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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Energy Res.</journal-id>
<journal-title-group>
<journal-title>Frontiers in Energy Research</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Energy Res.</abbrev-journal-title>
</journal-title-group>
<issn pub-type="epub">2296-598X</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">1764223</article-id>
<article-id pub-id-type="doi">10.3389/fenrg.2025.1764223</article-id>
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<article-categories>
<subj-group subj-group-type="heading">
<subject>Original Research</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>Benchmark model of the DC sending-end system with high-penetration renewable energy for voltage stability analysis</article-title>
<alt-title alt-title-type="left-running-head">Jiang et al.</alt-title>
<alt-title alt-title-type="right-running-head">
<ext-link ext-link-type="uri" xlink:href="https://doi.org/10.3389/fenrg.2025.1764223">10.3389/fenrg.2025.1764223</ext-link>
</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname>Jiang</surname>
<given-names>Minglei</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
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<contrib contrib-type="author">
<name>
<surname>Shi</surname>
<given-names>Shengyao</given-names>
</name>
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<sup>1</sup>
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<contrib contrib-type="author" corresp="yes">
<name>
<surname>Chao</surname>
<given-names>Pupu</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<uri xlink:href="https://loop.frontiersin.org/people/3308346"/>
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<contrib contrib-type="author">
<name>
<surname>Zhang</surname>
<given-names>Zhipeng</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
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<contrib contrib-type="author">
<name>
<surname>She</surname>
<given-names>Xin</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
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<contrib contrib-type="author">
<name>
<surname>Ma</surname>
<given-names>Kerui</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
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<contrib contrib-type="author">
<name>
<surname>Wang</surname>
<given-names>Kaiping</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
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<contrib contrib-type="author">
<name>
<surname>Zhang</surname>
<given-names>Dachi</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
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<contrib contrib-type="author">
<name>
<surname>Li</surname>
<given-names>Xin</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
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<aff id="aff1">
<label>1</label>
<institution>Research Institute of Economics and Technology, State Grid Jilin Electric Power Company Limited</institution>, <city>Changchun</city>, <country country="CN">China</country>
</aff>
<aff id="aff2">
<label>2</label>
<institution>School of Electrical Engineering, Dalian University of Technology</institution>, <city>Dalian</city>, <state>Liaoning</state>, <country country="CN">China</country>
</aff>
<author-notes>
<corresp id="c001">
<label>&#x2a;</label>Correspondence: Pupu Chao, <email xlink:href="mailto:chaopupu@dlut.edu.cn">chaopupu@dlut.edu.cn</email>
</corresp>
</author-notes>
<pub-date publication-format="electronic" date-type="pub" iso-8601-date="2026-01-26">
<day>26</day>
<month>01</month>
<year>2026</year>
</pub-date>
<pub-date publication-format="electronic" date-type="collection">
<year>2025</year>
</pub-date>
<volume>13</volume>
<elocation-id>1764223</elocation-id>
<history>
<date date-type="received">
<day>09</day>
<month>12</month>
<year>2025</year>
</date>
<date date-type="rev-recd">
<day>23</day>
<month>12</month>
<year>2025</year>
</date>
<date date-type="accepted">
<day>30</day>
<month>12</month>
<year>2025</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2026 Jiang, Shi, Chao, Zhang, She, Ma, Wang, Zhang and Li.</copyright-statement>
<copyright-year>2026</copyright-year>
<copyright-holder>Jiang, Shi, Chao, Zhang, She, Ma, Wang, Zhang and Li</copyright-holder>
<license>
<ali:license_ref start_date="2026-01-26">https://creativecommons.org/licenses/by/4.0/</ali:license_ref>
<license-p>This is an open-access article distributed under the terms of the <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution License (CC BY)</ext-link>. The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</license-p>
</license>
</permissions>
<abstract>
<sec>
<title>Introduction</title>
<p>With the increasing integration of renewable energy, the power grid is gradually facing multi-mode voltage stability problems, especially at the DC sending end. Thus, there is an urgent need to meet the voltage security and stability requirements of the DC sending-end power grid under different scenarios.</p>
</sec>
<sec>
<title>Methods</title>
<p>Based on the topology and operational data of an actual Chinese DC sending-end power grid, a high-penetration renewable-energy DC sending-end system was established using the Power System Analysis Synthesis Program. The system integrates 500 kV AC and &#xB1;800 kV DC networks, as well as renewable energy sources and synchronous generators. Typical multi-mode voltage stability scenarios, including transient overvoltage, low-high voltage interlocking, delayed voltage recovery and voltage collapse, were constructed under specific faults such as DC bipolar lockout and commutation failure. Key influencing factors of multi-mode voltage stability were systematically analyzed, including DC power output, the penetration of renewable energy, renewable energy control parameters, and the configuration of condenser.</p>
</sec>
<sec>
<title>Results</title>
<p>Simulation results indicate that the proposed model can well reflect the voltage stability characteristics under different scenarios and meet the requirements of voltage security and stability analysis for the high-penetration renewable energy DC transmission system.</p>
</sec>
<sec>
<title>Discussion</title>
<p>The established simplified model can serve as a basic platform for voltage stability analysis, providing a reliable foundation for subsequent related research on the voltage stability of DC sending-end power grids with high renewable energy penetration.</p>
</sec>
</abstract>
<kwd-group>
<kwd>benchmark system</kwd>
<kwd>DC sending-end grid</kwd>
<kwd>delayed voltage recovery</kwd>
<kwd>high penetration of renewable energy</kwd>
<kwd>transient overvoltage</kwd>
</kwd-group>
<funding-group>
<funding-statement>The author(s) declared that financial support was received for this work and/or its publication. This work was supported by the Science and Technology Project of State Grid Corporation of China (Grant No. SGJLJY00GPJS2400041) and the Strategic Consulting Project of Jilin Provincial Department of Science and Technology (Grant No. JL2023-09).</funding-statement>
</funding-group>
<counts>
<fig-count count="13"/>
<table-count count="6"/>
<equation-count count="3"/>
<ref-count count="19"/>
<page-count count="00"/>
</counts>
<custom-meta-group>
<custom-meta>
<meta-name>section-at-acceptance</meta-name>
<meta-value>Smart Grids</meta-value>
</custom-meta>
</custom-meta-group>
</article-meta>
</front>
<body>
<sec sec-type="intro" id="s1">
<label>1</label>
<title>Introduction</title>
<p>With the &#x2018;Dual Carbon&#x2019; goals, promoting energy transformation and the construction of a new-type power system have become important directions for the development of China&#x2019;s power industry. The installed capacity of renewable energy sources represented by wind power in the power grid has been continuously increasing (<xref ref-type="bibr" rid="B4">Jiang et al., 2022</xref>; <xref ref-type="bibr" rid="B11">Sun et al., 2022</xref>; <xref ref-type="bibr" rid="B16">Zhang and Kang, 2022</xref>). Meanwhile, to address the issue of power transmission from large-scale renewable energy bases in recent years, China has mainly adopted ultra-high voltage direct current (UHVDC) transmission lines, providing a solid guarantee for the efficient transmission of renewable energy power (<xref ref-type="bibr" rid="B9">Shi et al., 2022</xref>; <xref ref-type="bibr" rid="B18">Zhou et al., 2018</xref>).</p>
<p>However, in the DC sending-end system, as a large amount of renewable energy is connected to the grid, the grid&#x2019;s dynamic reactive power and voltage support capability has declined, and the problem of grid voltage stability has become increasingly prominent (<xref ref-type="bibr" rid="B7">Liu et al., 2020</xref>; <xref ref-type="bibr" rid="B2">Han et al., 2020</xref>; <xref ref-type="bibr" rid="B19">Zhou et al., 2022</xref>). At the same time, the interaction between renewable energy stations, the AC transmission grid, and DC has led to an increase in security and stability risks such as transient overvoltage and delayed voltage recovery, which have become the main factors restricting the consumption and transmission capacity of renewable energy (<xref ref-type="bibr" rid="B3">Han et al., 2024</xref>; <xref ref-type="bibr" rid="B14">Xin et al., 2019</xref>; <xref ref-type="bibr" rid="B10">Sun et al., 2021</xref>).</p>
<p>The benchmark system is the foundation for conducting power system research. Currently, in the context of the multi-form stability characteristics of the new-type power system with a high penetration of renewable energy, there are typical examples focusing on frequency and power angle stability issues (<xref ref-type="bibr" rid="B13">Wu et al., 2024</xref>; <xref ref-type="bibr" rid="B15">Xu et al., 2024</xref>; <xref ref-type="bibr" rid="B6">Li et al., 2023</xref>). Regarding the example systems for voltage stability with a high penetration of renewable energy, <xref ref-type="bibr" rid="B6">Li et al. (2023)</xref> focused on power angle and transient overvoltage issues and constructed a scenario where renewable energy and conventional power sources are bundled for transmission through AC and DC lines. <xref ref-type="bibr" rid="B17">Zhao et al. (2024)</xref> designed a DC receiving-end benchmark system that can reflect voltage collapse and sustained low voltage. The above-mentioned literature has constructed typical examples for the stability characteristics of the new-type power system, but there is still a lack of benchmark systems for the DC sending-end with a high penetration of renewable energy that can reflect multi-form voltage stability issues.</p>
<p>There are no typical benchmark systems for DC sending-end grids involving multi-form voltage stability issues. Existing studies mostly use the CIGRE HVDC as a standard example for analysis (<xref ref-type="bibr" rid="B12">Szechtman et al., 1991</xref>) and verify methods or strategies in actual power grids. <xref ref-type="bibr" rid="B5">Li et al. (2021)</xref> verified the effectiveness of the proposed measurement indicators for the transient overvoltage problem in the DC sending-end system in the CIGRE HVDC standard test system and actual DC sending-end systems. <xref ref-type="bibr" rid="B8">Ouyang et al. (2024)</xref> verified the control method of the rectifier station to suppress commutation failure overvoltage based on the CIGRE HVDC standard test model. <xref ref-type="bibr" rid="B1">Fu et al. (2016)</xref> analyzed the causes of delayed voltage recovery and the role of generators in the voltage recovery process and verified the optimization method in an actual power grid model. However, the examples currently used in research can only reflect some transient voltage issues in the system. Subsequent optimization and control strategy research based on these examples is difficult to take into account multi-form voltage stability issues. Moreover, the actual power grid model has a complex network structure and a large number of nodes, which can only be used for the verification of the effectiveness of theoretical methods and is difficult to support the mechanism analysis of transient voltage stability. In terms of multi-form voltage stability in high-penetration renewable energy DC sending-end grids, there is no example that can comprehensively reflect the transient voltage stability characteristics, and related optimization and strategy research work lacks an analysis and verification platform.</p>
<p>This paper addresses the multi-form voltage stability issues in high-penetration renewable energy DC sending-end systems. Based on the real-world grid configuration and data in China, a DC sending-end electromechanical transient benchmark system suitable for multi-form voltage stability analysis is established. The transmission grid is composed of 500 kV AC and &#xb1;800 kV UHVDC, and includes different types of power sources such as conventional energy, wind power, and photovoltaic power. Based on this benchmark, scenarios of overvoltage, low-high voltage interlocking, delayed voltage recovery, and voltage collapse with a high penetration of renewable energy are constructed, and the influence of factors, such as the penetration of renewable energy, renewable energy control parameters, DC transmission power, synchronous condenser configuration, and the proportion of induction motors on transient voltage stability, is analyzed. The results show that this benchmark can comprehensively reflect the impact of large-scale renewable energy access on the transient voltage of the DC sending-end system and can serve as a basic platform for voltage stability analysis and control strategy research.</p>
</sec>
<sec id="s2">
<label>2</label>
<title>Sending-end grid benchmark system with high penetration renewable energy</title>
<sec id="s2-1">
<label>2.1</label>
<title>Systematic overview</title>
<p>Based on the topology and data of an actual DC sending-end power grid in a region of China, a simulation benchmark of a DC sending-end grid with a high penetration of renewable energy has been established using the Power System Analysis Synthesis Program (PSASP). The system primarily employs a 500 kV AC and &#xb1;800 kV DC grid, comprising 420 nodes at different voltage levels. The AC receiving-end network and the DC receiving-end network are respectively equivalent to infinite bus systems. The structure of the transmission grid is illustrated in <xref ref-type="fig" rid="F1">Figure 1</xref>, and the node overview is summarized in <xref ref-type="table" rid="T1">Table 1</xref>. The UHVDC in the benchmark model is an ultra-high voltage DC based on line commutated converters (LCC-UHVDC). The converter stations adopt a bipolar structure, with each pole featuring a series connection of two 12-pulse converters. Specifically, the positive pole includes a positive pole high-voltage side converter and a positive pole low-voltage side converter, while the negative pole comprises a negative pole high-voltage side converter and a negative pole low-voltage side converter. Each converter is connected to the AC power grid through a converter transformer. The model structure of the UHVDC is shown in the <xref ref-type="fig" rid="F2">Figure 2</xref>.</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>The transmission grid structure diagram of the power system.</p>
</caption>
<graphic xlink:href="fenrg-13-1764223-g001.tif">
<alt-text content-type="machine-generated">Diagram of a power network with interconnected buses labeled B01 to B52. It includes symbols for regular power, wind power, photovoltaic, and converter stations, with various power outputs in megawatts. Lines indicate connections, and each node has specific power categories and amounts.</alt-text>
</graphic>
</fig>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>The overview of power system nodes.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Voltage level</th>
<th align="center">Nodes</th>
<th align="center">Notes</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">500 kV</td>
<td align="center">54</td>
<td align="center">AC transmission grid</td>
</tr>
<tr>
<td align="center">220 kV</td>
<td align="center">82</td>
<td align="center">Load nodes,transformer nodes</td>
</tr>
<tr>
<td align="center">Under 220 kV</td>
<td align="center">284</td>
<td align="center">Renewable, generator and capacitor nodes</td>
</tr>
<tr>
<td align="center">Total</td>
<td align="center">420</td>
<td align="center">&#x2014;</td>
</tr>
</tbody>
</table>
</table-wrap>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>The model structure of the UHVDC.</p>
</caption>
<graphic xlink:href="fenrg-13-1764223-g002.tif">
<alt-text content-type="machine-generated">Schematic diagram of a high-voltage direct current (HVDC) transmission system. It includes a sending-end AC bus at 500 kilovolts, positive and negative poles with high and low-voltage converters rated at plus or minus 800 kilovolts, and a receiving-end AC bus also at 500 kilovolts. The system shows bidirectional power flow through converters and transformers.</alt-text>
</graphic>
</fig>
</sec>
<sec id="s2-2">
<label>2.2</label>
<title>Lines and transformers overview</title>
<p>The system includes a total of 116 500 kV AC lines, 50 220 kV AC lines, 232 two-winding transformers, 38 three-winding transformers and one &#xb1;800 kV UHV DC transmission channel. The overview of the lines and transformers is shown in <xref ref-type="table" rid="T2">Table 2</xref>.</p>
<table-wrap id="T2" position="float">
<label>TABLE 2</label>
<caption>
<p>The overview of lines and transformers.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Line type</th>
<th align="center">Number</th>
<th colspan="2" align="center">Notes</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td rowspan="2" align="center">AC Tie lines</td>
<td rowspan="2" align="center">166</td>
<td align="center">500 kV AC grid</td>
<td align="center">116</td>
</tr>
<tr>
<td align="center">220 kV low-voltage lines</td>
<td align="center">50</td>
</tr>
<tr>
<td rowspan="3" align="center">Three-winding transformers</td>
<td rowspan="3" align="center">38</td>
<td align="center">525/230/66 kV</td>
<td align="center">27</td>
</tr>
<tr>
<td align="center">525/230/36 kV</td>
<td align="center">3</td>
</tr>
<tr>
<td align="center">242/66/10.5 kV</td>
<td align="center">8</td>
</tr>
<tr>
<td rowspan="3" align="center">Two-winding transformers</td>
<td rowspan="3" align="center">232</td>
<td align="center">Conventional unit<break/>Step-up transformers</td>
<td align="center">125</td>
</tr>
<tr>
<td align="center">Renewable energy unit transformers</td>
<td align="center">50</td>
</tr>
<tr>
<td align="center">Renewable energy station<break/>Step-up transformers</td>
<td align="center">50</td>
</tr>
<tr>
<td rowspan="2" align="center">DC line</td>
<td rowspan="2" align="center">1</td>
<td align="center">Rated voltage</td>
<td align="center">&#xb1;800 kV</td>
</tr>
<tr>
<td align="center">Rated power</td>
<td align="center">10000 MW</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
<sec id="s2-3">
<label>2.3</label>
<title>Power generation overview</title>
<p>The case study involves 134 thermal power units with an installed capacity of 35,142.5 MW; 51 renewable energy units of wind and photovoltaic power, with an installed capacity of 34,931.45 MW, including 31,173.45 MW of wind power and 3,758 MW of photovoltaic power. The penetration of renewable energy installed capacity is 49.85%. The overview of power source installed capacity is shown in <xref ref-type="table" rid="T3">Table 3</xref>.</p>
<table-wrap id="T3" position="float">
<label>TABLE 3</label>
<caption>
<p>The overview of power supply installation.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="center">Unit type</th>
<th rowspan="2" align="center">Thermal</th>
<th colspan="2" align="center">Renewable energy</th>
</tr>
<tr>
<th align="center">Wind</th>
<th align="center">PV</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">Capacity/MW</td>
<td align="center">35,142.5</td>
<td align="center">31,173.45</td>
<td align="center">3,758</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>In the simulation, the renewable energy installation at the renewable energy collection buses is summarized in <xref ref-type="table" rid="T4">Table 4</xref>.</p>
<table-wrap id="T4" position="float">
<label>TABLE 4</label>
<caption>
<p>The installed capacity overview of the renewable energy convergence bus power supply at the DC sending-end grid.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="center">Bus</th>
<th rowspan="2" align="center">Conventional/MW</th>
<th colspan="2" align="center">RE installation/MW</th>
<th rowspan="2" align="center">RE share</th>
</tr>
<tr>
<th align="center">Wind</th>
<th align="center">PV</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">B04</td>
<td align="center">470</td>
<td align="center">2,603</td>
<td align="center">100</td>
<td align="center">85.2%</td>
</tr>
<tr>
<td align="center">B06</td>
<td align="center">1,600</td>
<td align="center">99</td>
<td align="center">0</td>
<td align="center">5.8%</td>
</tr>
<tr>
<td align="center">B07</td>
<td align="center">500</td>
<td align="center">890.8</td>
<td align="center">89.5</td>
<td align="center">66.2%</td>
</tr>
<tr>
<td align="center">B08</td>
<td align="center">0</td>
<td align="center">1895</td>
<td align="center">45</td>
<td align="center">100.0%</td>
</tr>
<tr>
<td align="center">B09</td>
<td align="center">1,070</td>
<td align="center">2,306.5</td>
<td align="center">250</td>
<td align="center">70.5%</td>
</tr>
<tr>
<td align="center">B10</td>
<td align="center">0</td>
<td align="center">898.5</td>
<td align="center">0</td>
<td align="center">100.0%</td>
</tr>
<tr>
<td align="center">B11</td>
<td align="center">150</td>
<td align="center">1,442.5</td>
<td align="center">300</td>
<td align="center">92.1%</td>
</tr>
<tr>
<td align="center">B12</td>
<td align="center">0</td>
<td align="center">999.8</td>
<td align="center">0</td>
<td align="center">100.0%</td>
</tr>
<tr>
<td align="center">B15</td>
<td align="center">600</td>
<td align="center">594.5</td>
<td align="center">0</td>
<td align="center">49.8%</td>
</tr>
<tr>
<td align="center">B16</td>
<td align="center">330</td>
<td align="center">640.5</td>
<td align="center">150</td>
<td align="center">70.5%</td>
</tr>
<tr>
<td align="center">B17</td>
<td align="center">0</td>
<td align="center">1,000</td>
<td align="center">0</td>
<td align="center">100.0%</td>
</tr>
<tr>
<td align="center">B21</td>
<td align="center">400</td>
<td align="center">2057.2</td>
<td align="center">600</td>
<td align="center">86.9%</td>
</tr>
<tr>
<td align="center">B22</td>
<td align="center">0</td>
<td align="center">3,552.15</td>
<td align="center">650</td>
<td align="center">100.0%</td>
</tr>
<tr>
<td align="center">B23</td>
<td align="center">0</td>
<td align="center">1,592</td>
<td align="center">0</td>
<td align="center">100.0%</td>
</tr>
<tr>
<td align="center">B24</td>
<td align="center">0</td>
<td align="center">2,739.5</td>
<td align="center">100</td>
<td align="center">100.0%</td>
</tr>
<tr>
<td align="center">B30</td>
<td align="center">1,485</td>
<td align="center">1,137</td>
<td align="center">150</td>
<td align="center">46.4%</td>
</tr>
<tr>
<td align="center">B32</td>
<td align="center">0</td>
<td align="center">1748.1</td>
<td align="center">743.5</td>
<td align="center">100.0%</td>
</tr>
<tr>
<td align="center">B33</td>
<td align="center">0</td>
<td align="center">3,394.5</td>
<td align="center">0</td>
<td align="center">100.0%</td>
</tr>
<tr>
<td align="center">B34</td>
<td align="center">1,610</td>
<td align="center">788.9</td>
<td align="center">230</td>
<td align="center">38.8%</td>
</tr>
<tr>
<td align="center">B37</td>
<td align="center">1,360</td>
<td align="center">249.5</td>
<td align="center">0</td>
<td align="center">15.5%</td>
</tr>
<tr>
<td align="center">B40</td>
<td align="center">1820</td>
<td align="center">297</td>
<td align="center">0</td>
<td align="center">14.0%</td>
</tr>
<tr>
<td align="center">B51</td>
<td align="center">508.5</td>
<td align="center">99</td>
<td align="center">350</td>
<td align="center">46.9%</td>
</tr>
<tr>
<td align="center">B52</td>
<td align="center">660</td>
<td align="center">148.5</td>
<td align="center">0</td>
<td align="center">18.4%</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
<sec id="s2-4">
<label>2.4</label>
<title>Load and reactive power compensation overview</title>
<p>The system has a total active load of 14,346.07 MW and a total reactive load of 6,067.55 MVar, with the load evenly distributed throughout the system. In the renewable energy integration area, the loads are connected to the 220 kV buses and linked to the 500 kV buses via three-winding transformers. Reactive power compensation is provided by shunt capacitors and reactors. Specifically, the capacitor and reactor banks on the 500 kV lines are directly connected to the 500 kV buses, while those in the sub-500 kV network are connected to the low-voltage side buses of the three-winding transformers.</p>
</sec>
<sec id="s2-5">
<label>2.5</label>
<title>Basic system operating conditions</title>
<p>The basic operation mode of the system is shown in <xref ref-type="table" rid="T5">Table 5</xref>. The total output of conventional units in the system is 12,248 MW, the total output of renewable energy is 11,287.7 MW, the power transmitted through DC lines is 10,000 MW, and the penetration of renewable energy output is 47.96%.</p>
<table-wrap id="T5" position="float">
<label>TABLE 5</label>
<caption>
<p>The basic operating mode of the condition system.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th colspan="2" align="center">Power/MW</th>
<th rowspan="2" align="center">Load/MW</th>
<th rowspan="2" align="center">DC Export/MW</th>
<th rowspan="2" align="center">AC interface/MW</th>
<th rowspan="2" align="center">Loss/MW</th>
</tr>
<tr>
<th align="center">Conventional/MW</th>
<th align="center">RE/MW</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">12,248</td>
<td align="center">11,287.7</td>
<td align="center">15,320.5</td>
<td align="center">10,000</td>
<td align="center">2,234.46</td>
<td align="center">1,410.66</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
</sec>
<sec id="s3">
<label>3</label>
<title>Voltage stability characteristics of the sending-end power grid</title>
<p>A high-renewable-penetration DC sending-end power grid can exhibit multiple forms of voltage instability under different fault scenarios. Based on the established simulation system, various fault scenarios were constructed to analyze the influencing factors of these diverse forms of voltage stability.</p>
<sec id="s3-1">
<label>3.1</label>
<title>Transient overvoltage scenario</title>
<sec id="s3-1-1">
<label>3.1.1</label>
<title>Transient overvoltage scenario construction</title>
<p>During operation, UHVDC converter stations consume a significant amount of reactive power. When a large disturbance occurs in the DC power, the reactive power balance between the converter station and the sending-end grid is disrupted, causing a large surplus of reactive power to flood into the DC sending-end system. This results in transient overvoltage in the DC sending-end system.</p>
<p>A bipolar lockout fault occurs in the UHVDC system at <italic>t</italic> &#x3d; 1.0 s. The voltage at the sending-end converter bus rises, exhibiting transient overvoltage. The overvoltage state persists at the converter bus until the sending-end filter banks are tripped at <italic>t</italic> &#x3d; 1.3 s. The voltage waveform at the sending-end converter bus is shown in <xref ref-type="fig" rid="F3">Figure 3</xref>. The transient overvoltage at sending-end converter bus B19 reaches 1.42p.u., causing some renewable energy units in the vicinity of the DC link to trip due to overvoltage. The grid-connected terminal voltage and grid-connected power of some new energy sources are shown in <xref ref-type="fig" rid="F4">Figures 4A,B</xref> respectively. Starting from 1.15 s, the grid-connected terminal voltage of some new energy sources in the DC near-area successively exceeds 1.3 p.u., and these new energy sources trip off the grid one after another, with their grid-connected power dropping to zero.</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>Transient overvoltage after bipolar blocking fault.</p>
</caption>
<graphic xlink:href="fenrg-13-1764223-g003.tif">
<alt-text content-type="machine-generated">Graph showing bus voltage over time in per unit (p.u.). Voltage spikes to approximately 1.4 p.u. at around 1 second, then stabilizes slightly above 1.2 p.u. A vertical red dashed line indicates the cutoff of the sending-end filter bank.</alt-text>
</graphic>
</fig>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>The grid-connected terminal voltage and grid-connected power of some new energy sources. <bold>(A)</bold> The grid-connected terminal voltage of some new energy sources. <bold>(B)</bold> The grid-connected power of some new energy sources.</p>
</caption>
<graphic xlink:href="fenrg-13-1764223-g004.tif">
<alt-text content-type="machine-generated">Graphs (A) and (B) show active power over time in per unit (p.u.) for five different datasets labeled WT_B23_1, WT_B23_2, PV_B24, WT_B22_1, and WT_B22_2. Graph (A) depicts a fluctuation peaking near time equals one second and stabilizing, whereas graph (B) shows a steep initial increase stabilizing at higher values. Both graphs cover a time range from zero to five seconds.</alt-text>
</graphic>
</fig>
</sec>
<sec id="s3-1-2">
<label>3.1.2</label>
<title>Analysis of influencing factors for transient overvoltage</title>
<p>The reactive power surplus at the DC sending-end during fault periods is the primary cause of transient overvoltage in the system. Among various quantitative analysis methods for transient overvoltage, the Single-Branch Voltage Drop Method is widely adopted due to its simultaneous consideration of active and reactive power variations. The calculation formula of this method is shown in <xref ref-type="disp-formula" rid="e1">Equation 1</xref>:<disp-formula id="e1">
<mml:math id="m1">
<mml:mrow>
<mml:mo>&#x394;</mml:mo>
<mml:mi>U</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="&#x7c;">
<mml:mrow>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msup>
<mml:mi>S</mml:mi>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>R</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x394;</mml:mo>
<mml:mi>P</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="&#x7c;">
<mml:mrow>
<mml:msub>
<mml:mi>Q</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msup>
<mml:mi>S</mml:mi>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>X</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x394;</mml:mo>
<mml:mi>Q</mml:mi>
</mml:mrow>
<mml:msub>
<mml:mi>U</mml:mi>
<mml:mi mathvariant="normal">N</mml:mi>
</mml:msub>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(1)</label>
</disp-formula>
</p>
<p>Where &#x394;<italic>U</italic> represents the voltage increment at the converter bus; <italic>U</italic>
<sub>N</sub> denotes the rated voltage of the converter bus; <italic>X</italic> and <italic>R</italic> are the equivalent reactance and resistance, respectively; &#x394;<italic>P</italic> and &#x394;<italic>Q</italic> indicate the active and reactive power variations in the sending-end AC system before and after the fault occurrence; <italic>P</italic>
<sub>0</sub>, and <italic>Q</italic>
<sub>0</sub> are the initial active and reactive power values at the sending end under steady-state conditions, respectively; and <italic>S</italic> represents the short-circuit capacity of the converter station.</p>
<p>According to the formula, the overvoltage severity in the DC sending-end system is influenced by multiple factors, including the transmitted DC power and the configuration of synchronous condensers at the sending end. Furthermore, considering the high concentration of renewable energy in the vicinity of the DC sending-end within the model, this section analyzes the overvoltage stability characteristics of the test system by varying the renewable energy penetration level, its control parameters, the transmitted DC power, and the synchronous condenser configuration.</p>
<sec id="s3-1-2-1">
<label>3.1.2.1</label>
<title>Penetration of renewable energy</title>
<p>Under the basic operating condition, the committed capacity of renewable and thermal power units near the DC sending-end was modified while maintaining constant total generation output. Three scenarios with renewable energy penetration levels of 40%, 50%, and 60% at the DC sending-end were established. A bipolar lockout fault was applied at <italic>t</italic> &#x3d; 1.0 s. The voltage response characteristics at the sending-end converter bus B19 under these conditions are shown in <xref ref-type="fig" rid="F5">Figure 5</xref>.</p>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>Transient overvoltage curve under different penetrations of renewable energy.</p>
</caption>
<graphic xlink:href="fenrg-13-1764223-g005.tif">
<alt-text content-type="machine-generated">Graph showing bus voltage over time with renewable energy penetration levels at 40% (blue), 50% (red), and 60% (yellow). The voltage spikes sharply at 1 second, corresponding to cutting off the sending-end filter bank, then gradually stabilizes.</alt-text>
</graphic>
</fig>
<p>The simulation results demonstrate that the transient overvoltage at the sending-end bus caused by the DC blocking fault increases significantly with the rise in renewable energy penetration level.</p>
</sec>
<sec id="s3-1-2-2">
<label>3.1.2.2</label>
<title>Renewable energy control parameters</title>
<p>When transient overvoltage occurs at the DC sending-end converter bus, a large number of renewable energy sources in the nearby collection area will enter a high-voltage ride-through (HVRT) state. Therefore, different HVRT control parameters result in varying reactive power responses from renewable energy during the fault, consequently affecting the transient overvoltage levels at nearby buses.</p>
<p>The reactive current control strategy during high-voltage ride-through (HVRT) for renewable energy often employs the specified current control method. The control formula for the reactive current component <italic>I</italic>
<sub>qHV</sub> is shown in <xref ref-type="disp-formula" rid="e2">Equation 2</xref>:<disp-formula id="e2">
<mml:math id="m2">
<mml:mrow>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mtext>qHV</mml:mtext>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mi mathvariant="normal">q</mml:mi>
<mml:mo>_</mml:mo>
<mml:mtext>HV</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="&#x7c;">
<mml:mrow>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mtext>Hin</mml:mtext>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mi mathvariant="normal">t</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mi mathvariant="normal">q</mml:mi>
<mml:mo>_</mml:mo>
<mml:mtext>HV</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">q</mml:mi>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
<label>(2)</label>
</disp-formula>
</p>
<p>Where <italic>K</italic>
<sub>1q_HV</sub> is the HVRT reactive current calculation coefficient 1, <italic>K</italic>
<sub>2q_HV</sub> is the HVRT reactive current calculation coefficient 2, <italic>V</italic>
<sub>Hin</sub> is the HVRT entry threshold voltage, <italic>V</italic>
<sub>t</sub> is the terminal voltage magnitude, and <italic>I</italic>
<sub>q0</sub> is the initial reactive current. Since the initial reactive current <italic>I</italic>
<sub>q0</sub> is small and close to zero, the influence of <italic>K</italic>
<sub>2q_HV</sub> on the voltage during HVRT can be neglected. Therefore, the analysis primarily focuses on the impact of the calculation coefficient 1 <italic>K</italic>
<sub>1q_HV</sub> on the overvoltage.</p>
<p>Under the base operating condition, the first HVRT reactive current calculation coefficient, <italic>K</italic>
<sub>1q_HV</sub>, was configured to values of 1, 1.5, and 2 respectively. A bipolar lockout fault was applied to the DC system at <italic>t</italic> &#x3d; 1.0 s. The voltage response characteristics at the sending-end converter bus B19 are shown in <xref ref-type="fig" rid="F6">Figure 6</xref>.</p>
<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
<p>Transient overvoltage curve under different values of the first HVRT reactive current calculation coefficient (<italic>K</italic>
<sub>1q_HV</sub>).</p>
</caption>
<graphic xlink:href="fenrg-13-1764223-g006.tif">
<alt-text content-type="machine-generated">Graph depicting bus voltage in per unit over time, with three dashed lines representing different \(K_{1q\_HV}\) values: 1 (blue), 1.5 (red), and 2 (yellow). A significant peak occurs around 1 second, marked by a vertical arrow and the label &#x22;Cut off the sending-end filter bank.&#x22; An inset zooms into the peak region.</alt-text>
</graphic>
</fig>
<p>The simulation results show that the higher the renewable energy HVRT reactive current calculation coefficient 1 <italic>K</italic>
<sub>1q_HV</sub>, the lower the overvoltage at the system&#x2019;s sending-end bus.</p>
</sec>
<sec id="s3-1-2-3">
<label>3.1.2.3</label>
<title>DC transmitted power</title>
<p>Based on the base operating condition, the DC transmitted power was reduced while the sending-end filter banks were adjusted. Scenarios with DC transmitted power levels of 10,000 MW, 9,000 MW, and 8,000 MW were established. A bipolar lockout fault was applied at <italic>t</italic> &#x3d; 1.0 s. The voltage response characteristics at the sending-end converter bus B19 are shown in <xref ref-type="fig" rid="F7">Figure 7</xref>.</p>
<fig id="F7" position="float">
<label>FIGURE 7</label>
<caption>
<p>Transient overvoltage curve under different DC output power.</p>
</caption>
<graphic xlink:href="fenrg-13-1764223-g007.tif">
<alt-text content-type="machine-generated">Graph showing bus voltage (p.u.) over time. Three lines represent DC transmitted power levels of 10000 MW, 9000 MW, and 8000 MW. A vertical line marks the cutoff of the sending-end filter bank at around 1 second, followed by a transient increase in voltage.</alt-text>
</graphic>
</fig>
<p>The simulation results show that the higher the DC transmitted power, the more severe the transient overvoltage at both the sending-end converter bus and the nearby renewable generator terminal buses during a fault.</p>
</sec>
<sec id="s3-1-2-4">
<label>3.1.2.4</label>
<title>Synchronous condenser configuration</title>
<p>Synchronous condensers, as a common type of dynamic reactive power compensation equipment, can enhance system voltage stability and are widely used in DC sending-end systems. Under the base operating condition, two additional comparative cases were established by configuring one and two synchronous condensers, respectively, each with a rated capacity of 300 MVA, at the DC sending-end converter bus B19. A bipolar lockout fault was applied at <italic>t</italic> &#x3d; 1.0 s. The voltage response characteristics at the sending-end converter bus B19 are shown in <xref ref-type="fig" rid="F8">Figure 8</xref>.</p>
<fig id="F8" position="float">
<label>FIGURE 8</label>
<caption>
<p>Transient overvoltage curves under different synchronous condensers.</p>
</caption>
<graphic xlink:href="fenrg-13-1764223-g008.tif">
<alt-text content-type="machine-generated">Graph showing bus voltage (per unit) over time in seconds for three scenarios: SC 0 (blue), SC 1 (red), and SC 2 (yellow). Voltage spikes around 1 second, indicating the cutoff of the sending-end filter bank, then stabilizes.</alt-text>
</graphic>
</fig>
<p>The simulation results demonstrate that the installation of synchronous condensers can mitigate transient overvoltage during bipolar lockout faults. Furthermore, a higher total configured capacity of synchronous condensers results in lower transient overvoltage levels at the DC sending-end converter bus. In this paper, &#x201c;SC&#x201d; is the abbreviation for Synchronous Condenser.</p>
<p>In summary, a higher renewable energy penetration level, a smaller HVRT reactive current coefficient 1 <italic>K</italic>
<sub>1q_HV</sub>, a greater DC transmitted power, along with a lower configured capacity of synchronous condensers in the DC sending-end system will collectively lead to more severe transient overvoltage at the sending-end bus caused by DC block faults.</p>
</sec>
</sec>
</sec>
<sec id="s3-2">
<label>3.2</label>
<title>Low-high voltage cascade scenario</title>
<sec id="s3-2-1">
<label>3.2.1</label>
<title>Low-high voltage cascade scenario construction</title>
<p>Commutation failure is one of the most common faults in conventional UHVDC transmission systems. When a fault occurs in the receiving-end grid, it can affect the commutation voltage of the thyristors in the DC converter station, leading to commutation failure in the inverter.</p>
<p>Under the base operating condition, a DC commutation failure fault is set to occur at <italic>t</italic> &#x3d; 1.0 s. At the onset of commutation failure, the inverter side reduces its firing angle to improve the commutation margin. As the firing angle increases, the DC voltage at the receiving end drops rapidly, and the DC current rises sharply. This causes an increase in the firing angle of the sending-end converter, leading to higher reactive power absorption from the AC grid by the sending-end converter station. Consequently, the voltage at the sending-end converter bus decreases initially during the early stage of the fault. Subsequently, under the regulation of the Voltage Dependent Current Order Limiter (VDCOL), the DC current decreases rapidly, reducing the reactive power consumption at the sending end. The resulting significant surplus of reactive power at the sending end induces transient overvoltage at the sending-end converter bus, as shown in <xref ref-type="fig" rid="F9">Figure 9</xref>.</p>
<fig id="F9" position="float">
<label>FIGURE 9</label>
<caption>
<p>Low- and high-voltage interlock after DC single commutation failure.</p>
</caption>
<graphic xlink:href="fenrg-13-1764223-g009.tif">
<alt-text content-type="machine-generated">Graph depicting bus voltage in per unit versus time in seconds. The voltage initially remains constant at one per unit, spikes above 1.2 at around one second, then stabilizes above one per unit.</alt-text>
</graphic>
</fig>
</sec>
<sec id="s3-2-2">
<label>3.2.2</label>
<title>Analysis of influencing factors for the low-high voltage cascade</title>
<p>The impacts of various influencing factors including the penetration of renewable energy, renewable energy control parameters, DC transmission power, and synchronous condenser configuration on low-high voltage interlocking have been analyzed respectively. The impacts of the influencing factors on low-high voltage interlocking are illustrated in <xref ref-type="fig" rid="F10">Figure 10</xref>. A detailed analysis is conducted in the subsequent sections.</p>
<fig id="F10" position="float">
<label>FIGURE 10</label>
<caption>
<p>The impacts of the influencing factors on low-high voltage interlocking. <bold>(A)</bold> Low- and high-voltage interlocking curve under different penetrations of renewable energy. <bold>(B)</bold> Low- and high-voltage interlocking curve under different values of the first HVRT reactive current calculation coefficient (<italic>K</italic>
<sub>1q_HV</sub>). <bold>(C)</bold> Low- and high-voltage interlocking curve under different values of the first LVRT reactive current calculation coefficient (<italic>K</italic>
<sub>1q_LV</sub>). <bold>(D)</bold> Low- and high-voltage interlocking curve under different DC output power. <bold>(E)</bold> Low- and high-voltage interlocking curve under different synchronous condensers.</p>
</caption>
<graphic xlink:href="fenrg-13-1764223-g010.tif">
<alt-text content-type="machine-generated">Five graphs labeled A to E depict bus voltage over time in different scenarios. Graph A compares renewable energy penetration levels. Graph B examines three scenarios of \(K_{1Q\_HV}\). Graph C shows \(K_{1Q\_LV}\) levels. Graph D illustrates DC transmitted power variations. Graph E displays three cases of SC configurations. Each graph includes zoomed inserts highlighting specific voltage variations.</alt-text>
</graphic>
</fig>
<sec id="s3-2-2-1">
<label>3.2.2.1</label>
<title>Penetration of renewable energy</title>
<p>Based on the base operating condition and while maintaining constant total system power, three operational scenarios were configured by modifying the renewable energy penetration level at the DC sending-end to 40%, 50%, and 60% respectively. The system was subsequently set to experience a DC commutation failure fault at <italic>t</italic> &#x3d; 1.0 s. The voltage response characteristics at the sending-end converter bus B19 are shown in <xref ref-type="fig" rid="F10">Figure 10A</xref>.</p>
<p>The simulation results indicate that as the renewable energy penetration level increases during a DC commutation failure fault, the severity of the transient low voltage at the sending-end converter bus decreases, while the degree of transient over-voltage remains largely unchanged. This suggests that the renewable energy penetration level does not have a significant impact on a single DC commutation failure event.</p>
</sec>
<sec id="s3-2-2-2">
<label>3.2.2.2</label>
<title>Renewable energy control parameters</title>
<p>Under the base operating condition, the first renewable energy HVRT reactive current calculation coefficient, <italic>K</italic>
<sub>1q_HV</sub>, was configured to values of 0, 0.5, and 1 respectively. A DC commutation failure fault was applied to the system at <italic>t</italic> &#x3d; 1.0 s. The voltage response characteristics at the sending-end converter bus B19 are shown in <xref ref-type="fig" rid="F10">Figure 10B</xref>.</p>
<p>The simulation results demonstrate that the transient overvoltage at the sending-end bus progressively decreases as the renewable energy HVRT reactive current calculation coefficient 1 <italic>K</italic>
<sub>1q_HV</sub> increases.</p>
<p>The reactive current control strategy during low-voltage ride-through (LVRT) for renewable energy often employs the specified current control method. The formula for the reactive current component <italic>I</italic>
<sub>qLV</sub> during LVRT is shown in <xref ref-type="disp-formula" rid="e3">Equation 3</xref>.<disp-formula id="e3">
<mml:math id="m3">
<mml:mrow>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mtext>qLV</mml:mtext>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mi mathvariant="normal">q</mml:mi>
<mml:mo>_</mml:mo>
<mml:mtext>LV</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="&#x7c;">
<mml:mrow>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mtext>Lin</mml:mtext>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mi mathvariant="normal">t</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>K</mml:mi>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mi mathvariant="normal">q</mml:mi>
<mml:mo>_</mml:mo>
<mml:mtext>LV</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">q</mml:mi>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
<label>(3)</label>
</disp-formula>
</p>
<p>In the formula, <italic>K</italic>
<sub>1q_LV</sub> is the LVRT reactive current calculation coefficient 1, <italic>K</italic>
<sub>2q_LV</sub> is the LVRT reactive current calculation coefficient 2, and <italic>V</italic>
<sub>Lin</sub> is the LVRT entry threshold voltage. Since the initial reactive current <italic>I</italic>
<sub>q0</sub> during steady-state operation of renewable energy is small and essentially zero, adjusting the LVRT reactive current calculation coefficient 2 <italic>K</italic>
<sub>2q_LV</sub> has a negligible impact on the voltage during LVRT. Therefore, the analysis primarily focuses on the effect of the calculation coefficient <italic>K</italic>
<sub>1q_LV</sub> on the low-voltage response.</p>
<p>Under the base operating condition, the first LVRT reactive current calculation coefficient, <italic>K</italic>
<sub>1q_LV</sub>, was set to 0.5, 1, and 1.5, respectively. A DC commutation failure fault was applied to the system at <italic>t</italic> &#x3d; 1.0 s. The voltage response characteristics at the sending-end converter bus B19 are shown in <xref ref-type="fig" rid="F10">Figure 10C</xref>.</p>
<p>The simulation results indicate that as the renewable energy LVRT reactive current calculation coefficient 1 <italic>K</italic>
<sub>1q_LV</sub> increases, the low-voltage level at the sending-end bus caused by commutation failure becomes less severe, while the overvoltage severity increases.</p>
</sec>
<sec id="s3-2-2-3">
<label>3.2.2.3</label>
<title>DC transmission power</title>
<p>Based on the base operating condition and while maintaining constant total power delivery through both AC and DC transmission channels, scenarios with DC transmitted power levels of 10,000 MW, 9,000 MW, and 8,000 MW were established. A DC commutation failure fault was applied to the system at <italic>t</italic> &#x3d; 1.0 s. The voltage response characteristics at the sending-end converter bus B19 are shown in <xref ref-type="fig" rid="F10">Figure 10D</xref>.</p>
<p>The simulation results indicate that as the DC transmitted power increases, the transient low voltage at the sending-end converter bus during the fault decreases, while the transient overvoltage increases. Specifically, at DC transmitted power levels of 10,000 MW, 9,000 MW, and 8,000 MW, the transient low voltages caused by a single commutation failure are 0.662 p.u., 0.676 p.u., and 0.692 p.u., respectively, while the corresponding transient overvoltage values are 1.314 p.u., 1.266 p.u., and 1.223 p.u.</p>
</sec>
<sec id="s3-2-2-4">
<label>3.2.2.4</label>
<title>Synchronous condenser configuration</title>
<p>Based on the base operating condition, the DC sending-end converter bus B19 was configured with zero, one, and two synchronous condensers respectively, each with a rated capacity of 300 MVA. A DC commutation failure fault was applied to the system at <italic>t</italic> &#x3d; 1.0 s. The voltage response characteristics at the DC sending-end converter bus B19 are shown in <xref ref-type="fig" rid="F10">Figure 10E</xref>.</p>
<p>The simulation results demonstrate that configuring synchronous condensers can improve the transient low voltage and suppress the transient overvoltage during DC commutation failure events.</p>
<p>In summary, a higher renewable energy penetration level at the DC sending-end results in less severe transient low voltage during commutation failure events; a smaller HVRT reactive current calculation coefficient 1, <italic>K</italic>
<sub>1q_HV</sub>, leads to higher transient overvoltage; a smaller LVRT reactive current calculation coefficient 1, <italic>K</italic>
<sub>1q_LV</sub>, reduces both transient low voltage and overvoltage; while greater DC transmitted power and lower synchronous condenser capacity exacerbate both transient low voltage and overvoltage conditions.</p>
</sec>
</sec>
</sec>
<sec id="s3-3">
<label>3.3</label>
<title>Delayed voltage recovery scenario</title>
<sec id="s3-3-1">
<label>3.3.1</label>
<title>Voltage delayed recovery scenario construction</title>
<p>Under the base operating condition, the power sources and load overview for Bus B34 are summarized in <xref ref-type="table" rid="T6">Table 6</xref>. The load model comprises 40% static load, 30% unstable motor load, and 30% stable motor load.</p>
<table-wrap id="T6" position="float">
<label>TABLE 6</label>
<caption>
<p>The overview of power supply and load under B34 bus.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th colspan="3" align="center">Generation/MW</th>
<th colspan="2" align="center">Load absorption</th>
</tr>
<tr>
<th align="center">Conventional/MW</th>
<th align="center">Doubly-Fed/MW</th>
<th align="center">Direct-Drive/MW</th>
<th align="center">Active Power/MW</th>
<th align="center">Reactive Power/MVar</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">100</td>
<td align="center">598.9</td>
<td align="center">147</td>
<td align="center">1,015.47</td>
<td align="center">212.903</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>A three-phase short-circuit ground fault occurred at the 220 kV load bus under Node B34 at <italic>t</italic> &#x3d; 1.0 s, causing the regional voltage to rapidly drop to a very low level. The induction motors within the load began absorbing reactive power from the system. At <italic>t</italic> &#x3d; 1.5 s, after fault clearance, the induction motors became unstable and continued to draw a significant amount of reactive power, preventing the system voltage from recovering to its normal level. The voltage waveforms of some nodes under Bus B34 are shown in <xref ref-type="fig" rid="F11">Figure 11</xref>. Following the clearance of the short-circuit fault, the load bus voltage failed to recover normally, resulting in the terminal voltage of the wind turbines remaining below 0.9 p.u., thereby reducing the system&#x2019;s voltage stability.</p>
<fig id="F11" position="float">
<label>FIGURE 11</label>
<caption>
<p>Delayed voltage recovery after a fault.</p>
</caption>
<graphic xlink:href="fenrg-13-1764223-g011.tif">
<alt-text content-type="machine-generated">Graph showing bus voltage in per unit over time in seconds. The blue dashed line represents the load, showing a drop at one second. The orange and yellow dashed lines represent doubly-fed and direct-drive systems, both maintaining higher stability post-drop.</alt-text>
</graphic>
</fig>
</sec>
<sec id="s3-3-2">
<label>3.3.2</label>
<title>Analysis of influencing factors for delayed voltage recovery</title>
<p>The impacts of various influencing factors including the committed capacity of thermal power, proportion of unstable induction motors, renewable energy control parameter, and synchronous condenser configuration on delayed voltage recovery have been analyzed respectively. Delayed voltage recovery characteristics at renewable energy terminal buses under various influencing factors are illustrated in <xref ref-type="fig" rid="F12">Figure 12</xref>. A detailed analysis is conducted in the subsequent sections.</p>
<fig id="F12" position="float">
<label>FIGURE 12</label>
<caption>
<p>Delayed voltage recovery characteristics at renewable energy terminal buses under various influencing factors. <bold>(A)</bold> Effect of the committed capacity of nearby thermal power. <bold>(B)</bold> Effect of the proportion of unstable induction motors in the load. <bold>(C)</bold> Effect of different values of the first LVRT reactive current calculation coefficient (<italic>K</italic>
<sub>1q_LV</sub>). <bold>(D)</bold> Effect of the configured capacity of synchronous condensers.</p>
</caption>
<graphic xlink:href="fenrg-13-1764223-g012.tif">
<alt-text content-type="machine-generated">Four line graphs labeled A, B, C, and D show bus voltage over time from zero to five seconds. Graph A compares thermal commitment at 100 MW, 200 MW, and 300 MW, showing voltage drop and stabilization. Graph B displays bus voltage with unstable motors at 20%, 30%, and 40% with similar trends. Graph C illustrates varying \( K_{1Q\_LV} \) parameters at 0.5, 1, and 1.5, also showing voltage changes. Graph D compares scenarios SC 0, SC 1, and SC 2 with consistent voltage behavior. Each graph includes legends indicating line styles for different scenarios.</alt-text>
</graphic>
</fig>
<sec id="s3-3-2-1">
<label>3.3.2.1</label>
<title>Committed capacity of thermal power</title>
<p>Based on the base operating condition, the committed thermal power capacity connected to Bus B34 was adjusted to 100 MW, 200 MW, and 300 MW, respectively. A three-phase short-circuit fault was applied at the 220 kV load bus under Node B34 at <italic>t</italic> &#x3d; 1.0 s. The voltage waveforms at the renewable energy terminal buses under Bus B34 are shown in <xref ref-type="fig" rid="F12">Figure 12A</xref>.</p>
<p>The simulation results indicate that a higher committed capacity of thermal power near the renewable energy generation area supplies more reactive power during voltage dips, making the system less prone to delayed voltage recovery.</p>
</sec>
<sec id="s3-3-2-2">
<label>3.3.2.2</label>
<title>Proportion of unstable induction motors</title>
<p>Under the base operating condition, the proportion of unstable induction motors in the load was adjusted to 20%, 30%, and 40%, respectively. A three-phase short-circuit fault was applied at the 220 kV load bus under Node B34 at <italic>t</italic> &#x3d; 1.0 s. The voltage waveforms at the renewable energy terminal buses under Bus B34 are shown in <xref ref-type="fig" rid="F12">Figure 12B</xref>.</p>
<p>The simulation results indicate that a higher proportion of unstable induction motors leads to increased reactive power absorption by the motor load after a three-phase short-circuit fault, resulting in lower voltage at the load bus, decreased voltage at the renewable energy terminal bus, and a higher likelihood of delayed voltage recovery.</p>
</sec>
<sec id="s3-3-2-3">
<label>3.3.2.3</label>
<title>Renewable energy control parameter</title>
<p>Under the base operating condition, the first LVRT reactive current calculation coefficient, <italic>K</italic>
<sub>1q_LV</sub>, was set to 0.5, 1, and 1.5, respectively. A three-phase short-circuit fault was applied at the 220 kV load bus under Node B34 at <italic>t</italic> &#x3d; 1.0 s. The voltage waveforms at the renewable energy terminal buses under Bus B34 are shown in <xref ref-type="fig" rid="F12">Figure 12C</xref>.</p>
<p>The simulation results indicate that a larger LVRT reactive current calculation coefficient 1 <italic>K</italic>
<sub>1q_LV</sub> leads to a higher reactive current component during the fault, resulting in a less severe voltage dip. However, <italic>K</italic>
<sub>1q_LV</sub> has minimal impact on delayed voltage recovery.</p>
</sec>
<sec id="s3-3-2-4">
<label>3.3.2.4</label>
<title>Synchronous condenser configuration</title>
<p>Under the base operating condition, one and two synchronous condensers with a rated capacity of 50 MVA were configured at the 220 kV bus under Bus B34, forming two additional comparative cases. Subsequently, a three-phase short-circuit fault was applied at the 220 kV load bus under Node B34 at <italic>t</italic> &#x3d; 1.0 s. The voltage waveforms at the renewable energy terminal buses under Bus B34 are shown in <xref ref-type="fig" rid="F12">Figure 12D</xref>.</p>
<p>The simulation results demonstrate that the greater the configured capacity of synchronous condensers, the more reactive power is supplied during a voltage dip, making the system less susceptible to delayed voltage recovery.</p>
<p>In summary, the lower the committed thermal power capacity near the renewable energy area, the higher the proportion of unstable induction motors, and the less the configured capacity of synchronous condensers, the more severe the delayed voltage recovery phenomenon at the renewable energy terminal buses; while the LVRT reactive current calculation coefficient 1 <italic>K</italic>
<sub>1q_LV</sub> has minimal impact on delayed voltage recovery.</p>
</sec>
</sec>
</sec>
<sec id="s3-4">
<label>3.4</label>
<title>Voltage collapse scenario</title>
<p>A voltage collapse scenario has been established, and the impacts of various influencing factors including the penetration of renewable energy, DC transmission power, and synchronous condenser configuration on voltage collapse have been analyzed respectively. The analysis of the influencing factors under the voltage collapse scenario is illustrated in <xref ref-type="fig" rid="F13">Figure 13</xref>. A detailed analysis is conducted in the subsequent sections.</p>
<fig id="F13" position="float">
<label>FIGURE 13</label>
<caption>
<p>The analysis of the influencing factors under the voltage collapse scenario. <bold>(A)</bold> Voltage collapse curve after the AC fault. <bold>(B)</bold> Bus voltage of bus B04 under different penetrations of renewable energy. <bold>(C)</bold> Bus voltage of bus B04 under different DC output power. <bold>(D)</bold> Bus voltage of bus B04 under different synchronous condensers.</p>
</caption>
<graphic xlink:href="fenrg-13-1764223-g013.tif">
<alt-text content-type="machine-generated">Four subplots labeled A, B, C, and D display graphs of active power over time. A shows different power levels labeled B04, B10, B01, B03. B compares renewable energy penetration at 60%, 50%, and 40%. C compares direct current transmitted power at 8000 MW, 9000 MW, and 10000 MW. D compares scenarios labeled SC 0, SC 1, and SC 2. Each graph shows fluctuating power levels from 0 to 1.2 per unit over a 5-second duration.</alt-text>
</graphic>
</fig>
<sec id="s3-4-1">
<label>3.4.1</label>
<title>Voltage collapse scenario construction</title>
<p>On the basis of the basic operating condition, the proportion of renewable energy and the total system power are kept unchanged. At t &#x3d; 1.0 s, a three-phase permanent short-circuit fault occurs on one circuit of the double-circuit line between B09 and B10, near the B09 side. Subsequently, at t &#x3d; 1.2 s, the double-circuit line is tripped. After the line is removed, voltage collapse occurs at buses B04, B10, B01, and B03, as shown in <xref ref-type="fig" rid="F13">Figure 13A</xref>.</p>
</sec>
<sec id="s3-4-2">
<label>3.4.2</label>
<title>Analysis of influencing factors for voltage collapse</title>
<sec id="s3-4-2-1">
<label>3.4.2.1</label>
<title>Penetration of renewable energy</title>
<p>On the basis of the basic operating condition, while keeping the total system power unchanged, three scenarios are formed by adjusting the proportion of renewable energy at the DC sending end to 40%, 50%, and 60%, respectively. At t &#x3d; 1.0 s, a three-phase permanent short-circuit fault occurs on one circuit of the double-circuit line between B09 and B10, near the B09 side. Subsequently, at t &#x3d; 1.2 s, the double-circuit line is tripped. The voltage waveform of bus B04 after the AC fault is shown in <xref ref-type="fig" rid="F13">Figure 13B</xref>.</p>
<p>Simulation results indicate that the greater the proportion of renewable energy generation at the DC sending end, the more severe the voltage collapse after fault clearance, and that the share of renewable energy generation significantly impacts voltage collapse.</p>
</sec>
<sec id="s3-4-2-2">
<label>3.4.2.2</label>
<title>DC transmission power</title>
<p>On the basis of the basic operating condition, while keeping the total power of the AC and DC outgoing transmission channels unchanged, three scenarios are formed by adjusting the DC sending power to 10,000 MW, 9000 MW, and 8000 MW, respectively. At t &#x3d; 1.0 s, a three-phase permanent short-circuit fault occurs on one circuit of the double-circuit line between B09 and B10, near the B09 side. Subsequently, at t &#x3d; 1.2 s, the double-circuit line is tripped. The voltage waveform of bus B04 after the AC fault is shown in <xref ref-type="fig" rid="F13">Figure 13C</xref>.</p>
<p>Simulation results indicate that the greater the DC sending power, the more severe the voltage collapse after fault clearance, and the DC sending power significantly impacts the voltage collapse.</p>
</sec>
<sec id="s3-4-2-3">
<label>3.4.2.3</label>
<title>Synchronous condenser configuration</title>
<p>On the basis of the basic operating condition, one and two synchronous condensers with a rated capacity of 50 MVA each are configured on the 220 kV bus under Bus B34, forming two new comparative scenarios. At t &#x3d; 1.0 s, a three-phase permanent short-circuit fault occurs on one circuit of the double-circuit line between B09 and B10, near the B09 side. Subsequently, at t &#x3d; 1.2 s, the double-circuit line is tripped. The voltage waveform of bus B04 after the AC fault is shown in <xref ref-type="fig" rid="F13">Figure 13D</xref>.</p>
<p>Simulation results show that synchronous condensers provide voltage support after fault clearance. The more capacity of synchronous condensers configured, the less likely voltage collapse occurs after fault clearance.</p>
<p>In summary, a higher share of renewable energy generation, greater DC sending power, and a smaller capacity of synchronous condensers configured will make the renewable energy generator terminal voltage more susceptible to triggering voltage collapse after AC fault clearance.</p>
</sec>
</sec>
</sec>
</sec>
<sec sec-type="conclusion" id="s4">
<label>4</label>
<title>Conclusion</title>
<p>This paper addresses the modeling requirements for studying multi-form voltage stability in DC sending-end grids with high penetration of renewable energy. Based on real-world grid operational conditions, a simplified model of a DC sending-end grid suitable for electromechanical transient voltage stability analysis was developed. This test system effectively captures the multi-form voltage stability issues prevalent in DC sending-end grids with high renewable penetration in China, demonstrating various stability phenomena under different operating conditions, including transient overvoltage, low-high voltage cascades, delayed voltage recovery, and voltage collapse. Through analysis using this test system, the influencing factors of multi-form voltage stability were investigated. The results show that higher renewable penetration levels, greater DC transmitted power, and fewer synchronous condenser configurations not only exacerbate both transient low-voltage and overvoltage conditions but also increase the likelihood of voltage collapse. Additionally, less committed thermal power capacity near renewable energy areas, a higher proportion of unstable induction motors, and lower synchronous condenser capacity increase the likelihood of delayed voltage recovery at renewable energy terminals. While adjusting the key reactive current injection coefficients during HVRT and LVRT (<italic>K</italic>
<sub>1q_HV</sub>, <italic>K</italic>
<sub>1q_LV</sub>) can alleviate transient low-voltage and overvoltage issues, they have minimal impact on delayed voltage recovery. This test system can effectively support research on multi-form voltage stability characteristics and control strategies for DC sending-end systems with high renewable energy penetration.</p>
</sec>
</body>
<back>
<sec sec-type="data-availability" id="s5">
<title>Data availability statement</title>
<p>The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.</p>
</sec>
<sec sec-type="author-contributions" id="s6">
<title>Author contributions</title>
<p>MJ: Writing &#x2013; original draft, Resources, Funding acquisition, Conceptualization, Project administration, Supervision. SS: Formal Analysis, Writing &#x2013; original draft, Validation, Methodology. PC: Conceptualization, Writing &#x2013; original draft, Formal Analysis. ZZ: Data curation, Investigation, Writing &#x2013; review and editing, Formal Analysis. XS: Formal Analysis, Writing &#x2013; review and editing. KM: Methodology, Writing &#x2013; review and editing, Validation, Data curation. KW: Visualization, Writing &#x2013; review and editing, Data curation, Validation. DZ: Visualization, Writing &#x2013; review and editing. XL: Writing &#x2013; review and editing, Data curation, Visualization.</p>
</sec>
<ack>
<title>Acknowledgements</title>
<p>The authors gratefully acknowledge the State Grid Jilin Electric Power Company Limited for providing the grid operational data and technical support essential to this study. We also thank our research team members for their insightful discussions and collaboration.</p>
</ack>
<sec sec-type="COI-statement" id="s8">
<title>Conflict of interest</title>
<p>Authors MJ, SS, ZZ, XS, KM, KW, DZ, and XL were employed by State Grid Jilin Electric Power Company Limited.</p>
<p>The remaining author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<sec sec-type="ai-statement" id="s9">
<title>Generative AI statement</title>
<p>The author(s) declared that generative AI was not used in the creation of this manuscript.</p>
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<bold>Edited by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/3259328/overview">Yu Jin</ext-link>, Tianjin University, China</p>
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<fn fn-type="custom" custom-type="reviewed-by">
<p>
<bold>Reviewed by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/3314367/overview">Zhiping Dong</ext-link>, City University of Hong Kong, Hong Kong SAR, China</p>
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<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/3315618/overview">Shunguang Lei</ext-link>, Kunming University of Science and Technology, China</p>
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