Analytical Model for High Impedance Fault Analysis in Transmission Lines

<table class="table-group" id="tab1"><tr><td><table class="table"><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr class="thead"><td align="left">Parameter</td><td align="center">Value</td><td align="center"> </td></tr><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr><td align="left"><span style="width: 14.4674ptpx;"><svg height="12.4257pt" id="M137" style="vertical-align:-3.427751pt" version="1.1" viewbox="-0.0498162 -8.99795 14.4674 12.4257" width="14.4674pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M673 297H417L411 270C517 261 522 258 506 183L487 92C476 38 428 19 360 19C207 19 123 132 123 287C123 472 243 631 441 631C557 631 617 583 617 469L647 472C650 545 655 604 658 632C625 643 554 666 467 666C201 666 23 502 23 278C23 90 156 -16 339 -16C410 -16 501 6 569 24C566 43 567 70 573 101L589 183C604 259 607 262 667 271L673 297Z" id="g113-72"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="684" vert-adv-y="684"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,9.199,3.264)"><path d="M245 635C92 635 37 457 37 312C37 149 91 -12 244 -12C395 -12 449 166 449 312C449 469 395 635 245 635ZM243 598C332 598 358 454 358 312C358 173 334 26 245 26C158 26 128 174 128 313S152 598 243 598Z" id="g50-49"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg></span></td><td align="center">0.000932</td><td align="center"><span style="width: 10.3941ptpx;"><svg height="9.21094pt" id="M138" style="vertical-align:-0.2129908pt" version="1.1" viewbox="-0.0498162 -8.99795 10.3941 9.21094" width="10.3941pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M712 504L695 650H451L444 631C474 579 580 447 580 290C580 121 502 19 375 19C249 19 170 127 170 287C170 453 273 582 305 632L300 650H57L39 504L67 503C92 573 101 578 146 578H230C186 525 70 426 70 286C70 104 200 -15 374 -15C546 -15 681 109 681 289C681 429 570 526 519 578H608C648 578 661 569 685 503L712 504Z" id="g113-158"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="757" vert-adv-y="757"></glyph.data></g></svg></span></td></tr><tr><td align="left"><span style="width: 6.66793ptpx;"><svg height="6.42315pt" id="M139" style="vertical-align:-0.2129903pt" version="1.1" viewbox="-0.0498162 -6.21016 6.66793 6.42315" width="6.66793pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M471 456L444 459C426 433 414 430 388 430C324 430 270 434 216 434C103 434 51 374 23 338L43 317C96 366 146 380 221 375L154 109C149 86 147 68 147 52C147 4 168 -12 197 -12C240 -12 291 25 334 71L320 96C295 75 268 58 252 58C238 58 227 79 238 138C251 211 272 296 292 372C310 372 332 368 350 368C391 368 421 369 434 371C444 388 455 413 471 456Z" id="g113-241"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="483" vert-adv-y="483"></glyph.data></g></svg></span></td><td align="center">0.0298</td><td align="center">S</td></tr><tr><td align="left"><span style="width: 12.9035ptpx;"><svg height="12.4257pt" id="M140" style="vertical-align:-3.427751pt" version="1.1" viewbox="-0.0498162 -8.99795 12.9035 12.4257" width="12.9035pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><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" id="g113-87"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="709" vert-adv-y="709"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,7.641,3.264)"><path d="M245 635C92 635 37 457 37 312C37 149 91 -12 244 -12C395 -12 449 166 449 312C449 469 395 635 245 635ZM243 598C332 598 358 454 358 312C358 173 334 26 245 26C158 26 128 174 128 313S152 598 243 598Z" id="g50-49"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg></span></td><td align="center">11267</td><td align="center">V</td></tr><tr><td align="left"><span style="width: 5.62081ptpx;"><svg height="6.42315pt" id="M141" style="vertical-align:-0.2129903pt" version="1.1" viewbox="-0.0498162 -6.21016 5.62081 6.42315" width="5.62081pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M383 397C383 424 344 448 299 448C244 448 172 409 132 375C66 319 23 227 23 146C23 42 74 -12 146 -12C208 -12 298 30 359 103L343 124C315 95 248 48 192 48C145 48 111 85 111 163C111 228 129 294 151 330C171 363 201 401 241 401C275 401 302 384 325 356C332 347 339 344 348 348C373 360 383 381 383 397Z" id="g113-100"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="406" vert-adv-y="406"></glyph.data></g></svg></span></td><td align="center">299 792</td><td align="center">km/s</td></tr><tr><td align="left"><span style="width: 3.75774ptpx;"><svg height="9.89089pt" id="M142" style="vertical-align:-0.2129898pt" version="1.1" viewbox="-0.0498162 -9.6779 3.75774 9.89089" width="3.75774pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M238 681C243 705 239 712 230 712C217 712 156 682 75 674L70 648H105C148 648 153 641 144 598L39 110C18 11 35 -12 55 -12C90 -12 166 36 221 103L205 125C174 93 130 65 118 65C112 65 108 68 114 96L238 681Z" id="g113-109"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="269" vert-adv-y="269"></glyph.data></g></svg></span></td><td align="center">0.5</td><td align="center">km</td></tr><tr><td align="left"><span style="width: 8.77576ptpx;"><svg height="6.42315pt" id="M143" style="vertical-align:-0.2129903pt" version="1.1" viewbox="-0.0498162 -6.21016 8.77576 6.42315" width="8.77576pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M615 290C615 392 563 448 529 448C511 448 491 441 484 434L483 425C518 400 546 349 546 273C546 158 504 46 417 46C381 46 356 77 356 142C356 184 380 293 392 334L387 340L307 323C305 288 296 228 287 188C265 94 221 52 180 52C144 52 112 89 112 171C112 278 164 372 241 430L226 454C106 394 23 288 23 155C23 40 79 -12 139 -12C184 -12 245 32 285 85C292 31 322 -12 376 -12C423 -12 470 18 501 45C570 104 615 184 615 290Z" id="g113-246"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="638" vert-adv-y="638"></glyph.data></g></svg></span></td><td align="center">377</td><td align="center">rad/s</td></tr><tr class="table-tr"><td colspan="3"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Parameters for the first and second case of study. 

Mathematical Problems in Engineering

tab1

Table 1

Table 1: Analytical Model for High Impedance Fault Analysis in Transmission Lines 