<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD Journal Publishing DTD v2.3 20070202//EN" "journalpublishing.dtd">
<article article-type="research-article" dtd-version="2.3" xml:lang="EN" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">
<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Energy Res.</journal-id>
<journal-title>Frontiers in Energy Research</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Energy Res.</abbrev-journal-title>
<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">1081826</article-id>
<article-id pub-id-type="doi">10.3389/fenrg.2022.1081826</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Energy Research</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>A low-cost current flow controlling interline hybrid circuit breaker combined with SCR and H-bridge sub-module</article-title>
<alt-title alt-title-type="left-running-head">Zeng 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.2022.1081826">10.3389/fenrg.2022.1081826</ext-link>
</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname>Zeng</surname>
<given-names>Qingpeng</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/2071878/overview"/>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Zhu</surname>
<given-names>Jin</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1873925/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Guo</surname>
<given-names>Xinming</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Huo</surname>
<given-names>Qunhai</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1039977/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Yin</surname>
<given-names>Jingyuan</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1247746/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Wei</surname>
<given-names>Tongzhen</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
</contrib-group>
<aff id="aff1">
<sup>1</sup>
<institution>Institute of Electrical Engineering</institution>, <institution>Chinese Academy of Sciences</institution>, <addr-line>Beijing</addr-line>, <country>China</country>
</aff>
<aff id="aff2">
<sup>2</sup>
<institution>University of Chinese Academy of Sciences</institution>, <addr-line>Beijing</addr-line>, <country>China</country>
</aff>
<author-notes>
<fn fn-type="edited-by">
<p>
<bold>Edited by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1948207/overview">Tahir Khurshaid</ext-link>, Yeungnam University, South Korea</p>
</fn>
<fn fn-type="edited-by">
<p>
<bold>Reviewed by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1369477/overview">Liansheng Huang</ext-link>, Hefei Institutes of Physical Science (CAS), China</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1575728/overview">Tohid Rahimi</ext-link>, Carleton University, Canada</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Jin Zhu, <email>zhujin@mail.iee.ac.cn</email>
</corresp>
<fn fn-type="other">
<p>This article was submitted to Smart Grids, a section of the journal Frontiers in Energy Research</p>
</fn>
</author-notes>
<pub-date pub-type="epub">
<day>23</day>
<month>01</month>
<year>2023</year>
</pub-date>
<pub-date pub-type="collection">
<year>2022</year>
</pub-date>
<volume>10</volume>
<elocation-id>1081826</elocation-id>
<history>
<date date-type="received">
<day>27</day>
<month>10</month>
<year>2022</year>
</date>
<date date-type="accepted">
<day>28</day>
<month>11</month>
<year>2022</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2023 Zeng, Zhu, Guo, Huo, Yin and Wei.</copyright-statement>
<copyright-year>2023</copyright-year>
<copyright-holder>Zeng, Zhu, Guo, Huo, Yin and Wei</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/">
<p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). 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.</p>
</license>
</permissions>
<abstract>
<p>A massive number of DC circuit breaker is usually necessary to be installed to protect HVDC grids from DC faults, this will lead to high capital costs because large number of expensive IGBT-in-series are used. In this paper, an interline hybrid circuit breaker is proposed by the combination of SCR string and a small number of H-bridge modules (SCR-IHCB). The proposed SCR-IHCB has the capacity of blocking DC fault of two adjacent lines respectively by sharing only one main breaker branch (MB) mainly composed of low-cost SCR string and H-bridge module instead of IGBT-in-series string. The interline current flow control function is also integrated. Hence it has advantages of simple and compact topology, economical design compared with typical IGBT based HCB solutions. The operation process of the proposed SCR-IHCB is discussed in detail, and the performance is verified by MATLAB Simulink simulation and scale-down prototype experiment.</p>
</abstract>
<kwd-group>
<kwd>hybrid circuit breaker</kwd>
<kwd>interline</kwd>
<kwd>SCR string</kwd>
<kwd>current flow control</kwd>
<kwd>H-bridge submodule</kwd>
</kwd-group>
<contract-sponsor id="cn001">National Natural Science Foundation of China<named-content content-type="fundref-id">10.13039/501100001809</named-content>
</contract-sponsor>
</article-meta>
</front>
<body>
<sec id="s1">
<title>1 Introduction</title>
<p>Nowadays, HVDC grids have attracted significant attention, due to its inherent advantages such as flexible control of active and reactive power, low loss, system redundancy, and power reliability (<xref ref-type="bibr" rid="B8">Flourentzou et al., 2009</xref>; <xref ref-type="bibr" rid="B1">Akhmatov et al., 2014</xref>). While the HVDC grid offers several advantages, its engineering application still faces several challenges, one of which is the DC fault handling. The DC circuit breakers (DCCBs) is considered as an essential technology to isolate the fault area and maintain normal operations of non-fault areas in HVDC grids. There are three main groups of DCCB: mechanical DCCBs (<xref ref-type="bibr" rid="B28">Shi et al., 2015</xref>; <xref ref-type="bibr" rid="B19">Lin et al., 2016</xref>), solid-state DCCBs (<xref ref-type="bibr" rid="B5">Corzine and Ashton, 2012</xref>; <xref ref-type="bibr" rid="B26">Sano and Takasaki, 2014</xref>; <xref ref-type="bibr" rid="B3">Chang et al., 2016</xref>; <xref ref-type="bibr" rid="B15">Keshavarzi et al., 2017</xref>; <xref ref-type="bibr" rid="B18">Li et al., 2019</xref>; <xref ref-type="bibr" rid="B31">Wang et al., 2019</xref>; <xref ref-type="bibr" rid="B29">Shu et al., 2020</xref>; <xref ref-type="bibr" rid="B34">Zhang et al., 2020</xref>; <xref ref-type="bibr" rid="B33">Xu et al., 2021</xref>), and hybrid DCCBs(<xref ref-type="bibr" rid="B12">H&#xc4;FNER and JACOBSON, 2011</xref>; <xref ref-type="bibr" rid="B25">Sander et al., 2018</xref>). The hybrid DCCBs combine the merits of mechanical DCCBs and solid-state DCCBs and therefore is considered as an acceptable solution in HVDC grids. The classic hybrid DCCB (HCB) topology contains a main breaker branch (MB), an energy absorption branch and a transfer branch, the transfer branch consists of an ultra-fast mechanical disconnector (UFD) in series with load current switch (LCS). There are two main groups of HCBs based on the different MB technical routes.</p>
<p>One of the technical routes is IGBT based MB, the classic IGBT-in-series based HCB has been proposed by ABB and successfully tested (<xref ref-type="bibr" rid="B12">H&#xc4;FNER and JACOBSON, 2011</xref>; <xref ref-type="bibr" rid="B25">Sander et al., 2018</xref>). The State Grid Corporation of China (SGCC) proposed a full-bridge modular based MB to avoid the problem of IGBT-in-series synchronization control and has been used in Zhangbei four-terminal MMC-HVDC (Jia et al., 2020; Jinkun et al., 2020.). In order to further reduce the system cost, some integration solutions are proposed, multi-line DC circuit breakers are integrated into one equipment to reduce the number of unidirectional MBs (<xref ref-type="bibr" rid="B20">Liu et al., 2017</xref>; <xref ref-type="bibr" rid="B21">Majumder et al., 2017</xref>; <xref ref-type="bibr" rid="B22">Mokhberdoran et al., 2018a</xref>; <xref ref-type="bibr" rid="B16">Kontos et al., 2018</xref>; <xref ref-type="bibr" rid="B17">Li and Wang, 2018</xref>; <xref ref-type="bibr" rid="B32">Xiao et al., 2020</xref>; <xref ref-type="bibr" rid="B10">Guo et al., 2021</xref>; <xref ref-type="bibr" rid="B30">Wang et al., 2022</xref>), another solution integrated HCBs and current flow controllers (CFCs) into one equipment is proposed in (<xref ref-type="bibr" rid="B6">Cwikowski et al., 2018</xref>; <xref ref-type="bibr" rid="B23">Mokhberdoran et al., 2018b</xref>; <xref ref-type="bibr" rid="B35">Zhu et al., 2022</xref>.) to reduce the system loss. But there are still some drawbacks to the hybrid DCCB topology as follows:<list list-type="simple">
<list-item>
<p>(1) Large number of series connected full-controlled semiconductors, such as IGBTs or IGCTs, in the main breaker increase the investment severely (<xref ref-type="bibr" rid="B4">Chen et al., 2018</xref>).</p>
</list-item>
<list-item>
<p>(2) In future, large DC grids fault currents may exceed the interruption capacity of IGBT under serious fault conditions. The parallel connection of IGBTs is needed but also introduces challenges in terms of construction cost (<xref ref-type="bibr" rid="B7">Dong et al., 2021</xref>).</p>
</list-item>
</list>
</p>
<p>Another technical route is SCR based MB, The SCR based MB has advantages of larger capacity, and lower price. Since the current conducted through the SCR need to reach a value below its threshold current during the turn-off process of SCR, apply a reverse voltage is one of the possible solutions to ensure fast transition from conducting to blocking. The most important issue when designing an SCR-based HCB is reliably to generate a reverse voltage on SCR during the turn-off process so as to make the current conducted through the SCR reach a value below its threshold current(<xref ref-type="bibr" rid="B14">Jamshidi Far and Jovcic, 2018</xref>).</p>
<p>Coupled inductors or Z-source schemes are used to generate the required reverse voltage on SCR during the turn-off process in (<xref ref-type="bibr" rid="B24">Ray et al., 2019</xref>). In those schemes, the transient fault current through capacitors is used to generate a reverse voltage on SCRs, hence those schemes can only be passively turned-off in the condition of the high current rising rate.</p>
<p>A thyristor full-bridge based HCB topology is proposed in (<xref ref-type="bibr" rid="B11">Guo et al., 2020</xref>), which can pre-charge the capacitor with DC system voltage, and the reverse voltage is generated by discharge process of pre-charged capacitor. The full-bridge structure is used to pre-charge the capacitor with dc system voltage and switch the fault current path, the use of large number of thyristor strings also increases the system cost.</p>
<p>A SCR-HCB with multiple branches is proposed by Alstom in (<xref ref-type="bibr" rid="B9">Grieshaber et al., 2015</xref>), the capacitance voltage difference of different branches is used to generate the required reverse voltage. The inductor is no longer needed, but if n branches are required for each HCB, 2n number of thyristor strings are required for two adjacent lines, which also increases the number of components in the whole DC grid system.</p>
<p>A DCCB topology combing many SCRs with a few IGBTs-in-series is proposed in (<xref ref-type="bibr" rid="B29">Shu et al., 2020</xref>). The required reverse voltage can be generated by controlled IGBT. However, each DCCB requires two additional IGBT strings, the utilization of the device needs to be increased in multi-terminal system.</p>
<p>In this paper, an interlink hybrid DC circuit breaker (IHCB) based on the concept of sharing only one SCR string MB between two lines is proposed (SCR-IHCB) to increase the utilization of the device. Only a few H-bridge submodule is embedded in to generate the required reverse voltage of SCR turn-off process, and the current flow controlling function is also integrated into the IHCB. No additional capacitor pre-charge circuits and inductors are required, the proposed solution can interrupt the short circuit current of two lines independently and control the current flow if necessary. Therefore, compared to the traditional DCCB/CFC schemes, the proposed topology is simple and economical.</p>
</sec>
<sec id="s2">
<title>2 Proposed topology</title>
<sec id="s2-1">
<title>2.1 Basic structure of proposed SCR-IHCB</title>
<p>A novel IHCB is proposed in this paper and its detailed structure is shown in <xref ref-type="fig" rid="F1">Figure 1</xref>. MB is composed of an anti-parallel SCR string and a H-bridge sub module, connecting line 12 and line 13. <italic>MOV</italic>
<sub>
<italic>2</italic>
</sub> is used to protect IGBTs in H-bridge sub module. The transfer branch consisting of LCS and UFD is installed on each line. <italic>C</italic>
<sub>
<italic>1</italic>
</sub> can be charged through <italic>T</italic>
<sub>
<italic>1</italic>
</sub> to the limiting voltage of <italic>MOV</italic>
<sub>
<italic>1</italic>
</sub> to block the fault current and absorb the residual energy of the system.</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>Proposed SCR-IHCB topology and installation position in system. <bold>(A)</bold> Proposed topology; <bold>(B)</bold> Three-terminal meshed HVDC system under study.</p>
</caption>
<graphic xlink:href="fenrg-10-1081826-g001.tif"/>
</fig>
<p>There are three modes of operation: normal operation without current flow controlling (bypass mode), normal operation with current flow controlling (CFC mode), fault current blocking mode. Obviously, higher system integration, lower volume and cost are achieved because only 1&#xa0;MB mainly based on low-cost SCR string is used, and CFC function are integrated together.</p>
</sec>
<sec id="s2-2">
<title>2.2 Operation principles in different mode</title>
<sec id="s2-2-1">
<title>2.2.1 Bypass mode</title>
<p>When the multiterminal HVDC (MT-HVDC) system is running normally, <italic>LCS</italic>
<sub>
<italic>1</italic>
</sub>
<italic>/LCS</italic>
<sub>
<italic>2</italic>
</sub> and <italic>UFD</italic>
<sub>
<italic>1</italic>
</sub>
<italic>/UFD</italic>
<sub>
<italic>2</italic>
</sub> are all conducted, the SCR string (<italic>T</italic>
<sub>
<italic>0</italic>
</sub>) and H-bridge submodule are bypassed. There is no additional conduction loss and switching loss of semiconductor devices except <italic>LCS</italic>
<sub>
<italic>1</italic>
</sub>
<italic>/LCS</italic>
<sub>
<italic>2</italic>
</sub>.</p>
</sec>
<sec id="s2-2-2">
<title>2.2.2 Current flow control mode</title>
<p>When the current flow needs to be adjusted, the proposed SCR-IHCB can work in CFC mode, the working principle is similar with other interline power flow controllers as shown in (<xref ref-type="bibr" rid="B2">Balasubramaniam et al., 2015</xref>; <xref ref-type="bibr" rid="B27">Sau-Bassols and Gomis-Bellmunt, 2017</xref>). The possible states concerning the available switches are summarized in <xref ref-type="table" rid="T1">Table 1</xref>.</p>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>Switching states for CFC mode.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">State</th>
<th align="center">
<italic>S</italic>
<sub>1</sub>
</th>
<th align="center">
<italic>S</italic>
<sub>2</sub>
</th>
<th align="center">
<italic>S</italic>
<sub>3</sub>
</th>
<th align="center">
<italic>S</italic>
<sub>4</sub>
</th>
<th align="center">
<italic>S</italic>
<sub>5</sub>
</th>
<th align="center">
<italic>S</italic>
<sub>6</sub>
</th>
<th align="center">
<italic>S</italic>
<sub>7</sub>
</th>
<th align="center">
<italic>S</italic>
<sub>8</sub>
</th>
<th align="center">
<italic>V</italic>
<sub>1</sub>
</th>
<th align="center">
<italic>V</italic>
<sub>2</sub>
</th>
<th align="center">
<italic>V</italic>
<sub>C2</sub>
</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td colspan="12" align="center">Bypass Mode</td>
</tr>
<tr>
<td align="center">0</td>
<td align="center">1</td>
<td align="center">1</td>
<td align="center">1</td>
<td align="center">1</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">
<italic>&#x2212;</italic>
</td>
</tr>
<tr>
<td colspan="12" align="center">CFC Mode (<italic>I</italic>
<sub>12</sub> and <italic>I</italic>
<sub>13</sub> are going out the CFC and <italic>I</italic>
<sub>1</sub> is entering)</td>
</tr>
<tr>
<td align="center">1</td>
<td align="center">1</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">
<italic>&#x2212;E</italic>
</td>
<td align="center">&#x2191;</td>
</tr>
<tr>
<td align="center">2</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">1</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">1</td>
<td align="center">1</td>
<td align="center">0</td>
<td align="center">
<italic>E</italic>
</td>
<td align="center">0</td>
<td align="center">&#x2193;</td>
</tr>
<tr>
<td align="center">3</td>
<td align="center">1</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">1</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">1</td>
<td align="center">0</td>
<td align="center">
<italic>E</italic>
</td>
<td align="center">&#x2193;</td>
</tr>
<tr>
<td align="center">4</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">1</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">
<italic>&#x2212;E</italic>
</td>
<td align="center">0</td>
<td align="center">&#x2191;</td>
</tr>
<tr>
<td colspan="12" align="center">CFC Mode (<italic>I</italic>
<sub>12</sub> and <italic>I</italic>
<sub>13</sub> are entering the CFC and <italic>I</italic>
<sub>1</sub> is going out)</td>
</tr>
<tr>
<td align="center">5</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">1</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">
<italic>&#x2212;E</italic>
</td>
<td align="center">0</td>
<td align="center">&#x2191;</td>
</tr>
<tr>
<td align="center">6</td>
<td align="center">0</td>
<td align="center">1</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">1</td>
<td align="center">1</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">
<italic>E</italic>
</td>
<td align="center">&#x2193;</td>
</tr>
<tr>
<td align="center">7</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">1</td>
<td align="center">1</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">1</td>
<td align="center">
<italic>E</italic>
</td>
<td align="center">0</td>
<td align="center">&#x2193;</td>
</tr>
<tr>
<td align="center">8</td>
<td align="center">0</td>
<td align="center">1</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">0</td>
<td align="center">
<italic>&#x2212;E</italic>
</td>
<td align="center">&#x2191;</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>
<italic>E</italic> is the reference value of voltage over <italic>C</italic>
<sub>
<italic>2</italic>
</sub>.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<p>Where &#x201c;1&#x201d; represents the switch is ON and &#x201c;0&#x201d; represents the switch is OFF. In <xref ref-type="fig" rid="F2">Figure 2</xref>, one pair of states (state1 and state 2 in <xref ref-type="table" rid="T1">Table 1</xref>)f of current flow scenarios (<italic>I</italic>
<sub>
<italic>12</italic>
</sub> and <italic>I</italic>
<sub>
<italic>13</italic>
</sub> are going out the SCR-IHCB and <italic>I</italic>
<sub>
<italic>1</italic>
</sub> is entering) are considered as an example. In order to transfer power from line13 to line 12, the CFC should switch continuously in state 1 and state 2 by alternating conduction of <italic>S</italic>
<sub>
<italic>1</italic>
</sub> and <italic>S</italic>
<sub>
<italic>3</italic>
</sub>.</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>Operation stages of SCR-IHCB. <bold>(A)</bold> State 1; <bold>(B)</bold> State 2.</p>
</caption>
<graphic xlink:href="fenrg-10-1081826-g002.tif"/>
</fig>
<p>Below, the analytical analysis of the SCR-IHCB is performed for the pair of states (state 1 and state 2) presented before. Then, the analysis can be extended to the whole range of current configurations.</p>
<p>Taking state 1 as an example, capacitor <italic>C</italic>
<sub>
<italic>2</italic>
</sub> is charged by <italic>I</italic>
<sub>
<italic>13</italic>
</sub>, which is equivalent to inserting a negative voltage in series with line 13. In state 2, capacitor <italic>C</italic>
<sub>
<italic>2</italic>
</sub> is discharged by <italic>I</italic>
<sub>
<italic>12</italic>
</sub>, which is equivalent to inserting a positive voltage in series with line 12. Assuming <italic>D</italic> is the duty cycle of state 1. The average model of the three-terminal system with SCR-IHCB can be described as <xref ref-type="fig" rid="F3">Figure 3</xref>.</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>Average model of three-terminal DC grid with SCR-IHCB in current control mode.</p>
</caption>
<graphic xlink:href="fenrg-10-1081826-g003.tif"/>
</fig>
</sec>
<sec id="s2-2-3">
<title>2.2.3 Fault blocking mode</title>
<p>Take the DC short circuit fault of line12 when SCR-IHCB works in bypass mode as an example, the DC fault current blocking principle is given in <xref ref-type="fig" rid="F4">Figure 4</xref>. Before the fault occurs, the load currents may flow through the low-loss transfer branches in bypass mode as shown in <xref ref-type="fig" rid="F4">Figure 4A</xref> or in CFC mode such as shown in <xref ref-type="fig" rid="F2">Figure 2</xref>.</p>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>Operation of the SCR-IHCB for the transmission line fault. <bold>(A)</bold> Before <italic>t</italic>
<sub>2</sub>. <bold>(B)</bold> <italic>t</italic>
<sub>2</sub>-<italic>t</italic>
<sub>3</sub>. <bold>(C)</bold> <italic>t</italic>
<sub>3</sub>-<italic>t</italic>
<sub>4</sub> <bold>(D)</bold> <italic>t</italic>
<sub>4</sub>-<italic>t</italic>
<sub>5</sub> <bold>(E)</bold> <italic>t</italic>
<sub>5</sub>-<italic>t</italic>
<sub>6</sub> <bold>(F)</bold> <italic>t</italic>
<sub>6</sub>-<italic>t</italic>
<sub>7</sub>.</p>
</caption>
<graphic xlink:href="fenrg-10-1081826-g004.tif"/>
</fig>
<p>
<italic>Stage 1(t</italic>
<sub>
<italic>1-</italic>
</sub>
<italic>t</italic>
<sub>
<italic>3</italic>
</sub>
<italic>)</italic>: If a fault occurs on line12 at <italic>t</italic>
<sub>
<italic>1</italic>
</sub> and is detected at <italic>t</italic>
<sub>
<italic>2</italic>
</sub>, <italic>S</italic>
<sub>
<italic>5</italic>
</sub>, <italic>S</italic>
<sub>
<italic>7</italic>
</sub> and <italic>T</italic>
<sub>
<italic>0</italic>
</sub> will be switch on immediately, and then the IGBTs in <italic>LCS</italic>
<sub>
<italic>1</italic>
</sub> will all be switched off at <italic>t</italic>
<sub>
<italic>3</italic>
</sub>, as shown in <xref ref-type="fig" rid="F4">Figure 4B</xref>. The fault current is then commutated from transfer branch to the main breaker branches, and <italic>UFD</italic>
<sub>
<italic>1</italic>
</sub> will open within 2&#xa0;m.</p>
<p>
<italic>Stage 2(t</italic>
<sub>
<italic>3-</italic>
</sub>
<italic>t</italic>
<sub>
<italic>5</italic>
</sub>
<italic>)</italic>: With <italic>UFD</italic>
<sub>
<italic>1</italic>
</sub> in open position at <italic>t</italic>
<sub>
<italic>4</italic>
</sub> as shown in <xref ref-type="fig" rid="F4">Figure 4C</xref>. Then <italic>S</italic>
<sub>
<italic>7</italic>
</sub> switched off, and the <italic>S</italic>
<sub>
<italic>8</italic>
</sub> will be switched on, thyristor <italic>T</italic>
<sub>
<italic>1</italic>
</sub> will also be turned on immediately as shown in <xref ref-type="fig" rid="F4">Figure 4D</xref>. Initially, <italic>T</italic>
<sub>
<italic>0</italic>
</sub> still is on-state, capacitor voltage <italic>V</italic>
<sub>
<italic>c2</italic>
</sub> may suddenly increase in a short time, but its maximum value is strictly limited to the protection voltage <italic>V</italic>
<sub>
<italic>MOV2</italic>
</sub> by the parallel <italic>MOV</italic>
<sub>
<italic>2</italic>
</sub>, that will protect the IGBT <italic>S</italic>
<sub>
<italic>5</italic>
</sub>
<italic>-S</italic>
<sub>
<italic>8</italic>
</sub> from exceeding its maximum withstand voltage. Fault current will keep charging <italic>C</italic>
<sub>
<italic>1</italic>
</sub> from zero-voltage state. The capacitor voltage <italic>V</italic>
<sub>
<italic>c1</italic>
</sub> gradually increases from zero but it is smaller than the capacitor voltage of <italic>V</italic>
<sub>
<italic>c2</italic>
</sub> which has been pre-charged in interline CFC mode, and a reverse voltage <italic>V</italic>
<sub>
<italic>T0</italic>
</sub> <italic>(V</italic>
<sub>
<italic>T0</italic>
</sub> <italic>&#x3d; V</italic>
<sub>
<italic>c1</italic>
</sub>
<italic>(t) &#x2212;V</italic>
<sub>
<italic>c2</italic>
</sub>
<italic>)</italic> will hereby be generated, the equivalent circuit is shown in <xref ref-type="fig" rid="F5">Figure 5</xref>. The duration of reverse voltage should be larger than the requested recovery time, and the SCR string will be turn off reliably at <italic>t</italic>
<sub>
<italic>5</italic>
</sub> as shown in <xref ref-type="fig" rid="F4">Figure 4E</xref>.</p>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>Implified equivalent circuit of current commutation process. <bold>(A)</bold> <italic>t</italic>
<sub>3</sub>-<italic>t</italic>
<sub>4</sub> <bold>(B)</bold> <italic>t</italic>
<sub>4</sub>-<italic>t</italic>
<sub>5</sub>.</p>
</caption>
<graphic xlink:href="fenrg-10-1081826-g005.tif"/>
</fig>
<p>
<italic>Stage 3(t</italic>
<sub>
<italic>5-</italic>
</sub>
<italic>t</italic>
<sub>
<italic>7</italic>
</sub>
<italic>)</italic>: The fault current continuously charges <italic>C</italic>
<sub>
<italic>1</italic>
</sub>. When <italic>V</italic>
<sub>
<italic>c1</italic>
</sub> reaches the protection voltage of <italic>MOV</italic>
<sub>
<italic>1</italic>
</sub> at <italic>t</italic>
<sub>
<italic>6</italic>
</sub>, the current flowing through <italic>C</italic>
<sub>
<italic>1</italic>
</sub> is transferred to <italic>MOV</italic>
<sub>
<italic>1</italic>
</sub> as shown in <xref ref-type="fig" rid="F4">Figure 4F</xref>. Until fault current decreases to value that no longer maintain <italic>D</italic>
<sub>
<italic>1</italic>
</sub> conduction, the fault is cleared at <italic>t</italic>
<sub>
<italic>7</italic>
</sub>.</p>
</sec>
</sec>
</sec>
<sec id="s3">
<title>3 Parameters design and analysis</title>
<sec id="s3-1">
<title>3.1 Analysis of current commutation</title>
<p>Based on the fault blocking mode described in <xref ref-type="sec" rid="s2">Section 2</xref>, the process of current commutation starts when the IGBTs in <italic>LCS</italic>
<sub>
<italic>1</italic>
</sub> are switched off at <italic>t</italic>
<sub>
<italic>3.</italic>
</sub> Prior to the capacitor <italic>C</italic>
<sub>
<italic>1</italic>
</sub> is inserted at <italic>t</italic>
<sub>
<italic>4</italic>
</sub>, the fault current is fed into the fault node through healthy nodes, it means the current of other stations will inject into line12, the equivalent circuit is given in <xref ref-type="fig" rid="F5">Figure 5A</xref>. Ignoring the resistance of the IGBTs and thyristor which are much less than line resistance, the fault current <italic>i</italic>
<sub>
<italic>fault</italic>
</sub> can be written as below:<disp-formula id="e1">
<mml:math id="m1">
<mml:mrow>
<mml:mtable columnalign="center">
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:msub>
<mml:mi>i</mml:mi>
<mml:mrow>
<mml:mi>f</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>u</mml:mi>
<mml:mi>l</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>i</mml:mi>
<mml:mn>12</mml:mn>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>i</mml:mi>
<mml:mn>13</mml:mn>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mn mathvariant="italic">1</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mn>12</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:msup>
<mml:mi>e</mml:mi>
<mml:mfrac>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mi>R</mml:mi>
</mml:mrow>
<mml:mn>12</mml:mn>
</mml:msub>
</mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mn>12</mml:mn>
</mml:msub>
</mml:mfrac>
</mml:msup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2b;</mml:mo>
<mml:mfrac>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mn>3</mml:mn>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mn>12</mml:mn>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mn>13</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mfrac>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:msup>
<mml:mi>e</mml:mi>
<mml:mfrac>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>t</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mn>12</mml:mn>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mn>13</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mn>12</mml:mn>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mn>13</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mfrac>
</mml:msup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>&#x2264;</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>&#x2264;</mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>4</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:math>
<label>(1)</label>
</disp-formula>Where <italic>V</italic>
<sub>
<italic>1</italic>
</sub> and <italic>V</italic>
<sub>
<italic>3</italic>
</sub> are the voltage of station 1 and station 3 that assumed to remain constant value throughout the process, <italic>R</italic>
<sub>
<italic>12</italic>
</sub> and <italic>L</italic>
<sub>
<italic>12</italic>
</sub> is the resistance and inductance value of line12 to fault point, <italic>R</italic>
<sub>
<italic>13</italic>
</sub> and <italic>L</italic>
<sub>
<italic>13</italic>
</sub> is the resistance and inductance value of line13.</p>
<p>From <italic>t</italic>
<sub>
<italic>4</italic>
</sub> to <italic>t</italic>
<sub>
<italic>5</italic>
</sub>, the capacitor <italic>C</italic>
<sub>
<italic>1</italic>
</sub> and <italic>C</italic>
<sub>
<italic>2</italic>
</sub> are inserted into the system, the simplified equivalent circuit can be seen in <xref ref-type="fig" rid="F5">Figure 5B</xref>. For capacitor <italic>C</italic>
<sub>
<italic>2</italic>
</sub>, its voltage has a sudden increase in a short time and the maximum value is the clamping voltage of <italic>MOV</italic>
<sub>
<italic>2.</italic>
</sub> The current <italic>i</italic>
<sub>
<italic>12</italic>
</sub> will charge the capacitor <italic>C</italic>
<sub>
<italic>1</italic>
</sub> from zero until trigger the clamping voltage of <italic>MOV</italic>
<sub>
<italic>1</italic>
</sub> at <italic>t</italic>
<sub>
<italic>6</italic>
</sub>. According to <xref ref-type="fig" rid="F5">Figure 5B</xref>, the differential equations from <italic>t</italic>
<sub>
<italic>4</italic>
</sub> to <italic>t</italic>
<sub>
<italic>5</italic>
</sub> can be expressed as:<disp-formula id="e2">
<mml:math id="m2">
<mml:mrow>
<mml:mfenced open="{" close="" separators="|">
<mml:mrow>
<mml:mtable columnalign="left">
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mn>12</mml:mn>
</mml:msub>
<mml:mfrac>
<mml:mrow>
<mml:mi mathvariant="normal">d</mml:mi>
<mml:msub>
<mml:mi>i</mml:mi>
<mml:mn>12</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="normal">d</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:msub>
<mml:mi>i</mml:mi>
<mml:mn>12</mml:mn>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi mathvariant="normal">C</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mfrac>
<mml:mrow>
<mml:mi mathvariant="normal">d</mml:mi>
<mml:msub>
<mml:mi>u</mml:mi>
<mml:msub>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="normal">d</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mi mathvariant="normal">l</mml:mi>
<mml:mi mathvariant="normal">a</mml:mi>
<mml:mi mathvariant="normal">m</mml:mi>
<mml:mi>p</mml:mi>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:msub>
<mml:mi>i</mml:mi>
<mml:mn>12</mml:mn>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>i</mml:mi>
<mml:mn>12</mml:mn>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>4</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:math>
<label>(2)</label>
</disp-formula>where <italic>V</italic>
<sub>
<italic>clamp2</italic>
</sub> is the clamping voltage of <italic>MOV</italic>
<sub>
<italic>2</italic>
</sub>, the voltage of the capacitor <italic>C</italic>
<sub>
<italic>1</italic>
</sub> from <italic>t</italic>
<sub>
<italic>4</italic>
</sub> can be obtained:<disp-formula id="e3">
<mml:math id="m3">
<mml:mrow>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>&#x2061;</mml:mo>
<mml:mi>cos</mml:mi>
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:msqrt>
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mn>12</mml:mn>
</mml:msub>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:msqrt>
</mml:mrow>
</mml:mfrac>
<mml:mi>t</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:msqrt>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mn>12</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:msqrt>
<mml:msub>
<mml:mi>i</mml:mi>
<mml:mn>12</mml:mn>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>4</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mi>sin</mml:mi>
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:msqrt>
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mn>12</mml:mn>
</mml:msub>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:msqrt>
</mml:mrow>
</mml:mfrac>
<mml:mi>t</mml:mi>
<mml:mtext>&#x2003;</mml:mtext>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>4</mml:mn>
</mml:msub>
<mml:mo>&#x2264;</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>&#x2264;</mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>5</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(3)</label>
</disp-formula>
</p>
<p>Assuming <italic>T</italic>
<sub>
<italic>scr</italic>
</sub> is the minimum recovery time of SCR string, the SCR voltage <italic>V</italic>
<sub>
<italic>T0</italic>
</sub> can be expressed as:<disp-formula id="e4">
<mml:math id="m4">
<mml:mrow>
<mml:mtable columnalign="center">
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>&#x2061;</mml:mo>
<mml:mi>cos</mml:mi>
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:msqrt>
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mn>12</mml:mn>
</mml:msub>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:msqrt>
</mml:mrow>
</mml:mfrac>
<mml:mi>t</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:msqrt>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mn>12</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:msqrt>
<mml:msub>
<mml:mi>i</mml:mi>
<mml:mn>12</mml:mn>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>4</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mi>sin</mml:mi>
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:msqrt>
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mn>12</mml:mn>
</mml:msub>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:msqrt>
</mml:mrow>
</mml:mfrac>
<mml:mi>t</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mrow>
<mml:mi>c</mml:mi>
<mml:mi>l</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>m</mml:mi>
<mml:mi>p</mml:mi>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2264;</mml:mo>
<mml:mn>0</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>4</mml:mn>
</mml:msub>
<mml:mo>&#x2264;</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>&#x2264;</mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>4</mml:mn>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">s</mml:mi>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mi>r</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:math>
<label>(4)</label>
</disp-formula>
</p>
<p>The most important issue of parameter design of the proposed topology is to make sure that the duration of reverse voltage on the SCR string <italic>T</italic>
<sub>
<italic>0</italic>
</sub> must be larger than the minimum requested recovery time to make sure the current conducted thought the SCR reach a value below its threshold current and last long enough, thus the thyristor can be switched off reliably.</p>
<p>To meet the minimum recovery time of SCR under the worst situation, and the calculation process can be simplified:<disp-formula id="e5">
<mml:math id="m5">
<mml:mrow>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>v</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mi>max</mml:mi>
</mml:msub>
</mml:mfrac>
<mml:mo>&#x2265;</mml:mo>
<mml:mi>&#x3b1;</mml:mi>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mrow>
<mml:mi>s</mml:mi>
<mml:mi>c</mml:mi>
<mml:mi>r</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
<label>(5)</label>
</disp-formula>
</p>
<p>The capacitor <italic>C</italic>
<sub>
<italic>1</italic>
</sub> and voltage of <italic>C</italic>
<sub>
<italic>2</italic>
</sub> can be chosen as:<disp-formula id="e6">
<mml:math id="m6">
<mml:mrow>
<mml:mfenced open="{" close="" separators="|">
<mml:mrow>
<mml:mtable columnalign="center">
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>&#x2265;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mrow>
<mml:mi>s</mml:mi>
<mml:mi>c</mml:mi>
<mml:mi>r</mml:mi>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mi>max</mml:mi>
</mml:msub>
</mml:mrow>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mfrac>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2265;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mrow>
<mml:mi>s</mml:mi>
<mml:mi>c</mml:mi>
<mml:mi>r</mml:mi>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mi>max</mml:mi>
</mml:msub>
</mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mfrac>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:math>
<label>(6)</label>
</disp-formula>Where <italic>T</italic>
<sub>
<italic>rv</italic>
</sub> is the required reverse voltage time, <italic>T</italic>
<sub>
<italic>scr</italic>
</sub> is the minimum recovery time of <italic>T</italic>
<sub>
<italic>0</italic>
</sub>. <italic>I</italic>
<sub>
<italic>max</italic>
</sub> is the maximum allowed breaking current of SCR-IHCB. &#x3b1; is a redundancy factor and must be larger than 1.</p>
<p>According to Eqs. <xref ref-type="disp-formula" rid="e5">5</xref>, <xref ref-type="disp-formula" rid="e6">6</xref>, a larger redundancy factor &#x3b1; increases the reliability of SCR-IHCB, but the capacitor value <italic>C</italic>
<sub>
<italic>1</italic>
</sub> and <italic>V</italic>
<sub>
<italic>c2</italic>
</sub> becomes larger. A redundancy factor of 1.5&#x223c;2 is generally preferred. When the value of &#x3b1; is determined, the value of <italic>C</italic>
<sub>
<italic>1</italic>
</sub> and <italic>V</italic>
<sub>
<italic>C2</italic>
</sub> should be designed together, A smaller value of <italic>C</italic>
<sub>
<italic>1</italic>
</sub> means a faster blocking speed (<italic>t</italic>
<sub>
<italic>b</italic>
</sub> in <xref ref-type="fig" rid="F6">Figure 6</xref>) of the fault current because <italic>V</italic>
<sub>
<italic>c1</italic>
</sub> can rise to <italic>V</italic>
<sub>
<italic>DC</italic>
</sub> faster, but it also means that a higher <italic>V</italic>
<sub>
<italic>C2</italic>
</sub> value is required; a higher <italic>V</italic>
<sub>
<italic>c2</italic>
</sub> value also means higher withstand voltage of <italic>S</italic>
<sub>
<italic>5</italic>
</sub>
<italic>-S</italic>
<sub>
<italic>7</italic>
</sub>, IGBT-in-series or cascaded multi submodule topology can be used, but the cost and loss of the system will also increase. There exists a trade-off between system economy and fault current blocking speed, as shown in <xref ref-type="fig" rid="F6">Figure 6</xref>.</p>
<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
<p>The relationship between <italic>C</italic>
<sub>
<italic>1</italic>
</sub>, <italic>t</italic>
<sub>
<italic>b</italic>
</sub> and <italic>V</italic>
<sub>
<italic>c2</italic>
</sub>.</p>
</caption>
<graphic xlink:href="fenrg-10-1081826-g006.tif"/>
</fig>
</sec>
<sec id="s3-2">
<title>3.2 Parameters calculation of MOV</title>
<p>The rated voltage for the MOVs of the typical HCB should be greater than 1.5 times the system voltage to quickly reduce the fault current to zero:<disp-formula id="e7">
<mml:math id="m7">
<mml:mrow>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mrow>
<mml:mi>M</mml:mi>
<mml:mi>O</mml:mi>
<mml:mi>V</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2265;</mml:mo>
<mml:mn>1.5</mml:mn>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mrow>
<mml:mi>D</mml:mi>
<mml:mi>C</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
<label>(7)</label>
</disp-formula>
</p>
<p>The total absorbing energy <italic>E</italic>
<sub>
<italic>MOV</italic>
</sub> of MOV is associated with the energy storage components of system, which can be given by:<disp-formula id="e8">
<mml:math id="m8">
<mml:mrow>
<mml:msub>
<mml:mi>E</mml:mi>
<mml:mrow>
<mml:mi>M</mml:mi>
<mml:mi>O</mml:mi>
<mml:mi>V</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>D</mml:mi>
<mml:mi>C</mml:mi>
</mml:mrow>
</mml:msub>
<mml:msubsup>
<mml:mi>I</mml:mi>
<mml:mi>max</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
<mml:mo>&#x2212;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msubsup>
<mml:mi>V</mml:mi>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>o</mml:mi>
<mml:mi>v</mml:mi>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msubsup>
<mml:mo>&#x2212;</mml:mo>
<mml:msubsup>
<mml:mi>V</mml:mi>
<mml:mrow>
<mml:mi>D</mml:mi>
<mml:mi>C</mml:mi>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msubsup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(8)</label>
</disp-formula>where <italic>L</italic>
<sub>
<italic>DC</italic>
</sub> is the value of system equivalent inductance, <italic>I</italic>
<sub>
<italic>max</italic>
</sub> is the maximum value of fault current.</p>
</sec>
<sec id="s3-3">
<title>3.3 Device cost and loss analysis</title>
<p>In order to compare the improvements of the proposed SCR-IHCB, it is compared with the typical HCB&#x2b;CFC solution which is not integrated (three ABB&#x2019;s HCB solution (<xref ref-type="bibr" rid="B13">H&#xe4;fner and Jacobson, 2011</xref>) in three lines with one CFC (<xref ref-type="bibr" rid="B27">Sau-Bassols and Gomis-Bellmunt, 2017</xref>)) in 10kV/1&#xa0;kA three-port system, as shown in <xref ref-type="fig" rid="F7">Figure 7</xref>. 4.5&#xa0;kV IGBT(5SNA1200G452300) and 5.2&#xa0;kV thyristor(T1451N) are selected in the comparison. The relative conduction loss and device cost of two solutions in the same voltage level are shown in <xref ref-type="fig" rid="F8">Figure 8</xref>, where the ordinate is a relative value and &#x201c;1&#x201d; represents the maximum.</p>
<fig id="F7" position="float">
<label>FIGURE 7</label>
<caption>
<p>Detailed topologies of two solutions in 10kV/1&#xa0;kA three-port system <bold>(A)</bold> Proposed SCR-IHCB; <bold>(B)</bold> Typical HCB&#x2b;CFC solution.</p>
</caption>
<graphic xlink:href="fenrg-10-1081826-g007.tif"/>
</fig>
<fig id="F8" position="float">
<label>FIGURE 8</label>
<caption>
<p>Economic comparison with two solutions in 10&#xa0;kV three-port system.</p>
</caption>
<graphic xlink:href="fenrg-10-1081826-g008.tif"/>
</fig>
<p>As can be seen in <xref ref-type="fig" rid="F8">Figure 8</xref>, the device cost of the proposed solution is much lower than that of typical HCB&#x2b;CFC solution, because less HCBs are used and large number of fully-controlled semiconductor devices have been replaced by semi-controlled semiconductor devices.</p>
<p>The conduction loss in the proposed SCR-IHCB is much higher in CFC mode, but is lower in bypass mode compared with typical IGBT based HCB &#x2b; CFC solution. Because in bypass mode, only the conduction loss of LCS is added with the proposed solution, but both conduction loss of IGBTs in LCS and CFC parts are added with the typical solution. Considering the investment and conduction loss in different mode together, the comprehensive cost during operation strongly depends on how often the SCR-IHCB need to operate in CFC mode to ensure stable grid conditions, therefore the comprehensive cost could be much lower than the typical solution in the application scenario where inter line power flow control is only needed occasionally.</p>
</sec>
</sec>
<sec id="s4">
<title>4 Modeling and control methodology of CFC</title>
<p>In this section, the dynamic model of the proposed CFC is presented, using averaging technique where the terminals voltages are taken into consideration as setting values. Taking the first scenario for example, and the analysis can be extended to the rest of possible current configurations. We can see the current flow of the first scenario in the <xref ref-type="fig" rid="F2">Figure 2</xref>.</p>
<p>The following set of equations describes the circuit of <xref ref-type="fig" rid="F2">Figure 2A</xref>. This equivalent circuit was developed based on a reduction of the physical circuit layout, where: <italic>r</italic>
<sub>
<italic>xx</italic>
</sub> and <italic>L</italic>
<sub>
<italic>xx</italic>
</sub> are the resistance and the inductance of the line <italic>xx</italic> originated from the CFC bus and carrying an instantaneous current <italic>i</italic>
<sub>
<italic>x</italic>
</sub>, <italic>V</italic>
<sub>
<italic>c1</italic>
</sub> is the capacitor voltage, <italic>V</italic>
<sub>
<italic>1</italic>
</sub> is the voltage at the bus where the CFC is connected to, <italic>V</italic>
<sub>
<italic>2</italic>
</sub> and <italic>V</italic>
<sub>
<italic>3</italic>
</sub> are the voltages at the end terminals of the lines, respectively.<disp-formula id="e9">
<mml:math id="m9">
<mml:mrow>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:mtable columnalign="center">
<mml:mtr>
<mml:mtd>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mn>12</mml:mn>
</mml:msub>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mn>13</mml:mn>
</mml:msub>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mover accent="true">
<mml:mi>X</mml:mi>
<mml:mo>&#x2d9;</mml:mo>
</mml:mover>
<mml:mo>&#x3d;</mml:mo>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:mtable columnalign="center">
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>r</mml:mi>
<mml:mn>12</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>r</mml:mi>
<mml:mn>13</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mtd>
<mml:mtd>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mn>1</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mi>X</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:mtable columnalign="center">
<mml:mtr>
<mml:mtd>
<mml:mn>1</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mn>1</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mi>U</mml:mi>
</mml:mrow>
</mml:math>
<label>(9)</label>
</disp-formula>
<disp-formula id="e10">
<mml:math id="m10">
<mml:mrow>
<mml:mi>X</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:mtable columnalign="left">
<mml:mtr>
<mml:mtd>
<mml:msub>
<mml:mi>i</mml:mi>
<mml:mn>12</mml:mn>
</mml:msub>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:msub>
<mml:mi>i</mml:mi>
<mml:mn>13</mml:mn>
</mml:msub>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mrow>
<mml:mi>c</mml:mi>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>,</mml:mo>
<mml:mi>U</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:mtable columnalign="left">
<mml:mtr>
<mml:mtd>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mn>3</mml:mn>
</mml:msub>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(10)</label>
</disp-formula>
</p>
<p>Similarly, the state equations of <xref ref-type="fig" rid="F2">Figure 2B</xref>, where the capacitor is discharging into line12, are as follows:<disp-formula id="e11">
<mml:math id="m11">
<mml:mrow>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:mtable columnalign="center">
<mml:mtr>
<mml:mtd>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mn>12</mml:mn>
</mml:msub>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mn>13</mml:mn>
</mml:msub>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mi>C</mml:mi>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mover accent="true">
<mml:mi>X</mml:mi>
<mml:mo>&#x2d9;</mml:mo>
</mml:mover>
<mml:mo>&#x3d;</mml:mo>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:mtable columnalign="center">
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>r</mml:mi>
<mml:mn>12</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>r</mml:mi>
<mml:mn>13</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mi>X</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:mtable columnalign="center">
<mml:mtr>
<mml:mtd>
<mml:mn>1</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mn>1</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mi>U</mml:mi>
</mml:mrow>
</mml:math>
<label>(11)</label>
</disp-formula>
</p>
<p>Assume the duty ratio of the charging mode1 is <italic>D</italic>. Multiplying Eqs. <xref ref-type="disp-formula" rid="e8">8</xref>, <xref ref-type="disp-formula" rid="e10">10</xref> by <italic>D</italic> and <italic>(1&#x2212;D)</italic>, respectively, and adding the results to obtain the average model for the CFC for the scenario as follows:<disp-formula id="e12">
<mml:math id="m12">
<mml:mrow>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:mtable columnalign="center">
<mml:mtr>
<mml:mtd>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mn>12</mml:mn>
</mml:msub>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mn>13</mml:mn>
</mml:msub>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mover accent="true">
<mml:mi>X</mml:mi>
<mml:mo>&#x2d9;</mml:mo>
</mml:mover>
<mml:mo>&#x3d;</mml:mo>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:mtable columnalign="center">
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>r</mml:mi>
<mml:mn>12</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>D</mml:mi>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>r</mml:mi>
<mml:mn>13</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mtd>
<mml:mtd>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>D</mml:mi>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>D</mml:mi>
</mml:mrow>
</mml:mtd>
<mml:mtd>
<mml:mi>D</mml:mi>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mi>X</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:mtable columnalign="center">
<mml:mtr>
<mml:mtd>
<mml:mn>1</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mn>1</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mi>U</mml:mi>
</mml:mrow>
</mml:math>
<label>(12)</label>
</disp-formula>
</p>
<p>At steady state, Eq. <xref ref-type="disp-formula" rid="e11">11</xref> can be written as Eq. <xref ref-type="disp-formula" rid="e12">12</xref>:<disp-formula id="e13">
<mml:math id="m13">
<mml:mrow>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:mtable columnalign="center">
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>r</mml:mi>
<mml:mn>12</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>D</mml:mi>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>r</mml:mi>
<mml:mn>13</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mtd>
<mml:mtd>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>D</mml:mi>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>D</mml:mi>
</mml:mrow>
</mml:mtd>
<mml:mtd>
<mml:mi>D</mml:mi>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mi>X</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:mtable columnalign="center">
<mml:mtr>
<mml:mtd>
<mml:mn>1</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mn>1</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mi>U</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:math>
<label>(13)</label>
</disp-formula>
</p>
<p>Solving Eq. <xref ref-type="disp-formula" rid="e12">12</xref>, the steady-state value of capacitor voltage is obtained as:<disp-formula id="e14">
<mml:math id="m14">
<mml:mrow>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mi>c</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>r</mml:mi>
<mml:mn>12</mml:mn>
</mml:msub>
<mml:msub>
<mml:mi>i</mml:mi>
<mml:mn>12</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>D</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mn>3</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>r</mml:mi>
<mml:mn>12</mml:mn>
</mml:msub>
<mml:msub>
<mml:mi>i</mml:mi>
<mml:mn>12</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mi>D</mml:mi>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(14)</label>
</disp-formula>
</p>
<p>Eq. <xref ref-type="disp-formula" rid="e13">13</xref> gives an expression for the capacitor voltage as a function of the network parameters and the voltage drops across the cables connected to the CFC which represents the loading condition of the grid.</p>
<p>Given that the power taken from one line is equal to the power added to the other line, the power balancing between state 1 and state 2 as shown in <xref ref-type="fig" rid="F2">Figure 2</xref> is given by:<disp-formula id="e15">
<mml:math id="m15">
<mml:mrow>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mrow>
<mml:mi>c</mml:mi>
<mml:mn>2</mml:mn>
<mml:mo>_</mml:mo>
<mml:mi mathvariant="normal">r</mml:mi>
<mml:mi mathvariant="normal">e</mml:mi>
<mml:mi mathvariant="normal">f</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>D</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mn>12</mml:mn>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mrow>
<mml:mi>c</mml:mi>
<mml:mn>2</mml:mn>
<mml:mo>_</mml:mo>
<mml:mi mathvariant="normal">r</mml:mi>
<mml:mi mathvariant="normal">e</mml:mi>
<mml:mi mathvariant="normal">f</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mi>D</mml:mi>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mn>13</mml:mn>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:math>
<label>(15)</label>
</disp-formula>
</p>
<p>The relationship between <italic>I</italic>
<sub>
<italic>12</italic>
</sub> and <italic>I</italic>
<sub>
<italic>13</italic>
</sub> can be obtained from the above formula:<disp-formula id="e16">
<mml:math id="m16">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mn>12</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mn>13</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mi>D</mml:mi>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>D</mml:mi>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(16)</label>
</disp-formula>
</p>
<p>From the previous analysis the voltage ripple can be deduced and it is given by Eq. <xref ref-type="disp-formula" rid="e16">16</xref>.<disp-formula id="e17">
<mml:math id="m17">
<mml:mrow>
<mml:mo>&#x394;</mml:mo>
<mml:mi>U</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:msub>
<mml:mrow>
<mml:mi>D</mml:mi>
<mml:mi>I</mml:mi>
</mml:mrow>
<mml:mn>13</mml:mn>
</mml:msub>
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:mi>f</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>D</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mn>12</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>C</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:mi>f</mml:mi>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(17)</label>
</disp-formula>where &#x192; is the switching frequency of the CFC.</p>
<p>A block diagram for the control scheme is shown in <xref ref-type="fig" rid="F9">Figure 9</xref>. The control system has two nested PI controllers: an inner capacitor voltage controller and outer DC current controller. The outer controller regulates the DC line current by feeding a reference voltage to the inner voltage controller. The inner controller achieves the required capacitor voltage level by controlling the duty cycle.</p>
<fig id="F9" position="float">
<label>FIGURE 9</label>
<caption>
<p>PI controller for CFC mode of SCR-IHCB.</p>
</caption>
<graphic xlink:href="fenrg-10-1081826-g009.tif"/>
</fig>
</sec>
<sec id="s5">
<title>5 MTDC network Simulation Studies</title>
<p>In this section, a simplified three-terminal HVDC system is simulated. As shown in <xref ref-type="fig" rid="F1">Figure 1</xref>, the proposed SCR-IHCB topology is equipped at station 1 to adjust the power of line 12 and line 13. The practical parameter of the three-terminal HVDC system 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>Parameter of three-terminal HVDC system.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="3" align="center">Line parameter</th>
<th align="center">R (&#x3a9; <inline-formula id="inf1">
<mml:math id="m18">
<mml:mrow>
<mml:mi>&#x3a9;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>/km)</th>
<th align="center">0.01105</th>
</tr>
<tr>
<th align="center">L(MH/km)</th>
<th align="center">3.245</th>
</tr>
<tr>
<th align="center">C(<italic>&#x3bc;</italic>F/km)</th>
<th align="center">0.382</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">Station</td>
<td colspan="2" align="center">Length/km</td>
</tr>
<tr>
<td align="center">A1 to A2</td>
<td colspan="2" align="center">200</td>
</tr>
<tr>
<td align="center">A1 to A3</td>
<td colspan="2" align="center">300</td>
</tr>
<tr>
<td align="center">A2 to A3</td>
<td colspan="2" align="center">200</td>
</tr>
<tr>
<td rowspan="3" align="center">Converter Parameter</td>
<td align="center">AC voltage</td>
<td align="center">110&#xa0;kV</td>
</tr>
<tr>
<td align="center">DC voltage</td>
<td align="center">200&#xa0;kV</td>
</tr>
<tr>
<td align="center">Limiting current inductor</td>
<td align="center">100&#xa0;mH</td>
</tr>
<tr>
<td rowspan="3" align="center">SCR-IHCB Parameter</td>
<td align="center">Capacitor <italic>C</italic>
<sub>1</sub>
</td>
<td align="center">120&#xa0;<italic>&#x3bc;</italic>F</td>
</tr>
<tr>
<td align="center">Capacitor <italic>C</italic>
<sub>2</sub>
</td>
<td align="center">1mF/6&#xa0;kV</td>
</tr>
<tr>
<td align="center">Arrester protective voltage</td>
<td align="center">250&#xa0;kV</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>The currents flowing from the DC bus of station 1 and the transmission lines in presence of the SCR-IHCB are depicted in <xref ref-type="fig" rid="F10">Figure 10</xref>. The SCR-IHCB operates in the bypass mode for 0 &#x3c; <italic>t</italic> &#x3c; 2s. Thereafter, the CFC changes its operation mode to CFC mode at 2s. <xref ref-type="fig" rid="F10">Figures 10A, B</xref> implies that the SCR-IHCB can adjust the current bidirectionally in CFC mode. The short-circuit fault in line12 happens at time <italic>t</italic> &#x3d; 4s. It can be seen in <xref ref-type="fig" rid="F10">Figures 10A, B</xref> that the SCR-IHCB can quickly isolate the fault on line 12, and the transmission between station 1 and station 3 returned to normal (<italic>I</italic>
<sub>
<italic>1</italic>
</sub> <italic>&#x3d; I</italic>
<sub>
<italic>13</italic>
</sub>).</p>
<fig id="F10" position="float">
<label>FIGURE 10</label>
<caption>
<p>Performance of SCR-IHCB. <bold>(A)</bold> Current waveforms with forward power flow. <bold>(B)</bold> Reverse power flow. <bold>(C)</bold> Fault current transfer process. <bold>(D)</bold> Energy absorb by MOV<sub>1</sub>. <bold>(E)</bold> <italic>V</italic>
<sub>
<italic>T0</italic>
</sub>, <italic>V</italic>
<sub>
<italic>T1</italic>
</sub>, <italic>V</italic>
<sub>
<italic>c1</italic>
</sub> and <italic>V</italic>
<sub>
<italic>c2</italic>
</sub>. <bold>(F)</bold> Details of <italic>V</italic>
<sub>
<italic>T0</italic>
</sub>, <italic>V</italic>
<sub>
<italic>T1</italic>
</sub>, <italic>V</italic>
<sub>
<italic>c1</italic>
</sub> and <italic>V</italic>
<sub>
<italic>c2</italic>
</sub>. <bold>(G)</bold> Voltage of transfer branches. <bold>(H)</bold> Details of voltage of transfer branches. <bold>(I)</bold> <italic>V</italic>
<sub>
<italic>S5</italic>
</sub>
<italic>-V</italic>
<sub>
<italic>S8</italic>
</sub>. <bold>(J)</bold> <italic>I</italic>
<sub>
<italic>S5</italic>
</sub>
<italic>-I</italic>
<sub>
<italic>S8</italic>
</sub>. <bold>(K)</bold> <italic>V</italic>
<sub>
<italic>D1</italic>
</sub> and <italic>V</italic>
<sub>
<italic>D2</italic>
</sub>. <bold>(L)</bold> <italic>I</italic>
<sub>
<italic>D1</italic>
</sub> and <italic>I</italic>
<sub>
<italic>D2</italic>
</sub>.</p>
</caption>
<graphic xlink:href="fenrg-10-1081826-g010.tif"/>
</fig>
<p>As shown in <xref ref-type="fig" rid="F10">Figure 10C</xref>, before the fault is detected in <italic>t</italic> &#x3d; 4.001s, the SCR-IHCB is still working in CFC mode. when the system detects the fault, IHCB mode is activated, <italic>S</italic>
<sub>
<italic>5</italic>
</sub> and <italic>S</italic>
<sub>
<italic>7</italic>
</sub> conducts as mentioned above, the fault current goes through <italic>T</italic>
<sub>
<italic>0</italic>
</sub>, and <italic>I</italic>
<sub>
<italic>T0</italic>
</sub> started to rise rapidly. After 2&#xa0;m (waiting for the <italic>UFD</italic>
<sub>
<italic>1</italic>
</sub> completely open), the fault current was successfully transferred to charging path of the capacitor <italic>C</italic>
<sub>
<italic>1</italic>
</sub>, <italic>V</italic>
<sub>
<italic>c1</italic>
</sub> starts to rise (as shown in <xref ref-type="fig" rid="F10">Figure 10E</xref>), in less than 5&#xa0;m, the fault current (<italic>I</italic>
<sub>
<italic>c1</italic>
</sub>, <italic>I</italic>
<sub>
<italic>D1</italic>
</sub>) reaches the peak value 6.1&#xa0;kA. When <italic>V</italic>
<sub>
<italic>c1</italic>
</sub> reaches the protection voltage of MOV<sub>1</sub>(250&#xa0;kV as shown in <xref ref-type="fig" rid="F10">Figure 10E</xref>), the fault current is transferred to MOV path (<italic>I</italic>
<sub>
<italic>mov1</italic>
</sub> in <xref ref-type="fig" rid="F10">Figure 10C</xref>) and decreases to zero. The amount of absorbed energy of <italic>MOV</italic>
<sub>
<italic>1</italic>
</sub> reaches almost 3.6&#xa0;MJ as shown in <xref ref-type="fig" rid="F10">Figure 10D</xref>. When the fault current drops to zero, the value of <italic>V</italic>
<sub>
<italic>T0</italic>
</sub> return to <italic>V</italic>
<sub>
<italic>DC</italic>
</sub>
<italic>-V</italic>
<sub>
<italic>c2</italic>
</sub>, and the thyristor <italic>T</italic>
<sub>
<italic>1</italic>
</sub> needs to withstand a reverse voltage of <italic>V</italic>
<sub>
<italic>c1</italic>
</sub>
<italic>-V</italic>
<sub>
<italic>DC</italic>
</sub>, about 50&#xa0;kV as shown in <xref ref-type="fig" rid="F10">Figure 10E</xref>.</p>
<p>
<xref ref-type="fig" rid="F10">Figure 10F</xref> shows that the reverse voltage <italic>V</italic>
<sub>
<italic>T0</italic>
</sub> (<italic>V</italic>
<sub>
<italic>T0</italic>
</sub> <italic>&#x3d; V</italic>
<sub>
<italic>c1</italic>
</sub> <italic>&#x2212;V</italic>
<sub>
<italic>c2</italic>
</sub>) is generated at 4.003s, and the duration time is about 140us, much larger than the minimum requested recovery time of SCR string in (<xref ref-type="bibr" rid="B14">Jamshidi Far and Jovcic, 2018</xref>).</p>
<p>
<xref ref-type="fig" rid="F10">Figures 10G, H</xref> show the voltage waveform of two transfer branch, <italic>LCS</italic>
<sub>
<italic>1</italic>
</sub> and <italic>LCS</italic>
<sub>
<italic>2</italic>
</sub> works in CFC mode before fault is detected. <italic>UFD</italic>
<sub>
<italic>2</italic>
</sub> and <italic>LCS</italic>
<sub>
<italic>2</italic>
</sub> remain on-state to keep transmission of station1 and station 3 after fault blocking, <italic>LCS</italic>
<sub>
<italic>1</italic>
</sub> switch off at 4.001s, and the <italic>UFD</italic>
<sub>
<italic>1</italic>
</sub> takes 2&#xa0;m to completely open, then the voltage on <italic>UFD</italic>
<sub>
<italic>1</italic>
</sub> increases with <italic>V</italic>
<sub>
<italic>c1</italic>
</sub>.</p>
<p>
<xref ref-type="fig" rid="F10">Figures 10I, J</xref> show the voltage and current of the <italic>S</italic>
<sub>
<italic>5</italic>
</sub>
<italic>-S</italic>
<sub>
<italic>7</italic>
</sub>. Obviously, the operation sequence of <italic>S</italic>
<sub>
<italic>5</italic>
</sub>
<italic>-S</italic>
<sub>
<italic>8</italic>
</sub> is consistent with the theoretical analysis, and the maximum withstand voltage of <italic>S</italic>
<sub>
<italic>5</italic>
</sub>
<italic>-S</italic>
<sub>
<italic>8</italic>
</sub> is limited to the given voltage of <italic>V</italic>
<sub>
<italic>c2</italic>
</sub>, the maximum current is equal to the value when the fault current transferred from <italic>T</italic>
<sub>
<italic>0</italic>
</sub> branch to <italic>C</italic>
<sub>
<italic>1</italic>
</sub> branch.</p>
<p>
<xref ref-type="fig" rid="F10">Figures 10K, L</xref> show that the maximum withstand voltage and current of diode strings (<italic>D</italic>
<sub>
<italic>1</italic>
</sub> and <italic>D</italic>
<sub>
<italic>2</italic>
</sub>) are consistent with the maximum voltage of <italic>V</italic>
<sub>
<italic>c1</italic>
</sub> and maximum fault current.</p>
</sec>
<sec id="s6">
<title>6 Experimental Studies</title>
<p>Considering that the proposed SCR-IHCB topology is a symmetrical structure for fault blocking of two adjacent lines; therefore, the verification for the current opening process of one line is enough. A scale-down prototype is built for verifying the concept of the feasibility of the SCR-IHCB, as shown in <xref ref-type="fig" rid="F11">Figure 11A</xref>, the component marks in <xref ref-type="fig" rid="F11">Figure 11A</xref> are consistent with those in <xref ref-type="fig" rid="F1">Figure 1A</xref>. The diagram of the experimental system is depicted in <xref ref-type="fig" rid="F11">Figure 11B</xref> and the system parameters are listed in <xref ref-type="table" rid="T3">Table 3</xref>.</p>
<fig id="F11" position="float">
<label>FIGURE 11</label>
<caption>
<p>Experimental system. <bold>(A)</bold> Photograph of the scale down SCR-IHCB prototype. <bold>(B)</bold> Circuit diagram of three-terminal test platform.</p>
</caption>
<graphic xlink:href="fenrg-10-1081826-g011.tif"/>
</fig>
<table-wrap id="T3" position="float">
<label>TABLE 3</label>
<caption>
<p>Parameters of the experimental system.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Parameter</th>
<th align="center">Value</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">
<italic>U</italic>
<sub>
<italic>dc1</italic>
</sub>
</td>
<td align="center">200V</td>
</tr>
<tr>
<td align="center">
<italic>L</italic>
<sub>
<italic>12</italic>
</sub>
<italic>/L</italic>
<sub>
<italic>13</italic>
</sub>
<italic>/L</italic>
<sub>
<italic>23</italic>
</sub>
</td>
<td align="center">6mH/6mH/6&#xa0;mH</td>
</tr>
<tr>
<td align="center">
<italic>R</italic>
<sub>
<italic>12</italic>
</sub>
</td>
<td align="center">6&#x3a9;</td>
</tr>
<tr>
<td align="center">
<italic>R</italic>
<sub>
<italic>13</italic>
</sub>
</td>
<td align="center">1.2&#x3a9;</td>
</tr>
<tr>
<td align="center">
<italic>R</italic>
<sub>
<italic>23</italic>
</sub>
</td>
<td align="center">4.8&#x3a9;</td>
</tr>
<tr>
<td align="center">
<italic>R</italic>
<sub>
<italic>2</italic>
</sub>
</td>
<td align="center">18.6&#x3a9;</td>
</tr>
<tr>
<td align="center">
<italic>R</italic>
<sub>
<italic>3</italic>
</sub>
</td>
<td align="center">18.6&#x3a9;</td>
</tr>
<tr>
<td align="center">
<italic>V</italic>
<sub>
<italic>c2_ref</italic>
</sub>
</td>
<td align="center">30V</td>
</tr>
</tbody>
</table>
</table-wrap>
<sec id="s6-1">
<title>6.1 Fault current blocking</title>
<p>The fault blocking waveforms of the SCR-IHCB are shown in <xref ref-type="fig" rid="F12">Figure 12</xref>. It can be seen that after the fault occurs at <italic>t</italic>
<sub>
<italic>0</italic>
</sub>, after a detection time of 1&#xa0;m, the IGBT in LCS is turned OFF, fault current is transferred to main breaker branch at <italic>t</italic>
<sub>
<italic>1</italic>
</sub>. A 2&#xa0;m delay is set between <italic>t</italic>
<sub>
<italic>1</italic>
</sub> and <italic>t</italic>
<sub>
<italic>2</italic>
</sub> to simulate the opening time of mechanical switch. The IGBTs in main breaker branch is turned off at <italic>t</italic>
<sub>
<italic>2</italic>
</sub>, while <italic>C</italic>
<sub>
<italic>1</italic>
</sub> is charged and the fault current is successfully interrupted eventually at <italic>t</italic>
<sub>
<italic>3</italic>
</sub>.</p>
<fig id="F12" position="float">
<label>FIGURE 12</label>
<caption>
<p>Measured fault-interrupting waveforms of the DC Fault Mode.</p>
</caption>
<graphic xlink:href="fenrg-10-1081826-g012.tif"/>
</fig>
<p>The detailed waveforms of the thyristor <italic>T</italic>
<sub>
<italic>0</italic>
</sub> recovery stage is shown in <xref ref-type="fig" rid="F13">Figure 13</xref>. When the value of 220&#xa0;&#x3bc;F is chosen for <italic>C</italic>
<sub>
<italic>2</italic>
</sub>, the SCR-IHCB has <italic>&#x394;t</italic> &#x3e; 100us as shown in <xref ref-type="fig" rid="F13">Figure 13A</xref>, and the thyristor is turned off successfully, the fault current of the system (<italic>I</italic>
<sub>
<italic>sys</italic>
</sub>) is quickly transferred from <italic>T</italic>
<sub>
<italic>0</italic>
</sub> to <italic>T</italic>
<sub>
<italic>1</italic>
</sub> (<italic>I</italic>
<sub>
<italic>T0</italic>
</sub> and <italic>I</italic>
<sub>
<italic>T1</italic>
</sub> in <xref ref-type="fig" rid="F13">Figure 13A</xref>), the voltage of <italic>T</italic>
<sub>
<italic>0</italic>
</sub> (<italic>V</italic>
<sub>
<italic>T0</italic>
</sub>) rises as <italic>C</italic>
<sub>
<italic>1</italic>
</sub> is charged by the system fault current.</p>
<fig id="F13" position="float">
<label>FIGURE 13</label>
<caption>
<p>Measured waveforms during the thyristor recovery stage at <bold>(A)</bold> C<sub>2</sub> &#x3d; 220&#x3bc;F; <bold>(B)</bold> C<sub>2</sub> &#x3d; 100&#xa0;&#x3bc;F.</p>
</caption>
<graphic xlink:href="fenrg-10-1081826-g013.tif"/>
</fig>
<p>When the value of <italic>C</italic>
<sub>
<italic>2</italic>
</sub> is reduced to 100&#xa0;&#x3bc;F, the SCR-IHCB has <italic>&#x394;t</italic> &#x3c; 50us, smaller than <italic>t</italic>
<sub>
<italic>q</italic>
</sub> in datasheet of thyristor SKKT62 which is used in our experiment. It is obvious that the thyristor has failed to turn off, the fault current of the system (<italic>I</italic>
<sub>
<italic>sys</italic>
</sub>) continues to flow through <italic>T</italic>
<sub>
<italic>0</italic>
</sub>, Capacitor <italic>C</italic>
<sub>
<italic>1</italic>
</sub> and capacitor <italic>C</italic>
<sub>
<italic>2</italic>
</sub> are connected in parallel, and the voltage rises synchronously.</p>
</sec>
<sec id="s6-2">
<title>6.2 Current control</title>
<p>The CFC function is also verified by experiments, as shown in <xref ref-type="fig" rid="F14">Figure 14</xref>. At the beginning, the current at line 12 <italic>(I</italic>
<sub>
<italic>12</italic>
</sub>) is 12A and at line 13 (<italic>I</italic>
<sub>
<italic>13</italic>
</sub>) is 6A at first. At <italic>t</italic> &#x3d; 10&#xa0;m, the CFC begins to work and the current at line 13 (<italic>I</italic>
<sub>
<italic>13</italic>
</sub>) begins to increase and the current at line 12 (<italic>I</italic>
<sub>
<italic>12</italic>
</sub>) decreases meanwhile. After 5&#xa0;m, the line current forms a new steady state. It can be found that the controller can keep capacitor voltage constant at 30V (<italic>V</italic>
<sub>
<italic>c2</italic>
</sub>) during current regulation.</p>
<fig id="F14" position="float">
<label>FIGURE 14</label>
<caption>
<p>Measured fault-interrupting waveforms of the current control mode.</p>
</caption>
<graphic xlink:href="fenrg-10-1081826-g014.tif"/>
</fig>
</sec>
</sec>
<sec sec-type="conclusion" id="s7">
<title>7 Conclusion</title>
<p>In this paper, a SCR string and H-bridge module based interline hybrid circuit breaker topology with current flow control function is proposed. The operation principles in normal operation mode and DC fault mode are analyzed, the parameters design principle is also presented in detail. The simulation and experiment results from a meshed HVDC grid model confirm the operational performance of the proposed topology. Compared with other solutions, the topology design is more economical and simpler because only one bidirectional SCR string and only one H-bridge module is needed for two adjacent lines, no additional capacitor pre-charge circuits and inductors are required, the current flow control function is also integrated without additional components.</p>
</sec>
</body>
<back>
<sec sec-type="data-availability" id="s8">
<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 id="s9">
<title>Author contributions</title>
<p>QZ: Writing&#x2014;Original Draft, Experimental Studies and Visualization. JZ: Conceptualization, Methodology and Supervision. XG: Writing&#x2014;Original Draft and Simulation Studies. QH: Editing, Parameters Design. JY: Process Analysis, Supervision. TW: Supervision.</p>
</sec>
<sec id="s10">
<title>Funding</title>
<p>This work was supported in part by the National Natural Science Foundation of China under Grant 51607171, in part by The Institute of Electrical Engineering, CAS under Grant E155610301 and E155610201.</p>
</sec>
<ack>
<p>This is a brief acknowledgement of the contributions of individual colleagues, institutions, or agencies that assisted the writers&#x2019; efforts in the writing of this article.</p>
</ack>
<sec sec-type="COI-statement" id="s11">
<title>Conflict of interest</title>
<p>The authors declare that the research 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="disclaimer" id="s12">
<title>Publisher&#x2019;s note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
<ref-list>
<title>References</title>
<ref id="B1">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Akhmatov</surname>
<given-names>V.</given-names>
</name>
<name>
<surname>Callavik</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Franck</surname>
<given-names>C. M.</given-names>
</name>
<name>
<surname>Rye</surname>
<given-names>S. E.</given-names>
</name>
<name>
<surname>Ahndorf</surname>
<given-names>T.</given-names>
</name>
<name>
<surname>Bucher</surname>
<given-names>M. K.</given-names>
</name>
<etal/>
</person-group> (<year>2014</year>). <article-title>Technical guidelines and prestandardization work for first HVDC grids</article-title>. <source>IEEE Trans. Power Deliv.</source> <volume>29</volume> (<issue>1</issue>), <fpage>327</fpage>&#x2013;<lpage>335</lpage>. <pub-id pub-id-type="doi">10.1109/TPWRD.2013.2273978</pub-id>
</citation>
</ref>
<ref id="B2">
<citation citation-type="confproc">
<person-group person-group-type="author">
<name>
<surname>Balasubramaniam</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Liang</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Ugalde-Loo</surname>
<given-names>C. E.</given-names>
</name>
</person-group> (<year>2015</year>). &#x201c;<article-title>Control, dynamics and operation of a dual H-bridge current flow controller</article-title>,&#x201d; in <conf-name>IEEE Energy Conversion Congress and Exposition</conf-name> (<publisher-loc>Montreal, Canada</publisher-loc>: <publisher-name>ECCE</publisher-name>). <pub-id pub-id-type="doi">10.1109/ecce.2015.7309996</pub-id>
</citation>
</ref>
<ref id="B3">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Chang</surname>
<given-names>A. H.</given-names>
</name>
<name>
<surname>Sennett</surname>
<given-names>B. R.</given-names>
</name>
<name>
<surname>Avestruz</surname>
<given-names>A.-T.</given-names>
</name>
<name>
<surname>Leeb</surname>
<given-names>S. B.</given-names>
</name>
<name>
<surname>Kirtley</surname>
<given-names>J. L.</given-names>
</name>
</person-group> (<year>2016</year>). <article-title>Analysis and design of DC system protection using Z-source circuit breaker</article-title>. <source>IEEE Trans. Power Electron.</source> <volume>31</volume> (<issue>2</issue>), <fpage>1036</fpage>&#x2013;<lpage>1049</lpage>. <pub-id pub-id-type="doi">10.1109/TPEL.2015.2415775</pub-id>
</citation>
</ref>
<ref id="B4">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Chen</surname>
<given-names>Z.</given-names>
</name>
<name>
<surname>Yu</surname>
<given-names>Z.</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>X.</given-names>
</name>
<name>
<surname>Wei</surname>
<given-names>T.</given-names>
</name>
<name>
<surname>Lyu</surname>
<given-names>G.</given-names>
</name>
<name>
<surname>Qu</surname>
<given-names>L.</given-names>
</name>
<etal/>
</person-group> (<year>2018</year>). <article-title>Analysis and experiments for IGBT, IEGT, and IGCT in hybrid DC circuit breaker</article-title>. <source>IEEE Trans. Ind. Electron.</source> <volume>65</volume> (<issue>4</issue>), <fpage>2883</fpage>&#x2013;<lpage>2892</lpage>. <pub-id pub-id-type="doi">10.1109/TIE.2017.2764863</pub-id>
</citation>
</ref>
<ref id="B5">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Corzine</surname>
<given-names>K. A.</given-names>
</name>
<name>
<surname>Ashton</surname>
<given-names>R. W.</given-names>
</name>
</person-group> (<year>2012</year>). <article-title>A new Z-source DC circuit breaker</article-title>. <source>IEEE Trans. Power Electron.</source> <volume>27</volume> (<issue>6</issue>), <fpage>2796</fpage>&#x2013;<lpage>2804</lpage>. <pub-id pub-id-type="doi">10.1109/tpel.2011.2178125</pub-id>
</citation>
</ref>
<ref id="B6">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Cwikowski</surname>
<given-names>O.</given-names>
</name>
<name>
<surname>Sau-Bassols</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Chang</surname>
<given-names>B.</given-names>
</name>
<name>
<surname>Prieto-Araujo</surname>
<given-names>E.</given-names>
</name>
<name>
<surname>Barnes</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Gomis-Bellmunt</surname>
<given-names>O.</given-names>
</name>
<etal/>
</person-group> (<year>2018</year>). <article-title>Integrated HVDC circuit breakers with current flow control capability</article-title>. <source>IEEE Trans. Power Deliv.</source> <volume>33</volume> (<issue>1</issue>), <fpage>371</fpage>&#x2013;<lpage>380</lpage>. <pub-id pub-id-type="doi">10.1109/TPWRD.2017.2711963</pub-id>
</citation>
</ref>
<ref id="B7">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Dong</surname>
<given-names>Z.</given-names>
</name>
<name>
<surname>Ren</surname>
<given-names>R.</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>W.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>F. F.</given-names>
</name>
<name>
<surname>Tolbert</surname>
<given-names>L. M.</given-names>
</name>
</person-group> (<year>2021</year>). <article-title>Instability issue of paralleled dies in an SiC power module in solid-state circuit breaker applications</article-title>. <source>IEEE Trans. Power Electron.</source> <volume>36</volume> (<issue>10</issue>), <fpage>11763</fpage>&#x2013;<lpage>11773</lpage>. <pub-id pub-id-type="doi">10.1109/TPEL.2021.3068608</pub-id>
</citation>
</ref>
<ref id="B8">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Flourentzou</surname>
<given-names>N.</given-names>
</name>
<name>
<surname>Agelidis</surname>
<given-names>V. G.</given-names>
</name>
<name>
<surname>Demetriades</surname>
<given-names>G. D.</given-names>
</name>
</person-group> (<year>2009</year>). <article-title>VSC-based HVDC power transmission systems: An overview</article-title>. <source>IEEE Trans. Power Electron.</source> <volume>24</volume> (<issue>3</issue>), <fpage>592</fpage>&#x2013;<lpage>602</lpage>. <pub-id pub-id-type="doi">10.1109/TPEL.2008.2008441</pub-id>
</citation>
</ref>
<ref id="B9">
<citation citation-type="confproc">
<person-group person-group-type="author">
<name>
<surname>Grieshaber</surname>
<given-names>W.</given-names>
</name>
<name>
<surname>Davidson</surname>
<given-names>C. C.</given-names>
</name>
<name>
<surname>Whitehouse</surname>
<given-names>R. S.</given-names>
</name>
<name>
<surname>Dupraz</surname>
<given-names>J.-P.</given-names>
</name>
<name>
<surname>Barker</surname>
<given-names>C. D.</given-names>
</name>
</person-group> (<year>2015</year>). &#x201c;<article-title>A new ultra-fast HVDC Circuit breaker for meshed DC networks</article-title>,&#x201d; in <conf-name>11th IET International Conference on AC and DC Power Transmission</conf-name> (<publisher-loc>Birmingham, UK)</publisher-loc>: <publisher-name>Institution of Engineering and Technology</publisher-name>), <fpage>047</fpage>. <pub-id pub-id-type="doi">10.1049/cp.2015.0021</pub-id>
</citation>
</ref>
<ref id="B10">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Guo</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Li</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Gu</surname>
<given-names>G.</given-names>
</name>
<name>
<surname>Zeng</surname>
<given-names>D.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>G.</given-names>
</name>
</person-group> (<year>2021</year>). <article-title>A multiport DC circuit breaker for high-voltage DC grids</article-title>. <source>IEEE J. Emerg. Sel. Top. Power Electron.</source> <volume>9</volume> (<issue>3</issue>), <fpage>3216</fpage>&#x2013;<lpage>3228</lpage>. <pub-id pub-id-type="doi">10.1109/JESTPE.2020.3018646</pub-id>
</citation>
</ref>
<ref id="B11">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Guo</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>G.</given-names>
</name>
<name>
<surname>Zeng</surname>
<given-names>D.</given-names>
</name>
<name>
<surname>Li</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Chao</surname>
<given-names>H.</given-names>
</name>
</person-group> (<year>2020</year>). <article-title>A thyristor full-bridge-based DC circuit breaker</article-title>. <source>IEEE Trans. Power Electron.</source> <volume>35</volume> (<issue>1</issue>), <fpage>1111</fpage>&#x2013;<lpage>1123</lpage>. <pub-id pub-id-type="doi">10.1109/TPEL.2019.2915808</pub-id>
</citation>
</ref>
<ref id="B12">
<citation citation-type="confproc">
<person-group person-group-type="author">
<name>
<surname>H&#xe4;fner</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Jacobson</surname>
<given-names>B.</given-names>
</name>
</person-group> (<year>2011</year>). &#x201c;<article-title>Proactive hybrid HVDC breakers-A key innovation for reliable HVDC grids</article-title>,&#x201d; in <conf-name>Integrating Supergrids and Microgrids International Symposium</conf-name> (<publisher-loc>Bologna, Italy)</publisher-loc>, <fpage>1</fpage>&#x2013;<lpage>8</lpage>.</citation>
</ref>
<ref id="B13">
<citation citation-type="confproc">
<person-group person-group-type="author">
<name>
<surname>H&#xe4;fner</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Jacobson</surname>
<given-names>B.</given-names>
</name>
</person-group> (<year>2011</year>). &#x201c;<article-title>Proactive hybrid HVDC breakers-a key innovation for reliable HVDC grids</article-title>,&#x201d; in <conf-name>Proceedings of the international symposium on integrating supergrids and microgrids</conf-name> (<publisher-loc>Bologna, Italy)</publisher-loc>, <fpage>1</fpage>&#x2013;<lpage>8</lpage>.</citation>
</ref>
<ref id="B14">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Jamshidi Far</surname>
<given-names>A.</given-names>
</name>
<name>
<surname>Jovcic</surname>
<given-names>D.</given-names>
</name>
</person-group> (<year>2018</year>). <article-title>Design, modeling and control of hybrid DC circuit breaker based on fast thyristors</article-title>. <source>IEEE Trans. Power Deliv.</source> <volume>33</volume> (<issue>2</issue>), <fpage>919</fpage>&#x2013;<lpage>927</lpage>. <pub-id pub-id-type="doi">10.1109/TPWRD.2017.2761022</pub-id>
</citation>
</ref>
<ref id="B15">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Keshavarzi</surname>
<given-names>D.</given-names>
</name>
<name>
<surname>Ghanbari</surname>
<given-names>T.</given-names>
</name>
<name>
<surname>Farjah</surname>
<given-names>E.</given-names>
</name>
</person-group> (<year>2017</year>). <article-title>A Z-source-based bidirectional DC circuit breaker with Fault Current limitation and interruption capabilities</article-title>. <source>IEEE Trans. Power Electron.</source> <volume>32</volume> (<issue>9</issue>), <fpage>6813</fpage>&#x2013;<lpage>6822</lpage>. <pub-id pub-id-type="doi">10.1109/TPEL.2016.2624147</pub-id>
</citation>
</ref>
<ref id="B16">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Kontos</surname>
<given-names>E.</given-names>
</name>
<name>
<surname>Ramirez-Elizondo</surname>
<given-names>L. M.</given-names>
</name>
<name>
<surname>Franck</surname>
<given-names>C. M.</given-names>
</name>
<name>
<surname>Bauer</surname>
<given-names>P.</given-names>
</name>
<name>
<surname>Bauer</surname>
<given-names>P.</given-names>
</name>
</person-group> (<year>2018</year>). <article-title>Multiline breaker for HVDC applications</article-title>. <source>IEEE Trans. Power Deliv.</source> <volume>33</volume> (<issue>3</issue>), <fpage>1469</fpage>&#x2013;<lpage>1478</lpage>. <pub-id pub-id-type="doi">10.1109/TPWRD.2017.2754649</pub-id>
</citation>
</ref>
<ref id="B17">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Li</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>S.</given-names>
</name>
</person-group> (<year>2018</year>). <article-title>Interlink hybrid DC circuit breaker</article-title>. <source>IEEE Trans. Ind. Electron.</source> <volume>65</volume> (<issue>11</issue>), <fpage>8677</fpage>&#x2013;<lpage>8686</lpage>. <pub-id pub-id-type="doi">10.1109/TIE.2018.2803778</pub-id>
</citation>
</ref>
<ref id="B18">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Li</surname>
<given-names>W.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Wu</surname>
<given-names>X.</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>X.</given-names>
</name>
</person-group> (<year>2019</year>). <article-title>A novel solid-state circuit breaker for on-board DC microgrid system</article-title>. <source>IEEE Trans. Ind. Electron.</source> <volume>66</volume> (<issue>7</issue>), <fpage>5715</fpage>&#x2013;<lpage>5723</lpage>. <pub-id pub-id-type="doi">10.1109/TIE.2018.2854559</pub-id>
</citation>
</ref>
<ref id="B19">
<citation citation-type="confproc">
<person-group person-group-type="author">
<name>
<surname>Lin</surname>
<given-names>W.</given-names>
</name>
<name>
<surname>Jovcic</surname>
<given-names>D.</given-names>
</name>
<name>
<surname>Nguefeu</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Saad</surname>
<given-names>H.</given-names>
</name>
</person-group> (<year>2016</year>). &#x201c;<article-title>Modelling of high power mechanical DC circuit breaker</article-title>,&#x201d; in <conf-name>IEEE PES Asia-Pacific Power and Energy Engineering Conference</conf-name> (<publisher-loc>Brisbane, Australia</publisher-loc>: <publisher-name>APPEEC</publisher-name>), <fpage>1</fpage>&#x2013;<lpage>5</lpage>. <pub-id pub-id-type="doi">10.1109/APPEEC.2015.7381002</pub-id>
</citation>
</ref>
<ref id="B20">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Liu</surname>
<given-names>G.</given-names>
</name>
<name>
<surname>Xu</surname>
<given-names>F.</given-names>
</name>
<name>
<surname>Xu</surname>
<given-names>Z.</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>Z.</given-names>
</name>
<name>
<surname>Tang</surname>
<given-names>G.</given-names>
</name>
</person-group> (<year>2017</year>). <article-title>Assembly HVDC breaker for HVDC grids with modular multilevel converters</article-title>. <source>IEEE Trans. Power Electron.</source> <volume>32</volume> (<issue>2</issue>), <fpage>931</fpage>&#x2013;<lpage>941</lpage>. <pub-id pub-id-type="doi">10.1109/TPEL.2016.2540808</pub-id>
</citation>
</ref>
<ref id="B21">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Majumder</surname>
<given-names>R.</given-names>
</name>
<name>
<surname>Barupati</surname>
<given-names>P.</given-names>
</name>
<name>
<surname>Jonsson</surname>
<given-names>T. U.</given-names>
</name>
<name>
<surname>Velotto</surname>
<given-names>G.</given-names>
</name>
</person-group> (<year>2017</year>). <article-title>An alternative method to build DC switchyard with hybrid DC breaker for DC grid</article-title>. <source>IEEE Trans. Power Deliv.</source> <volume>32</volume> (<issue>2</issue>), <fpage>713</fpage>&#x2013;<lpage>722</lpage>. <pub-id pub-id-type="doi">10.1109/TPWRD.2016.2582923</pub-id>
</citation>
</ref>
<ref id="B22">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Mokhberdoran</surname>
<given-names>A.</given-names>
</name>
<name>
<surname>Gomis-Bellmunt</surname>
<given-names>O.</given-names>
</name>
<name>
<surname>Silva</surname>
<given-names>N.</given-names>
</name>
<name>
<surname>Carvalho</surname>
<given-names>A.</given-names>
</name>
</person-group> (<year>2018a</year>). <article-title>Current flow controlling hybrid DC circuit breaker</article-title>. <source>IEEE Trans. Power Electron.</source> <volume>33</volume> (<issue>2</issue>), <fpage>1323</fpage>&#x2013;<lpage>1334</lpage>. <pub-id pub-id-type="doi">10.1109/TPEL.2017.2688412</pub-id>
</citation>
</ref>
<ref id="B23">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Mokhberdoran</surname>
<given-names>A.</given-names>
</name>
<name>
<surname>Van Hertem</surname>
<given-names>D.</given-names>
</name>
<name>
<surname>Silva</surname>
<given-names>N.</given-names>
</name>
<name>
<surname>Leite</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Carvalho</surname>
<given-names>A.</given-names>
</name>
</person-group> (<year>2018b</year>). <article-title>Multiport hybrid HVDC circuit breaker</article-title>. <source>IEEE Trans. Ind. Electron.</source> <volume>65</volume> (<issue>1</issue>), <fpage>309</fpage>&#x2013;<lpage>320</lpage>. <pub-id pub-id-type="doi">10.1109/TIE.2017.2719608</pub-id>
</citation>
</ref>
<ref id="B24">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Ray</surname>
<given-names>A.</given-names>
</name>
<name>
<surname>Rajashekara</surname>
<given-names>K.</given-names>
</name>
<name>
<surname>Banavath</surname>
<given-names>S. N.</given-names>
</name>
<name>
<surname>Pramanick</surname>
<given-names>S. K.</given-names>
</name>
</person-group> (<year>2019</year>). <article-title>Coupled inductor-based zero current switching hybrid DC circuit breaker topologies</article-title>. <source>IEEE Trans. Ind. Appl.</source> <volume>55</volume> (<issue>5</issue>), <fpage>5360</fpage>&#x2013;<lpage>5370</lpage>. <pub-id pub-id-type="doi">10.1109/TIA.2019.2926467</pub-id>
</citation>
</ref>
<ref id="B25">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Sander</surname>
<given-names>R.</given-names>
</name>
<name>
<surname>Suriyah</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Leibfried</surname>
<given-names>T.</given-names>
</name>
</person-group> (<year>2018</year>). <article-title>Characterization of a countercurrent injection-based HVDC circuit breaker</article-title>. <source>IEEE Trans. Power Electron.</source> <volume>33</volume> (<issue>4</issue>), <fpage>2948</fpage>&#x2013;<lpage>2956</lpage>. <pub-id pub-id-type="doi">10.1109/TPEL.2017.2709785</pub-id>
</citation>
</ref>
<ref id="B26">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Sano</surname>
<given-names>K.</given-names>
</name>
<name>
<surname>Takasaki</surname>
<given-names>M.</given-names>
</name>
</person-group> (<year>2014</year>). <article-title>A surgeless solid-state DC circuit breaker for voltage-source-converter-based HVDC systems</article-title>. <source>IEEE Trans. Ind. Appl.</source> <volume>50</volume> (<issue>4</issue>), <fpage>2690</fpage>&#x2013;<lpage>2699</lpage>. <pub-id pub-id-type="doi">10.1109/TIA.2013.2293819</pub-id>
</citation>
</ref>
<ref id="B27">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Sau-Bassols</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Gomis-Bellmunt</surname>
<given-names>O.</given-names>
</name>
</person-group> (<year>2017</year>). <article-title>Modelling and control of an interline current flow controller for meshed HVDC grids</article-title>. <source>IEEE Trans. Power Deliv.</source> <volume>32</volume> (<issue>1</issue>), <fpage>11</fpage>&#x2013;<lpage>22</lpage>. <pub-id pub-id-type="doi">10.1109/TPWRD.2015.2513160</pub-id>
</citation>
</ref>
<ref id="B28">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Shi</surname>
<given-names>Z. Q.</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>Y. K.</given-names>
</name>
<name>
<surname>Jia</surname>
<given-names>S. L.</given-names>
</name>
<name>
<surname>Song</surname>
<given-names>X. C.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>L. J.</given-names>
</name>
<name>
<surname>Chen</surname>
<given-names>M.</given-names>
</name>
</person-group> (<year>2015</year>). <article-title>Design and numerical investigation of A HVDC vacuum switch based on artificial current zero</article-title>. <source>IEEE Trans. Dielectr. Electr. Insul.</source> <volume>22</volume> (<issue>1</issue>), <fpage>135</fpage>&#x2013;<lpage>141</lpage>. <pub-id pub-id-type="doi">10.1109/TDEI.2014.004533</pub-id>
</citation>
</ref>
<ref id="B29">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Shu</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Ma</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Liu</surname>
<given-names>T.</given-names>
</name>
<name>
<surname>He</surname>
<given-names>Z.</given-names>
</name>
</person-group> (<year>2020</year>). <article-title>An active Z-source DC circuit breaker combined with SCR and IGBT</article-title>. <source>IEEE Trans. Power Electron.</source> <volume>35</volume> (<issue>10</issue>), <fpage>10003</fpage>&#x2013;<lpage>10007</lpage>. <pub-id pub-id-type="doi">10.1109/TPEL.2020.2980543</pub-id>
</citation>
</ref>
<ref id="B30">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Wang</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Ming</surname>
<given-names>W.</given-names>
</name>
<name>
<surname>Ugalde Loo</surname>
<given-names>C. E.</given-names>
</name>
<name>
<surname>Liang</surname>
<given-names>J.</given-names>
</name>
</person-group> (<year>2022</year>). <article-title>A low-loss integrated circuit breaker for HVDC applications</article-title>. <source>IEEE Trans. Power Deliv.</source> <volume>37</volume> (<issue>1</issue>), <fpage>472</fpage>&#x2013;<lpage>485</lpage>. <pub-id pub-id-type="doi">10.1109/TPWRD.2021.3063515</pub-id>
</citation>
</ref>
<ref id="B31">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Wang</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Li</surname>
<given-names>W.</given-names>
</name>
<name>
<surname>Wu</surname>
<given-names>Xuanyu.</given-names>
</name>
<name>
<surname>Wu</surname>
<given-names>Xiaohua.</given-names>
</name>
</person-group> (<year>2019</year>). <article-title>A novel bidirectional solid-state circuit breaker for DC microgrid</article-title>. <source>IEEE Trans. Ind. Electron.</source> <volume>66</volume> (<issue>7</issue>), <fpage>5707</fpage>&#x2013;<lpage>5714</lpage>. <pub-id pub-id-type="doi">10.1109/TIE.2018.2878191</pub-id>
</citation>
</ref>
<ref id="B32">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Xiao</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Xu</surname>
<given-names>Z.</given-names>
</name>
<name>
<surname>Xiao</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Gan</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Xu</surname>
<given-names>F.</given-names>
</name>
<name>
<surname>Dai</surname>
<given-names>L.</given-names>
</name>
</person-group> (<year>2020</year>). <article-title>Components sharing based integrated HVDC circuit breaker for meshed HVDC grids</article-title>. <source>IEEE Trans. Power Deliv.</source> <volume>35</volume> (<issue>4</issue>), <fpage>1856</fpage>&#x2013;<lpage>1866</lpage>. <pub-id pub-id-type="doi">10.1109/TPWRD.2019.2955726</pub-id>
</citation>
</ref>
<ref id="B33">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Xu</surname>
<given-names>X.</given-names>
</name>
<name>
<surname>Chen</surname>
<given-names>W.</given-names>
</name>
<name>
<surname>Liu</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Sun</surname>
<given-names>R.</given-names>
</name>
<name>
<surname>Li</surname>
<given-names>Z.</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>B.</given-names>
</name>
</person-group> (<year>2021</year>). <article-title>An efficient and reliable solid-state circuit breaker based on mixture device</article-title>. <source>IEEE Trans. Power Electron.</source> <volume>36</volume> (<issue>9</issue>), <fpage>9767</fpage>&#x2013;<lpage>9771</lpage>. <pub-id pub-id-type="doi">10.1109/TPEL.2021.3067316</pub-id>
</citation>
</ref>
<ref id="B34">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Zhang</surname>
<given-names>X.</given-names>
</name>
<name>
<surname>Yu</surname>
<given-names>Z.</given-names>
</name>
<name>
<surname>Chen</surname>
<given-names>Z.</given-names>
</name>
<name>
<surname>Zhao</surname>
<given-names>B.</given-names>
</name>
<name>
<surname>Zeng</surname>
<given-names>R.</given-names>
</name>
</person-group> (<year>2020</year>). <article-title>Optimal design of diode-bridge bidirectional solid-state switch using standard recovery diodes for 500-kV high-voltage DC breaker</article-title>. <source>IEEE Trans. Power Electron.</source> <volume>35</volume> (<issue>2</issue>), <fpage>1165</fpage>&#x2013;<lpage>1170</lpage>. <pub-id pub-id-type="doi">10.1109/TPEL.2019.2930739</pub-id>
</citation>
</ref>
<ref id="B35">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Zhu</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Guo</surname>
<given-names>X.</given-names>
</name>
<name>
<surname>Yang</surname>
<given-names>X.</given-names>
</name>
<name>
<surname>Mi</surname>
<given-names>Z.</given-names>
</name>
<name>
<surname>Wei</surname>
<given-names>T.</given-names>
</name>
</person-group> (<year>2022</year>). <article-title>Integrated topology of multi-line DC circuit breaker and power flow controller</article-title>. <source>IEEE Trans. Power Deliv.</source> <volume>37</volume> (<issue>3</issue>), <fpage>2112</fpage>&#x2013;<lpage>2121</lpage>. <pub-id pub-id-type="doi">10.1109/TPWRD.2021.3104667</pub-id>
</citation>
</ref>
</ref-list>
</back>
</article>