An Optimization Model and Modified Harmony Search Algorithm for Microgrid Planning with ESS

<table class="table-group" id="tab1"><tr><td><table class="table"><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr class="thead"><td class="align_left" rowspan="2">Unit</td><td class="align_center" colspan="3">Parameter</td></tr><tr class="thead"><td class="align_center"><span style="width: 20.4566ptpx;"><svg height="14.1649pt" id="M139" style="vertical-align:-5.529pt" version="1.1" viewbox="-0.0498162 -8.6359 20.4566 14.1649" width="20.4566pt" 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="M645 631C614 643 545 666 457 666C215 666 23 519 23 283C23 90 158 -16 337 -16C412 -16 489 2 522 10C543 39 590 127 606 167L580 181C519 89 459 18 348 18C201 18 122 136 122 287C122 464 244 632 435 632C544 632 602 595 608 472L639 475C643 526 645 581 645 631Z" id="g113-68"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="668" vert-adv-y="668" xpluscharwidth="8.684"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,8.619,3.132)"><path d="M606 650H137L129 618C217 609 221 609 203 518L129 129C115 46 106 40 26 32L18 0H300L307 32C210 40 203 45 218 129L249 305H358C454 305 455 296 457 219H491L531 425H497C465 353 463 350 366 350H259L300 569C306 605 310 611 346 611H444C522 611 535 598 541 578C550 557 553 519 552 485L588 489L606 650Z" id="g50-71"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="630" vert-adv-y="630" xpluscharwidth="14.3519811"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,13.716,3.132)"><path d="M98 134C72 134 46 117 46 90C46 73 55 65 60 64C95 55 124 32 124 -4C124 -42 95 -68 44 -89L57 -123C122 -104 194 -60 194 22C194 94 136 134 98 134Z" id="g50-45"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="237" vert-adv-y="237" xpluscharwidth="15.87269289"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,15.873,3.132)"><path d="M400 606C400 634 383 656 353 656C316 656 294 620 294 593C294 564 317 545 343 545C375 545 400 573 400 606ZM366 351C379 413 381 451 356 451C323 451 251 408 183 341L199 313C223 335 267 365 277 365C285 365 284 354 277 312C245 132 222 27 193 -100C182 -148 160 -188 131 -188C113 -188 90 -178 75 -170C64 -164 55 -168 48 -175C38 -185 24 -203 24 -222S48 -257 71 -257C89 -257 131 -241 186 -192C243 -141 286 -46 310 74L366 351Z" id="g50-107"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="430" vert-adv-y="430" xpluscharwidth="19.7859871"></glyph.data></g></svg></span></td><td class="align_center"><span style="width: 27.1245ptpx;"><svg height="14.1649pt" id="M140" style="vertical-align:-5.529pt" version="1.1" viewbox="-0.0498162 -8.6359 27.1245 14.1649" width="27.1245pt" 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="M645 631C614 643 545 666 457 666C215 666 23 519 23 283C23 90 158 -16 337 -16C412 -16 489 2 522 10C543 39 590 127 606 167L580 181C519 89 459 18 348 18C201 18 122 136 122 287C122 464 244 632 435 632C544 632 602 595 608 472L639 475C643 526 645 581 645 631Z" id="g113-68"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="668" vert-adv-y="668" xpluscharwidth="8.684"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,8.619,3.132)"><path d="M46 650V618C122 613 130 611 130 522V128C130 46 123 40 40 32V0H319V32C227 40 217 42 217 128V279L292 260C303 259 322 258 338 261C436 272 534 337 534 467C534 534 508 580 469 609C428 640 371 650 299 650H46ZM217 558C217 585 220 596 228 603C235 610 256 615 284 615C367 615 435 571 435 463C435 339 358 304 291 304C256 304 229 310 217 317V558Z" id="g58-78"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="573" vert-adv-y="573" xpluscharwidth="13.83328281"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,13.833,3.132)"><path d="M698 650H468V617C551 609 555 599 536 543C506 457 432 264 379 129H377C311 297 238 488 212 560C196 604 198 609 271 617V650H21V617C80 612 98 603 127 532C183 396 268 173 335 -9H370C445 196 551 450 578 511C615 602 630 609 698 617V650Z" id="g58-84"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="717" vert-adv-y="717" xpluscharwidth="20.35767849"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,20.358,3.132)"><path d="M98 134C72 134 46 117 46 90C46 73 55 65 60 64C95 55 124 32 124 -4C124 -42 95 -68 44 -89L57 -123C122 -104 194 -60 194 22C194 94 136 134 98 134Z" id="g50-45"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="237" vert-adv-y="237" xpluscharwidth="22.51469289"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,22.515,3.132)"><path d="M400 606C400 634 383 656 353 656C316 656 294 620 294 593C294 564 317 545 343 545C375 545 400 573 400 606ZM366 351C379 413 381 451 356 451C323 451 251 408 183 341L199 313C223 335 267 365 277 365C285 365 284 354 277 312C245 132 222 27 193 -100C182 -148 160 -188 131 -188C113 -188 90 -178 75 -170C64 -164 55 -168 48 -175C38 -185 24 -203 24 -222S48 -257 71 -257C89 -257 131 -241 186 -192C243 -141 286 -46 310 74L366 351Z" id="g50-107"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="430" vert-adv-y="430" xpluscharwidth="26.427987100000003"></glyph.data></g></svg></span></td><td class="align_center"><span style="width: 23.2334ptpx;"><svg height="14.1649pt" id="M141" style="vertical-align:-5.529pt" version="1.1" viewbox="-0.0498162 -8.6359 23.2334 14.1649" width="23.2334pt" 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="M645 631C614 643 545 666 457 666C215 666 23 519 23 283C23 90 158 -16 337 -16C412 -16 489 2 522 10C543 39 590 127 606 167L580 181C519 89 459 18 348 18C201 18 122 136 122 287C122 464 244 632 435 632C544 632 602 595 608 472L639 475C643 526 645 581 645 631Z" id="g113-68"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="668" vert-adv-y="668" xpluscharwidth="8.684"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,8.619,3.132)"><path d="M1013 650H775L768 618L793 615C853 608 859 601 837 545C792 433 708 266 639 131H637L537 639H503L251 132H249L190 552C183 602 190 607 235 614L262 618L269 650H25L18 618C92 610 95 608 107 525L184 -9H221L475 494H479L576 -9H613L884 526C928 607 934 609 1005 618L1013 650Z" id="g50-88"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="1025" vert-adv-y="1025" xpluscharwidth="17.94646925"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,16.482,3.132)"><path d="M98 134C72 134 46 117 46 90C46 73 55 65 60 64C95 55 124 32 124 -4C124 -42 95 -68 44 -89L57 -123C122 -104 194 -60 194 22C194 94 136 134 98 134Z" id="g50-45"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="237" vert-adv-y="237" xpluscharwidth="18.63869289"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,18.639,3.132)"><path d="M400 606C400 634 383 656 353 656C316 656 294 620 294 593C294 564 317 545 343 545C375 545 400 573 400 606ZM366 351C379 413 381 451 356 451C323 451 251 408 183 341L199 313C223 335 267 365 277 365C285 365 284 354 277 312C245 132 222 27 193 -100C182 -148 160 -188 131 -188C113 -188 90 -178 75 -170C64 -164 55 -168 48 -175C38 -185 24 -203 24 -222S48 -257 71 -257C89 -257 131 -241 186 -192C243 -141 286 -46 310 74L366 351Z" id="g50-107"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="430" vert-adv-y="430" xpluscharwidth="22.551987099999998"></glyph.data></g></svg></span></td></tr><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr><td class="align_left">DG<sub>1</sub></td><td class="align_center">0.35 yuan/kWh</td><td class="align_center">—</td><td class="align_center">—</td></tr><tr><td class="align_left">DG<sub>2</sub></td><td class="align_center">0.35 yuan/kWh</td><td class="align_center">—</td><td class="align_center">—</td></tr><tr><td class="align_left">DG<sub>3</sub></td><td class="align_center">—</td><td class="align_center">0.95 yuan/kWh</td><td class="align_center">—</td></tr><tr><td class="align_left">DG<sub>4</sub></td><td class="align_center">—</td><td class="align_center">—</td><td class="align_center">0.55 yuan/kWh</td></tr><tr class="table-tr"><td colspan="4"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Parameter values of the DG units in the MG.

Discrete Dynamics in Nature and Society

tab1

Table 1

Table 1: An Optimization Model and Modified Harmony Search Algorithm for Microgrid Planning with ESS 