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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/62c53fa1a7803f6965b7711a/bg1.jpg"><div class="c x0 y1 w2 h0"><div class="t m0 x1 h2 y2 ff1 fs0 fc0 sc0 ls0 ws0">Matlab Code of R<span class="_ _0"></span>obust Gener<span class="_ _0"></span>alized Maximum-likelihood </div><div class="t m0 x2 h2 y3 ff1 fs0 fc0 sc0 ls0 ws0">Estimator f<span class="_ _0"></span>or P<span class="_ _0"></span>ow<span class="_ _0"></span>er S<span class="_ _0"></span>yst<span class="_ _0"></span>em State Est<span class="_ _0"></span>imator using Pr<span class="_ _0"></span>ojection </div><div class="t m0 x3 h2 y4 ff1 fs0 fc0 sc0 ls0 ws0">Statistics<span class="ff2"> </span></div><div class="t m0 x4 h2 y5 ff1 fs0 fc0 sc0 ls0 ws0">Junbo Zhao, Lamine Mili<span class="ff2"> </span></div><div class="t m0 x5 h3 y6 ff1 fs1 fc0 sc0 ls0 ws0">R<span class="_ _0"></span>obust <span class="_ _1"></span>power <span class="_ _1"></span>s<span class="_ _0"></span>yst<span class="_ _0"></span>em <span class="_ _1"></span>state <span class="_ _1"></span>estimator <span class="_ _1"></span>is <span class="_ _1"></span>of <span class="_ _1"></span>vital <span class="_ _1"></span>importance <span class="_ _1"></span>f<span class="_ _0"></span>or <span class="_ _1"></span>monitoring <span class="_ _1"></span>and </div><div class="t m0 x5 h3 y7 ff1 fs1 fc0 sc0 ls0 ws0">control <span class="_ _0"></span>applications. Based <span class="ls1">on</span> <span class="_ _0"></span>our <span class="_ _0"></span>experience, w<span class="_ _0"></span>e find<span class="_ _0"></span> that the <span class="_ _0"></span>robust <span class="_ _0"></span>gener<span class="_ _0"></span>alized </div><div class="t m0 x5 h3 y8 ff1 fs1 fc0 sc0 ls0 ws0">maximum-lik<span class="_ _0"></span>elihood <span class="_ _2"></span>(GM)-estimator <span class="_ _2"></span>using <span class="_ _2"></span>pro<span class="_ _0"></span>jection <span class="_ _2"></span>statistics <span class="_ _2"></span>is <span class="_ _2"></span>one of <span class="_ _2"></span>the <span class="_ _2"></span>best </div><div class="t m0 x5 h3 y9 ff1 fs1 fc0 sc0 ls0 ws0">method <span class="_ _1"></span>in <span class="_ _1"></span>the <span class="_ _1"></span>liter<span class="_ _0"></span>atur<span class="_ _0"></span>e<span class="ls2">. <span class="_ _3"></span></span><span class="sc1">It <span class="_ _3"></span>is <span class="_ _3"></span>rob<span class="_ _0"></span>u<span class="_ _0"></span>st <span class="_ _3"></span>to<span class="_ _0"></span> <span class="_ _3"></span>mult<span class="_ _0"></span>iple<span class="_ _0"></span> <span class="_ _3"></span>inter<span class="_ _4"></span>ac<span class="_ _4"></span>ting <span class="_ _3"></span>and<span class="_ _4"></span> <span class="_ _1"></span>conf<span class="_ _4"></span>orm<span class="_ _4"></span>ing <span class="_ _1"></span>ba<span class="_ _4"></span>d </span></div><div class="t m0 x5 h3 ya ff1 fs1 fc0 sc1 ls0 ws0">dat<span class="_ _0"></span>a, <span class="_ _4"></span>bad <span class="_ _4"></span>le<span class="_ _4"></span>ver<span class="_ _4"></span>age<span class="_ _0"></span> <span class="_ _4"></span>poin<span class="_ _4"></span>ts, b<span class="_ _0"></span>ad<span class="_ _0"></span> <span class="_ _4"></span>zer<span class="_ _4"></span>o in<span class="_ _4"></span>jecti<span class="_ _4"></span>ons <span class="_ _4"></span>as <span class="_ _4"></span>well<span class="_ _4"></span> as<span class="_ _4"></span> s<span class="_ _0"></span>ome <span class="_ _4"></span>typ<span class="_ _4"></span>es <span class="_ _4"></span>of <span class="_ _4"></span>cybe<span class="_ _4"></span>r a<span class="_ _0"></span>tta<span class="_ _4"></span>cks<span class="sc0 ls3">. </span></div><div class="t m0 x5 h3 yb ff1 fs1 fc0 sc0 ls0 ws0">In <span class="_ _5"> </span>addition, <span class="_ _5"> </span><span class="sc1">its <span class="_ _5"> </span>com<span class="_ _4"></span>pu<span class="_ _4"></span>ting <span class="_ _5"> </span>eff<span class="_ _4"></span>icien<span class="_ _4"></span>cy <span class="_ _5"> </span>is <span class="_ _5"> </span>h<span class="_ _4"></span>igh <span class="_ _5"> </span>t<span class="_ _4"></span>hat <span class="_ _5"> </span>ma<span class="_ _4"></span>ke<span class="_ _4"></span>s <span class="_ _5"> </span>it <span class="_ _5"> </span>suitab<span class="_ _4"></span>le <span class="_ _5"> </span>fo<span class="_ _4"></span>r <span class="_ _5"> </span>onli<span class="_ _0"></span>ne<span class="_ _4"></span> </span></div><div class="t m0 x5 h3 yc ff1 fs1 fc0 sc1 ls0 ws0">appl<span class="_ _4"></span>ication<span class="_ _4"></span>s<span class="sc0 ls2">. <span class="ls0">Besides the good <span class="_ _2"></span>break<span class="_ _4"></span>down <span class="_ _2"></span>point of the <span class="_ _2"></span>GM-est<span class="_ _2"></span>imator<span class="_ _6"></span>, it<span class="_ _2"></span> has <span class="_ _2"></span><span class="sc1">a hig<span class="_ _4"></span>h </span></span></span></div><div class="t m0 x5 h3 yd ff1 fs1 fc0 sc1 ls0 ws0">stat<span class="_ _4"></span>istica<span class="_ _4"></span>l <span class="_ _7"> </span>eff<span class="_ _4"></span>icien<span class="_ _4"></span>cy <span class="_ _8"> </span>und<span class="_ _4"></span>er <span class="_ _8"> </span>Ga<span class="_ _4"></span>ussian<span class="_ _4"></span> <span class="_ _8"> </span>or <span class="_ _8"> </span>ot<span class="_ _0"></span>her<span class="_ _4"></span> <span class="_ _8"> </span>thick<span class="_ _4"></span>-ta<span class="_ _4"></span>iled <span class="_ _8"> </span>n<span class="_ _4"></span>on-Ga<span class="_ _4"></span>ussia<span class="_ _0"></span>n </div><div class="t m0 x5 h3 ye ff1 fs1 fc0 sc1 ls0 ws0">mea<span class="_ _4"></span>sure<span class="_ _4"></span>men<span class="_ _4"></span>t <span class="_ _9"> </span>no<span class="_ _4"></span>ise<span class="sc0 ls2">. <span class="_ _9"> </span><span class="ls0">The <span class="_ _a"> </span>original <span class="_ _a"> </span>version <span class="_ _a"> </span>of <span class="_ _9"> </span>the <span class="_ _9"> </span>GM-estimator <span class="_ _a"> </span>using <span class="_ _9"> </span>SCAD<span class="_ _4"></span>A </span></span></div><div class="t m0 x5 h3 yf ff1 fs1 fc0 sc0 ls0 ws0">measurements w<span class="_ _4"></span>as proposed by Mili and his co<span class="_ _4"></span>lleagues in 1996 [1]<span class="ls2">. <span class="_ _a"> </span></span> <span class="_ _5"> </span><span class="ff2"> </span></div><div class="t m0 x5 h3 y10 ff2 fs1 fc0 sc0 ls0 ws0"> </div><div class="t m0 x5 h3 y11 ff1 fs1 fc0 sc0 ls0 ws0">Here, <span class="_ _4"></span>w<span class="_ _4"></span>e <span class="_ _4"></span>would <span class="_ _b"></span>lik<span class="_ _0"></span>e <span class="_ _b"></span>to <span class="_ _4"></span>shar<span class="_ _0"></span>e <span class="_ _b"></span>the <span class="_ _4"></span>Matlab <span class="_ _4"></span>code <span class="_ _b"></span>of <span class="_ _b"></span>the <span class="_ _4"></span>GM<span class="_ _2"></span>-estimator <span class="_ _b"></span>to <span class="_ _b"></span>all <span class="_ _b"></span>research<span class="_ _0"></span>ers<span class="ls3">. </span></div><div class="t m0 x5 h3 y12 ff1 fs1 fc0 sc0 ls0 ws0">W<span class="_ _b"></span>e also <span class="_ _4"></span>invite <span class="_ _4"></span>each of <span class="_ _4"></span>you <span class="_ _4"></span>to <span class="_ _0"></span>test <span class="_ _4"></span>the method <span class="_ _4"></span>an<span class="_ _2"></span>d <span class="_ _4"></span>giv<span class="_ _4"></span>e us <span class="_ _4"></span>your <span class="_ _4"></span>feedback if <span class="_ _4"></span>you<span class="_ _0"></span> ha<span class="_ _4"></span>ve </div><div class="t m0 x5 h3 y13 ff1 fs1 fc0 sc0 ls0 ws0">any<span class="_ _6"></span>. The <span class="_ _4"></span>code <span class="_ _4"></span>attached is <span class="_ _4"></span>to <span class="_ _4"></span>implement<span class="_ _2"></span> <span class="_ _4"></span>the GM-estimator <span class="_ _b"></span>proposed <span class="_ _4"></span>by <span class="_ _0"></span>Mili <span class="_ _4"></span>in<span class="_ _2"></span> <span class="_ _4"></span>[R1]. </div><div class="t m0 x5 h3 y14 ff1 fs1 fc0 sc0 ls0 ws0">The <span class="_ _2"></span>test <span class="_ _c"></span>sy<span class="_ _4"></span>stems <span class="_ _c"></span>include <span class="_ _c"></span>IEEE <span class="_ _2"></span>14<span class="_ _2"></span>-bus, <span class="_ _c"></span>30-bus <span class="_ _2"></span>and <span class="_ _c"></span>11<span class="_ _0"></span>8-bus <span class="_ _c"></span>sy<span class="_ _4"></span>stems. <span class="_ _c"></span>Only <span class="_ _2"></span>SCAD<span class="_ _4"></span>A </div><div class="t m0 x5 h3 y15 ff1 fs1 fc0 sc0 ls0 ws0">measurements ar<span class="_ _0"></span>e included. W<span class="_ _b"></span>e hav<span class="_ _4"></span>e included detailed comments of the code. <span class="_ _a"> </span><span class="ff2"> </span></div><div class="t m0 x5 h3 y16 ff2 fs1 fc0 sc0 ls0 ws0"> </div><div class="t m0 x5 h3 y17 ff1 fs1 fc0 sc1 ls0 ws0">Wh<span class="_ _0"></span>en <span class="_ _4"></span>you<span class="_ _4"></span> use <span class="_ _4"></span>this c<span class="_ _0"></span>ode<span class="_ _0"></span> f<span class="_ _0"></span>or <span class="_ _4"></span>you<span class="_ _4"></span>r futu<span class="_ _4"></span>re r<span class="_ _4"></span>esea<span class="_ _4"></span>rc<span class="_ _4"></span>h and <span class="_ _4"></span>public<span class="_ _4"></span>ation<span class="_ _4"></span>s<span class="_ _2"></span><span class="sc0 ls2">, <span class="_ _4"></span><span class="sc1 ls0">we w<span class="_ _4"></span>ould<span class="_ _4"></span> </span></span></div><div class="t m0 x5 h3 y18 ff1 fs1 fc0 sc1 ls0 ws0">app<span class="_ _4"></span>recia<span class="_ _4"></span>te i<span class="_ _4"></span>f yo<span class="_ _4"></span>u cit<span class="_ _4"></span>e the<span class="_ _4"></span> two<span class="_ _4"></span> paper<span class="_ _4"></span>s [R1<span class="_ _4"></span>-R2]<span class="sc0">. Please let us know if y<span class="_ _4"></span>ou hav<span class="_ _4"></span>e any </span></div><div class="t m0 x5 h3 y19 ff1 fs1 fc0 sc0 ls0 ws0">problems in using this cod<span class="_ _4"></span>e.<span class="_ _2"></span> Y<span class="_ _b"></span>ou<span class="_ _0"></span>r feedback and<span class="_ _0"></span> comments are highl<span class="_ _4"></span>y appreciated.<span class="ff2"> </span></div><div class="t m0 x5 h3 y1a ff2 fs1 fc0 sc0 ls0 ws0"> </div><div class="t m0 x5 h3 y1b ff1 fs1 fc0 sc0 ls0 ws0">Best reg<span class="_ _0"></span>ards,<span class="ff2"> </span></div><div class="t m0 x5 h3 y1c ff1 fs1 fc0 sc0 ls0 ws0">Junbo Zhao and Lamine Mili<span class="ff2"> </span></div><div class="t m0 x5 h3 y1d ff2 fs1 fc0 sc0 ls0 ws0"> </div><div class="t m0 x5 h3 y1e ff1 fs1 fc0 sc0 ls0 ws0">Email: <span class="fc1">zjunbo@vt.edu</span><span class="ls2">, </span><span class="fc1">lmili@vt<span class="_ _2"></span>.edu</span> <span class="_ _d"> </span><span class="ff2"> </span></div><div class="t m0 x5 h3 y1f ff1 fs1 fc0 sc0 ls0 ws0">Br<span class="_ _4"></span>adley Department of Electrical an<span class="_ _2"></span>d Comput<span class="_ _4"></span>er E<span class="_ _2"></span>ngineering <span class="_ _d"> </span><span class="ff2"> </span></div><div class="t m0 x5 h3 y20 ff1 fs1 fc0 sc0 ls0 ws0">Virginia P<span class="_ _4"></span>olyt<span class="_ _0"></span>echnic Institute and State Uni<span class="_ _0"></span>v<span class="_ _4"></span>ersity<span class="_ _2"></span><span class="ff2"> </span></div><div class="t m0 x5 h3 y21 ff2 fs1 fc0 sc0 ls0 ws0"> </div><div class="t m0 x5 h3 y22 ff1 fs1 fc0 sc0 ls0 ws0">[R1] L. Mili, M. Cheniae, N. Vichar<span class="_ _4"></span>e,<span class="_ _2"></span> and P<span class="_ _e"></span>. Rousseeu<span class="_ _4"></span>w<span class="_ _b"></span>, ``R<span class="_ _4"></span>obust state estimati<span class="_ _2"></span>on </div><div class="t m0 x6 h3 y23 ff1 fs1 fc0 sc0 ls0 ws0">based on projection statistics,<span class="_ _b"></span>" IEEE T<span class="_ _b"></span>rans. Po<span class="_ _4"></span>wer Sy<span class="_ _4"></span>st<span class="_ _2"></span>, v<span class="_ _4"></span>ol. 11, no.<span class="_ _2"></span> 2, p<span class="_ _2"></span>p<span class="ls2">. </span></div><div class="t m0 x6 h3 y24 ff1 fs1 fc0 sc0 ls0 ws0">1118<span class="ls4">--</span>1127, 1996.<span class="ff2"> </span></div><div class="t m0 x5 h3 y25 ff1 fs1 fc0 sc0 ls0 ws0">[R2] J. B. <span class="_ _d"> </span> <span class="_ _d"> </span>Zhao, M. Netto, L. Mili, "<span class="_ _e"></span>A robust iter<span class="_ _4"></span>ated ext<span class="_ _4"></span>en<span class="_ _2"></span>ded Kalman filter for </div><div class="t m0 x6 h3 y26 ff1 fs1 fc0 sc0 ls0 ws0">power s<span class="_ _0"></span>yst<span class="_ _0"></span>em d<span class="_ _0"></span>ynamic state estimation<span class="_ _0"></span>", IEEE T<span class="_ _4"></span>r<span class="_ _4"></span>an<span class="_ _2"></span>s. on Pow<span class="_ _4"></span>er Syst<span class="_ _4"></span>ems, </div><div class="t m0 x6 h3 y27 ff1 fs1 fc0 sc0 ls0 ws0">DOI:10.1109/TPWR<span class="_ _4"></span>S.<span class="_ _2"></span>2016.262834<span class="_ _0"></span>4, in press.<span class="ff2"> </span></div></div><a class="l" rel='nofollow' onclick='return false;'><div class="d m1"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m1"></div></a></div><div class="pi" data-data='{"ctm":[1.611792,0.000000,0.000000,1.611792,0.000000,0.000000]}'></div></div>
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