A MapReduce Based High Performance Neural Network in Enabling Fast Stability Assessment of Power Systems

<table class="table-group" id="tab8"><tr><td><table class="table"><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr class="thead"><td class="align_left" rowspan="2"> </td><td class="align_center" colspan="2"> 68-node system</td><td class="align_center" colspan="2"> Sichuan power grid</td></tr><tr class="thead"><td class="align_center">Stable</td><td class="align_center">Unstable</td><td class="align_center">Stable</td><td class="align_center">Unstable</td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td class="align_left"><i>N</i>-1</td><td class="align_center">688</td><td class="align_center">112</td><td class="align_center">758</td><td class="align_center">42</td></tr><tr><td class="align_left"><i>N</i>-2</td><td class="align_center">621</td><td class="align_center">179</td><td class="align_center">682</td><td class="align_center">118</td></tr><tr><td class="align_left"><i>N</i>-<i>k</i>  <svg height="11.5564pt" id="M141" style="vertical-align:-2.26807pt" version="1.1" viewbox="-0.0498162 -9.28833 36.8796 11.5564" width="36.8796pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,4.498,0)"><path d="M480 416C480 431 465 448 438 448C388 448 312 383 252 330C217 299 188 273 155 237H153L257 680C262 700 263 712 253 712C240 712 183 684 97 674L92 648L126 647C166 646 172 645 163 606L23 -6L29 -12C51 -5 77 2 107 8C115 62 130 128 142 180C153 193 179 220 204 241C231 170 259 106 288 54C317 0 336 -12 358 -12C381 -12 423 2 477 80L460 100C434 74 408 54 398 54C385 54 374 65 351 107C326 154 282 241 263 299C296 332 351 377 403 377C424 377 436 372 445 368C449 366 456 368 462 375C472 386 480 402 480 416Z" id="g113-108"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="503" vert-adv-y="503"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,14.669,0)"><path d="M531 285V335L57 550V494L473 310L57 127V71L531 285ZM531 -40V10H57V-40H531Z" id="g117-94"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,25.932,0)"><path d="M285 378C315 398 338 416 353 432C373 451 384 474 384 503C384 579 325 635 236 635H235C182 635 136 610 108 579L65 516L85 496C110 533 150 575 205 575C258 575 300 543 300 481C300 407 232 369 141 339L147 310C163 315 188 321 211 321C268 321 338 284 338 192C338 94 288 40 217 40C160 40 119 68 93 91C85 98 77 97 69 91C60 84 47 71 46 58C44 46 48 35 62 22C75 10 116 -12 162 -12C234 -12 424 62 424 224C424 297 373 359 285 376V378Z" id="g113-52"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,32.172,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data></g></svg></td><td class="align_center">436</td><td class="align_center">364</td><td class="align_center">523</td><td class="align_center">277</td></tr><tr class="table-tr"><td colspan="5"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Mathematical Problems in Engineering

tab8

Table 8

Table 8: A MapReduce Based High Performance Neural Network in Enabling Fast Stability Assessment of Power Systems 