Analysis of Constraint-Handling in Metaheuristic Approaches for the Generation and Transmission Expansion Planning Problem with Renewable Energy

<table class="table-group" id="tab10"><tr><td><table class="table"><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr class="thead"><td class="align_left">Operating condition</td><td class="align_center">Hours</td><td class="align_center">Cost <svg height="11.439pt" id="M274" style="vertical-align:-2.15067pt" version="1.1" viewbox="-0.0498162 -9.28833 51.851 11.439" width="51.851pt" 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="M290 -163V-135C183 -126 181 -122 181 -44V583C181 662 184 666 290 675V703H120V-163H290Z" id="g113-92"></path></g><g transform="matrix(.013,0,0,-0.013,4.485,0)"><path d="M263 363V584C343 572 363 521 380 464L408 470C399 526 392 562 387 596C376 598 367 601 353 604C328 612 296 617 263 617V693H228V615C122 603 67 532 67 453C67 376 123 329 193 300L228 284V41C132 52 93 131 75 189L45 181C54 130 66 71 73 50C113 24 170 9 228 9V-76H263V11C370 24 434 90 434 185C434 275 367 325 292 352L263 363ZM228 376C171 398 136 431 136 484C136 530 164 578 228 584V376ZM263 272L275 267C345 236 359 196 359 150C359 96 325 50 263 42V272Z"></path></g><g transform="matrix(.013,0,0,-0.013,10.748,0)"><path d="M368 703H309L44 -163H104L368 703Z" id="g113-48"></path></g><g transform="matrix(.013,0,0,-0.013,16.11,0)"><path d="M861 0V28C774 35 771 41 768 147L759 509C756 612 762 614 851 622V650H681L449 149L221 650H57V622C148 613 153 609 144 479L130 271C123 166 117 123 111 88C104 46 85 34 26 28V0H259V28C192 35 169 42 167 90C166 130 166 173 170 256L185 541H187L411 7H431L675 555H679L683 147C683 41 680 35 598 28V0H861Z" id="g121-75"></path></g><g transform="matrix(.013,0,0,-0.013,27.692,0)"><path d="M956 650H736V622C814 613 818 602 804 542C789 471 733 275 691 141H689C628 314 570 476 514 641H485C434 478 377 312 323 142H321C277 284 238 419 199 554C184 605 186 613 259 622V650H16V622C77 615 92 606 117 524C172 346 228 170 281 -11H312C363 151 419 312 475 488H477C528 343 597 150 652 -11H683C765 269 826 458 848 522C878 605 887 613 956 622V650Z" id="g121-85"></path></g><g transform="matrix(.013,0,0,-0.013,40.159,0)"><path d="M513 0V26C455 31 447 37 447 103V278C447 398 390 449 309 449C255 449 202 412 166 376V712C127 700 67 684 19 677V653C85 647 87 643 87 580V103C87 37 79 31 19 26L18 0H231V26C171 32 166 39 166 103V341C194 373 232 392 270 392C337 392 368 351 368 269V103C368 38 360 32 302 26V0H513Z" id="g121-102"></path></g><g transform="matrix(.013,0,0,-0.013,47.101,0)"><path d="M226 -163V703H56V676C162 667 165 662 165 584V-43C165 -122 162 -126 56 -136V-163H226Z" id="g113-94"></path></g></svg></td></tr><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr><td class="align_left"><span style="width: 11.0876ptpx;"><svg height="9.14241pt" id="M275" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -5.96091 11.0876 9.14241" width="11.0876pt" 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="M445 282C445 390 384 448 297 448C266 448 231 437 189 418C96 376 23 279 23 151C23 65 66 -12 169 -12C233 -12 294 18 337 53C411 113 445 201 445 282ZM355 280C355 161 302 62 243 36C231 31 219 30 207 30C147 30 111 78 111 154C111 302 180 380 220 399C231 404 246 407 264 407C311 407 355 367 355 280Z" id="g113-112"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.019,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path></g></svg></span></td><td class="align_center">6000</td><td class="align_center">100</td></tr><tr><td class="align_left"><span style="width: 11.0876ptpx;"><svg height="9.14241pt" id="M276" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -5.96091 11.0876 9.14241" width="11.0876pt" 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="M445 282C445 390 384 448 297 448C266 448 231 437 189 418C96 376 23 279 23 151C23 65 66 -12 169 -12C233 -12 294 18 337 53C411 113 445 201 445 282ZM355 280C355 161 302 62 243 36C231 31 219 30 207 30C147 30 111 78 111 154C111 302 180 380 220 399C231 404 246 407 264 407C311 407 355 367 355 280Z" id="g113-112"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.019,3.132)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z" id="g50-51"></path></g></svg></span></td><td class="align_center">2760</td><td class="align_center">100</td></tr><tr class="table-tr"><td colspan="3"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Time for each operating condition and weighting factor for each operating condition not satisfying clean energy’s goal.</div>

Complexity

tab10

Table 10

Table 10: Analysis of Constraint-Handling in Metaheuristic Approaches for the Generation and Transmission Expansion Planning Problem with Renewable Energy 

Table 10 | Analysis of Constraint-Handling in Metaheuristic Approaches for the Generation and Transmission Expansion Planning Problem with Renewable Energy 