their reliability. This approach employs a stringent failure criterion, leading to a conservative predicted lifespan. This method achieved a prediction accuracy of 85.648% compared to the benchmarks in GB/T 2423.50-2012, validating the accuracy of our model and the effectiveness of our simulation technology under stringent conditions. This research provides vital theoretical data and serves as an essential tool for guiding the precise maintenance of equipment in varying environmental humidity levels. Full article
(This article belongs to the Special Issue Advanced Monitoring of Smart Critical Infrastructures)
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<p>Temperature and Humidity Variations Across Different Materials (<b>a</b>) variation of temperature and humidity between different materials; (<b>b</b>) variation of humidity and relative humidity between different materials.</p>
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<p>Analyzing the Sensitivity of Af to Humidity, Temperature and Activation Energy.</p>
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<p>Finite element simulation flowchart.</p>
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<p>Key component structure diagram (<b>a</b>) exploded view of electrolytic capacitor with each component structure; (<b>b</b>) exploded view of optocoupler with each component structure.</p>
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<p>Moist air domain establishment and meshing.</p>
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<p>Simulation results of moisture diffusion (<b>a</b>) transient residual diagram; (<b>b</b>) distribution of water vapor pressure on electrolytic capacitor surface.</p>
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<p>Humidity diffusion analysis diagram (<b>a</b>) humidity distribution of aluminum electrolytic capacitors; (<b>b</b>) relative humidity changes of different materials of electrolytic capacitor.</p>
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<p>Humidity diffusion analysis diagram (<b>a</b>) humidity distribution of the photocoupler; (<b>b</b>) relative humidity changes of different materials of photocoupler.</p>
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<p>Relationship between the ambient humidity and internal component’s humidity of the device (<b>a</b>) the impact of ambient temperature and humidity on the relative humidity of polyethylene; (<b>b</b>) the impact of ambient temperature and humidity on the relative humidity of epoxy.</p>
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<p>Variation of electrolytic capacitor life with temperature and humidity (<b>a</b>) taking the humidity of polyethylene as the judgment basis; (<b>b</b>) taking the humidity of epoxy as the judgment basis.</p>
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<p>Fitting surface of electrolytic capacitor life with environmental temperature and humidity.</p>
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<p>Fitting surface of optocoupler life with environmental temperature and humidity.</p>
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14 pages, 5374 KiB  
Article
Physics-Informed Neural Network-Based VSC Back-to-Back HVDC Impedance Model and Grid Stability Estimation
by Minhyeok Chang, Yoongun Jung, Seokjun Kang and Gilsoo Jang
Electronics 2024, 13(13), 2590; https://doi.org/10.3390/electronics13132590 - 1 Jul 2024
Viewed by 545
Abstract
With the increase in the number of power electronic devices in power systems, various techniques for assessing their stability have emerged. Among these techniques, impedance model-based stability analysis techniques have been widely used. However, conducting such analyses across multiple operating points requires abundant [...] Read more.
With the increase in the number of power electronic devices in power systems, various techniques for assessing their stability have emerged. Among these techniques, impedance model-based stability analysis techniques have been widely used. However, conducting such analyses across multiple operating points requires abundant impedance measurement data from power electronic devices. In this paper, we propose a method for constructing impedance models of equipment with fewer impedance measurement data in voltage-source converter (VSC) back-to-back high-voltage direct current (HVDC) systems using physics-informed neural networks. Furthermore, given the power system states, we present a neural network approach to estimate grid stability at different operating points. Validation via PSCAD/EMTDC simulations and a PyTorch neural network confirmed the adequacy of these models. Full article
(This article belongs to the Special Issue Advances in Enhancing Energy and Power System Stability and Control)
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Figure 1
<p>VSC back-to-back HVDC schematic diagram.</p>
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<p>VSC back-to-back HVDC control diagram.</p>
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<p>Perturb-and-observe-based impedance identification.</p>
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<p>Proposed physics-informed neural network-based impedance model.</p>
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<p>Proposed neural network-based stability estimation model of VSC back-to-back HVDC.</p>
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<p>Magnitude of <math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="bold-italic">Y</mi> </mrow> <mrow> <mi>d</mi> <mi>d</mi> </mrow> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="bold-italic">Y</mi> </mrow> <mrow> <mi>d</mi> <mi>q</mi> </mrow> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="bold-italic">Y</mi> </mrow> <mrow> <mi>q</mi> <mi>d</mi> </mrow> </msub> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="bold-italic">Y</mi> </mrow> <mrow> <mi>q</mi> <mi>q</mi> </mrow> </msub> </mrow> </semantics></math> for VSC-1 (<b>a</b>–<b>d</b>) and VSC-2 (<b>e</b>–<b>h</b>).</p>
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<p>Magnitude of <math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="bold-italic">Y</mi> </mrow> <mrow> <mi>d</mi> <mi>d</mi> </mrow> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="bold-italic">Y</mi> </mrow> <mrow> <mi>d</mi> <mi>q</mi> </mrow> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="bold-italic">Y</mi> </mrow> <mrow> <mi>q</mi> <mi>d</mi> </mrow> </msub> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="bold-italic">Y</mi> </mrow> <mrow> <mi>q</mi> <mi>q</mi> </mrow> </msub> </mrow> </semantics></math> for VSC-1 (<b>a</b>–<b>d</b>) and VSC-2 (<b>e</b>–<b>h</b>).</p>
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<p>Average neural network data loss.</p>
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<p>Neural network-based stability estimation model training setup.</p>
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<p>Modified IEEE-39 bus with VSC back-to-back HVDC.</p>
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18 pages, 5756 KiB  
Article
Fault-Tolerant Three-Vector Model-Predictive-Control-Based Grid-Connected Control Strategy for Offshore Wind Farms
by Jiahui Wu, Jiangyong Li, Haiyun Wang, Guodong Li and Yalun Ru
Electronics 2024, 13(12), 2316; https://doi.org/10.3390/electronics13122316 - 13 Jun 2024
Viewed by 498
Abstract
In the conventional dual-loop vector control strategy of Voltage Source Converter-based High Voltage Direct Current (VSC-HVDC) systems employed in offshore wind farms, challenges such as complex PI parameter-tuning and slow response speed exist. Furthermore, a single-phase bridge-arm fault in the converter station can [...] Read more.
In the conventional dual-loop vector control strategy of Voltage Source Converter-based High Voltage Direct Current (VSC-HVDC) systems employed in offshore wind farms, challenges such as complex PI parameter-tuning and slow response speed exist. Furthermore, a single-phase bridge-arm fault in the converter station can lead to a change in system parameters, resulting in the failure of the original control strategy. Hence, this paper proposes a fault-tolerant control strategy for grid-connected offshore wind farms, based on model predictive control (MPC). Firstly, the predictive models for both normal and fault-tolerant states of the grid-side converter station are established based on the system structure of the grid-side converter station and a super-local model. Subsequently, a cost function is constructed using the power error, with the optimization objective set as the value function. This approach allows for accurate prediction of the future switching states of the grid-tied inverter to track the reference power. Finally, a simulation model of the offshore wind power grid system is established in the MATLAB/Simulink (2022a) environment. The results demonstrate that the grid-side converter station can effectively operate in a fault-tolerant manner under the proposed control strategy, thereby enhancing the disturbance resistance and fault-recovery capabilities of the offshore wind VSC-HVDC system. Full article
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<p>Offshore wind farm grid integration diagram.</p>
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<p>Topology diagram of the OWF-VSC.</p>
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<p>OWF-VSC control strategy.</p>
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<p>Topology diagram of the fault-tolerant GS-VSC.</p>
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<p>Vector range.</p>
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<p>The GS-VSC fault-tolerant MPC strategy.</p>
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<p>Response curves for grid-side AC three-phase faults under two types of control: (<b>a</b>) DC bus voltage and (<b>b</b>) the GS-VSC’s reactive power.</p>
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<p>Response curves for reactive power glitch under two controls: (<b>a</b>) DC bus voltage and (<b>b</b>) the GS-VSC’s reactive power.</p>
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<p>Response curves for a reactive power glitch under two controls: (<b>a</b>) DC bus voltage and (<b>b</b>) the GS-VSC’s reactive power.</p>
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<p>Response curves for single-phase bridge-arm faults under both controls: (<b>a</b>) DC bus voltage; (<b>b</b>) grid-connected current waveforms under fault-free conventional double closed-loop control; (<b>c</b>) grid-connected current waveforms under fault-tolerant conventional dual-loop control; (<b>d</b>) grid-connected current waveforms under fault-tolerant three-vector MPC control; (<b>e</b>) THD of grid-connected current under fault-free conventional double closed-loop control; (<b>f</b>) THD of grid-connected current under fault-tolerant conventional double closed-loop control; and (<b>g</b>) THD of grid-connected current under fault-tolerant three-vector MPC control.</p>
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<p>Response curves for single-phase bridge-arm faults under both controls: (<b>a</b>) DC bus voltage; (<b>b</b>) grid-connected current waveforms under fault-free conventional double closed-loop control; (<b>c</b>) grid-connected current waveforms under fault-tolerant conventional dual-loop control; (<b>d</b>) grid-connected current waveforms under fault-tolerant three-vector MPC control; (<b>e</b>) THD of grid-connected current under fault-free conventional double closed-loop control; (<b>f</b>) THD of grid-connected current under fault-tolerant conventional double closed-loop control; and (<b>g</b>) THD of grid-connected current under fault-tolerant three-vector MPC control.</p>
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<p>Response curves for single-phase bridge-arm faults under both controls: (<b>a</b>) DC bus voltage; (<b>b</b>) grid-connected current waveforms under fault-free conventional double closed-loop control; (<b>c</b>) grid-connected current waveforms under fault-tolerant conventional dual-loop control; (<b>d</b>) grid-connected current waveforms under fault-tolerant three-vector MPC control; (<b>e</b>) THD of grid-connected current under fault-free conventional double closed-loop control; (<b>f</b>) THD of grid-connected current under fault-tolerant conventional double closed-loop control; and (<b>g</b>) THD of grid-connected current under fault-tolerant three-vector MPC control.</p>
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<p>Harmonic distortion ratio comparison.</p>
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8 pages, 500 KiB  
Data Descriptor
Data for Optimal Estimation of Under-Frequency Load Shedding Scheme Parameters by Considering Virtual Inertia Injection
by Santiago Bustamante-Mesa, Jorge W. Gonzalez-Sanchez, Sergio D. Saldarriaga-Zuluaga, Jesús M. López-Lezama and Nicolás Muñoz-Galeano
Data 2024, 9(6), 80; https://doi.org/10.3390/data9060080 - 13 Jun 2024
Viewed by 597
Abstract
The data presented in this paper are related to the paper entitled “Optimal Estimation of Under-Frequency Load Shedding Scheme Parameters by Considering Virtual Inertia Injection”, available in the Energies journal. Here, data are included to show the results of an Under-Frequency Load Shedding [...] Read more.
The data presented in this paper are related to the paper entitled “Optimal Estimation of Under-Frequency Load Shedding Scheme Parameters by Considering Virtual Inertia Injection”, available in the Energies journal. Here, data are included to show the results of an Under-Frequency Load Shedding (UFLS) scheme that considers the injection of virtual inertia by a VSC-HVDC link. The data obtained in six cases which were considered and analyzed are shown. In this paper, each case represents a different frequency response configuration in the event of generation loss, taking into account the presence or absence of a VSC-HVDC link, traditional and optimized UFLS schemes, as well as the injection of virtual inertia by the VSC-HVDC link. Data for each example contain the state of the relay, threshold, position in every delay, load shed, and relay configuration parameters. Data were obtained through Digsilent Power Factory and Python simulations. The purpose of this dataset is so that other researchers can reproduce the results reported in our paper. Full article
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<p>Co-simulation framework using Digsilent Power Factory/Python for the UFLS scheme.</p>
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17 pages, 3753 KiB  
Article
Research on Fault Identification of Hybrid Multi-Feed High-Voltage Direct Current System Based on Line Commutated Converter and Voltage Source Converter
by Ting Wang, Kun Chen, Long’en Zhang, Xingyang Hu, Hengxuan Li and Pangqi Ye
Energies 2024, 17(9), 2215; https://doi.org/10.3390/en17092215 - 4 May 2024
Cited by 1 | Viewed by 743
Abstract
With the rapid development of voltage source converter (VSC) and line commutated converter (LCC) technology and the relative concentration of power and load, the inverter station of the flexible DC system is fed into the same AC bus with the conventional DC rectifier [...] Read more.
With the rapid development of voltage source converter (VSC) and line commutated converter (LCC) technology and the relative concentration of power and load, the inverter station of the flexible DC system is fed into the same AC bus with the conventional DC rectifier station, and the high-voltage direct current (HVDC) parallel hybrid feed system is formed in structure. As the electrical distance between the converter stations is very close, when a fault occurs in the near area, the current on the AC wiring on the VSC side will fluctuate greatly, resulting in the misoperation of the AC wiring protection. For this reason, this paper proposes a fault identification method based on VSC/LCC hybrid multi-fed HVDC system, which discriminates the fault and outputs the protection signal according to the protection criterion, and logically judges the combination of the output protection signal to identify the fault type. The simulation results show that the method can identify all kinds of faults of hybrid multi-feed DC system and solve the problem of protection misoperation of the hybrid multi-feed DC system. Full article
(This article belongs to the Section F6: High Voltage)
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<p>LCC-HVDC system protection logic diagram: (<b>a</b>) converter transformer differential protection; (<b>b</b>) converter DC differential protection.</p>
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<p>LCC-HVDC system protection logic diagram: (<b>a</b>) grounding electrode overvoltage protection; (<b>b</b>) DC line traveling wave protection.</p>
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<p>Simulation model of AC feed bus current differential protection in near area AC system.</p>
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<p>Schematic diagram of fault setting in protection area of near area AC system.</p>
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<p>Electrical quantity and action signal of AC feed bus BC phase-to-phase short circuit fault in near area AC system: (<b>a</b>) current difference of three phases A, B, and C; (<b>b</b>) signal output of current differential protection.</p>
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<p>Automatic reclosing of BC interphase short circuit fault of AC feed bus in near area AC system.</p>
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<p>Waveform of AC single-phase ground fault on inverter side of LCC HVDC system.</p>
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<p>Voltage and current waveforms: (<b>a</b>) DC positive bus current; (<b>b</b>) DC voltage.</p>
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<p>Current value in case of serious failure: (<b>a</b>) phase A current of AC connection bus; (<b>b</b>) phase A upper bridge arm current.</p>
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<p>Current value in the case of a common failure: (<b>a</b>) phase A current of AC connection bus; (<b>b</b>) phase A upper bridge arm current.</p>
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<p>Flow chart of fault identification logic judgment for LCC HVDC system.</p>
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<p>Flow chart of fault identification logic judgment for VSC HVDC system.</p>
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<p>Signal of uni-polar ground fault or bipolar short circuit fault of LCC HVDC DC line.</p>
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<p>LCC HVDC AC bus single-phase grounding automatic re-closing signal.</p>
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17 pages, 4832 KiB  
Article
Fault Detection and VSC-HVDC Network Dynamics Analysis for the Faults in Its Host AC Networks
by Kiran Rana, Nand Kishor, Richa Negi and Monalisa Biswal
Appl. Sci. 2024, 14(6), 2378; https://doi.org/10.3390/app14062378 - 12 Mar 2024
Cited by 1 | Viewed by 808
Abstract
High-voltage direct current (HVDC) transmission is preferred over high-voltage alternating current (HVAC) for long power lines for asynchronous power grid interconnection and high-level renewable energy integration. The control and protection functions associated with HVDC systems help with fast and secure clearance of faults. [...] Read more.
High-voltage direct current (HVDC) transmission is preferred over high-voltage alternating current (HVAC) for long power lines for asynchronous power grid interconnection and high-level renewable energy integration. The control and protection functions associated with HVDC systems help with fast and secure clearance of faults. The control and protection challenges in the embedded HVDC network are of great concern for the stable and secure operation of an HVDC network. The DC fault current may reach an extremely high level in a rather short period because of the low impedance in a DC system, which is dangerous for converters, and disturbances in the AC network directly influence the performance of the HVDC system. Sometimes, faults on the AC side may lead to disconnection or failure of the DC link, causing reliability problems as well as huge economic losses. AC and DC protection solutions are being developed for HVDC systems to enhance their sustainability and reliability. As such, AC and DC faults should be detected and cleared at a faster rate. Therefore, in this article, the feasibility of the synchro-squeezed transform (SST) is analyzed for detection purposes. For more accurate and faster detection, the signal is first decomposed using the empirical mode decomposition (EMD) technique, and then the SST is applied. A discrete Teager energy (DTE) spectrum is obtained with the processed signal, which works as the detection index. The algorithm shows low sampling frequency requirements, with higher efficiency and reliability for the purpose. PSCAD/EMTDC version 4.6 software and MATLAB 2022a software is used for the modeling and simulation. Full article
(This article belongs to the Special Issue Power Systems: Protection and Connection with Converters)
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<p>Flowchart of proposed technique.</p>
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<p>MMC HVDC network.</p>
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<p>(<b>a</b>) Current signal for AG fault. (<b>b</b>) Current signal for ABG fault. (<b>c</b>) Current signal for AB fault. (<b>d</b>) Current signal for ABC fault.</p>
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<p>Current signal decomposition for ABC faults.</p>
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<p>(<b>a</b>) DTE index for AG fault. (<b>b</b>) DTE index for ABG fault. (<b>c</b>) DTE index for AB fault. (<b>d</b>) DTE index for ABC fault.</p>
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<p>TFRs obtained for AG fault (<b>a</b>) using HHT and (<b>b</b>) using SST.</p>
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<p>TFRs obtained for AB fault (<b>a</b>) using HHT and (<b>b</b>) using SST.</p>
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<p>TFRs obtained for ABG fault (<b>a</b>) using HHT and (<b>b</b>) using SST.</p>
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<p>TFRs obtained for ABC fault (<b>a</b>) using HHT and (<b>b</b>) using SST.</p>
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<p>(<b>a</b>) Current waveform during zero-crossing fault. (<b>b</b>) Current waveform during peak crossing fault. (<b>c</b>) DTE during zero-crossing fault. (<b>d</b>) DTE during peak crossing fault.</p>
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<p>Results for SLS. (<b>a</b>) Current waveform for phase A, (<b>b</b>) DTE for phase A during SLS.</p>
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<p>Results for the presence of noise in the signal. (<b>a</b>) Current waveform for phase A, (<b>b</b>) DTE for phase A in the presence of various SNRs.</p>
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15 pages, 5071 KiB  
Article
Frequency Stability Control Strategy for Voltage Source Converter-Based Multi-Terminal DC Transmission System
by Chao Xing, Mingqun Liu, Junzhen Peng, Yuhong Wang, Chengbo Shang, Zongsheng Zheng, Jianquan Liao and Shilin Gao
Energies 2024, 17(5), 1195; https://doi.org/10.3390/en17051195 - 2 Mar 2024
Cited by 1 | Viewed by 632
Abstract
The voltage source converter-based multi-terminal DC transmission (VSC-MTDC) system can use additional frequency control to respond to the frequency change of faulty AC system. However, the control coefficient of traditional additional frequency control is mostly fixed, and the control flexibility is insufficient, so [...] Read more.
The voltage source converter-based multi-terminal DC transmission (VSC-MTDC) system can use additional frequency control to respond to the frequency change of faulty AC system. However, the control coefficient of traditional additional frequency control is mostly fixed, and the control flexibility is insufficient, so it cannot be adjusted adaptively according to the frequency change of the system. Therefore, a frequency control strategy of the VSC-MTDC system based on fuzzy logic control is proposed. Based on the DC voltage slope controller, this strategy introduces an additional frequency controller based on fuzzy logic control, takes the frequency deviation and frequency change rate as the additional controller input, and dynamically adjusts the control quantity through the fuzzy logic control link to realize the adaptive adjustment of the VSC-MTDC system to the AC system’s frequency. Finally, a three-terminal flexible HVDC system is built on the PSCAD/EMTDC simulation platform for simulation verification. The results show that the proposed control strategy can effectively use the flexible DC system to support the frequency of the AC system and significantly improve the frequency stability of the faulty AC system. Full article
(This article belongs to the Section F: Electrical Engineering)
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<p>Constant DC voltage slope control characteristics.</p>
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<p>Constant DC voltage slope control block diagram.</p>
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<p>Structure of fuzzy logic controller.</p>
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<p>Membership function corresponding to <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>f</mi> </mrow> </semantics></math>.</p>
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<p>Membership function corresponding to <math display="inline"><semantics> <mrow> <mrow> <mrow> <mi mathvariant="normal">d</mi> <mi>f</mi> </mrow> <mo>/</mo> <mrow> <mi mathvariant="normal">d</mi> <mi>t</mi> </mrow> </mrow> </mrow> </semantics></math>.</p>
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<p>Membership function corresponding to <math display="inline"><semantics> <mrow> <msubsup> <mi>P</mi> <mi>ref</mi> <mo>′</mo> </msubsup> </mrow> </semantics></math>.</p>
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<p>Additional frequency controller based on fuzzy logic control.</p>
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<p>Three-terminal flexible HVDC system.</p>
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<p>Frequency of <span class="html-italic">S</span><sub>1</sub> AC system.</p>
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<p>Frequency of <span class="html-italic">S</span><sub>2</sub> AC system.</p>
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<p>Frequency of <span class="html-italic">S</span><sub>3</sub> AC system.</p>
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<p>Active power of converter station VSC1.</p>
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<p>Active power of converter station VSC2.</p>
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<p>Active power of converter station VSC3.</p>
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<p>Frequency of <span class="html-italic">S</span><sub>1</sub> AC system.</p>
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<p>Frequency of <span class="html-italic">S</span><sub>2</sub> AC system.</p>
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<p>Frequency of <span class="html-italic">S</span><sub>3</sub> AC system.</p>
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<p>Active power of converter station VSC1.</p>
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<p>Active power of converter station VSC2.</p>
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<p>Active power of converter station VSC3.</p>
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<p>Frequency of <span class="html-italic">S</span><sub>1</sub> AC system.</p>
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<p>Frequency of <span class="html-italic">S</span><sub>3</sub> AC system.</p>
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<p>Active power of converter station VSC1.</p>
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<p>Active power of converter station VSC3.</p>
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23 pages, 3948 KiB  
Article
A P-Q Coordination Control Strategy of VSC-HVDC and BESS for LVRT Recovery Performance Enhancement
by Zhen Wang, Jialiang Wu, Ruixu Liu and Yu Shan
Electronics 2024, 13(4), 741; https://doi.org/10.3390/electronics13040741 - 12 Feb 2024
Cited by 1 | Viewed by 748
Abstract
Voltage source converter (VSC)-based multi-terminal direct current (MTDC) transmission technology has been a research focus, and the low-voltage ride-through (LVRT) and recovery in receiving-end systems is one of the major problems to consider. A coordinated control strategy for a VSC-MTDC system is proposed [...] Read more.
Voltage source converter (VSC)-based multi-terminal direct current (MTDC) transmission technology has been a research focus, and the low-voltage ride-through (LVRT) and recovery in receiving-end systems is one of the major problems to consider. A coordinated control strategy for a VSC-MTDC system is proposed to improve the frequency and voltage dynamics in the receiving-end system during the LVRT and recovery processes. A battery energy storage system (BESS) plays a significant role in providing frequency and voltage support with its flexible power control capability. During the LVRT process, the BESS can provide reactive current injection and active current absorption to improve system stability in the AC side, and during the recovery process, an adaptive current limitation method is proposed for the BESS converter to dynamically adjust the active and reactive power outputs according to the frequency and voltage deviation severity. Meanwhile, the coordination of the sending-end systems and DC chopper can reduce the power output to avoid DC overvoltage during LVRT, and it can also provide frequency support to the receiving-end system with the DC voltage transmitting frequency information during the recovery process. A simulation was carried out on the MATLAB/Simulink platform, and a three-terminal VSC-MTDC system was used to validate the effectiveness of the proposed strategy. Full article
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<p>The diagram of the studied three-terminal VSC-HVDC system.</p>
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<p>The diagram of the overall control strategy.</p>
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<p>The effects of <span class="html-italic">f<sub>BA</sub></span> and <span class="html-italic">V<sub>t</sub></span><sub>,<span class="html-italic">BA</span></sub> on the active and reactive current limitations. (<b>a</b>) The effect of <span class="html-italic">f<sub>BA</sub></span> and <span class="html-italic">V<sub>t</sub></span><sub>,<span class="html-italic">BA</span></sub> on active current limitation; (<b>b</b>) the effect of <span class="html-italic">f<sub>BA</sub></span> and <span class="html-italic">V<sub>t</sub></span><sub>,<span class="html-italic">BA</span></sub> on reactive current limitation.</p>
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<p>The coordination chart of the equipment under the proposed control strategy during the LVRT and recovery processes.</p>
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<p>The diagrams of the system <span class="html-italic">V<sub>t</sub></span>-<span class="html-italic">I<sub>d</sub></span> characteristics. (<b>a</b>) when the grid voltage drop <span class="html-italic">E</span> changes; (<b>b</b>) when the grid impedance amplitude <span class="html-italic">Z<sub>g</sub></span> changes; (<b>c</b>) when the grid impedance angle <span class="html-italic">θ<sub>g</sub></span> changes; (<b>d</b>) when the proportional coefficient <span class="html-italic">k<sub>q</sub></span> changes; (<b>e</b>) when the proportional coefficient <span class="html-italic">k<sub>d</sub></span> changes.</p>
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<p>The simulation results for deep voltage drop in receiving-end system AC1. (<b>a</b>) The frequency in system AC1; (<b>b</b>) the terminal voltage in system AC1; (<b>c</b>) the active power output of the BESS converter; (<b>d</b>) the reactive power output of the BESS converter; (<b>e</b>) the active power output of the receiving-end converter; (<b>f</b>) the reactive power output of the receiving-end converter; (<b>g</b>) the DC voltage of the DC transmission line; (<b>h</b>) the current in DC chopper.</p>
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<p>The simulation results for deep voltage drop in receiving-end system AC1. (<b>a</b>) The frequency in system AC1; (<b>b</b>) the terminal voltage in system AC1; (<b>c</b>) the active power output of the BESS converter; (<b>d</b>) the reactive power output of the BESS converter; (<b>e</b>) the active power output of the receiving-end converter; (<b>f</b>) the reactive power output of the receiving-end converter; (<b>g</b>) the DC voltage of the DC transmission line; (<b>h</b>) the current in DC chopper.</p>
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<p>The simulation results for light voltage drop in receiving-end system AC1. (<b>a</b>) The frequency in system AC1; (<b>b</b>) the terminal voltage in system AC1; (<b>c</b>) the active power output of the BESS converter; (<b>d</b>) the reactive power output of the BESS converter; (<b>e</b>) the active power output of the receiving-end converter; (<b>f</b>) the reactive power output of the receiving-end converter; (<b>g</b>) the DC voltage of the DC transmission line; (<b>h</b>) the active power output of the sending-end system AC2 and WF.</p>
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<p>The diagram of the modified sending-end system AC2 with SGs, load nodes, and a BESS.</p>
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<p>The simulation results for deep voltage drop in sending-end system AC2. (<b>a</b>) The frequency in system AC2; (<b>b</b>) the terminal voltage in system AC2; (<b>c</b>) the active power output of the BESS converter; (<b>d</b>) the reactive power output of the BESS converter; (<b>e</b>) the active power output of the sending-end converter; (<b>f</b>) the reactive power output of the sending-end converter; (<b>g</b>) the DC voltage of the DC transmission line; (<b>h</b>) the active power output of the receiving-end converter and WF.</p>
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<p>The simulation results for deep voltage drop in sending-end system AC2. (<b>a</b>) The frequency in system AC2; (<b>b</b>) the terminal voltage in system AC2; (<b>c</b>) the active power output of the BESS converter; (<b>d</b>) the reactive power output of the BESS converter; (<b>e</b>) the active power output of the sending-end converter; (<b>f</b>) the reactive power output of the sending-end converter; (<b>g</b>) the DC voltage of the DC transmission line; (<b>h</b>) the active power output of the receiving-end converter and WF.</p>
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<p>The diagram of the generator governor and turbine.</p>
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20 pages, 2905 KiB  
Article
Optimal Estimation of Under-Frequency Load Shedding Scheme Parameters by Considering Virtual Inertia Injection
by Santiago Bustamante-Mesa, Jorge W. Gonzalez-Sanchez, Sergio D. Saldarriaga-Zuluaga, Jesús M. López-Lezama and Nicolás Muñoz-Galeano
Energies 2024, 17(2), 279; https://doi.org/10.3390/en17020279 - 5 Jan 2024
Cited by 2 | Viewed by 1090
Abstract
Under-frequency load shedding (UFLS) schemes are the latest safety measures applied for safeguarding the integrity of the grid against abrupt frequency imbalances. The overall inertia of electrical power systems is expected to decrease with an increased penetration of renewable energy as well as [...] Read more.
Under-frequency load shedding (UFLS) schemes are the latest safety measures applied for safeguarding the integrity of the grid against abrupt frequency imbalances. The overall inertia of electrical power systems is expected to decrease with an increased penetration of renewable energy as well as elements connected through power electronic interfaces. However, voltage source converter-based high voltage direct current (VSC-HVDC) links can provide virtual inertia through a control loop that allows for a reaction to occur at certain frequency fluctuations. This paper evaluates a UFLS scheme that considers the injection of virtual inertia through a VSC-HVDC link. A genetic algorithm (GA) is used to determine the location of the UFLS relays, the activation threshold of each stage, the delay time and the percentage of load shedding at each stage. It was found that the virtual inertia causes the nadir to delay and sometimes reach a greater depth. Furthermore, the implemented GA approximates the frequency response to the limits set with the constraints, reducing the load shedding but achieving a steeper nadir and a lower steady-state frequency level than traditional UFLS. The simulations were performed using the IEEE 39-bus test system. Full article
(This article belongs to the Section F: Electrical Engineering)
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<p>Generic block diagram of inertial control on VSC-HVDC links.</p>
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<p>Basic parameters of the UFLS scheme.</p>
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<p>Flowchart of the implemented genetic algorithm (GA).</p>
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<p>Example of an individual or candidate solution.</p>
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<p>Co-Simulation framework for the UFLS scheme.</p>
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<p>IEEE 39-bus test system with VSC-HVDC link.</p>
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<p>Simplified model of the wind farm and the VSC-HVDC link.</p>
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<p>Comparison between the frequency response of cases 1 and 2.</p>
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<p>Frequency response under generation loss, cases 3, 4, 5 and 6. (<b>a</b>) Time window of 90 s. (<b>b</b>) Nadir region, range of 17 s between 3 and 19 s of the simulations.</p>
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<p>Frequency response under generation loss, cases 3, 4, 5 and 6. (<b>a</b>) Time window of 90 s. (<b>b</b>) Nadir region, range of 17 s between 3 and 19 s of the simulations.</p>
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<p>Comparison between load shedding using the UFLS scheme of case studies 3, 4, 5 and 6.</p>
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17 pages, 6840 KiB  
Article
A Multi-Terminal Control Method for AC Grids Based on a Hybrid High-Voltage Direct Current with Cascaded MMC Converters
by Lei Liu, Xiaopeng Li, Qin Jiang, Yufei Teng, Mingju Chen, Yongfei Wang, Xueyang Zeng, Yiping Luo and Pengyu Pan
Electronics 2023, 12(23), 4799; https://doi.org/10.3390/electronics12234799 - 27 Nov 2023
Cited by 1 | Viewed by 830
Abstract
The hybrid high-voltage direct current (HVDC) transmission system with cascaded MMC converters has become a promising alternative for possessing the technical merits of both line-commuted converter (LCC) and voltage source converter (VSC), resulting in favorable characteristics and potential control of good prospect. This [...] Read more.
The hybrid high-voltage direct current (HVDC) transmission system with cascaded MMC converters has become a promising alternative for possessing the technical merits of both line-commuted converter (LCC) and voltage source converter (VSC), resulting in favorable characteristics and potential control of good prospect. This paper pays heightened attention to the feasible power and DC voltage control modes of a hybrid HVDC system; characteristics of master–slave control show higher flexibility than the LCC-VSC HVDC system, which demonstrates that the exceptional potential can serve to stability support the AC power grids. To optimize the control effect, besides damping level to attenuate power oscillations, the robustness suitable for various faults is also considered to obtain a multi-objective control problem. A detailed solution is proceeding using the TLS-ESPRIT identification algorithm and H2/H hybrid robust control theory. This motivates multi-terminal controllers in the LCC rectifier and MMC inverters, which immensely improve the stability of both sending and receiving girds at the same time. According to the parameters of the actual hybrid HVDC project, the simulation model is established in PSCAD v4.6.2 software, and proposed control methods have been verified to satisfy damping objectives and perform well in multiple operating scenarios. Full article
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<p>The configuration of the BHT-JS hybrid HVDC system.</p>
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<p>Control modes of LCC converters.</p>
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<p>The CPC diagram.</p>
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<p>The power and UI characteristics of a hybrid cascaded HVDC system.</p>
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<p>Diagram of the robust control model.</p>
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<p>Diagram of damping requirements.</p>
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<p>The supplementary damping controller of the rectifier LCC converter for sending AC grid.</p>
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<p>The supplementary damping controller of MMC2 in CPC for ending AC grid.</p>
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<p>The pole locations of <b><span class="html-italic">G</span><sub>1</sub></b> with and without controller.</p>
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<p>The rotor speed of the sending AC system.</p>
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<p>The rotor speed of the receiving AC system.</p>
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<p>The DC power of the LCC inverter.</p>
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<p>The DC power of the MMC1 inverter.</p>
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<p>The rotor speed of the sending AC system.</p>
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<p>The rotor speed of the receiving AC system.</p>
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<p>The DC power of the LCC inverter.</p>
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<p>The DC power of the MMC1 inverter.</p>
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<p>The rotor speed of the sending AC system.</p>
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<p>The rotor speed of the receiving AC system.</p>
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<p>The active power of the LCC inverter.</p>
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<p>The DC power of the MMC1 inverter.</p>
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3795 KiB  
Proceeding Paper
Nonlinear Control Design of Three-Level Neutral-Point-Clamped-Based High-Voltage Direct Current Systems for Enhanced Availability during AC Faults with Semi-Experimental Validation
by Ilyass El Myasse, Aziz Watil, Abdelmounime El Magri and Ambe Harrison
Eng. Proc. 2023, 56(1), 35; https://doi.org/10.3390/ASEC2023-15336 - 26 Oct 2023
Cited by 4 | Viewed by 461
Abstract
This research paper addresses the issue of enhancing the operational availability of NPC three-level converter-based high-voltage direct current (HVDC) transport systems during alternating current (AC) grid fault conditions. During short-circuit faults in power transmission lines, voltage sags can occur, causing fluctuations in the [...] Read more.
This research paper addresses the issue of enhancing the operational availability of NPC three-level converter-based high-voltage direct current (HVDC) transport systems during alternating current (AC) grid fault conditions. During short-circuit faults in power transmission lines, voltage sags can occur, causing fluctuations in the DC link voltage of converter systems. These voltage sags have the potential to induce a reversed power flow and trip the VSC-HVDC transmission system. The objective of this paper is to develop a nonlinear control technique that investigates the fault ride-through (FRT) capability of VSC-HVDC transmission system characteristics during voltage sag events. To achieve this, we conduct semi-experimental investigations using Processor-in-the-Loop (PIL) simulations and analyze the results. Symmetrical and asymmetrical voltage sag events with different remaining voltages are applied to an AC grid, and their effects are observed for varying durations. The proposed nonlinear control technique aims to mitigate the impact of voltage sags on the operational availability of HVDC transport systems. By analyzing the semi-experimental results, we aim to gain insights into the FRT capability of the VSC-HVDC transmission system. Full article
(This article belongs to the Proceedings of The 4th International Electronic Conference on Applied Sciences)
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<p>Topology of three-phase NPC-based HVDC transmission system.</p>
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<p>PIL test of the suggested approach using an eZdsp F28335 Discovery board.</p>
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<p>The performance of the proposed strategy under three-phase voltage sags.</p>
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22 pages, 10826 KiB  
Article
Analysis of Onshore Synthetic Inertia and Primary Control Reserve Contributions of Alternating Current-Side Meshed Offshore Grids with Voltage-Source Converter and Diode Rectifier Unit High-Voltage Direct Current Connections
by Michael Herrmann, Merlin Alkemper and Lutz Hofmann
Energies 2023, 16(18), 6700; https://doi.org/10.3390/en16186700 - 19 Sep 2023
Viewed by 904
Abstract
The increasing use of renewable energy sources in place of conventional generation units is leading to a reduction in onshore inertia and to the development of offshore wind park grids connected by multiple high-voltage direct current (HVDC) connections to the onshore alternating current [...] Read more.
The increasing use of renewable energy sources in place of conventional generation units is leading to a reduction in onshore inertia and to the development of offshore wind park grids connected by multiple high-voltage direct current (HVDC) connections to the onshore alternating current (AC) grid. For AC-side meshed offshore grids with voltage-source converter (VSC) and diode rectifier unit (DRU) HVDC connections towards onshore grids, this study focuses on the energetic feasibility of synthetic inertia (SI) and primary control reserve (PCR) contributions triggered locally at the onshore converters of both connection types. To this end, the obstacles preventing contributions for VSC HVDC connections and the mechanisms allowing contributions for DRU HVDC connections are identified first. Based on these findings, the article proposes an enhancement of the offshore HVDC converter controls that is continuously active and allows locally triggered onshore contributions at all onshore HVDC converters of both connection types without using communication and requiring only minimal system knowledge. Additional simulations confirm that, although the enhancement is continuously active, the operational performance of the offshore HVDC converter controls for normal offshore grid operation and its robustness against offshore AC-side faults are not affected. Full article
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<p>Expected development of the fundamental offshore grid structure of future erections: (<b>a</b>) dedicated HVDC connections; (<b>b</b>) AC-side parallel HVDC connections; (<b>c</b>) AC-side meshed HVDC connections; (<b>d</b>) AC- and DC-side meshed HVDC connections.</p>
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<p>Use of a dedicated (<b>a</b>) VSC and (<b>b</b>) DRU HVDC connection for OWP connection.</p>
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<p>Layout of the offshore AC-side meshed grid model with the three main nodes A, B and C and with indication of the cable connection lengths (green), rated HVDC transmission power (orange), and rated OWP power (blue) [<a href="#B50-energies-16-06700" class="html-bibr">50</a>].</p>
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<p>Layout of an offshore DRU HVDC converter including reactive power compensation and harmonic filters in the offshore grid model in <a href="#energies-16-06700-f003" class="html-fig">Figure 3</a> [<a href="#B14-energies-16-06700" class="html-bibr">14</a>,<a href="#B15-energies-16-06700" class="html-bibr">15</a>,<a href="#B16-energies-16-06700" class="html-bibr">16</a>,<a href="#B49-energies-16-06700" class="html-bibr">49</a>,<a href="#B50-energies-16-06700" class="html-bibr">50</a>].</p>
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<p>Structure of the offshore HVDC converter controls [<a href="#B50-energies-16-06700" class="html-bibr">50</a>].</p>
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<p>Block diagram of the voltage control in <a href="#energies-16-06700-f005" class="html-fig">Figure 5</a>: (<b>a</b>) d-axis component control path; (<b>b</b>) q-axis component control path [<a href="#B50-energies-16-06700" class="html-bibr">50</a>].</p>
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<p>Block diagram of the current controls of each converter in <a href="#energies-16-06700-f005" class="html-fig">Figure 5</a> with the distinct components highlighted in different colours [<a href="#B50-energies-16-06700" class="html-bibr">50</a>].</p>
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<p>Structure of the onshore HVDC converter controls [<a href="#B50-energies-16-06700" class="html-bibr">50</a>].</p>
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<p>Block diagram of the onshore converter controls in <a href="#energies-16-06700-f008" class="html-fig">Figure 8</a> [<a href="#B50-energies-16-06700" class="html-bibr">50</a>].</p>
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<p>Block diagram of the DC voltage path of the onshore converter controls extended by the simplified modeling of onshore SI and PCR contributions (red).</p>
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<p>Active power response of an onshore HVDC converter for the defined active power schedule used to model SI and PCR contributions.</p>
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<p>AC-side active power curves of the (<b>a</b>) onshore and (<b>b</b>) offshore HVDC converters for the active power schedule triggered at HVDC 5 (VSC HVDC connection) in grid model variant 1.</p>
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<p>DC-side voltage curve at the onshore converter of HVDC 5 for the active power schedule triggered at HVDC 5 (VSC HVDC connection) in grid model variant 1.</p>
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<p>AC-side active power curves of (<b>a</b>) all onshore and (<b>b</b>) the offshore VSC HVDC converters for the active power schedule triggered at HVDC 1 (DRU HVDC connection) in grid model variant 2.</p>
Full article ">Figure 15
<p>DC-side voltage curve at the onshore converter of HVDC 1 for the active power schedule triggered at HVDC 1 (DRU HVDC connection) in grid model variant 2.</p>
Full article ">Figure 16
<p>Onshore (<b>a</b>) AC-side active power curves of the HVDC connections and (<b>b</b>) DC-side voltage curves of the DRU HVDC connections for the active power schedule triggered at HVDC 4 (DRU HVDC connection) in grid model variant 4.</p>
Full article ">Figure 17
<p>Simplified steady-state circuit of the DC link of a VSC HVDC connection with indication of the onshore (blue) and offshore (green) side.</p>
Full article ">Figure 18
<p>Block diagram of the offshore current controls extended by the proposed enhancement (red) to allow for onshore contributions.</p>
Full article ">Figure 19
<p>AC-side active power curves of the (<b>a</b>) onshore and (<b>b</b>) offshore HVDC converters for the active power schedule triggered at HVDC 5 (VSC HVDC connection) in grid model variant 1 using the enhanced offshore controls.</p>
Full article ">Figure 20
<p>DC-side voltage curve at the onshore converter of HVDC 5 for the active power schedule triggered at HVDC 5 (VSC HVDC connection) in grid model variant 1 using the enhanced offshore controls.</p>
Full article ">Figure 21
<p>AC-side active power curves of (<b>a</b>) all onshore and (<b>b</b>) the offshore VSC HVDC converters for the active power schedule triggered at HVDC 5 (VSC HVDC connection) in grid model variant 3 using the enhanced offshore controls.</p>
Full article ">Figure 22
<p>AC-side active power curves of (<b>a</b>) all onshore and (<b>b</b>) the offshore VSC HVDC converters for the active power schedule triggered at HVDC 5 (VSC HVDC connection) in grid model variant 4 using the enhanced offshore controls.</p>
Full article ">Figure 23
<p>Onshore (<b>a</b>) AC-side active power curves of the HVDC connections and (<b>b</b>) DC-side voltage curves of the DRU HVDC connections for the active power schedule triggered at HVDC 4 (DRU HVDC connection) in grid model variant 4 using the enhanced offshore controls.</p>
Full article ">Figure 24
<p>(<b>a</b>) Voltage curves at node A; AC-side active power curves of the offshore HVDC converters for the offshore AC voltage setpoint increase (event 1) in grid model variant 1 (<b>b</b>) with and (<b>c</b>) without the offshore control enhancement.</p>
Full article ">Figure 25
<p>AC-side active power curves of the onshore HVDC converters for the OWP generation decrease (event 4) in grid model variant 4 (<b>a</b>) with and (<b>b</b>) without the offshore control enhancement.</p>
Full article ">Figure 26
<p>AC-side current curves of the offshore converter of HVDC 2 for the three-phase short circuit at node A (event 6) in grid model variant 3 (<b>a</b>) with and (<b>b</b>) without the offshore control enhancement.</p>
Full article ">Figure 27
<p>AC-side active power curves of the offshore HVDC converters for the tripping of HVDC 2 (event 8) in grid model variant 1 (<b>a</b>) with and (<b>b</b>) without the offshore control enhancement.</p>
Full article ">
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