Operation of Parallel Inverters in Microgrid Using New Adaptive PI Controllers Based on Least Mean Fourth Technique

<table class="fixed-width table-group" id="tab1"><tr><td><table class="table"><colgroup><col style="width:18.06em"/><col style="width:13.95em"/></colgroup><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr class="thead"><td class="align_left">Parameter/Description</td><td class="align_center">Values</td></tr><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr><td class="align_left">Voltage level</td><td class="align_center">= 6.6 kV</td></tr><tr><td class="align_left">Microgrid rating/base</td><td class="align_center">= 2.5 MVA</td></tr><tr><td class="align_left">Power Rating/inverter</td><td class="align_center">= 0.75MVA</td></tr><tr><td class="align_left">Feeder impedance <svg height="14.4911pt" id="M9" style="vertical-align:-5.52898pt" version="1.1" viewbox="-0.0498162 -8.96212 15.4446 14.4911" width="15.4446pt" 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="M669 636L663 650H260C230 650 221 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class="align_left">Transformer Tr<sub>1</sub>, Tr<sub>2</sub> rating</td><td class="align_center">= 2.5 MVA</td></tr><tr><td class="align_left">Transformer Tr<sub>1</sub> voltage ratio</td><td class="align_center">= <svg height="9.49473pt" id="M11" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -9.28833 86.2559 9.49473" width="86.2559pt" 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="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"></path></g><g transform="matrix(.013,0,0,-0.013,6.24,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,9.204,0)"><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 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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"></path></g><g transform="matrix(.013,0,0,-0.013,32.663,0)"><path d="M697 650H468L461 623L492 619C539 613 547 605 518 546C481 471 367 264 278 116H276C239 278 197 500 186 567C180 604 185 613 226 619L252 623L260 650H24L17 623C78 617 92 613 108 533L216 -11H247C365 200 515 462 560 529C616 612 624 615 689 623L697 650Z"></path></g><g transform="matrix(.013,0,0,-0.013,43.822,0)"><path d="M116 412C83 412 59 388 59 355C59 321 83 297 115 297S170 321 170 355C170 388 147 412 116 412ZM114 -12C147 -12 171 11 171 46C171 78 147 103 115 103C84 103 60 78 60 46C60 11 84 -12 114 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,50.418,0)"><path d="M137 343C167 482 260 545 321 574C357 591 397 603 429 609L423 641C382 634 335 622 295 608C189 570 37 457 37 238C37 84 125 -12 242 -12C362 -12 447 89 447 209C447 311 374 393 267 393C247 393 226 386 204 376L137 343ZM227 337C318 337 361 256 361 173C361 105 336 22 258 22C176 22 126 120 126 240C126 266 127 291 132 310C155 323 189 337 227 337Z"></path></g><g transform="matrix(.013,0,0,-0.013,56.658,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,59.622,0)"><path d="M137 343C167 482 260 545 321 574C357 591 397 603 429 609L423 641C382 634 335 622 295 608C189 570 37 457 37 238C37 84 125 -12 242 -12C362 -12 447 89 447 209C447 311 374 393 267 393C247 393 226 386 204 376L137 343ZM227 337C318 337 361 256 361 173C361 105 336 22 258 22C176 22 126 120 126 240C126 266 127 291 132 310C155 323 189 337 227 337Z"></path></g><g transform="matrix(.013,0,0,-0.013,70.278,0)"><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"></path></g><g transform="matrix(.013,0,0,-0.013,76.818,0)"><path d="M697 650H468L461 623L492 619C539 613 547 605 518 546C481 471 367 264 278 116H276C239 278 197 500 186 567C180 604 185 613 226 619L252 623L260 650H24L17 623C78 617 92 613 108 533L216 -11H247C365 200 515 462 560 529C616 612 624 615 689 623L697 650Z"></path></g></svg></td></tr><tr><td class="align_left">Transformer Tr<sub>1</sub>, Tr<sub>2</sub> resistance</td><td class="align_center"><span style="width: 64.7995ptpx;"><svg height="11.7782pt" id="M12" style="vertical-align:-3.42938pt" version="1.1" viewbox="-0.0498162 -8.34882 64.7995 11.7782" width="64.7995pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g 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transform="matrix(.013,0,0,-0.013,57.623,0)"><path d="M515 96L502 119C471 88 431 62 423 62C416 62 411 70 417 101C440 223 469 341 497 448H486L412 422L380 277C330 188 210 57 152 57C137 57 126 69 139 124L195 366C210 431 205 448 182 448C155 448 89 413 23 350L36 326C73 354 103 376 112 376C118 376 118 365 113 340L61 118C54 90 52 68 52 51C52 0 75 -12 98 -12S151 -3 181 17C242 58 305 119 362 193H364L345 104C323 3 339 -12 359 -12C390 -12 464 35 515 96Z"></path></g></svg></span></td></tr><tr><td class="align_left">Transformers Tr<sub>1</sub>, Tr<sub>2</sub> inductance</td><td class="align_center"><span style="width: 46.0093ptpx;"><svg height="11.7782pt" id="M13" style="vertical-align:-3.42938pt" version="1.1" viewbox="-0.0498162 -8.34882 46.0093 11.7782" width="46.0093pt" 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="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g 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304ZM482 289C482 161 380 33 304 33C278 33 248 51 233 69L303 396C326 400 352 403 369 403C428 403 482 380 482 289Z"></path></g><g transform="matrix(.013,0,0,-0.013,38.833,0)"><path d="M515 96L502 119C471 88 431 62 423 62C416 62 411 70 417 101C440 223 469 341 497 448H486L412 422L380 277C330 188 210 57 152 57C137 57 126 69 139 124L195 366C210 431 205 448 182 448C155 448 89 413 23 350L36 326C73 354 103 376 112 376C118 376 118 365 113 340L61 118C54 90 52 68 52 51C52 0 75 -12 98 -12S151 -3 181 17C242 58 305 119 362 193H364L345 104C323 3 339 -12 359 -12C390 -12 464 35 515 96Z"></path></g></svg></span></td></tr><tr><td class="align_left">Transformer Tr<sub>1</sub>, Tr<sub>2</sub> rating</td><td class="align_center">= 2.5 MVA</td></tr><tr><td class="align_left">Transformer Tr<sub>2</sub> voltage ratio</td><td class="align_center">= <svg height="9.49473pt" id="M14" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -9.28833 84.3508 9.49473" width="84.3508pt" 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class="tbody-hr"/></td></tr></table></td></tr></table>

Mathematical Problems in Engineering

tab1

Table 1

Table 1: Operation of Parallel Inverters in Microgrid Using New Adaptive PI Controllers Based on Least Mean Fourth Technique 