The Extension of Auxiliary Problem Principle for Solving Dynamic Economic Dispatch Problem in Power Systems

<table class="table-group" id="tab3"><tr><td><table class="table"><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr class="thead"><td class="align_left">Case</td><td class="align_center">Parameter</td><td class="align_center">Iteration</td><td class="align_center"><span style="width: 90.9303ptpx;"><svg height="14.5263pt" id="M140" style="vertical-align:-2.268101pt" version="1.1" viewbox="-0.0498162 -12.2582 90.9303 14.5263" width="90.9303pt" 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="M797 0V26C739 32 732 36 732 103V296C732 394 682 449 605 449C576 449 550 437 529 423C504 407 475 389 446 366C425 418 382 449 334 449C303 449 279 437 253 421C222 403 201 385 180 371V452C135 432 85 419 41 411V388C99 379 102 374 102 310V103C102 38 93 32 27 26V0H238V26C189 32 180 38 180 103V338C210 363 250 390 289 390C351 390 377 348 377 275V103C377 37 368 32 306 26V0H520V26C465 32 456 38 456 101V296C456 314 455 326 453 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230V280H52V230H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,68.354,0)"><path d="M689 332C689 394 670 448 646 448C620 448 597 421 597 396C597 386 600 381 608 372C619 359 620 334 620 315C620 150 538 45 454 45C414 45 386 67 386 122C386 138 388 158 394 180L457 426L452 432L377 416L315 156C302 100 259 45 216 45C176 45 148 67 148 122C148 133 152 158 156 180C162 212 173 259 194 332C201 357 206 384 206 405C206 430 198 448 174 448C125 448 66 406 23 342L43 319C84 368 110 383 121 383C126 383 128 382 128 377C128 370 127 359 122 343C99 268 84 204 77 156C74 137 70 111 70 104C70 25 125 -12 180 -12C228 -12 276 12 319 50C338 8 378 -12 418 -12C549 -12 689 166 689 332Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,77.611,-5.741)"><path d="M485 418C485 434 469 451 441 451C389 451 312 387 255 335C221 304 194 278 159 242H157L259 678C264 698 264 710 255 710C242 710 183 681 96 673L90 643L128 642C165 641 171 640 162 602L24 -5L31 -12C51 -4 81 4 110 9L145 181C154 195 180 220 205 242C233 170 263 106 291 53C318 1 335 -12 360 -12C383 -12 425 0 483 82L463 105C437 79 411 57 400 57C388 57 378 68 355 110C329 156 288 244 268 298C299 333 355 376 405 376C426 376 440 373 448 368C453 365 465 368 468 373C477 386 485 405 485 418Z"></path></g><g transform="matrix(.013,0,0,-0.013,82.759,0)"><path d="M162 -163V703H101V-163H162Z"></path></g><g transform="matrix(.013,0,0,-0.013,86.178,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"></path></g></svg></span></td></tr><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr><td class="align_left">Case1</td><td class="align_center"><i>c</i> = 1, <i>β</i> = 9.1<i>c</i></td><td class="align_center">Fail</td><td class="align_center">0.3987</td></tr><tr><td class="align_left">Case2</td><td class="align_center"><i>c</i> = 10, <i>β</i> = 9.1<i>c</i></td><td class="align_center">Fail</td><td class="align_center">0.0589</td></tr><tr><td class="align_left">Case3</td><td class="align_center"><i>c</i> = 100, <i>β</i> = 9.1<i>c</i></td><td class="align_center">Fail</td><td class="align_center">0.0061</td></tr><tr><td class="align_left">Case4</td><td class="align_center"><i>c</i> = 1000, <i>β</i> = 9.1<i>c</i></td><td class="align_center">Fail</td><td class="align_center">6.1481 × 10<sup>−4</sup></td></tr><tr><td class="align_left">Case5</td><td class="align_center"><i>c</i> = 10000, <i>β</i> <i>=</i> 9.1<i>c</i></td><td class="align_center">22</td><td class="align_center">6.2349 × 10<sup>−5</sup></td></tr><tr class="table-tr"><td colspan="4"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>The simulation results based on APP-like algorithm for test system.</div>

Journal of Mathematics

tab3

Table 3

Table 3: The Extension of Auxiliary Problem Principle for Solving Dynamic Economic Dispatch Problem in Power Systems 