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

<table class="table-group" id="tab12"><tr><td><table class="table"><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr class="thead"><td class="align_left">Type of generator</td><td class="align_center"><span style="width: 51.851ptpx;"><svg height="11.439pt" id="M282" 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></span></td></tr><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr><td class="align_left">Candidate wind generator <svg height="15.2199pt" id="M283" style="vertical-align:-3.2957pt" version="1.1" viewbox="-0.0498162 -11.9242 15.8934 15.2199" width="15.8934pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,.705,-2.897)"><path d="M470 619L451 641C422 610 391 595 348 595C316 595 288 601 248 612C197 628 172 633 138 633C97 633 43 615 0 555L19 532C54 562 86 578 130 578C166 578 189 571 222 562C267 549 301 540 337 540C381 540 434 557 470 619Z" id="g119-25"></path></g><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M405 650H141L135 622C222 616 230 610 215 535L133 116C118 41 113 33 29 28L23 0H289L295 28C209 33 205 40 219 116L298 535C312 609 317 616 399 622L405 650Z" id="g113-74"></path></g><g transform="matrix(.0091,0,0,-0.0091,4.719,3.132)"><path d="M396 114C349 71 317 59 274 59C216 59 123 104 123 241C123 342 180 400 246 400C283 400 317 386 348 359C355 352 361 348 366 348C378 348 401 371 402 394C402 405 398 413 385 424C369 437 337 451 294 451H293C254 451 193 434 141 394C73 342 39 277 39 198C39 90 114 -12 243 -12C303 -12 371 31 415 90L396 114Z" id="g58-97"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.796,3.132)"><path d="M708 439H523V409C587 401 594 395 581 344C562 272 534 184 513 118H511C468 225 428 330 391 434H361C318 317 283 217 244 121H242C218 196 193 273 170 349C157 394 160 401 220 409V439H10V409C60 403 67 394 86 343C127 224 165 109 201 -10H233C273 101 314 199 353 299C393 195 432 99 475 -10H507C554 126 596 251 627 334C648 390 657 401 708 409V439Z" id="g58-117"></path></g></svg></td><td class="align_center">700,000</td></tr><tr><td class="align_left">Candidate conventional generator <svg height="15.2153pt" id="M284" style="vertical-align:-3.2911pt" version="1.1" viewbox="-0.0498162 -11.9242 9.08855 15.2153" width="9.08855pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,.705,-2.897)"><path d="M470 619L451 641C422 610 391 595 348 595C316 595 288 601 248 612C197 628 172 633 138 633C97 633 43 615 0 555L19 532C54 562 86 578 130 578C166 578 189 571 222 562C267 549 301 540 337 540C381 540 434 557 470 619Z" id="g119-25"></path></g><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M405 650H141L135 622C222 616 230 610 215 535L133 116C118 41 113 33 29 28L23 0H289L295 28C209 33 205 40 219 116L298 535C312 609 317 616 399 622L405 650Z" id="g113-74"></path></g><g transform="matrix(.0091,0,0,-0.0091,4.719,3.132)"><path d="M387 400C387 425 348 451 303 451C247 451 176 414 132 376C69 322 24 228 24 148C24 43 74 -12 147 -12C211 -12 301 33 363 103L346 128C319 99 249 51 193 51C148 51 112 84 112 165C112 230 130 287 154 330C170 359 199 400 243 400C277 400 304 383 326 354C333 345 343 343 354 348C378 360 387 382 387 400Z" id="g50-100"></path></g></svg></td><td class="align_center">700,000</td></tr><tr class="table-tr"><td colspan="2"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Complexity

tab12

Table 12

Table 12: Analysis of Constraint-Handling in Metaheuristic Approaches for the Generation and Transmission Expansion Planning Problem with Renewable Energy 

Table 12 | Analysis of Constraint-Handling in Metaheuristic Approaches for the Generation and Transmission Expansion Planning Problem with Renewable Energy 