Voltage Stability Analysis of Front-End Speed Controlled Wind Turbine Integrated into Regional Power Grid Based on Bifurcation Theory

<table class="table-group" id="tab2"><tr><td><table class="table"><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr class="thead"><td class="align_left" rowspan="2">Parameter</td><td class="align_center" colspan="2">Bifurcation point</td></tr><tr class="thead"><td class="align_center"><i>H</i><sub>1</sub></td><td class="align_center">LP</td></tr><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr><td class="align_left"><i>δ</i><sub><i>m</i></sub></td><td class="align_center">3.234323</td><td class="align_center">3.221205</td></tr><tr><td class="align_left"><i>ω</i></td><td class="align_center">0</td><td class="align_center">0</td></tr><tr><td class="align_left"><span style="width: 13.7222ptpx;"><svg height="15.3797pt" id="M45" style="vertical-align:-3.9436pt" version="1.1" viewbox="-0.0498162 -11.4361 13.7222 15.3797" width="13.7222pt" 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="M593 650H142L136 622C219 616 224 611 209 531L130 120C114 39 108 34 23 28L17 0H501C518 32 557 130 568 158L540 169C519 132 495 93 469 70C439 43 409 35 332 35C272 35 241 37 225 50C211 61 211 89 222 149L253 320H350C441 320 443 312 441 239H471L510 434H481C455 366 448 358 360 358H260L303 572C311 613 312 615 348 615H431C509 615 522 603 532 581C544 555 546 531 545 491L574 493C583 555 592 631 593 650Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.008,-5.741)"><path d="M310 541L304 571C290 586 211 619 185 610L80 76L131 52L310 541Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.943,3.784)"><path d="M538 684C542 703 539 710 529 710C512 710 455 682 363 674L361 644H396C444 644 448 642 438 594L405 438C373 450 347 451 336 451C288 451 200 416 147 374C69 312 24 207 24 113C24 29 60 -12 94 -12C126 -12 156 4 196 30C231 53 296 100 346 166H348L328 81C311 10 325 -12 348 -12C380 -12 450 24 512 98L495 125C466 97 431 70 417 70C408 70 408 80 411 98L538 684ZM390 373L361 240C336 196 210 56 145 56C132 56 113 73 113 131C113 216 156 338 220 379C243 394 266 402 303 402C331 402 375 388 390 373Z"></path></g></svg></span></td><td class="align_center">−0.891554</td><td class="align_center">−0.887648</td></tr><tr><td class="align_left"><span style="width: 13.1285ptpx;"><svg height="17.5627pt" id="M46" style="vertical-align:-6.1266pt" version="1.1" viewbox="-0.0498162 -11.4361 13.1285 17.5627" width="13.1285pt" 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="M593 650H142L136 622C219 616 224 611 209 531L130 120C114 39 108 34 23 28L17 0H501C518 32 557 130 568 158L540 169C519 132 495 93 469 70C439 43 409 35 332 35C272 35 241 37 225 50C211 61 211 89 222 149L253 320H350C441 320 443 312 441 239H471L510 434H481C455 366 448 358 360 358H260L303 572C311 613 312 615 348 615H431C509 615 522 603 532 581C544 555 546 531 545 491L574 493C583 555 592 631 593 650Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.008,-5.741)"><path d="M310 541L304 571C290 586 211 619 185 610L80 76L131 52L310 541Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.943,3.784)"><path d="M481 430L460 436C440 442 393 451 366 451C348 451 325 448 313 446C267 437 195 409 147 367C79 308 24 211 24 105C24 37 56 -12 93 -12C121 -12 156 1 199 32C246 66 313 122 349 168H351L286 -147C274 -205 261 -215 210 -224L199 -226L193 -255L438 -243L442 -214L417 -212C364 -208 359 -200 370 -140L433 204C455 324 469 389 481 430ZM391 385C382 336 366 260 358 238C321 178 209 59 143 59C129 59 115 83 115 131C115 207 152 317 220 373C243 392 282 403 314 403C348 403 374 395 391 385Z"></path></g></svg></span></td><td class="align_center">0.049883</td><td class="align_center">0.049893</td></tr><tr><td class="align_left"><i>E</i><sub><i>fd</i></sub></td><td class="align_center">0.003010</td><td class="align_center">0.000133</td></tr><tr><td class="align_left"><i>θ</i></td><td class="align_center">0.036403</td><td class="align_center">0.023048</td></tr><tr><td class="align_left"><span style="width: 7.11985ptpx;"><svg height="6.1673pt" id="M47" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -5.96091 7.11985 6.1673" width="7.11985pt" 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="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><td class="align_center">1.004215</td><td class="align_center">1.000187</td></tr><tr><td class="align_left"><i>Q</i><sub>1</sub></td><td class="align_center">1.294855</td><td class="align_center">1.296925</td></tr><tr class="table-tr"><td colspan="3"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>The parameter value of each bifurcation point (in p.u.).</div>

Complexity

tab2

Table 2

Table 2: Voltage Stability Analysis of Front-End Speed Controlled Wind Turbine Integrated into Regional Power Grid Based on Bifurcation Theory 