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<div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/624f7b5274bc5c01053ffa51/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">﹫<span class="_ _0"></span></div><div class="t m0 x2 h3 y2 ff2 fs1 fc0 sc0 ls0 ws0">第</div><div class="t m0 x3 h4 y3 ff3 fs1 fc0 sc0 ls0 ws0">39</div><div class="t m0 x4 h3 y2 ff2 fs1 fc0 sc0 ls0 ws0">卷<span class="_ _1"> </span>第</div><div class="t m0 x5 h4 y3 ff3 fs1 fc0 sc0 ls0 ws0">4</div><div class="t m0 x6 h3 y2 ff2 fs1 fc0 sc0 ls0 ws0">期</div><div class="t m0 x7 h4 y4 ff3 fs1 fc0 sc0 ls0 ws0">2019</div><div class="t m0 x8 h3 y5 ff2 fs1 fc0 sc0 ls0 ws0">年</div><div class="t m0 x9 h4 y4 ff3 fs1 fc0 sc0 ls0 ws0">4</div><div class="t m0 xa h3 y5 ff2 fs1 fc0 sc0 ls0 ws0">月</div><div class="t m0 xb h5 y6 ff4 fs0 fc0 sc0 ls1 ws0">电力自动化设备</div><div class="t m0 xc h6 y7 ff3 fs2 fc0 sc0 ls0 ws0">Electric<span class="_ _2"> </span>P<span class="_ _3"></span>ower<span class="_ _2"> </span>Automation<span class="_ _2"> </span>Equipment</div><div class="t m0 xd h4 y3 ff3 fs1 fc0 sc0 ls0 ws0">Vol．<span class="_ _3"></span>39<span class="_ _4"> </span>No．<span class="_ _3"></span>4</div><div class="t m0 xe h4 y4 ff3 fs1 fc0 sc0 ls0 ws0">Apr．<span class="_ _1"> </span>2019</div><div class="t m0 x5 h7 y8 ff2 fs3 fc0 sc0 ls2 ws0">三电平逆变器的改进无模型预测电流控制</div><div class="t m0 xf h8 y9 ff4 fs4 fc0 sc0 ls0 ws0">金<span class="_ _5"> </span>涛</div><div class="t m0 x10 h9 ya ff3 fs5 fc0 sc0 ls0 ws0">1</div><div class="t m0 x11 h8 yb ff4 fs4 fc0 sc0 ls0 ws0">，</div><div class="t m0 x12 h8 y9 ff4 fs4 fc0 sc0 ls0 ws0">沈学<span class="_ _3"></span>宇</div><div class="t m0 x13 h9 ya ff3 fs5 fc0 sc0 ls0 ws0">1</div><div class="t m0 x14 h8 yb ff4 fs4 fc0 sc0 ls0 ws0">，</div><div class="t m0 x15 h8 y9 ff4 fs4 fc0 sc0 ls0 ws0">苏泰<span class="_ _3"></span>新</div><div class="t m0 x16 h9 ya ff3 fs5 fc0 sc0 ls0 ws0">1</div><div class="t m0 x17 h8 yb ff4 fs4 fc0 sc0 ls0 ws0">，</div><div class="t m0 x18 h8 y9 ff4 fs4 fc0 sc0 ls0 ws0">郭敬<span class="_ _3"></span>东</div><div class="t m0 x19 h9 ya ff3 fs5 fc0 sc0 ls0 ws0">2</div><div class="t m0 x1a h3 yc ff4 fs1 fc0 sc0 ls0 ws0">（<span class="_ _2"> </span><span class="ff3">1．</span></div><div class="t m0 x1b h3 yd ff4 fs1 fc0 sc0 ls3 ws0">福州大学<span class="_ _6"> </span>电气工程与自动化学院</div><div class="t m0 x1c h3 yc ff4 fs1 fc0 sc0 ls0 ws0">，</div><div class="t m0 xf h3 yd ff4 fs1 fc0 sc0 ls0 ws0">福建<span class="_ _1"> </span>福<span class="_ _3"></span>州</div><div class="t m0 x11 h3 yc ff4 fs1 fc0 sc0 ls0 ws0">，<span class="_ _7"></span><span class="ff3">350116<span class="ff4">；<span class="_ _8"> </span></span>2．</span></div><div class="t m0 x1d h3 yd ff4 fs1 fc0 sc0 ls3 ws0">国网福建省电力有限公司电力科学研究院</div><div class="t m0 x1e h3 yc ff4 fs1 fc0 sc0 ls0 ws0">，</div><div class="t m0 x1f h3 yd ff4 fs1 fc0 sc0 ls0 ws0">福建<span class="_ _1"> </span>福<span class="_ _3"></span>州</div><div class="t m0 x20 h3 yc ff4 fs1 fc0 sc0 ls0 ws0">，<span class="_ _7"></span><span class="ff3">350007<span class="ff4">）</span></span></div><div class="t m0 x21 h5 ye ff2 fs0 fc0 sc0 ls0 ws0">摘要</div><div class="t m0 x22 h5 yf ff2 fs0 fc0 sc0 ls0 ws0">：</div><div class="t m0 x23 h5 ye ff4 fs0 fc0 sc0 ls4 ws0">针对传统模型预测控制对系统模型的<span class="_ _3"></span>依<span class="_ _3"></span>赖<span class="_ _3"></span>性强</div><div class="t m0 x24 ha yf ff5 fs0 fc0 sc0 ls0 ws0">、</div><div class="t m0 x25 h5 ye ff4 fs0 fc0 sc0 ls5 ws0">鲁棒性差的问题</div><div class="t m0 x26 h5 yf ff4 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x27 h5 ye ff4 fs0 fc0 sc0 ls5 ws0">提出一种应用于三相三电平中性点</div><div class="t m0 x21 h5 y10 ff4 fs0 fc0 sc0 ls0 ws0">箝位<span class="_ _3"></span>型</div><div class="t m0 x28 h5 y11 ff4 fs0 fc0 sc0 ls0 ws0">（<span class="_ _6"> </span><span class="ff3">NP<span class="_ _3"></span>C<span class="_ _3"></span></span>）</div><div class="t m0 x29 h5 y12 ff4 fs0 fc0 sc0 ls4 ws0">逆变器的改进无模型预测电流控制方法</div><div class="t m0 x2a ha y11 ff5 fs0 fc0 sc0 ls0 ws0">。</div><div class="t m0 x2b h5 y12 ff4 fs0 fc0 sc0 ls4 ws0">该方法利用当前时刻检<span class="ls6">测的负载电流和上一次计算</span></div><div class="t m0 x21 h5 y13 ff4 fs0 fc0 sc0 ls4 ws0">的电流差分矢量预测下一时刻的输出电流<span class="_ _3"></span>值</div><div class="t m0 x2c h5 y14 ff4 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x2d h5 y13 ff4 fs0 fc0 sc0 ls5 ws0">其无需任何系统模型参数</div><div class="t m0 x27 h5 y14 ff4 fs0 fc0 sc0 ls0 ws0">；</div><div class="t m0 x2e h5 y13 ff4 fs0 fc0 sc0 ls5 ws0">通过引入计数因子</div><div class="t m0 x2f h5 y14 ff4 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x30 h5 y13 ff4 fs0 fc0 sc0 ls0 ws0">及<span class="_ _3"></span>时<span class="_ _9"></span>更<span class="_ _3"></span>新<span class="_ _9"></span>电<span class="_ _3"></span>流</div><div class="t m0 x21 h5 y15 ff4 fs0 fc0 sc0 ls0 ws0">差分</div><div class="t m0 x22 h5 y16 ff4 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x23 h5 y15 ff4 fs0 fc0 sc0 ls4 ws0">并在下一控制周期内应用所选择的使给定代价函数最小的逆变器开<span class="_ _3"></span>关状<span class="_ _3"></span>态</div><div class="t m0 x31 h5 y16 ff4 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x32 h5 y15 ff4 fs0 fc0 sc0 ls6 ws0">有效地控制负载电流</div><div class="t m0 x33 ha y16 ff5 fs0 fc0 sc0 ls0 ws0">。</div><div class="t m0 x34 h5 y15 ff4 fs0 fc0 sc0 ls0 ws0">该</div><div class="t m0 x21 h5 y17 ff4 fs0 fc0 sc0 ls4 ws0">算法在一个采样间隔内只需对负载电流进行一次采样</div><div class="t m0 x2a h5 y18 ff4 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x35 h5 y19 ff4 fs0 fc0 sc0 ls0 ws0">但其<span class="_ _3"></span>运算<span class="_ _3"></span>量大</div><div class="t m0 x36 h5 y18 ff4 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x37 h5 y19 ff4 fs0 fc0 sc0 ls6 ws0">对系统处理器要求较高</div><div class="t m0 x30 ha y18 ff5 fs0 fc0 sc0 ls0 ws0">。</div><div class="t m0 x38 h5 y19 ff4 fs0 fc0 sc0 ls0 ws0">仿<span class="_ _3"></span>真<span class="_ _3"></span>和<span class="_ _3"></span>实<span class="_ _3"></span>验</div><div class="t m0 x21 h5 y1a ff4 fs0 fc0 sc0 ls0 ws0">结果<span class="_ _3"></span>表明</div><div class="t m0 x7 h5 y1b ff4 fs0 fc0 sc0 ls0 ws0">：</div><div class="t m0 x39 h5 y1c ff4 fs0 fc0 sc0 ls4 ws0">所提控制策略具有良好的稳态特性和动态响应速度</div><div class="t m0 x3a h5 y1b ff4 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x3b h5 y1c ff4 fs0 fc0 sc0 ls6 ws0">且能<span class="_ _a"></span>消除<span class="_ _a"></span>负载参数变化对控制系统稳定性的</div><div class="t m0 x21 h5 y1d ff4 fs0 fc0 sc0 ls0 ws0">影响</div><div class="t m0 x22 ha y1e ff5 fs0 fc0 sc0 ls0 ws0">。</div><div class="t m0 x21 h5 y1f ff2 fs0 fc0 sc0 ls0 ws0">关键<span class="_ _3"></span>词</div><div class="t m0 x28 h5 y20 ff2 fs0 fc0 sc0 ls0 ws0">：</div><div class="t m0 x3c h5 y1f ff4 fs0 fc0 sc0 ls4 ws0">无模型预测电流控制</div><div class="t m0 x3d h5 y20 ff4 fs0 fc0 sc0 ls0 ws0">；</div><div class="t m0 x3e h5 y1f ff4 fs0 fc0 sc0 ls0 ws0">三电<span class="_ _3"></span>平</div><div class="t m0 x3f hb y20 ff3 fs0 fc0 sc0 ls0 ws0">NP<span class="_ _3"></span>C</div><div class="t m0 x11 h5 y1f ff4 fs0 fc0 sc0 ls0 ws0">逆变<span class="_ _3"></span>器</div><div class="t m0 x40 h5 y20 ff4 fs0 fc0 sc0 ls0 ws0">；</div><div class="t m0 x41 h5 y1f ff4 fs0 fc0 sc0 ls0 ws0">模型<span class="_ _3"></span>参数</div><div class="t m0 x42 h5 y20 ff4 fs0 fc0 sc0 ls0 ws0">；</div><div class="t m0 x43 h5 y1f ff4 fs0 fc0 sc0 ls0 ws0">代价<span class="_ _3"></span>函数</div><div class="t m0 x21 h5 y21 ff2 fs0 fc0 sc0 ls0 ws0">中图<span class="_ _3"></span>分类<span class="_ _3"></span>号</div><div class="t m0 x44 h5 y22 ff2 fs0 fc0 sc0 ls0 ws0">：<span class="_ _2"> </span><span class="ff3">T<span class="_ _a"></span>M<span class="_ _b"> </span>464</span></div><div class="t m0 x45 h5 y21 ff2 fs0 fc0 sc0 ls0 ws0">文献<span class="_ _3"></span>标识<span class="_ _3"></span>码</div><div class="t m0 x46 h5 y22 ff2 fs0 fc0 sc0 ls0 ws0">：<span class="_ _2"> </span><span class="ff3">A<span class="_ _c"> </span>DOI</span>：<span class="_ _d"> </span><span class="ff3">10<span class="_ _3"></span>．<span class="_ _3"></span>16081<span class="_ _e"> </span>/<span class="_ _f"></span>j<span class="_"> </span>．<span class="_ _10"></span>iss<span class="_ _a"></span>n<span class="_ _3"></span>．<span class="_ _3"></span>1006</span></div><div class="t m0 x47 hb y23 ff3 fs0 fc0 sc0 ls0 ws0">－</div><div class="t m0 x48 hb y22 ff3 fs0 fc0 sc0 ls0 ws0">6047<span class="_ _3"></span>．<span class="_ _3"></span>2019．<span class="_ _3"></span>04<span class="_ _3"></span>．<span class="_ _3"></span>013</div><div class="t m0 x21 hc y24 ff3 fs4 fc0 sc0 ls0 ws0">0</div><div class="t m0 x1b h8 y25 ff2 fs4 fc0 sc0 ls0 ws0">引言</div><div class="t m0 x22 h5 y26 ff6 fs0 fc0 sc0 ls0 ws0">近年<span class="_ _3"></span>来</div><div class="t m0 x44 h5 y27 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x49 h5 y26 ff6 fs0 fc0 sc0 ls4 ws0">随着处理器计算速度的<span class="_ _3"></span>不断<span class="_ _3"></span>提<span class="_ _3"></span>高</div><div class="t m0 x2d h5 y27 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x4a h5 y26 ff6 fs0 fc0 sc0 ls0 ws0">模<span class="_ _3"></span>型</div><div class="t m0 x21 h5 y28 ff6 fs0 fc0 sc0 ls0 ws0">预测<span class="_ _3"></span>控<span class="_ _3"></span>制</div><div class="t m0 x4b h5 y29 ff3 fs0 fc0 sc0 ls0 ws0">MP<span class="_ _3"></span>C<span class="_ _f"></span><span class="ff6">（<span class="_ _11"> </span></span>Model<span class="_ _1"> </span>P<span class="_ _3"></span>redictive<span class="_ _1"> </span>Control<span class="_ _10"></span><span class="ff6">）</span></div><div class="t m0 xb h5 y2a ff6 fs0 fc0 sc0 ls0 ws0">在<span class="_ _10"></span>电<span class="_ _10"></span>力<span class="_ _f"></span>电</div><div class="t m0 x21 h5 y2b ff6 fs0 fc0 sc0 ls4 ws0">子变换器方面的应用受到了广大<span class="ls6">国内外学者越来越</span></div><div class="t m0 x21 h5 y2c ff6 fs0 fc0 sc0 ls0 ws0">多的<span class="_ _3"></span>关注</div><div class="t m0 x7 ha y2d ff5 fs0 fc0 sc0 ls0 ws0">。</div><div class="t m0 x44 h5 y2e ff6 fs0 fc0 sc0 ls0 ws0">文献</div><div class="t m0 x9 h5 y2d ff6 fs0 fc0 sc0 ls0 ws0">［<span class="_ _12"></span><span class="ff3">1<span class="_ _13"></span><span class="ff6">］</span></span></div><div class="t m0 x4c h5 y2e ff6 fs0 fc0 sc0 ls0 ws0">首次<span class="_ _3"></span>将</div><div class="t m0 x4d hb y2d ff3 fs0 fc0 sc0 ls0 ws0">MP<span class="_ _3"></span>C</div><div class="t m0 x1c h5 y2e ff6 fs0 fc0 sc0 ls4 ws0">引入电力电子变换</div><div class="t m0 x21 h5 y2f ff6 fs0 fc0 sc0 ls0 ws0">器控<span class="_ _3"></span>制</div><div class="t m0 x28 h5 y30 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x3c h5 y31 ff6 fs0 fc0 sc0 ls4 ws0">并取得较好的控制效果</div><div class="t m0 x4e ha y30 ff5 fs0 fc0 sc0 ls0 ws0">。</div><div class="t m0 x4f h3 y32 ff2 fs1 fc0 sc0 ls0 ws0">收稿<span class="_ _3"></span>日期</div><div class="t m0 x3c h3 y33 ff2 fs1 fc0 sc0 ls0 ws0">：<span class="_ _8"> </span><span class="ff3">2018</span></div><div class="t m0 x50 h4 y34 ff3 fs1 fc0 sc0 ls0 ws0">－</div><div class="t m0 x51 h4 y33 ff3 fs1 fc0 sc0 ls0 ws0">05</div><div class="t m0 x52 h4 y34 ff3 fs1 fc0 sc0 ls0 ws0">－</div><div class="t m0 xa h3 y33 ff3 fs1 fc0 sc0 ls0 ws0">11<span class="ff4">；</span></div><div class="t m0 x53 h3 y32 ff2 fs1 fc0 sc0 ls0 ws0">修回<span class="_ _3"></span>日期</div><div class="t m0 x54 h3 y33 ff2 fs1 fc0 sc0 ls0 ws0">：<span class="_ _8"> </span><span class="ff3">2018</span></div><div class="t m0 x55 h4 y34 ff3 fs1 fc0 sc0 ls0 ws0">－</div><div class="t m0 x56 h4 y33 ff3 fs1 fc0 sc0 ls0 ws0">12</div><div class="t m0 x57 h4 y34 ff3 fs1 fc0 sc0 ls0 ws0">－</div><div class="t m0 x3f h4 y33 ff3 fs1 fc0 sc0 ls0 ws0">14</div><div class="t m0 x4f h3 y35 ff2 fs1 fc0 sc0 ls0 ws0">基金<span class="_ _3"></span>项目</div><div class="t m0 x3c h3 y36 ff2 fs1 fc0 sc0 ls0 ws0">：</div><div class="t m0 x7 h3 y35 ff4 fs1 fc0 sc0 ls0 ws0">欧盟</div><div class="t m0 x8 h4 y36 ff3 fs1 fc0 sc0 ls0 ws0">FP<span class="_ _3"></span>7</div><div class="t m0 xa h3 y35 ff4 fs1 fc0 sc0 ls7 ws0">国际<span class="_ _a"></span>科技合作基金资助项目</div><div class="t m0 x58 h3 y36 ff4 fs1 fc0 sc0 ls0 ws0">（<span class="_ _2"> </span><span class="ff3">909880</span>）<span class="_ _2"> </span>；</div><div class="t m0 x4f h3 y37 ff4 fs1 fc0 sc0 ls3 ws0">国家自然科学基金资助项目</div><div class="t m0 x59 h3 y38 ff4 fs1 fc0 sc0 ls0 ws0">（<span class="_ _d"> </span><span class="ff3">61304260</span>）</div><div class="t m0 x4f h4 y39 ff3 fs1 fc0 sc0 ls0 ws0">Project<span class="_ _6"> </span>su<span class="_ _a"></span>ppo<span class="_ _a"></span>rted<span class="_ _6"> </span>by<span class="_ _6"> </span>th<span class="_ _a"></span>e<span class="_ _6"> </span>FP7<span class="_ _6"> </span>Inte<span class="_ _a"></span>rnatio<span class="_ _a"></span>na<span class="_ _a"></span>l<span class="_ _6"> </span>Scien<span class="_ _a"></span>ce<span class="_ _6"> </span>＆<span class="_ _2"> </span>Tec<span class="_ _a"></span>hno<span class="_ _a"></span>logy</div><div class="t m0 x4f h3 y3a ff3 fs1 fc0 sc0 ls0 ws0">Cooperat<span class="_ _a"></span>ion<span class="_ _b"> </span>F<span class="_ _a"></span>oun<span class="_ _a"></span>datio<span class="_ _a"></span>n<span class="_ _2"> </span>of<span class="_ _6"> </span>EU<span class="ff4">（<span class="_ _8"> </span></span>909<span class="_ _a"></span>8<span class="_ _a"></span>80<span class="ff4">）<span class="_ _14"> </span></span>an<span class="_ _a"></span>d<span class="_ _6"> </span>th<span class="_ _a"></span>e<span class="_ _6"> </span>N<span class="_ _a"></span>ation<span class="_ _a"></span>al<span class="_ _2"> </span>Natur<span class="_ _a"></span>al</div><div class="t m0 x4f h3 y3b ff3 fs1 fc0 sc0 ls0 ws0">Sc<span class="_ _a"></span>ienc<span class="_ _a"></span>e<span class="_ _6"> </span>Fou<span class="_ _a"></span>nda<span class="_ _a"></span>tion<span class="_ _6"> </span>of<span class="_ _6"> </span>Ch<span class="_ _a"></span>ina<span class="ff4">（<span class="_ _d"> </span></span>61<span class="_ _a"></span>3<span class="_ _a"></span>04<span class="_ _a"></span>26<span class="_ _a"></span>0<span class="ff4">）</span></div><div class="t m0 x22 h5 y3c ff7 fs0 fc0 sc0 ls0 ws0">!<span class="_ _15"></span><span class="ff6 ls4">按照控制变量的不同</span></div><div class="t m0 x5a h5 y3d ff6 fs0 fc0 sc0 ls0 ws0">，<span class="_ _16"></span><span class="ff3">MP<span class="_ _3"></span>C</span></div><div class="t m0 x5b h5 y3c ff6 fs0 fc0 sc0 ls6 ws0">可以分为模型预测</div><div class="t m0 x21 h5 y3e ff6 fs0 fc0 sc0 ls0 ws0">电流控制</div><div class="t m0 x5c h5 y3f ff3 fs0 fc0 sc0 ls0 ws0">MPCC<span class="_ _9"></span><span class="ff6">（<span class="_ _b"> </span></span>M<span class="_ _a"></span>ode<span class="_ _a"></span>l<span class="_ _1"> </span>Predic<span class="_ _a"></span>tive<span class="_ _11"> </span>Curr<span class="_ _a"></span>ent<span class="_ _17"> </span>Co<span class="_ _a"></span>ntrol<span class="_ _3"></span><span class="ff6">）</span></div><div class="t m0 x5d hd y40 ff6 fs6 fc0 sc0 ls0 ws0">［<span class="_ _13"></span><span class="ff3">2<span class="_ _13"></span><span class="ff6">］</span></span></div><div class="t m0 x21 h5 y41 ff6 fs0 fc0 sc0 ls0 ws0">和模<span class="_ _3"></span>型预<span class="_ _3"></span>测直<span class="_ _9"></span>接<span class="_ _3"></span>功<span class="_ _9"></span>率<span class="_ _9"></span>控<span class="_ _9"></span>制</div><div class="t m0 x5e h5 y42 ff3 fs0 fc0 sc0 ls0 ws0">MP<span class="_ _3"></span>DP<span class="_ _3"></span>C<span class="_ _10"></span><span class="ff6">（<span class="_ _11"> </span></span>Model<span class="_ _11"> </span>P<span class="_ _3"></span>redictive</div><div class="t m0 x21 h5 y43 ff3 fs0 fc0 sc0 ls0 ws0">Direct<span class="_ _b"> </span>P<span class="_ _3"></span>ow<span class="_ _3"></span>er<span class="_ _b"> </span>Control<span class="_ _3"></span><span class="ff6">）</span></div><div class="t m0 x53 hd y44 ff6 fs6 fc0 sc0 ls0 ws0">［<span class="_ _13"></span><span class="ff3">3<span class="_ _13"></span><span class="ff6">］</span></span></div><div class="t m0 x5f hb y43 ff5 fs0 fc0 sc0 ls0 ws0">。<span class="ff3">MP<span class="_ _9"></span>CC</span></div><div class="t m0 x60 h5 y45 ff6 fs0 fc0 sc0 ls8 ws0">根据不同情况获得</div><div class="t m0 x21 h5 y46 ff6 fs0 fc0 sc0 ls0 ws0">参考<span class="_ _3"></span>电流<span class="_ _3"></span>值</div><div class="t m0 x44 h5 y47 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x49 h5 y46 ff6 fs0 fc0 sc0 ls8 ws0">然后通过模型预测<span class="ls9">控制器使输出电流</span></div><div class="t m0 x21 h5 y48 ff6 fs0 fc0 sc0 ls0 ws0">跟踪<span class="_ _3"></span>参<span class="_ _3"></span>考<span class="_ _9"></span>电<span class="_ _10"></span>流</div><div class="t m0 x51 ha y49 ff5 fs0 fc0 sc0 ls0 ws0">。</div><div class="t m0 x61 h5 y48 ff6 fs0 fc0 sc0 ls0 ws0">目<span class="_ _9"></span>前</div><div class="t m0 x62 h5 y49 ff6 fs0 fc0 sc0 ls0 ws0">，<span class="_ _18"></span><span class="ff3">MP<span class="_ _3"></span>CC</span></div><div class="t m0 x63 h5 y48 ff6 fs0 fc0 sc0 lsa ws0">已经在电机控制</div><div class="t m0 x46 hd y4a ff6 fs6 fc0 sc0 ls0 ws0">［<span class="_ _13"></span><span class="ff3">4-<span class="_ _13"></span>5<span class="_ _13"></span><span class="ff6">］</span></span></div><div class="t m0 x64 ha y49 ff5 fs0 fc0 sc0 ls0 ws0">、</div><div class="t m0 x21 h5 y4b ff6 fs0 fc0 sc0 ls0 ws0">并网<span class="_ _3"></span>逆变</div><div class="t m0 x65 hd y4c ff6 fs6 fc0 sc0 ls0 ws0">［<span class="_ _13"></span><span class="ff3">6-<span class="_ _13"></span>7<span class="_ _13"></span><span class="ff6">］</span></span></div><div class="t m0 x49 h5 y4b ff6 fs0 fc0 sc0 ls0 ws0">等<span class="_ _3"></span>多<span class="_ _9"></span>个<span class="_ _9"></span>方<span class="_ _9"></span>面<span class="_ _9"></span>得<span class="_ _9"></span>到<span class="_ _9"></span>应<span class="_ _10"></span>用</div><div class="t m0 x66 ha y4d ff5 fs0 fc0 sc0 ls0 ws0">。</div><div class="t m0 x67 h5 y4b ff6 fs0 fc0 sc0 ls0 ws0">该<span class="_ _9"></span>控<span class="_ _9"></span>制<span class="_ _9"></span>方<span class="_ _9"></span>法<span class="_ _10"></span>具</div><div class="t m0 x21 h5 y4e ff6 fs0 fc0 sc0 ls0 ws0">有响<span class="_ _3"></span>应速<span class="_ _3"></span>度快</div><div class="t m0 x29 ha y4f ff5 fs0 fc0 sc0 ls0 ws0">、</div><div class="t m0 x68 h5 y4e ff6 fs0 fc0 sc0 ls0 ws0">输<span class="_ _3"></span>出<span class="_ _9"></span>效<span class="_ _9"></span>果<span class="_ _9"></span>好</div><div class="t m0 x69 ha y4f ff5 fs0 fc0 sc0 ls0 ws0">、</div><div class="t m0 x54 h5 y4e ff6 fs0 fc0 sc0 ls9 ws0">可直接给出开关状态</div><div class="t m0 x64 ha y4f ff5 fs0 fc0 sc0 ls0 ws0">、</div><div class="t m0 x21 h5 y50 ff6 fs0 fc0 sc0 ls4 ws0">可同时对多种控制目标进行控制等优势</div><div class="t m0 x6a hd y51 ff6 fs6 fc0 sc0 ls0 ws0">［<span class="_ _13"></span><span class="ff3">8<span class="_ _13"></span><span class="ff6">］</span></span></div><div class="t m0 x58 ha y52 ff5 fs0 fc0 sc0 ls0 ws0">。</div><div class="t m0 x2c h5 y50 ff6 fs0 fc0 sc0 ls0 ws0">但<span class="_ _3"></span>传<span class="_ _3"></span>统</div><div class="t m0 x21 hb y53 ff3 fs0 fc0 sc0 ls0 ws0">MP<span class="_ _3"></span>CC</div><div class="t m0 x6b h5 y54 ff6 fs0 fc0 sc0 ls4 ws0">依赖于精确的系统<span class="_ _3"></span>模型</div><div class="t m0 x6c h5 y53 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x6d h5 y54 ff6 fs0 fc0 sc0 ls0 ws0">在<span class="_ _3"></span>实<span class="_ _9"></span>际<span class="_ _3"></span>电<span class="_ _9"></span>路<span class="_ _3"></span>中</div><div class="t m0 x2d h5 y53 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x4a h5 y54 ff6 fs0 fc0 sc0 ls0 ws0">当<span class="_ _3"></span>电</div><div class="t m0 x21 h5 y55 ff6 fs0 fc0 sc0 ls0 ws0">阻</div><div class="t m0 x6e ha y56 ff5 fs0 fc0 sc0 ls0 ws0">、</div><div class="t m0 x6f h5 y57 ff6 fs0 fc0 sc0 ls4 ws0">电感等参数随温度</div><div class="t m0 x70 ha y56 ff5 fs0 fc0 sc0 ls0 ws0">、</div><div class="t m0 x5f h5 y57 ff6 fs0 fc0 sc0 ls6 ws0">电磁<span class="_ _a"></span>场和<span class="_ _a"></span>其他外界环境条件</div><div class="t m0 x21 h5 y58 ff6 fs0 fc0 sc0 ls0 ws0">的变<span class="_ _3"></span>化<span class="_ _10"></span>而<span class="_ _f"></span>发<span class="_ _e"></span>生<span class="_ _10"></span>改<span class="_ _f"></span>变<span class="_ _e"></span>时</div><div class="t m0 x70 h5 y59 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x71 h5 y58 ff6 fs0 fc0 sc0 lsb ws0">会直接导致控制器性<span class="_ _3"></span>能的</div><div class="t m0 x21 h5 y5a ff6 fs0 fc0 sc0 ls0 ws0">下降</div><div class="t m0 x72 hd y5b ff6 fs6 fc0 sc0 ls0 ws0">［<span class="_ _13"></span><span class="ff3">9-<span class="_ _13"></span>10<span class="_ _19"></span><span class="ff6">］</span></span></div><div class="t m0 x73 ha y5c ff5 fs0 fc0 sc0 ls0 ws0">。</div><div class="t m0 x22 h5 y5d ff6 fs0 fc0 sc0 ls4 ws0">为了解决这个问题</div><div class="t m0 x5f h5 y5e ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x74 h5 y5d ff6 fs0 fc0 sc0 ls0 ws0">文<span class="_ _3"></span>献</div><div class="t m0 x3d h5 y5e ff6 fs0 fc0 sc0 ls0 ws0">［<span class="_ _1a"></span><span class="ff3">11<span class="_ _1b"></span><span class="ff6">］</span></span></div><div class="t m0 x66 h5 y5d ff6 fs0 fc0 sc0 ls8 ws0">提出了一种自校</div><div class="t m0 x21 h5 y5f ff6 fs0 fc0 sc0 ls0 ws0">正</div><div class="t m0 x75 hb y60 ff3 fs0 fc0 sc0 ls0 ws0">MP<span class="_ _3"></span>CC</div><div class="t m0 x76 h5 y5f ff6 fs0 fc0 sc0 ls0 ws0">策略</div><div class="t m0 x29 h5 y60 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x68 h5 y5f ff6 fs0 fc0 sc0 ls4 ws0">实时修正预测模型</div><div class="t m0 x77 h5 y60 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x78 h5 y5f ff6 fs0 fc0 sc0 ls0 ws0">有效<span class="_ _3"></span>消除<span class="_ _3"></span>了<span class="_ _3"></span>模<span class="_ _3"></span>型</div><div class="t m0 x21 h5 y61 ff6 fs0 fc0 sc0 ls0 ws0">参数<span class="_ _3"></span>时变<span class="_ _3"></span>对控<span class="_ _9"></span>制<span class="_ _9"></span>系<span class="_ _9"></span>统<span class="_ _3"></span>的<span class="_ _9"></span>影<span class="_ _9"></span>响</div><div class="t m0 x79 h5 y62 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x63 h5 y61 ff6 fs0 fc0 sc0 ls9 ws0">但在观察电感参数过</div><div class="t m0 x21 h5 y63 ff6 fs0 fc0 sc0 ls0 ws0">程中<span class="_ _3"></span>使用<span class="_ _3"></span>的是<span class="_ _9"></span>低<span class="_ _9"></span>通<span class="_ _9"></span>滤<span class="_ _3"></span>波<span class="_ _9"></span>器</div><div class="t m0 x5a h5 y64 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x69 h5 y65 ff6 fs0 fc0 sc0 ls9 ws0">会直接影响电感的观测</div><div class="t m0 x21 h5 y66 ff6 fs0 fc0 sc0 ls0 ws0">效果</div><div class="t m0 x22 ha y67 ff5 fs0 fc0 sc0 ls0 ws0">。</div><div class="t m0 x28 h5 y66 ff6 fs0 fc0 sc0 ls0 ws0">文献</div><div class="t m0 x7a h5 y67 ff6 fs0 fc0 sc0 ls0 ws0">［<span class="_ _12"></span><span class="ff3">12<span class="_ _13"></span><span class="ff6">］</span></span></div><div class="t m0 x61 h5 y66 ff6 fs0 fc0 sc0 ls8 ws0">通过实<span class="_ _a"></span>时在线监测电路电感值</div><div class="t m0 x7b h5 y67 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x7c h5 y66 ff6 fs0 fc0 sc0 ls0 ws0">实</div><div class="t m0 x21 h5 y68 ff6 fs0 fc0 sc0 ls4 ws0">现对三相变换器的</div><div class="t m0 x7d h5 y69 ff3 fs0 fc0 sc0 ls0 ws0">MP<span class="_ _3"></span>DP<span class="_ _3"></span>C<span class="_ _3"></span><span class="ff6">，</span></div><div class="t m0 x7e h5 y6a ff6 fs0 fc0 sc0 ls6 ws0">但也同样存在类似的问</div><div class="t m0 x21 h5 y6b ff6 fs0 fc0 sc0 ls0 ws0">题</div><div class="t m0 x6e ha y6c ff5 fs0 fc0 sc0 ls0 ws0">。</div><div class="t m0 x22 h5 y6b ff6 fs0 fc0 sc0 ls0 ws0">文献</div><div class="t m0 x73 h5 y6c ff6 fs0 fc0 sc0 ls0 ws0">［<span class="_ _12"></span><span class="ff3">13<span class="_ _3"></span>-<span class="_ _1c"></span>1<span class="_ _a"></span>4<span class="_ _13"></span><span class="ff6">］</span></span></div><div class="t m0 xa h5 y6b ff6 fs0 fc0 sc0 ls9 ws0">通过构造扰动观测器减少模型参</div><div class="t m0 x7f h5 y6d ff6 fs0 fc0 sc0 ls4 ws0">数失配对控制系统造成的影响</div><div class="t m0 x80 h5 y6e ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x81 h5 y6d ff6 fs0 fc0 sc0 ls6 ws0">提高系统的鲁棒性</div><div class="t m0 x82 h5 y6e ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x7f h5 y6f ff6 fs0 fc0 sc0 ls4 ws0">但观测器带来的计算延时问题会<span class="ls6">严重影响整个系统</span></div><div class="t m0 x7f h5 y70 ff6 fs0 fc0 sc0 ls0 ws0">的控<span class="_ _3"></span>制<span class="_ _3"></span>性<span class="_ _9"></span>能</div><div class="t m0 x83 ha y71 ff5 fs0 fc0 sc0 ls0 ws0">。</div><div class="t m0 x84 h5 y70 ff6 fs0 fc0 sc0 ls0 ws0">文<span class="_ _9"></span>献</div><div class="t m0 x85 h5 y71 ff6 fs0 fc0 sc0 ls0 ws0">［<span class="_ _1a"></span><span class="ff3">15<span class="_ _1b"></span><span class="ff6">］</span></span></div><div class="t m0 x86 h5 y70 ff6 fs0 fc0 sc0 lsc ws0">提出一种无模型预测<span class="_ _3"></span>电流</div><div class="t m0 x7f h5 y72 ff6 fs0 fc0 sc0 ls0 ws0">控制</div><div class="t m0 x43 h5 y73 ff3 fs0 fc0 sc0 ls0 ws0">MF<span class="_ _a"></span>P<span class="_ _3"></span>CC<span class="_ _3"></span><span class="ff6">（<span class="_ _b"> </span></span>M<span class="_ _a"></span>odel-<span class="_ _1c"></span>Fre<span class="_ _a"></span>e<span class="_ _17"> </span>P<span class="_ _3"></span>redi<span class="_ _a"></span>ctive<span class="_ _11"> </span>Curr<span class="_ _a"></span>ent<span class="_ _11"> </span>Contr<span class="_ _a"></span>ol<span class="_ _3"></span><span class="ff6">）<span class="_ _b"> </span>，</span></div><div class="t m0 x7f h5 y74 ff6 fs0 fc0 sc0 ls8 ws0">该<span class="_ _a"></span>控<span class="_ _a"></span>制<span class="_ _a"></span>方<span class="_ _a"></span>法<span class="_ _a"></span>在不使用电机参数的情况<span class="_ _3"></span>下</div><div class="t m0 x87 h5 y75 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x88 h5 y74 ff6 fs0 fc0 sc0 ls0 ws0">只<span class="_ _9"></span>利<span class="_ _9"></span>用<span class="_ _9"></span>定</div><div class="t m0 x7f h5 y76 ff6 fs0 fc0 sc0 ls4 ws0">子电流与过去时刻的电流差分<span class="ls6">来实现电流预测</span></div><div class="t m0 x33 ha y77 ff5 fs0 fc0 sc0 ls0 ws0">。</div><div class="t m0 x34 h5 y76 ff6 fs0 fc0 sc0 ls0 ws0">但</div><div class="t m0 x7f h5 y78 ff6 fs0 fc0 sc0 ls0 ws0">该方<span class="_ _3"></span>法在<span class="_ _3"></span>每个<span class="_ _3"></span>采<span class="_ _9"></span>样<span class="_ _9"></span>周<span class="_ _9"></span>期<span class="_ _9"></span>中</div><div class="t m0 x89 h5 y79 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x8a h5 y78 ff6 fs0 fc0 sc0 ls9 ws0">必须对电流进行</div><div class="t m0 x8b hb y79 ff3 fs0 fc0 sc0 ls0 ws0">2</div><div class="t m0 x33 h5 y78 ff6 fs0 fc0 sc0 ls0 ws0">次<span class="_ _9"></span>采</div><div class="t m0 x7f h5 y7a ff6 fs0 fc0 sc0 ls0 ws0">样</div><div class="t m0 x8c h5 y7b ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x8d h5 y7a ff6 fs0 fc0 sc0 ls0 ws0">在</div><div class="t m0 x16 hb y7b ff3 fs0 fc0 sc0 ls0 ws0">2</div><div class="t m0 x8e h5 y7a ff6 fs0 fc0 sc0 ls4 ws0">次采样的固定延迟时<span class="ls6">间选择不当的情况下</span></div><div class="t m0 x82 h5 y7b ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x7f h5 y7c ff6 fs0 fc0 sc0 ls4 ws0">会导致检测到电流尖峰</div><div class="t m0 x8f ha y7d ff5 fs0 fc0 sc0 ls0 ws0">。</div><div class="t m0 x32 h5 y7c ff6 fs0 fc0 sc0 ls6 ws0">而关<span class="_ _a"></span>于延迟时间的选择更</div><div class="t m0 x7f h5 y7e ff6 fs0 fc0 sc0 ls4 ws0">多的是依赖于研究者的经验</div><div class="t m0 x90 h5 y7f ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x91 h5 y7e ff6 fs0 fc0 sc0 ls6 ws0">缺乏确定的指导准则</div><div class="t m0 x82 h5 y7f ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x7f h5 y80 ff6 fs0 fc0 sc0 ls0 ws0">从而<span class="_ _3"></span>限制<span class="_ _3"></span>了</div><div class="t m0 x92 hb y81 ff3 fs0 fc0 sc0 ls0 ws0">MFP<span class="_ _3"></span>CC</div><div class="t m0 x93 h5 y80 ff6 fs0 fc0 sc0 ls0 ws0">的普<span class="_ _3"></span>及和<span class="_ _3"></span>使用</div><div class="t m0 x1f hd y82 ff6 fs6 fc0 sc0 ls0 ws0">［<span class="_ _13"></span><span class="ff3">16<span class="_ _19"></span><span class="ff6">］</span></span></div><div class="t m0 x30 ha y81 ff5 fs0 fc0 sc0 ls0 ws0">。</div><div class="t m0 x94 h5 y83 ff6 fs0 fc0 sc0 ls0 ws0">针对<span class="_ _3"></span>上述<span class="_ _3"></span>问<span class="_ _3"></span>题</div><div class="t m0 x95 h5 y84 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x93 h5 y83 ff6 fs0 fc0 sc0 ls9 ws0">本文将对三相三电平中性点箝</div><div class="t m0 x7f h5 y85 ff6 fs0 fc0 sc0 ls0 ws0">位型</div><div class="t m0 x94 h5 y86 ff6 fs0 fc0 sc0 ls0 ws0">（<span class="_ _b"> </span><span class="ff3">NP<span class="_ _3"></span>C<span class="_ _3"></span></span>）</div><div class="t m0 x83 h5 y85 ff6 fs0 fc0 sc0 ls8 ws0">逆变器进行数学建模</div><div class="t m0 x96 h5 y86 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 xd h5 y85 ff6 fs0 fc0 sc0 ls0 ws0">在<span class="_ _3"></span>此<span class="_ _9"></span>基<span class="_ _9"></span>础<span class="_ _9"></span>上<span class="_ _9"></span>提<span class="_ _9"></span>出</div><div class="t m0 x7f h5 y87 ff6 fs0 fc0 sc0 lsd ws0">一<span class="_ _1b"></span>种<span class="_ _1b"></span>改进无模型预测<span class="_ _3"></span>电流控<span class="_ _3"></span>制</div><div class="t m0 x47 h5 y88 ff3 fs0 fc0 sc0 ls0 ws0">IMFP<span class="_ _3"></span>CC<span class="_ _e"> </span><span class="ff6">（<span class="_ _11"> </span></span>Improved</div><div class="t m0 x7f h5 y89 ff3 fs0 fc0 sc0 ls0 ws0">Model-<span class="_ _1d"></span>Free<span class="_ _b"> </span>P<span class="_ _9"></span>redictive<span class="_ _1"> </span>Current<span class="_ _1"> </span>Control<span class="_ _10"></span><span class="ff6">）<span class="_ _b"> </span>，</span></div><div class="t m0 x97 h5 y8a ff6 fs0 fc0 sc0 ls0 ws0">该<span class="_ _f"></span>控<span class="_ _f"></span>制<span class="_ _f"></span>方<span class="_ _f"></span>法</div><div class="t m0 x7f h5 y8b ff6 fs0 fc0 sc0 ls8 ws0">在<span class="_ _a"></span>无<span class="_ _a"></span>模<span class="_ _a"></span>型<span class="_ _a"></span>预<span class="_ _a"></span>测控制的基础上进行改进</div><div class="t m0 x98 h5 y8c ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x99 h5 y8b ff6 fs0 fc0 sc0 ls0 ws0">在<span class="_ _9"></span>一<span class="_ _9"></span>个<span class="_ _9"></span>控<span class="_ _9"></span>制</div><div class="t m0 x7f h5 y8d ff6 fs0 fc0 sc0 ls8 ws0">周<span class="_ _a"></span>期<span class="_ _a"></span>内<span class="_ _a"></span>仅<span class="_ _a"></span>对<span class="_ _a"></span>负载电流进行一次采样</div><div class="t m0 xe h5 y8e ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x9a h5 y8d ff6 fs0 fc0 sc0 ls0 ws0">降<span class="_ _9"></span>低<span class="_ _9"></span>了<span class="_ _9"></span>硬<span class="_ _9"></span>件<span class="_ _10"></span>系</div><div class="t m0 x7f h5 y8f ff6 fs0 fc0 sc0 ls0 ws0">统的<span class="_ _3"></span>设计<span class="_ _3"></span>要<span class="_ _3"></span>求</div><div class="t m0 x9b ha y90 ff5 fs0 fc0 sc0 ls0 ws0">。</div><div class="t m0 x9c h5 y8f ff6 fs0 fc0 sc0 ls0 ws0">同<span class="_ _3"></span>时</div><div class="t m0 x9d h5 y90 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x9e h5 y8f ff6 fs0 fc0 sc0 ls9 ws0">所提控制策略通过计数因子</div><div class="t m0 x7f h5 y91 ff6 fs0 fc0 sc0 ls8 ws0">及<span class="_ _a"></span>时<span class="_ _a"></span>更<span class="_ _a"></span>新<span class="_ _a"></span>不<span class="_ _a"></span>同开关状态下的电流差分</div><div class="t m0 x98 h5 y92 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x99 h5 y93 ff6 fs0 fc0 sc0 ls0 ws0">利<span class="_ _9"></span>用<span class="_ _9"></span>每<span class="_ _9"></span>个<span class="_ _9"></span>控</div><div class="t m0 x7f h5 y94 ff6 fs0 fc0 sc0 ls8 ws0">制<span class="_ _a"></span>周<span class="_ _a"></span>期<span class="_ _a"></span>的<span class="_ _a"></span>采<span class="_ _a"></span>样值与电流差分<span class="ls9">矢量进行求和运算</span></div><div class="t m0 x9f h5 y95 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x34 h5 y94 ff6 fs0 fc0 sc0 ls0 ws0">实</div><div class="t m0 x7f h5 y96 ff6 fs0 fc0 sc0 ls4 ws0">现对输出电流的预测</div><div class="t m0 xa0 h5 y97 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 xa1 h5 y96 ff6 fs0 fc0 sc0 ls0 ws0">其无<span class="_ _3"></span>需依<span class="_ _3"></span>赖<span class="_ _3"></span>负<span class="_ _3"></span>载<span class="_ _3"></span>参<span class="_ _3"></span>数</div><div class="t m0 xa2 h5 y97 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 xa3 h5 y96 ff6 fs0 fc0 sc0 ls0 ws0">具<span class="_ _3"></span>有<span class="_ _3"></span>较</div><div class="t m0 x7f h5 y98 ff6 fs0 fc0 sc0 ls0 ws0">强的<span class="_ _3"></span>鲁棒<span class="_ _3"></span>性</div><div class="t m0 xa4 ha y99 ff5 fs0 fc0 sc0 ls0 ws0">。</div><div class="t m0 x9b h5 y98 ff6 fs0 fc0 sc0 ls0 ws0">最后<span class="_ _3"></span>利用</div><div class="t m0 xa5 hb y99 ff3 fs0 fc0 sc0 ls0 ws0">Simulink</div><div class="t m0 xa6 h5 y98 ff6 fs0 fc0 sc0 ls6 ws0">实时仿真实验平台</div><div class="t m0 x7f h5 y9a ff6 fs0 fc0 sc0 ls8 ws0">对<span class="_ _a"></span>本<span class="_ _a"></span>文<span class="_ _a"></span>所<span class="_ _a"></span>提<span class="_ _a"></span>算法进行实验验证</div><div class="t m0 xa7 h5 y9b ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 xa8 h5 y9a ff6 fs0 fc0 sc0 ls9 ws0">实验结果验证了所</div><div class="t m0 x7f h5 y9c ff6 fs0 fc0 sc0 ls4 ws0">提控制算法的正确性和有效性</div><div class="t m0 x80 ha y9d ff5 fs0 fc0 sc0 ls0 ws0">。</div><div class="t m0 x2b hc y9e ff3 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m0 x42 h8 y9f ff2 fs4 fc0 sc0 lse ws0">三电平逆变器的</div><div class="t m0 x8f hc y9e ff3 fs4 fc0 sc0 ls0 ws0">MP<span class="_ _3"></span>CC</div><div class="t m0 x2b hb ya0 ff3 fs0 fc0 sc0 ls0 ws0">1<span class="_ _3"></span>．<span class="_ _3"></span>1</div><div class="t m0 x43 h5 ya1 ff2 fs0 fc0 sc0 ls0 ws0">系统<span class="_ _3"></span>建模</div><div class="t m0 x94 h5 ya2 ff6 fs0 fc0 sc0 ls0 ws0">三电<span class="_ _3"></span>平</div><div class="t m0 x92 hb ya3 ff3 fs0 fc0 sc0 ls0 ws0">NP<span class="_ _3"></span>C</div><div class="t m0 xa9 h5 ya2 ff6 fs0 fc0 sc0 lsc ws0">逆变器与动态阻感负载连接电路</div><div class="t m0 x7f h5 ya4 ff6 fs0 fc0 sc0 ls0 ws0">如图</div><div class="t m0 x43 hb ya5 ff3 fs0 fc0 sc0 ls0 ws0">1</div><div class="t m0 xaa h5 ya4 ff6 fs0 fc0 sc0 ls0 ws0">所示</div><div class="t m0 xa4 ha ya5 ff5 fs0 fc0 sc0 ls0 ws0">。</div><div class="t m0 x9b h5 ya4 ff6 fs0 fc0 sc0 ls0 ws0">图中</div><div class="t m0 x95 h5 ya5 ff6 fs0 fc0 sc0 ls0 ws0">，<span class="_ _16"></span><span class="ff8">V</span></div><div class="t m0 x9d he ya6 ff3 fs6 fc0 sc0 ls0 ws0">dc</div><div class="t m0 xab h5 ya4 ff6 fs0 fc0 sc0 ls0 ws0">为直<span class="_ _3"></span>流电<span class="_ _3"></span>压</div><div class="t m0 xac h5 ya5 ff6 fs0 fc0 sc0 ls0 ws0">；<span class="_ _6"> </span><span class="ff8">C</span></div><div class="t m0 x9a he ya6 ff3 fs6 fc0 sc0 ls0 ws0">1</div><div class="t m0 xad h5 ya4 ff6 fs0 fc0 sc0 ls0 ws0">和</div><div class="t m0 xae hf ya5 ff8 fs0 fc0 sc0 ls0 ws0">C</div><div class="t m0 x20 he ya6 ff3 fs6 fc0 sc0 ls0 ws0">2</div><div class="t m0 xa3 h5 ya4 ff6 fs0 fc0 sc0 ls0 ws0">为<span class="_ _3"></span>直<span class="_ _3"></span>流</div><div class="t m0 x7f h5 ya7 ff6 fs0 fc0 sc0 ls0 ws0">侧电<span class="_ _3"></span>容</div><div class="t m0 xaa h5 ya8 ff6 fs0 fc0 sc0 ls0 ws0">；<span class="_ _2"> </span><span class="ff8">Ｒ</span></div><div class="t m0 xaf h5 ya7 ff6 fs0 fc0 sc0 ls0 ws0">为<span class="_ _9"></span>负<span class="_ _9"></span>载<span class="_ _9"></span>电<span class="_ _9"></span>阻</div><div class="t m0 x9e h5 ya8 ff6 fs0 fc0 sc0 ls0 ws0">；<span class="_ _b"> </span><span class="ff8">L</span></div><div class="t m0 xb0 h5 ya7 ff6 fs0 fc0 sc0 ls0 ws0">为<span class="_ _9"></span>负<span class="_ _9"></span>载<span class="_ _10"></span>电<span class="_ _10"></span>感</div><div class="t m0 xb1 h5 ya8 ff6 fs0 fc0 sc0 ls0 ws0">；<span class="_ _b"> </span><span class="ff8">v</span></div><div class="t m0 xb2 he ya9 ff3 fs6 fc0 sc0 ls0 ws0">ao</div><div class="t m0 xae ha ya8 ff5 fs0 fc0 sc0 ls0 ws0">、<span class="_ _18"></span><span class="ff8">v</span></div><div class="t m0 xb3 he ya9 ff3 fs6 fc0 sc0 ls0 ws0">bo</div><div class="t m0 xb4 ha ya8 ff5 fs0 fc0 sc0 ls0 ws0">、<span class="_ _18"></span><span class="ff8">v</span></div><div class="t m0 xb5 he ya9 ff3 fs6 fc0 sc0 ls0 ws0">co</div><div class="t m0 x34 h5 ya7 ff6 fs0 fc0 sc0 ls0 ws0">和</div><div class="t m0 x7f hf yaa ff8 fs0 fc0 sc0 ls0 ws0">i</div><div class="t m0 xb6 he yab ff3 fs6 fc0 sc0 ls0 ws0">a</div><div class="t m0 xb7 ha yaa ff5 fs0 fc0 sc0 ls0 ws0">、<span class="_ _16"></span><span class="ff8">i</span></div><div class="t m0 x8d he yab ff3 fs6 fc0 sc0 ls0 ws0">b</div><div class="t m0 xb8 ha yaa ff5 fs0 fc0 sc0 ls0 ws0">、<span class="_ _16"></span><span class="ff8">i</span></div><div class="t m0 xb9 he yab ff3 fs6 fc0 sc0 ls0 ws0">c</div><div class="t m0 xba h5 yac ff6 fs0 fc0 sc0 ls0 ws0">分别<span class="_ _3"></span>为</div><div class="t m0 xbb hb yaa ff3 fs0 fc0 sc0 ls0 ws0">NP<span class="_ _3"></span>C</div><div class="t m0 x93 h5 yac ff6 fs0 fc0 sc0 ls4 ws0">逆变器输出的各相电压和电流</div><div class="t m0 x82 ha yaa ff5 fs0 fc0 sc0 ls0 ws0">。</div><div class="t m0 x94 h5 yad ff6 fs0 fc0 sc0 ls0 ws0">由空<span class="_ _3"></span>间矢<span class="_ _3"></span>量<span class="_ _3"></span>的<span class="_ _3"></span>原<span class="_ _9"></span>理<span class="_ _9"></span>可<span class="_ _9"></span>推<span class="_ _9"></span>得</div><div class="t m0 xa7 h5 yae ff6 fs0 fc0 sc0 ls0 ws0">，<span class="_ _7"></span><span class="ff3">NP<span class="_ _3"></span>C</span></div><div class="t m0 x9a h5 yad ff6 fs0 fc0 sc0 ls0 ws0">逆<span class="_ _3"></span>变<span class="_ _10"></span>器<span class="_ _9"></span>输<span class="_ _9"></span>出<span class="_ _9"></span>的</div><div class="t m0 x7f h5 yaf ff6 fs0 fc0 sc0 ls0 ws0">电压<span class="_ _3"></span>矢量<span class="_ _3"></span>为</div><div class="t m0 xa4 h5 yb0 ff6 fs0 fc0 sc0 ls0 ws0">：</div></div><div class="pi" data-data='{"ctm":[1.612029,0.000000,0.000000,1.612029,-22.847616,-6.854301]}'></div></div>
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<div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/624f7b5274bc5c01053ffa51/bg2.jpg"><div class="t m0 x1 h3 yb1 ff2 fs1 fc0 sc0 ls0 ws0">第</div><div class="t m0 xbc h4 yb2 ff3 fs1 fc0 sc0 ls0 ws0">4</div><div class="t m0 xbd h3 yb1 ff2 fs1 fc0 sc0 ls0 ws0">期</div><div class="t m0 x55 h10 yb3 ff6 fs2 fc0 sc0 ls0 ws0">金<span class="_ _1e"> </span>涛</div><div class="t m0 xbe h10 yb4 ff6 fs2 fc0 sc0 ls0 ws0">，</div><div class="t m0 xbf h10 yb3 ff6 fs2 fc0 sc0 ls0 ws0">等</div><div class="t m0 xb h10 yb4 ff6 fs2 fc0 sc0 ls0 ws0">：</div><div class="t m0 xc0 h10 yb3 ff6 fs2 fc0 sc0 lsf ws0">三电平逆变器的改进无模型预测电流控制</div><div class="t m0 xc1 h2 yb5 ff1 fs0 fc0 sc0 ls0 ws0">﹫<span class="_ _0"></span></div><div class="t m0 xc2 h3 yb6 ff2 fs1 fc0 sc0 ls0 ws0">图</div><div class="t m0 xc3 h4 yb7 ff3 fs1 fc0 sc0 ls0 ws0">1</div><div class="t m0 x5c h3 yb6 ff2 fs1 fc0 sc0 ls0 ws0">三电<span class="_ _3"></span>平</div><div class="t m0 x52 h4 yb7 ff3 fs1 fc0 sc0 ls0 ws0">NP<span class="_ _3"></span>C</div><div class="t m0 x53 h3 yb6 ff2 fs1 fc0 sc0 ls3 ws0">逆变器带动态阻感负载的电路</div><div class="t m0 xc3 h4 yb8 ff3 fs1 fc0 sc0 ls0 ws0">Fig．<span class="_ _3"></span>1<span class="_ _4"> </span>Circuit<span class="_ _6"> </span>of<span class="_ _6"> </span>three-<span class="_ _19"></span>leve<span class="_ _a"></span>l<span class="_ _1f"> </span>NP<span class="_ _3"></span>C<span class="_ _6"> </span>inverter<span class="_ _6"> </span>with</div><div class="t m0 x50 h4 yb9 ff3 fs1 fc0 sc0 ls0 ws0">dynamic<span class="_ _6"> </span>resistiv<span class="_ _a"></span>e<span class="_ _3"></span>-<span class="_ _1d"></span>inductiv<span class="_ _a"></span>e<span class="_ _1f"> </span>load</div><div class="t m0 xc4 h11 yba ff9 fs0 fc0 sc0 ls0 ws0">v</div><div class="t m0 x9 hb ybb ff3 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 xc5 hb ybc ff3 fs0 fc0 sc0 ls0 ws0">2</div><div class="t m0 xc5 hb ybd ff3 fs0 fc0 sc0 ls0 ws0">3</div><div class="t m0 xc6 h5 yba ff6 fs0 fc0 sc0 ls0 ws0">（<span class="_ _1f"> </span><span class="ff9">v</span></div><div class="t m0 xc7 he ybe ff3 fs6 fc0 sc0 ls0 ws0">ao</div><div class="t m0 xc8 hb ybb ff3 fs0 fc0 sc0 ls0 ws0">+</div><div class="t m0 xc9 h12 ybf ffa fs0 fc0 sc0 ls0 ws0">α</div><div class="t m0 x5e h11 yba ff9 fs0 fc0 sc0 ls0 ws0">v</div><div class="t m0 x4d he ybe ff3 fs6 fc0 sc0 ls0 ws0">bo</div><div class="t m0 xca hb ybb ff3 fs0 fc0 sc0 ls0 ws0">+</div><div class="t m0 xcb h12 ybf ffa fs0 fc0 sc0 ls0 ws0">α</div><div class="t m0 xcc he yc0 ff3 fs6 fc0 sc0 ls0 ws0">2</div><div class="t m0 x1c h11 yba ff9 fs0 fc0 sc0 ls0 ws0">v</div><div class="t m0 x77 he ybe ff3 fs6 fc0 sc0 ls0 ws0">co</div><div class="t m0 xcd h5 yba ff6 fs0 fc0 sc0 ls0 ws0">）<span class="_ _20"> </span>（<span class="_ _6"> </span><span class="ff3">1<span class="_ _3"></span></span>）</div><div class="t m0 x21 h5 yc1 ff6 fs0 fc0 sc0 ls0 ws0">其中</div><div class="t m0 x22 h5 yc2 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x23 h12 yc1 ffa fs0 fc0 sc0 ls0 ws0">α</div><div class="t m0 x2 hb yc3 ff3 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x65 hb yc2 ff3 fs0 fc0 sc0 ls0 ws0">e</div><div class="t m0 x4b he yc4 ff3 fs6 fc0 sc0 ls0 ws0">j2</div><div class="t m0 x7a h13 yc5 ffb fs6 fc0 sc0 ls0 ws0">π</div><div class="t m0 xce he yc4 ff8 fs6 fc0 sc0 ls0 ws0">/<span class="_ _3"></span><span class="ff3">3</span></div><div class="t m0 x8 h5 yc1 ff6 fs0 fc0 sc0 ls4 ws0">为单位旋转矢量</div><div class="t m0 x6c h5 yc2 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 xcf h5 yc1 ff6 fs0 fc0 sc0 ls0 ws0">表示</div><div class="t m0 xd0 hb yc2 ff3 fs0 fc0 sc0 ls0 ws0">120<span class="_ _3"></span>°</div><div class="t m0 xd1 h5 yc1 ff6 fs0 fc0 sc0 ls0 ws0">相位<span class="_ _3"></span>差</div><div class="t m0 x7b ha yc2 ff5 fs0 fc0 sc0 ls0 ws0">。</div><div class="t m0 x22 h5 yc6 ff6 fs0 fc0 sc0 ls0 ws0">基于<span class="_ _3"></span>图</div><div class="t m0 xce hb yc7 ff3 fs0 fc0 sc0 ls0 ws0">1</div><div class="t m0 x29 h5 yc6 ff6 fs0 fc0 sc0 ls9 ws0">所<span class="_ _a"></span>示的系统主电路图</div><div class="t m0 xd2 h5 yc7 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x67 h5 yc6 ff6 fs0 fc0 sc0 ls0 ws0">利<span class="_ _9"></span>用<span class="_ _9"></span>基<span class="_ _9"></span>尔<span class="_ _9"></span>霍<span class="_ _10"></span>夫</div><div class="t m0 x21 h5 yc8 ff6 fs0 fc0 sc0 ls4 ws0">定理可得负载电流动态方程为</div><div class="t m0 x3e h5 yc9 ff6 fs0 fc0 sc0 ls0 ws0">：</div><div class="t m0 x5c h11 yca ff9 fs0 fc0 sc0 ls0 ws0">v</div><div class="t m0 xd3 he ycb ff8 fs6 fc0 sc0 ls0 ws0">x<span class="ff3">o</span></div><div class="t m0 x4 hb ycc ff3 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x29 hf yca ff8 fs0 fc0 sc0 ls0 ws0">L</div><div class="t m0 xd4 hb ycd ff3 fs0 fc0 sc0 ls0 ws0">d<span class="_ _3"></span><span class="ff9">i</span></div><div class="t m0 x5 h14 yce ff8 fs6 fc0 sc0 ls0 ws0">x</div><div class="t m0 x52 hb ycf ff3 fs0 fc0 sc0 ls0 ws0">d<span class="_ _3"></span><span class="ff8">t</span></div><div class="t m0 xd5 hb ycc ff3 fs0 fc0 sc0 ls0 ws0">+</div><div class="t m0 xc6 hf yca ff8 fs0 fc0 sc0 ls0 ws0">Ｒ<span class="_ _3"></span><span class="ff9">i</span></div><div class="t m0 xd6 h14 ycb ff8 fs6 fc0 sc0 ls0 ws0">x</div><div class="t m0 x5f hb ycc ff3 fs0 fc0 sc0 ls0 ws0">+</div><div class="t m0 x74 h11 yca ff9 fs0 fc0 sc0 ls0 ws0">v</div><div class="t m0 xd7 h14 ycb ff8 fs6 fc0 sc0 ls0 ws0">NO</div><div class="t m0 x6c hf yca ff8 fs0 fc0 sc0 ls0 ws0">x</div><div class="t m0 xcf h15 yd0 ffc fs0 fc0 sc0 ls0 ws0">∈</div><div class="t m0 xd8 h5 yca ff6 fs0 fc0 sc0 ls0 ws0">｛<span class="_ _2"> </span><span class="ff3">a<span class="_ _3"></span></span>，<span class="_ _16"></span><span class="ff3">b<span class="_ _3"></span><span class="ff6">，<span class="_ _16"></span><span class="ff3">c<span class="_ _3"></span><span class="ff6">｝<span class="_ _21"> </span>（<span class="_ _6"> </span></span>2<span class="_ _3"></span><span class="ff6">）</span></span></span></span></div><div class="t m0 x21 h5 yd1 ff6 fs0 fc0 sc0 ls0 ws0">其中</div><div class="t m0 x22 h5 yd2 ff6 fs0 fc0 sc0 ls0 ws0">，<span class="_ _16"></span><span class="ff8">x</span></div><div class="t m0 x2 h5 yd1 ff6 fs0 fc0 sc0 ls4 ws0">表示逆变器输出的</div><div class="t m0 x5e hb yd2 ff3 fs0 fc0 sc0 ls0 ws0">a<span class="_ _3"></span><span class="ff5">、<span class="_ _16"></span><span class="ff3">b<span class="ff5">、<span class="_ _16"></span><span class="ff3">c</span></span></span></span></div><div class="t m0 x1c h5 yd1 ff6 fs0 fc0 sc0 ls0 ws0">三相</div><div class="t m0 xd9 ha yd2 ff5 fs0 fc0 sc0 ls0 ws0">。</div><div class="t m0 x22 h5 yd3 ff6 fs0 fc0 sc0 ls0 ws0">结合<span class="_ _3"></span>式</div><div class="t m0 x44 h5 yd4 ff6 fs0 fc0 sc0 ls0 ws0">（<span class="_ _6"> </span><span class="ff3">2<span class="_ _3"></span></span>）<span class="_ _1f"> </span>，</div><div class="t m0 x61 h5 yd3 ff6 fs0 fc0 sc0 ls0 ws0">利用<span class="_ _3"></span>前向<span class="_ _3"></span>欧<span class="_ _3"></span>拉<span class="_ _3"></span>公<span class="_ _3"></span>式<span class="_ _9"></span>对<span class="_ _3"></span>式</div><div class="t m0 xda h5 yd4 ff6 fs0 fc0 sc0 ls0 ws0">（<span class="_ _1f"> </span><span class="ff3">1<span class="_ _3"></span></span>）</div><div class="t m0 x2c h5 yd3 ff6 fs0 fc0 sc0 ls0 ws0">进<span class="_ _3"></span>行<span class="_ _9"></span>离</div><div class="t m0 x21 h5 yd5 ff6 fs0 fc0 sc0 ls0 ws0">散化</div><div class="t m0 x22 h5 yd6 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x23 h5 yd5 ff6 fs0 fc0 sc0 ls0 ws0">可得<span class="_ _3"></span>到在</div><div class="t m0 xdb hf yd6 ff8 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 xdc hb yd7 ff3 fs0 fc0 sc0 ls0 ws0">+</div><div class="t m0 xc5 hb yd8 ff3 fs0 fc0 sc0 ls0 ws0">1</div><div class="t m0 xc6 h5 yd5 ff6 fs0 fc0 sc0 ls4 ws0">时刻输出电流的预测值为</div><div class="t m0 x2d h5 yd6 ff6 fs0 fc0 sc0 ls0 ws0">：</div><div class="t m0 x76 h11 yd9 ff9 fs0 fc0 sc0 ls0 ws0">i</div><div class="t m0 x4b he yda ff3 fs6 fc0 sc0 ls0 ws0">pre</div><div class="t m0 xdd h5 yd9 ff6 fs0 fc0 sc0 ls0 ws0">（<span class="_ _1f"> </span><span class="ff8">k</span></div><div class="t m0 x51 hb ydb ff3 fs0 fc0 sc0 ls0 ws0">+</div><div class="t m0 xdb hb ydc ff3 fs0 fc0 sc0 ls0 ws0">1</div><div class="t m0 xdc h5 yd9 ff6 fs0 fc0 sc0 ls0 ws0">）</div><div class="t m0 xc5 hb ydb ff3 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x62 hb ydd ff3 fs0 fc0 sc0 ls0 ws0">1</div><div class="t m0 xde hb yde ff3 fs0 fc0 sc0 ls0 ws0">－</div><div class="t m0 xc8 hf ydf ff8 fs0 fc0 sc0 ls0 ws0">ＲT</div><div class="t m0 xdf he ye0 ff3 fs6 fc0 sc0 ls0 ws0">s</div><div class="t m0 xc9 hf ye1 ff8 fs0 fc0 sc0 ls0 ws0">L</div><div class="t m1 x4c h16 ye2 ffd fs7 fc0 sc0 ls0 ws0">(<span class="_ _22"> </span>)</div><div class="t m0 xe0 h5 yd9 ff9 fs0 fc0 sc0 ls0 ws0">i<span class="_"> </span><span class="ff6">（<span class="_ _b"> </span><span class="ff8">k<span class="_ _3"></span></span>）</span></div><div class="t m0 x55 hb ydb ff3 fs0 fc0 sc0 ls0 ws0">+</div><div class="t m0 x45 hf ye3 ff8 fs0 fc0 sc0 ls0 ws0">T</div><div class="t m0 xd0 he ye4 ff3 fs6 fc0 sc0 ls0 ws0">s</div><div class="t m0 xcd hf ye5 ff8 fs0 fc0 sc0 ls0 ws0">L</div><div class="t m0 xe1 h5 yd9 ff9 fs0 fc0 sc0 ls0 ws0">v<span class="_ _3"></span><span class="ff6">（<span class="_ _1f"> </span><span class="ff8">k<span class="_ _3"></span></span>）<span class="_ _23"> </span>（<span class="_ _6"> </span><span class="ff3">3<span class="_ _3"></span></span>）</span></div><div class="t m0 x21 h5 ye6 ff6 fs0 fc0 sc0 ls0 ws0">其中</div><div class="t m0 x22 h5 ye7 ff6 fs0 fc0 sc0 ls0 ws0">，<span class="_ _16"></span><span class="ff8">T</span></div><div class="t m0 xbd he ye8 ff3 fs6 fc0 sc0 ls0 ws0">s</div><div class="t m0 xe2 h5 ye6 ff6 fs0 fc0 sc0 ls0 ws0">为采<span class="_ _3"></span>样<span class="_ _3"></span>时<span class="_ _9"></span>间</div><div class="t m0 x4c h5 ye7 ff6 fs0 fc0 sc0 ls0 ws0">；</div><div class="t m0 x62 h5 ye6 ff6 fs0 fc0 sc0 ls0 ws0">上<span class="_ _3"></span>标</div><div class="t m0 xe3 hb ye7 ff5 fs0 fc0 sc0 ls0 ws0">“<span class="_ _19"></span><span class="ff3">pre<span class="_ _9"></span><span class="ff5">”</span></span></div><div class="t m0 x60 h5 ye6 ff6 fs0 fc0 sc0 ls0 ws0">表<span class="_ _3"></span>示<span class="_ _9"></span>预<span class="_ _9"></span>测<span class="_ _9"></span>变<span class="_ _9"></span>量</div><div class="t m0 x4a ha ye7 ff5 fs0 fc0 sc0 ls0 ws0">。</div><div class="t m0 x7c h5 ye6 ff6 fs0 fc0 sc0 ls0 ws0">逆</div><div class="t m0 x21 h5 ye9 ff6 fs0 fc0 sc0 ls0 ws0">变<span class="_ _3"></span>器在</div><div class="t m0 x2 hf yea ff8 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 xe4 hb yeb ff3 fs0 fc0 sc0 ls0 ws0">+</div><div class="t m0 x3 hb yea ff3 fs0 fc0 sc0 ls0 ws0">1</div><div class="t m0 xdd h5 ye9 ff6 fs0 fc0 sc0 ls4 ws0">时刻的负载电流值</div><div class="t m0 xe5 h11 yea ff9 fs0 fc0 sc0 ls0 ws0">i</div><div class="t m0 xe6 he yec ff3 fs6 fc0 sc0 ls0 ws0">pre</div><div class="t m0 xd8 h5 yea ff6 fs0 fc0 sc0 ls0 ws0">（<span class="_ _1f"> </span><span class="ff8">k</span></div><div class="t m0 xe7 hb yeb ff3 fs0 fc0 sc0 ls0 ws0">+</div><div class="t m0 xe1 h5 yea ff3 fs0 fc0 sc0 ls0 ws0">1<span class="_ _3"></span><span class="ff6">）</span></div><div class="t m0 xe8 h5 ye9 ff6 fs0 fc0 sc0 ls0 ws0">可以<span class="_ _3"></span>由三<span class="_ _3"></span>电</div><div class="t m0 x21 h5 yed ff6 fs0 fc0 sc0 ls0 ws0">平</div><div class="t m0 x75 hb yee ff3 fs0 fc0 sc0 ls0 ws0">NP<span class="_ _3"></span>C</div><div class="t m0 xe9 h5 yed ff6 fs0 fc0 sc0 ls0 ws0">逆变<span class="_ _3"></span>器产<span class="_ _3"></span>生<span class="_ _3"></span>的</div><div class="t m0 xc7 hb yee ff3 fs0 fc0 sc0 ls0 ws0">27</div><div class="t m0 xd7 h5 yed ff6 fs0 fc0 sc0 ls0 ws0">个<span class="_ _3"></span>电<span class="_ _9"></span>压<span class="_ _3"></span>矢<span class="_ _9"></span>量</div><div class="t m0 xea h5 yee ff9 fs0 fc0 sc0 ls0 ws0">v<span class="_ _3"></span><span class="ff6">（<span class="_ _11"> </span><span class="ff8">k<span class="_ _3"></span></span>）</span></div><div class="t m0 xeb h5 yed ff6 fs0 fc0 sc0 ls0 ws0">来<span class="_ _3"></span>预<span class="_ _9"></span>测</div><div class="t m0 x64 ha yee ff5 fs0 fc0 sc0 ls0 ws0">。</div><div class="t m0 x21 h5 yef ff6 fs0 fc0 sc0 ls0 ws0">进一<span class="_ _3"></span>步地</div><div class="t m0 x7 h5 yf0 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x39 h5 yef ff6 fs0 fc0 sc0 ls0 ws0">考虑<span class="_ _3"></span>延时<span class="_ _3"></span>补偿</div><div class="t m0 x74 h5 yf0 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 xd7 h5 yef ff6 fs0 fc0 sc0 ls0 ws0">需计<span class="_ _3"></span>算在</div><div class="t m0 xcd hf yf0 ff8 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 x57 hb yf1 ff3 fs0 fc0 sc0 ls0 ws0">+</div><div class="t m0 xea hb yf0 ff3 fs0 fc0 sc0 ls0 ws0">2</div><div class="t m0 xbf h5 yef ff6 fs0 fc0 sc0 ls0 ws0">时刻<span class="_ _3"></span>电流<span class="_ _3"></span>预</div><div class="t m0 x21 h5 yf2 ff6 fs0 fc0 sc0 ls0 ws0">测值</div><div class="t m0 x22 ha yf3 ff5 fs0 fc0 sc0 ls0 ws0">。</div><div class="t m0 x28 h5 yf2 ff6 fs0 fc0 sc0 ls4 ws0">为了避免由于参考电流阶<span class="ls6">跃变化而使实际电</span></div><div class="t m0 x21 h5 yf4 ff6 fs0 fc0 sc0 ls0 ws0">流量<span class="_ _3"></span>产生<span class="_ _3"></span>较大<span class="_ _9"></span>的<span class="_ _9"></span>电<span class="_ _9"></span>流<span class="_ _3"></span>尖<span class="_ _9"></span>峰</div><div class="t m0 x5a h5 yf5 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x69 h5 yf6 ff6 fs0 fc0 sc0 ls9 ws0">采用矢量角度补偿法计</div><div class="t m0 x21 h5 yf7 ff6 fs0 fc0 sc0 ls0 ws0">算未<span class="_ _3"></span>来参<span class="_ _3"></span>考值</div><div class="t m0 x29 h5 yf8 ff6 fs0 fc0 sc0 ls0 ws0">：</div><div class="t m0 x68 h11 yf9 ff9 fs0 fc0 sc0 ls0 ws0">i</div><div class="t m0 xd4 he yfa ff3 fs6 fc0 sc0 ls0 ws0">*</div><div class="t m0 xec h5 yf9 ff6 fs0 fc0 sc0 ls0 ws0">（<span class="_ _1f"> </span><span class="ff8">k</span></div><div class="t m0 xc6 hb yfb ff3 fs0 fc0 sc0 ls0 ws0">+</div><div class="t m0 x62 h5 yf9 ff3 fs0 fc0 sc0 ls0 ws0">2<span class="_ _3"></span><span class="ff6">）</span></div><div class="t m0 xc8 hb yfb ff3 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 xe3 h11 yf9 ff9 fs0 fc0 sc0 ls0 ws0">i</div><div class="t m0 xed he yfa ff3 fs6 fc0 sc0 ls0 ws0">*</div><div class="t m0 x7e h5 yf9 ff6 fs0 fc0 sc0 ls0 ws0">（<span class="_ _1f"> </span><span class="ff8">k<span class="_ _3"></span></span>）<span class="_ _1f"> </span><span class="ff3">e</span></div><div class="t m0 x1c he yfa ff3 fs6 fc0 sc0 ls0 ws0">2j<span class="ff8">wT</span></div><div class="t m0 xcd h17 yfc ff3 fs8 fc0 sc0 ls0 ws0">s</div><div class="t m0 xee h5 yf9 ff6 fs0 fc0 sc0 ls0 ws0">（<span class="_ _6"> </span><span class="ff3">4<span class="_ _3"></span></span>）</div><div class="t m0 x21 h5 yfd ff6 fs0 fc0 sc0 ls0 ws0">其中</div><div class="t m0 x22 h5 yfe ff6 fs0 fc0 sc0 ls0 ws0">，<span class="_ _7"></span><span class="ff8">w</span></div><div class="t m0 x3c h5 yfd ff6 fs0 fc0 sc0 ls5 ws0">为参考电流矢量的工频角速度</div><div class="t m0 xef h5 yfe ff6 fs0 fc0 sc0 ls0 ws0">；</div><div class="t m0 xda h5 yfd ff6 fs0 fc0 sc0 ls0 ws0">上<span class="_ _3"></span>标</div><div class="t m0 xf0 hb yfe ff5 fs0 fc0 sc0 ls0 ws0">“<span class="_ _18"></span><span class="ff3">*<span class="_ _6"> </span><span class="ff5">”</span></span></div><div class="t m0 x7c h5 yfd ff6 fs0 fc0 sc0 ls0 ws0">表</div><div class="t m0 x21 h5 yff ff6 fs0 fc0 sc0 ls0 ws0">示参<span class="_ _3"></span>考值</div><div class="t m0 x7 ha y100 ff5 fs0 fc0 sc0 ls0 ws0">。</div><div class="t m0 x44 h5 yff ff6 fs0 fc0 sc0 ls0 ws0">由此<span class="_ _3"></span>可见</div><div class="t m0 xf1 h5 y100 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x70 h5 yff ff6 fs0 fc0 sc0 ls4 ws0">代价函数可以定义如下</div><div class="t m0 xf2 h5 y100 ff6 fs0 fc0 sc0 ls0 ws0">：</div><div class="t m0 xf3 hf y101 ff8 fs0 fc0 sc0 ls0 ws0">g</div><div class="t m0 x6f hb y102 ff3 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x6b h11 y101 ff9 fs0 fc0 sc0 ls0 ws0">i</div><div class="t m0 xbd he y103 ff3 fs6 fc0 sc0 ls0 ws0">*</div><div class="t m0 xbd h18 y104 ffe fs6 fc0 sc0 ls0 ws0">α</div><div class="t m0 xe2 h5 y101 ff6 fs0 fc0 sc0 ls0 ws0">（<span class="_ _1f"> </span><span class="ff8">k</span></div><div class="t m0 xf4 hb y102 ff3 fs0 fc0 sc0 ls0 ws0">+</div><div class="t m0 x4 h5 y105 ff3 fs0 fc0 sc0 ls0 ws0">2<span class="_ _3"></span><span class="ff6">）</span></div><div class="t m0 x68 hb y102 ff3 fs0 fc0 sc0 ls0 ws0">－</div><div class="t m0 x52 h11 y101 ff9 fs0 fc0 sc0 ls0 ws0">i</div><div class="t m0 xf5 he y103 ff3 fs6 fc0 sc0 ls0 ws0">pre</div><div class="t m0 xf5 h18 y104 ffe fs6 fc0 sc0 ls0 ws0">α</div><div class="t m0 xf6 h5 y101 ff6 fs0 fc0 sc0 ls0 ws0">（<span class="_ _1f"> </span><span class="ff8">k</span></div><div class="t m0 x62 hb y102 ff3 fs0 fc0 sc0 ls0 ws0">+</div><div class="t m0 xde h5 y105 ff3 fs0 fc0 sc0 ls0 ws0">2<span class="_ _3"></span><span class="ff6">）</span></div><div class="t m0 xed hb y102 ff3 fs0 fc0 sc0 ls0 ws0">+</div><div class="t m0 xca h11 y101 ff9 fs0 fc0 sc0 ls0 ws0">i</div><div class="t m0 x6c he y103 ff3 fs6 fc0 sc0 ls0 ws0">*</div><div class="t m0 x6c h18 y104 ffe fs6 fc0 sc0 ls0 ws0">β</div><div class="t m0 x4e h5 y101 ff6 fs0 fc0 sc0 ls0 ws0">（<span class="_ _1f"> </span><span class="ff8">k</span></div><div class="t m0 x77 hb y102 ff3 fs0 fc0 sc0 ls0 ws0">+</div><div class="t m0 xcd h5 y105 ff3 fs0 fc0 sc0 ls0 ws0">2<span class="_ _3"></span><span class="ff6">）</span></div><div class="t m0 xea hb y102 ff3 fs0 fc0 sc0 ls0 ws0">－</div><div class="t m0 x6a h11 y101 ff9 fs0 fc0 sc0 ls0 ws0">i</div><div class="t m0 xf7 he y103 ff3 fs6 fc0 sc0 ls0 ws0">pre</div><div class="t m0 xf7 h18 y104 ffe fs6 fc0 sc0 ls0 ws0">β</div><div class="t m0 x10 h5 y101 ff6 fs0 fc0 sc0 ls0 ws0">（<span class="_ _1f"> </span><span class="ff8">k</span></div><div class="t m0 x2c hb y102 ff3 fs0 fc0 sc0 ls0 ws0">+</div><div class="t m0 x2d h5 y105 ff3 fs0 fc0 sc0 ls0 ws0">2<span class="_ _3"></span><span class="ff6">）</span></div><div class="t m0 xee h5 y106 ff6 fs0 fc0 sc0 ls0 ws0">（<span class="_ _6"> </span><span class="ff3">5<span class="_ _3"></span></span>）</div><div class="t m0 x21 h5 y61 ff6 fs0 fc0 sc0 ls0 ws0">其中</div><div class="t m0 x22 h5 y62 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x23 h5 y61 ff6 fs0 fc0 sc0 ls0 ws0">下标</div><div class="t m0 x3 ha y62 ff5 fs0 fc0 sc0 ls0 ws0">“</div><div class="t m0 xdd h19 y61 ffe fs0 fc0 sc0 ls0 ws0">α</div><div class="t m0 x50 ha y62 ff5 fs0 fc0 sc0 ls0 ws0">”</div><div class="t m0 xc4 h5 y61 ff6 fs0 fc0 sc0 ls0 ws0">和</div><div class="t m0 x52 ha y62 ff5 fs0 fc0 sc0 ls0 ws0">“</div><div class="t m0 xc5 h19 y61 ffe fs0 fc0 sc0 ls0 ws0">β</div><div class="t m0 x6 ha y62 ff5 fs0 fc0 sc0 ls0 ws0">”</div><div class="t m0 xf1 h5 y61 ff6 fs0 fc0 sc0 ls6 ws0">表示<span class="_ _a"></span>相应<span class="_ _a"></span>状态量在两相静止坐</div><div class="t m0 x21 h5 y63 ff6 fs0 fc0 sc0 ls4 ws0">标系下的表达形式</div><div class="t m0 xf8 ha y64 ff5 fs0 fc0 sc0 ls0 ws0">。</div><div class="t m0 xf1 h5 y65 ff6 fs0 fc0 sc0 ls6 ws0">预测<span class="_ _a"></span>控制<span class="_ _a"></span>器将使用系统的离散</div><div class="t m0 x21 h5 y66 ff6 fs0 fc0 sc0 ls4 ws0">时间模型来计算逆变器每一个电<span class="ls6">压矢量对应的输出</span></div><div class="t m0 x21 h5 y107 ff6 fs0 fc0 sc0 ls0 ws0">电流<span class="_ _3"></span>预测<span class="_ _3"></span>值</div><div class="t m0 x44 h5 y108 ff6 fs0 fc0 sc0 ls0 ws0">；</div><div class="t m0 x49 h5 y107 ff6 fs0 fc0 sc0 ls8 ws0">再通过选择使代价<span class="ls9">函数最小的开关状</span></div><div class="t m0 x21 h5 y109 ff6 fs0 fc0 sc0 ls0 ws0">态</div><div class="t m0 x6e h5 y10a ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x6f h5 y109 ff6 fs0 fc0 sc0 ls4 ws0">将其应用于下一采样时刻</div><div class="t m0 xe0 h5 y10a ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x3e h5 y109 ff6 fs0 fc0 sc0 ls6 ws0">实现对逆变器的最优</div><div class="t m0 x21 h5 y10b ff6 fs0 fc0 sc0 ls0 ws0">输出<span class="_ _3"></span>控制</div><div class="t m0 x7 ha y10c ff5 fs0 fc0 sc0 ls0 ws0">。</div><div class="t m0 x21 hb y10d ff3 fs0 fc0 sc0 ls0 ws0">1<span class="_ _3"></span>．<span class="_ _3"></span>2</div><div class="t m0 xf9 h5 y10e ff2 fs0 fc0 sc0 ls4 ws0">模型参数变化的影响</div><div class="t m0 x22 h5 y10f ff6 fs0 fc0 sc0 ls0 ws0">由<span class="_ _3"></span>于<span class="_ _10"></span>以<span class="_ _10"></span>上</div><div class="t m0 x68 hb y110 ff3 fs0 fc0 sc0 ls0 ws0">MP<span class="_ _3"></span>CC</div><div class="t m0 xfa h5 y10f ff6 fs0 fc0 sc0 lsa ws0">的实现过程存在着非线性属</div><div class="t m0 x21 h5 y111 ff6 fs0 fc0 sc0 ls0 ws0">性</div><div class="t m0 x6e h5 y112 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x6f h5 y111 ff6 fs0 fc0 sc0 ls4 ws0">因此无法对其进行根轨迹分析</div><div class="t m0 xf h5 y112 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x45 h5 y111 ff6 fs0 fc0 sc0 ls6 ws0">而且进行闭合回</div><div class="t m0 x21 h5 y113 ff6 fs0 fc0 sc0 ls0 ws0">路稳<span class="_ _3"></span>定性<span class="_ _3"></span>分<span class="_ _3"></span>析<span class="_ _3"></span>也<span class="_ _9"></span>是<span class="_ _9"></span>更<span class="_ _9"></span>为<span class="_ _9"></span>复<span class="_ _9"></span>杂<span class="_ _10"></span>的</div><div class="t m0 xe5 ha y114 ff5 fs0 fc0 sc0 ls0 ws0">。</div><div class="t m0 xd8 h5 y113 ff6 fs0 fc0 sc0 ls0 ws0">因<span class="_ _9"></span>此</div><div class="t m0 xea h5 y114 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x6a h5 y113 ff6 fs0 fc0 sc0 ls0 ws0">本<span class="_ _9"></span>文<span class="_ _9"></span>将<span class="_ _9"></span>根<span class="_ _9"></span>据</div><div class="t m0 x21 h5 y115 ff6 fs0 fc0 sc0 ls4 ws0">控制器性能来分析参数变化对系统的影响</div><div class="t m0 x10 ha y116 ff5 fs0 fc0 sc0 ls0 ws0">。</div><div class="t m0 x94 h5 y117 ff6 fs0 fc0 sc0 ls0 ws0">将式</div><div class="t m0 xfb h5 y118 ff6 fs0 fc0 sc0 ls0 ws0">（<span class="_ _6"> </span><span class="ff3">3<span class="_ _3"></span></span>）</div><div class="t m0 xfc h5 y117 ff6 fs0 fc0 sc0 ls4 ws0">改写为如下形式</div><div class="t m0 xfd h5 y118 ff6 fs0 fc0 sc0 ls0 ws0">：</div><div class="t m0 xfe h11 y119 ff9 fs0 fc0 sc0 ls0 ws0">i</div><div class="t m0 xff he y11a ff3 fs6 fc0 sc0 ls0 ws0">pre</div><div class="t m0 xbb h5 y119 ff6 fs0 fc0 sc0 ls0 ws0">（<span class="_ _1f"> </span><span class="ff8">k</span></div><div class="t m0 x100 hb y11b ff3 fs0 fc0 sc0 ls0 ws0">+</div><div class="t m0 x101 h5 y11c ff3 fs0 fc0 sc0 ls0 ws0">1<span class="_ _3"></span><span class="ff6">）</span></div><div class="t m0 x102 hb y11b ff3 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x103 h5 y119 ff8 fs0 fc0 sc0 ls0 ws0">C<span class="_ _3"></span>'<span class="_ _9"></span><span class="ff9">i<span class="_"> </span><span class="ff6">（<span class="_ _b"> </span></span></span>k<span class="_ _3"></span><span class="ff6">）</span></div><div class="t m0 x80 hb y11b ff3 fs0 fc0 sc0 ls0 ws0">+</div><div class="t m0 x104 h5 y119 ff8 fs0 fc0 sc0 ls0 ws0">C<span class="_ _3"></span>″<span class="ff9">v<span class="_ _3"></span><span class="ff6">（<span class="_ _1f"> </span></span></span>k<span class="_ _3"></span><span class="ff6">）<span class="_ _24"> </span>（<span class="_ _6"> </span><span class="ff3">6<span class="_ _3"></span></span>）</span></div><div class="t m0 x7f h5 y11d ff6 fs0 fc0 sc0 ls0 ws0">其中</div><div class="t m0 x94 h5 y11e ff6 fs0 fc0 sc0 ls0 ws0">，<span class="_ _16"></span><span class="ff8">C<span class="_ _3"></span>'</span></div><div class="t m0 x105 hb y11f ff3 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x106 hb y11e ff3 fs0 fc0 sc0 ls0 ws0">1</div><div class="t m0 xa4 hb y11f ff3 fs0 fc0 sc0 ls0 ws0">－</div><div class="t m0 xfc hf y11e ff8 fs0 fc0 sc0 ls0 ws0">ＲT</div><div class="t m0 x107 he y120 ff3 fs6 fc0 sc0 ls0 ws0">s</div><div class="t m0 x19 h5 y11e ff8 fs0 fc0 sc0 ls0 ws0">/<span class="_ _f"></span>L<span class="_ _3"></span><span class="ff6">；<span class="_ _1f"> </span></span>C<span class="_ _3"></span>″</div><div class="t m0 x108 hb y11f ff3 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x86 hf y11e ff8 fs0 fc0 sc0 ls0 ws0">T</div><div class="t m0 x89 he y120 ff3 fs6 fc0 sc0 ls0 ws0">s</div><div class="t m0 x109 ha y11e ff8 fs0 fc0 sc0 ls0 ws0">/<span class="_ _f"></span>L<span class="_ _3"></span><span class="ff5">。</span></div><div class="t m0 x81 h5 y11d ff6 fs0 fc0 sc0 ls0 ws0">由<span class="_ _9"></span>式</div><div class="t m0 x10a h5 y11e ff6 fs0 fc0 sc0 ls0 ws0">（<span class="_ _1f"> </span><span class="ff3">6<span class="_ _9"></span></span>）</div><div class="t m0 x87 h5 y11d ff6 fs0 fc0 sc0 ls0 ws0">可<span class="_ _9"></span>知</div><div class="t m0 xb4 h5 y11e ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x33 h5 y11d ff6 fs0 fc0 sc0 ls0 ws0">预<span class="_ _9"></span>测</div><div class="t m0 x7f h5 y121 ff6 fs0 fc0 sc0 ls0 ws0">电流<span class="_ _3"></span>包含<span class="_ _3"></span>以下</div><div class="t m0 x26 hb y122 ff3 fs0 fc0 sc0 ls0 ws0">2</div><div class="t m0 x9c h5 y121 ff6 fs0 fc0 sc0 ls0 ws0">个<span class="_ _3"></span>部<span class="_ _9"></span>分</div><div class="t m0 x103 h5 y122 ff6 fs0 fc0 sc0 ls0 ws0">：</div><div class="t m0 x10b h5 y121 ff6 fs0 fc0 sc0 ls9 ws0">一部分与输出负载电流矢</div><div class="t m0 x7f h5 y123 ff6 fs0 fc0 sc0 ls0 ws0">量方<span class="_ _3"></span>向相<span class="_ _3"></span>同</div><div class="t m0 xa4 h5 y124 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 xfe h5 y125 ff6 fs0 fc0 sc0 ls8 ws0">另一部分与实际<span class="ls9">电路电压矢量方向相</span></div><div class="t m0 x7f h5 y126 ff6 fs0 fc0 sc0 ls0 ws0">同</div><div class="t m0 x8c ha y127 ff5 fs0 fc0 sc0 ls0 ws0">。</div><div class="t m0 x94 h5 y126 ff6 fs0 fc0 sc0 ls4 ws0">负载参数变化对预测电流的影响如图</div><div class="t m0 x10c hb y127 ff3 fs0 fc0 sc0 ls0 ws0">2</div><div class="t m0 x10d h5 y126 ff6 fs0 fc0 sc0 ls0 ws0">所示</div><div class="t m0 x10e ha y127 ff5 fs0 fc0 sc0 ls0 ws0">。</div><div class="t m0 x84 h3 y128 ff2 fs1 fc0 sc0 ls0 ws0">图</div><div class="t m0 x19 h4 y129 ff3 fs1 fc0 sc0 ls0 ws0">2</div><div class="t m0 x101 h3 y128 ff2 fs1 fc0 sc0 ls3 ws0">负载参数变化的影响</div><div class="t m0 x10f h4 y12a ff3 fs1 fc0 sc0 ls0 ws0">Fig．<span class="_ _3"></span>2<span class="_ _4"> </span>Effect<span class="_ _6"> </span>of<span class="_ _6"> </span>load<span class="_ _1f"> </span>paramete<span class="_ _a"></span>r<span class="_ _1f"> </span>variation</div><div class="t m0 x94 h5 y12b ff6 fs0 fc0 sc0 ls0 ws0">一方<span class="_ _3"></span>面</div><div class="t m0 xa4 h5 y12c ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 xfe h5 y12b ff6 fs0 fc0 sc0 lsa ws0">负<span class="_ _a"></span>载电阻发生变化仅影响</div><div class="t m0 x87 h5 y12c ff8 fs0 fc0 sc0 ls0 ws0">C<span class="_ _3"></span>'<span class="_ _9"></span><span class="ff6">，</span></div><div class="t m0 x10d h5 y12b ff6 fs0 fc0 sc0 ls0 ws0">因<span class="_ _9"></span>此<span class="_ _10"></span>将</div><div class="t m0 x7f h5 y12d ff6 fs0 fc0 sc0 ls0 ws0">使预<span class="_ _3"></span>测电<span class="_ _3"></span>流发<span class="_ _9"></span>生<span class="_ _9"></span>径<span class="_ _9"></span>向<span class="_ _3"></span>移<span class="_ _9"></span>动</div><div class="t m0 x89 h5 y12e ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x8a h5 y12d ff6 fs0 fc0 sc0 ls9 ws0">从而导致预测电流振幅</div><div class="t m0 x7f h5 y12f ff6 fs0 fc0 sc0 ls0 ws0">发生<span class="_ _3"></span>变化</div><div class="t m0 xfb h5 y130 ff6 fs0 fc0 sc0 ls0 ws0">；</div><div class="t m0 xaf h5 y12f ff6 fs0 fc0 sc0 ls0 ws0">另一<span class="_ _3"></span>方面</div><div class="t m0 x110 h5 y130 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 xa0 h5 y12f ff6 fs0 fc0 sc0 ls6 ws0">负载<span class="_ _a"></span>电感<span class="_ _a"></span>发生变化会导致预测</div><div class="t m0 x7f h5 y131 ff6 fs0 fc0 sc0 ls0 ws0">负载<span class="_ _3"></span>电流<span class="_ _3"></span>矢量<span class="_ _9"></span>发<span class="_ _9"></span>生<span class="_ _9"></span>改<span class="_ _3"></span>变</div><div class="t m0 x103 h5 y132 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x10b h5 y131 ff6 fs0 fc0 sc0 ls9 ws0">从而会引起电流纹波发生</div><div class="t m0 x7f h5 y133 ff6 fs0 fc0 sc0 ls8 ws0">变<span class="_ _a"></span>化<span class="_ _a"></span>且<span class="_ _a"></span>电<span class="_ _a"></span>流<span class="_ _a"></span>幅值产生小幅度变动</div><div class="t m0 x96 h5 y134 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x48 h5 y135 ff6 fs0 fc0 sc0 ls9 ws0">原因在于电感的</div><div class="t m0 x7f h5 y136 ff6 fs0 fc0 sc0 ls4 ws0">改变会同时影响</div><div class="t m0 x2e hf y137 ff8 fs0 fc0 sc0 ls0 ws0">C<span class="_ _3"></span>'</div><div class="t m0 x101 h5 y136 ff6 fs0 fc0 sc0 ls0 ws0">和</div><div class="t m0 xa1 hf y137 ff8 fs0 fc0 sc0 ls0 ws0">C<span class="_ _3"></span>″</div><div class="t m0 x86 h5 y136 ff6 fs0 fc0 sc0 ls0 ws0">这</div><div class="t m0 x111 hb y137 ff3 fs0 fc0 sc0 ls0 ws0">2</div><div class="t m0 x91 h5 y136 ff6 fs0 fc0 sc0 ls0 ws0">个权<span class="_ _3"></span>重系<span class="_ _3"></span>数</div><div class="t m0 x112 ha y137 ff5 fs0 fc0 sc0 ls0 ws0">。</div><div class="t m0 x2b hc y138 ff3 fs4 fc0 sc0 ls0 ws0">2<span class="_ _5"> </span>IMFP<span class="_ _3"></span>CC</div><div class="t m0 x113 h8 y139 ff2 fs4 fc0 sc0 lse ws0">在三电平逆变器中的应用</div><div class="t m0 x2b hb y13a ff3 fs0 fc0 sc0 ls0 ws0">2<span class="_ _3"></span>．<span class="_ _3"></span>1<span class="_ _25"> </span>IMFP<span class="_ _3"></span>CC</div><div class="t m0 x113 h5 y13b ff2 fs0 fc0 sc0 ls0 ws0">算法<span class="_ _3"></span>的原<span class="_ _3"></span>理</div><div class="t m0 x94 hb y13c ff3 fs0 fc0 sc0 ls0 ws0">MFP<span class="_ _3"></span>CC</div><div class="t m0 x36 h5 y13d ff6 fs0 fc0 sc0 ls4 ws0">的基本思想如下</div><div class="t m0 x114 h5 y13c ff6 fs0 fc0 sc0 ls0 ws0">：</div><div class="t m0 x115 h5 y13d ff6 fs0 fc0 sc0 ls5 ws0">由于控制器的采样频</div><div class="t m0 x7f h5 y13e ff6 fs0 fc0 sc0 ls0 ws0">率很<span class="_ _3"></span>高</div><div class="t m0 xaa h5 y13f ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x8e h5 y13e ff6 fs0 fc0 sc0 ls8 ws0">且<span class="_ _a"></span>在<span class="_ _a"></span>每个控制周期中<span class="ls9">仅有一个开关状态被</span></div><div class="t m0 x7f h5 y140 ff6 fs0 fc0 sc0 ls0 ws0">使用</div><div class="t m0 x94 h5 y141 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x116 h5 y140 ff6 fs0 fc0 sc0 ls8 ws0">可<span class="_ _a"></span>以<span class="_ _a"></span>认<span class="_ _a"></span>为在该控制周期<span class="ls9">内负载电流是线性变</span></div><div class="t m0 x7f h5 y142 ff6 fs0 fc0 sc0 ls0 ws0">化的</div><div class="t m0 x94 h5 y143 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x116 h5 y144 ff6 fs0 fc0 sc0 ls8 ws0">因<span class="_ _a"></span>此<span class="_ _a"></span>只<span class="_ _a"></span>需通过计算每个<span class="ls9">控制周期前后两端电</span></div><div class="t m0 x7f h5 y145 ff6 fs0 fc0 sc0 ls0 ws0">流的<span class="_ _3"></span>差分</div><div class="t m0 xfb h5 y146 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 xaf h5 y145 ff6 fs0 fc0 sc0 ls4 ws0">即可对负载电流进行预测</div><div class="t m0 x2f ha y146 ff5 fs0 fc0 sc0 ls0 ws0">。</div><div class="t m0 x94 h5 y147 ff6 fs0 fc0 sc0 ls9 ws0">为<span class="_ _a"></span>了<span class="_ _a"></span>减<span class="_ _1b"></span>小<span class="_ _a"></span>用于存储电流差分矢量矩阵的大小</div><div class="t m0 x82 h5 y148 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x7f h5 y149 ff6 fs0 fc0 sc0 ls0 ws0">本文<span class="_ _3"></span>在两<span class="_ _10"></span>相<span class="_ _10"></span>静<span class="_ _9"></span>止<span class="_ _11"> </span><span class="ffe">αβ<span class="_ _b"> </span></span>坐<span class="_ _10"></span>标<span class="_ _10"></span>系<span class="_ _10"></span>下<span class="_ _10"></span>实<span class="_ _10"></span>现</div><div class="t m0 x10a hb y14a ff3 fs0 fc0 sc0 ls0 ws0">IMFP<span class="_ _3"></span>CC<span class="_ _3"></span><span class="ff5">。</span></div><div class="t m0 x33 h5 y149 ff6 fs0 fc0 sc0 ls0 ws0">由<span class="_ _9"></span>于</div><div class="t m0 x7f h5 y14b ff6 fs0 fc0 sc0 ls0 ws0">三电<span class="_ _3"></span>平</div><div class="t m0 xba hb y14c ff3 fs0 fc0 sc0 ls0 ws0">NP<span class="_ _3"></span>C</div><div class="t m0 x36 h5 y14b ff6 fs0 fc0 sc0 ls0 ws0">逆变<span class="_ _3"></span>器<span class="_ _9"></span>存<span class="_ _3"></span>在</div><div class="t m0 x10b hb y14c ff3 fs0 fc0 sc0 ls0 ws0">27</div><div class="t m0 x90 h5 y14b ff6 fs0 fc0 sc0 ls0 ws0">种<span class="_ _3"></span>开<span class="_ _9"></span>关<span class="_ _3"></span>状<span class="_ _9"></span>态</div><div class="t m0 x117 h5 y14c ff6 fs0 fc0 sc0 ls0 ws0">｛<span class="_ _6"> </span><span class="ff8">S</span></div><div class="t m0 x118 he y14d ff3 fs6 fc0 sc0 ls0 ws0">1</div><div class="t m0 x119 h5 y14c ff6 fs0 fc0 sc0 ls0 ws0">，<span class="_ _7"></span><span class="ff8">S</span></div><div class="t m0 xc1 he y14d ff3 fs6 fc0 sc0 ls0 ws0">2</div><div class="t m0 x33 h5 y14c ff6 fs0 fc0 sc0 ls0 ws0">，<span class="_ _7"></span><span class="fff">…<span class="ff6">，</span></span></div><div class="t m0 x7f hf y14e ff8 fs0 fc0 sc0 ls0 ws0">S</div><div class="t m0 x11a he y14f ff3 fs6 fc0 sc0 ls0 ws0">27</div><div class="t m0 x11b h5 y14e ff6 fs0 fc0 sc0 ls0 ws0">｝<span class="_ _2"> </span>，</div><div class="t m0 x43 h5 y150 ff6 fs0 fc0 sc0 lsc ws0">在<span class="_ _a"></span>控<span class="_ _1b"></span>制器进行滚动计算寻优的过程中其所消</div><div class="t m0 x7f h5 y151 ff6 fs0 fc0 sc0 ls4 ws0">耗的时间不能忽略</div><div class="t m0 x95 h5 y152 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x110 h5 y151 ff6 fs0 fc0 sc0 ls0 ws0">为此</div><div class="t m0 x31 h5 y152 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x32 h5 y151 ff6 fs0 fc0 sc0 ls6 ws0">采用<span class="_ _a"></span>两步预测值对控制器</div><div class="t m0 x7f h5 y153 ff6 fs0 fc0 sc0 ls0 ws0">进行<span class="_ _3"></span>延时<span class="_ _3"></span>补偿</div><div class="t m0 x113 hb y154 ff5 fs0 fc0 sc0 ls0 ws0">。<span class="ff3">IMFP<span class="_ _3"></span>CC</span></div><div class="t m0 x10b h5 y153 ff6 fs0 fc0 sc0 ls0 ws0">工作<span class="_ _3"></span>原理<span class="_ _3"></span>如图</div><div class="t m0 x11c hb y154 ff3 fs0 fc0 sc0 ls0 ws0">3</div><div class="t m0 x11d h5 y153 ff6 fs0 fc0 sc0 ls0 ws0">所示</div><div class="t m0 x11e h5 y154 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x33 h5 y153 ff6 fs0 fc0 sc0 ls0 ws0">可见</div><div class="t m0 x7f h5 y155 ff6 fs0 fc0 sc0 ls0 ws0">只要<span class="_ _3"></span>根据</div><div class="t m0 x10f hf y156 ff8 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 xa4 h5 y157 ff6 fs0 fc0 sc0 ls4 ws0">时刻采样得到的负载<span class="_ _3"></span>电流<span class="_ _3"></span>值<span class="_ _3"></span>和</div><div class="t m0 x118 hb y156 ff3 fs0 fc0 sc0 ls0 ws0">2</div><div class="t m0 xa3 h5 y157 ff6 fs0 fc0 sc0 ls0 ws0">个<span class="_ _3"></span>电<span class="_ _3"></span>流</div><div class="t m0 x7f h5 y158 ff6 fs0 fc0 sc0 ls0 ws0">差分<span class="_ _3"></span>矢量</div><div class="t m0 xfb h5 y159 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 xaf h5 y158 ff6 fs0 fc0 sc0 ls0 ws0">即可<span class="_ _3"></span>实<span class="_ _3"></span>现<span class="_ _9"></span>对</div><div class="t m0 x108 hf y159 ff8 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 x31 hb y15a ff3 fs0 fc0 sc0 ls0 ws0">+</div><div class="t m0 xb0 hb y15b ff3 fs0 fc0 sc0 ls0 ws0">2</div><div class="t m0 x11f h5 y158 ff6 fs0 fc0 sc0 ls8 ws0">时刻电流的预测</div><div class="t m0 xa3 ha y159 ff5 fs0 fc0 sc0 ls0 ws0">。</div><div class="t m0 x33 h5 y158 ff6 fs0 fc0 sc0 ls0 ws0">值<span class="_ _3"></span>得</div><div class="t m0 x7f h5 y15c ff6 fs0 fc0 sc0 ls0 ws0">注意<span class="_ _3"></span>的是</div><div class="t m0 xfb h5 y15d ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 xaf h5 y15c ff6 fs0 fc0 sc0 ls8 ws0">为<span class="_ _a"></span>了得到电流差分<span class="ls9">且避免检测到由于开</span></div><div class="t m0 x7f h5 y15e ff6 fs0 fc0 sc0 ls4 ws0">关动作而产生的电流尖峰</div><div class="t m0 x32 h5 y15f ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x120 h5 y15e ff6 fs0 fc0 sc0 ls0 ws0">在第</div><div class="t m0 xa8 hf y15f ff8 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 x1f h5 y15e ff6 fs0 fc0 sc0 ls0 ws0">个<span class="_ _3"></span>控<span class="_ _3"></span>制<span class="_ _3"></span>周<span class="_ _3"></span>期<span class="_ _3"></span>中</div><div class="t m0 x9f h5 y15f ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x34 h5 y15e ff6 fs0 fc0 sc0 ls0 ws0">负</div><div class="t m0 x7f h5 y160 ff6 fs0 fc0 sc0 ls8 ws0">载<span class="_ _a"></span>电<span class="_ _a"></span>流<span class="_ _a"></span>应<span class="_ _a"></span>该<span class="_ _a"></span>在开关状态应用之前进行<span class="_ _3"></span>采样</div><div class="t m0 x121 h5 y161 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x10d h5 y160 ff6 fs0 fc0 sc0 ls0 ws0">最<span class="_ _9"></span>终<span class="_ _9"></span>得</div><div class="t m0 x7f h5 y162 ff6 fs0 fc0 sc0 ls0 ws0">到</div><div class="t m0 x122 hf y163 ff8 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 x42 hb y164 ff3 fs0 fc0 sc0 ls0 ws0">+</div><div class="t m0 x3a hb y165 ff3 fs0 fc0 sc0 ls0 ws0">2</div><div class="t m0 x17 h5 y166 ff6 fs0 fc0 sc0 ls4 ws0">时刻负载电流的预测值为</div><div class="t m0 x1e h5 y163 ff6 fs0 fc0 sc0 ls0 ws0">：</div><div class="t m0 x8c h11 y167 ff9 fs0 fc0 sc0 ls0 ws0">i</div><div class="t m0 x122 he y168 ff3 fs6 fc0 sc0 ls0 ws0">pre</div><div class="t m0 x122 h14 y169 ff8 fs6 fc0 sc0 ls0 ws0">x</div><div class="t m0 x94 h5 y167 ff6 fs0 fc0 sc0 ls0 ws0">（<span class="_ _1f"> </span><span class="ff8">k</span></div><div class="t m0 x17 hb y16a ff3 fs0 fc0 sc0 ls0 ws0">+</div><div class="t m0 x18 h5 y16b ff3 fs0 fc0 sc0 ls0 ws0">2<span class="_ _3"></span><span class="ff6">）</span></div><div class="t m0 x36 hd y169 ff8 fs6 fc0 sc0 ls0 ws0">S<span class="ff6">（<span class="_ _8"> </span></span>k</div><div class="t m0 x123 he y16c ff3 fs6 fc0 sc0 ls0 ws0">+</div><div class="t m0 x124 hd y169 ff3 fs6 fc0 sc0 ls0 ws0">1<span class="ff6">）</span></div><div class="t m0 xa9 hb y16a ff3 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x101 h11 y167 ff9 fs0 fc0 sc0 ls0 ws0">i</div><div class="t m0 x110 h14 y169 ff8 fs6 fc0 sc0 ls0 ws0">x</div><div class="t m0 x125 h5 y167 ff6 fs0 fc0 sc0 ls0 ws0">（<span class="_ _1f"> </span><span class="ff8">k<span class="_ _3"></span></span>）</div><div class="t m0 x32 hd y169 ff8 fs6 fc0 sc0 ls0 ws0">S<span class="ff6">（<span class="_ _8"> </span></span>k</div><div class="t m0 x11f he y16c ff3 fs6 fc0 sc0 ls0 ws0">－</div><div class="t m0 x126 hd y169 ff3 fs6 fc0 sc0 ls0 ws0">1<span class="ff6">）</span></div><div class="t m0 x115 hb y16a ff3 fs0 fc0 sc0 ls0 ws0">+</div><div class="t m0 x81 h1a y16d ffb fs0 fc0 sc0 ls0 ws0">Δ</div><div class="t m0 x47 h11 y167 ff9 fs0 fc0 sc0 ls0 ws0">i</div><div class="t m0 x1f hd y169 ff8 fs6 fc0 sc0 ls0 ws0">x<span class="_ _26"> </span>S<span class="ff6">（<span class="_ _8"> </span></span>k<span class="ff6">）</span></div><div class="t m0 x97 hb y16a ff3 fs0 fc0 sc0 ls0 ws0">+</div><div class="t m0 x127 h1a y16d ffb fs0 fc0 sc0 ls0 ws0">Δ</div><div class="t m0 x88 h11 y167 ff9 fs0 fc0 sc0 ls0 ws0">i</div><div class="t m0 x118 hd y169 ff8 fs6 fc0 sc0 ls0 ws0">x<span class="_ _27"> </span>S<span class="ff6">（<span class="_ _8"> </span></span>k</div><div class="t m0 x33 he y16c ff3 fs6 fc0 sc0 ls0 ws0">+</div><div class="t m0 xb5 hd y169 ff3 fs6 fc0 sc0 ls0 ws0">1<span class="ff6">）</span></div><div class="t m0 xb5 h5 y16e ff6 fs0 fc0 sc0 ls0 ws0">（<span class="_ _6"> </span><span class="ff3">7<span class="_ _3"></span></span>）</div><div class="t m0 x7f h5 y16f ff6 fs0 fc0 sc0 ls0 ws0">其中</div><div class="t m0 x128 h5 y170 ff6 fs0 fc0 sc0 ls0 ws0">，<span class="_ _28"></span><span class="ff8">x</span></div><div class="t m0 x16 h15 y16f ffc fs0 fc0 sc0 ls0 ws0">∈</div><div class="t m0 x8e h5 y170 ff6 fs0 fc0 sc0 ls0 ws0">｛</div><div class="t m0 x129 h19 y16f ffe fs0 fc0 sc0 ls0 ws0">α</div><div class="t m0 x12a h5 y170 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x83 h19 y16f ffe fs0 fc0 sc0 ls0 ws0">β</div><div class="t m0 xfc h5 y170 ff6 fs0 fc0 sc0 ls0 ws0">｝<span class="_ _d"> </span>；<span class="_ _2"> </span><span class="ff8">S<span class="_"> </span></span>（<span class="_ _1f"> </span><span class="ff8">k<span class="_"> </span></span>）</div><div class="t m0 x110 h15 y16f ffc fs0 fc0 sc0 ls0 ws0">∈</div><div class="t m0 x12b h5 y170 ff6 fs0 fc0 sc0 ls0 ws0">｛<span class="_ _2"> </span><span class="ff8">S</span></div><div class="t m0 x12c he y171 ff3 fs6 fc0 sc0 ls0 ws0">1</div><div class="t m0 x10b h5 y170 ff6 fs0 fc0 sc0 ls0 ws0">，<span class="_ _16"></span><span class="ff8">S</span></div><div class="t m0 x8a he y171 ff3 fs6 fc0 sc0 ls0 ws0">2</div><div class="t m0 x12d h5 y170 ff6 fs0 fc0 sc0 ls0 ws0">，<span class="_ _16"></span><span class="fff">…<span class="ff6">，<span class="_ _16"></span><span class="ff8">S</span></span></span></div><div class="t m0 x1f he y171 ff3 fs6 fc0 sc0 ls0 ws0">27</div><div class="t m0 x12e h5 y170 ff6 fs0 fc0 sc0 ls0 ws0">｝<span class="_ _d"> </span>；<span class="_ _6"> </span><span class="ff9">i</span></div><div class="t m0 x12f h14 y171 ff8 fs6 fc0 sc0 ls0 ws0">x</div><div class="t m0 x11c h5 y170 ff6 fs0 fc0 sc0 ls0 ws0">（<span class="_ _1f"> </span><span class="ff8">k<span class="_ _3"></span></span>）</div><div class="t m0 x130 hd y171 ff8 fs6 fc0 sc0 ls0 ws0">S<span class="ff6">（<span class="_ _8"> </span></span>k</div><div class="t m0 x33 he ya9 ff3 fs6 fc0 sc0 ls0 ws0">－</div><div class="t m0 xb5 hd y171 ff3 fs6 fc0 sc0 ls0 ws0">1<span class="ff6">）</span></div><div class="t m0 x34 h5 y16f ff6 fs0 fc0 sc0 ls0 ws0">表</div><div class="t m0 x7f h5 y172 ff6 fs0 fc0 sc0 ls0 ws0">示在<span class="_ _3"></span>开关<span class="_ _3"></span>状态</div><div class="t m0 x26 h5 y173 ff8 fs0 fc0 sc0 ls0 ws0">S<span class="_ _3"></span><span class="ff6">（<span class="_ _1f"> </span></span>k</div><div class="t m0 x131 hb y174 ff3 fs0 fc0 sc0 ls0 ws0">－</div><div class="t m0 x110 h5 y173 ff3 fs0 fc0 sc0 ls0 ws0">1<span class="_ _3"></span><span class="ff6">）</span></div><div class="t m0 x9e h5 y172 ff6 fs0 fc0 sc0 ls0 ws0">的<span class="_ _3"></span>作<span class="_ _9"></span>用<span class="_ _3"></span>下</div><div class="t m0 x132 h5 y173 ff6 fs0 fc0 sc0 ls0 ws0">，<span class="_ _7"></span><span class="ff8">k</span></div><div class="t m0 x133 h5 y172 ff6 fs0 fc0 sc0 ls5 ws0">时刻的采样电流</div><div class="t m0 x7f h5 y175 ff6 fs0 fc0 sc0 ls0 ws0">值</div><div class="t m0 x8c h5 y176 ff6 fs0 fc0 sc0 ls0 ws0">，</div><div class="t m0 x8d h5 y175 ff6 fs0 fc0 sc0 ls0 ws0">同理</div><div class="t m0 x8e h5 y176 ff6 fs0 fc0 sc0 ls0 ws0">，<span class="_ _16"></span><span class="ff9">i</span></div><div class="t m0 x134 h14 y177 ff8 fs6 fc0 sc0 ls0 ws0">x</div><div class="t m0 x12a h5 y176 ff6 fs0 fc0 sc0 ls0 ws0">（<span class="_ _b"> </span><span class="ff8">k</span></div><div class="t m0 xff hb y178 ff3 fs0 fc0 sc0 ls0 ws0">+</div><div class="t m0 x123 h5 y176 ff3 fs0 fc0 sc0 ls0 ws0">1<span class="_ _3"></span><span class="ff6">）</span></div><div class="t m0 x101 hd y177 ff8 fs6 fc0 sc0 ls0 ws0">S<span class="ff6">（<span class="_ _8"> </span></span>k<span class="ff6">）</span></div><div class="t m0 xa1 ha y176 ff5 fs0 fc0 sc0 ls0 ws0">、<span class="_ _16"></span><span class="ff9">i</span></div><div class="t m0 xa5 h14 y177 ff8 fs6 fc0 sc0 ls0 ws0">x</div><div class="t m0 x86 h5 y176 ff6 fs0 fc0 sc0 ls0 ws0">（<span class="_ _1f"> </span><span class="ff8">k</span></div><div class="t m0 x8a hb y178 ff3 fs0 fc0 sc0 ls0 ws0">+</div><div class="t m0 x135 h5 y176 ff3 fs0 fc0 sc0 ls0 ws0">2<span class="_ _3"></span><span class="ff6">）</span></div><div class="t m0 x136 hd y177 ff8 fs6 fc0 sc0 ls0 ws0">S<span class="ff6">（<span class="_ _8"> </span></span>k</div><div class="t m0 x48 he y179 ff3 fs6 fc0 sc0 ls0 ws0">+</div><div class="t m0 x137 hd y177 ff3 fs6 fc0 sc0 ls0 ws0">1<span class="ff6">）</span></div><div class="t m0 x9a h5 y175 ff6 fs0 fc0 sc0 ls0 ws0">分<span class="_ _9"></span>别<span class="_ _9"></span>表<span class="_ _9"></span>示<span class="_ _9"></span>在<span class="_ _10"></span>开</div><div class="t m0 x7f h5 y17a ff6 fs0 fc0 sc0 ls0 ws0">关状<span class="_ _3"></span>态</div><div class="t m0 xba h5 y17b ff8 fs0 fc0 sc0 ls0 ws0">S<span class="_ _3"></span><span class="ff6">（<span class="_ _1f"> </span></span>k<span class="_ _3"></span><span class="ff6">）</span></div><div class="t m0 x36 h5 y17a ff6 fs0 fc0 sc0 ls0 ws0">和</div><div class="t m0 x124 h5 y17b ff8 fs0 fc0 sc0 ls0 ws0">S<span class="_ _3"></span><span class="ff6">（<span class="_ _b"> </span></span>k</div><div class="t m0 x138 hb y116 ff3 fs0 fc0 sc0 ls0 ws0">+</div><div class="t m0 xa0 h5 y17b ff3 fs0 fc0 sc0 ls0 ws0">1<span class="_ _3"></span><span class="ff6">）</span></div><div class="t m0 x103 h5 y17a ff6 fs0 fc0 sc0 ls0 ws0">的<span class="_ _3"></span>作<span class="_ _9"></span>用<span class="_ _9"></span>下</div><div class="t m0 x47 h5 y17b ff6 fs0 fc0 sc0 ls0 ws0">，<span class="_ _7"></span><span class="ff8">k</span></div><div class="t m0 xe hb y116 ff3 fs0 fc0 sc0 ls0 ws0">+</div><div class="t m0 x30 hb y17b ff3 fs0 fc0 sc0 ls0 ws0">1</div><div class="t m0 x97 h5 y17a ff6 fs0 fc0 sc0 ls0 ws0">和</div><div class="t m0 x139 hf y17b ff8 fs0 fc0 sc0 ls0 ws0">k</div><div class="t m0 x119 hb y116 ff3 fs0 fc0 sc0 ls0 ws0">+</div><div class="t m0 x8b hb y17b ff3 fs0 fc0 sc0 ls0 ws0">2</div><div class="t m0 x33 h5 y17a ff6 fs0 fc0 sc0 ls0 ws0">时<span class="_ _3"></span>刻</div></div><div class="pi" data-data='{"ctm":[1.612029,0.000000,0.000000,1.612029,-22.847616,-6.854301]}'></div></div>
