Enhanced Instantaneous Power Theory with Average Algorithm for Indirect Current Controlled Three-Level Inverter-Based Shunt Active Power Filter under Dynamic State Conditions

<div>Simulation waveforms of (a) overall DC-Bus voltage <svg height="11.9087pt" id="M147" style="vertical-align:-3.2728pt" version="1.1" viewbox="-0.0498162 -8.6359 16.6438 11.9087" width="16.6438pt" 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="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(.0091,0,0,-0.0091,7.332,3.132)"><path d="M517 51L485 54C448 58 441 63 441 115V712C404 700 337 684 285 678V653C357 648 362 645 362 580V437C339 446 309 449 295 449C159 449 38 340 38 201C38 61 143 -12 223 -12C234 -12 261 -6 301 17L362 53V-12C420 9 495 22 517 26V51ZM362 85C338 67 301 51 266 51C201 51 128 109 128 228C128 373 212 411 259 411C296 411 338 395 362 360V85Z" id="g190-101"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="528" vert-adv-y="528"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,12.137,3.132)"><path d="M390 111C344 68 312 56 269 56C212 56 118 102 118 241C118 346 175 401 241 401C277 401 312 388 342 360C350 352 355 349 361 349C372 349 394 371 394 392C394 403 391 411 378 422C362 436 329 449 288 449H287C250 449 190 432 138 392C71 341 37 274 37 197C37 90 112 -12 238 -12C297 -12 363 32 407 90L390 111Z" id="g190-100"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="423" vert-adv-y="423"></glyph.data></g></svg>, (b) upper capacitor voltage <svg height="11.9087pt" id="M148" style="vertical-align:-3.2728pt" version="1.1" viewbox="-0.0498162 -8.6359 21.0921 11.9087" width="21.0921pt" 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="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(.0091,0,0,-0.0091,7.332,3.132)"><path d="M517 51L485 54C448 58 441 63 441 115V712C404 700 337 684 285 678V653C357 648 362 645 362 580V437C339 446 309 449 295 449C159 449 38 340 38 201C38 61 143 -12 223 -12C234 -12 261 -6 301 17L362 53V-12C420 9 495 22 517 26V51ZM362 85C338 67 301 51 266 51C201 51 128 109 128 228C128 373 212 411 259 411C296 411 338 395 362 360V85Z" id="g190-101"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="528" vert-adv-y="528"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,12.137,3.132)"><path d="M390 111C344 68 312 56 269 56C212 56 118 102 118 241C118 346 175 401 241 401C277 401 312 388 342 360C350 352 355 349 361 349C372 349 394 371 394 392C394 403 391 411 378 422C362 436 329 449 288 449H287C250 449 190 432 138 392C71 341 37 274 37 197C37 90 112 -12 238 -12C297 -12 363 32 407 90L390 111Z" id="g190-100"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="423" vert-adv-y="423"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,16.018,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg>, (c) lower capacitor voltage <svg height="11.9087pt" id="M149" style="vertical-align:-3.2728pt" version="1.1" viewbox="-0.0498162 -8.6359 21.0921 11.9087" width="21.0921pt" 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="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(.0091,0,0,-0.0091,7.332,3.132)"><path d="M517 51L485 54C448 58 441 63 441 115V712C404 700 337 684 285 678V653C357 648 362 645 362 580V437C339 446 309 449 295 449C159 449 38 340 38 201C38 61 143 -12 223 -12C234 -12 261 -6 301 17L362 53V-12C420 9 495 22 517 26V51ZM362 85C338 67 301 51 266 51C201 51 128 109 128 228C128 373 212 411 259 411C296 411 338 395 362 360V85Z" id="g190-101"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="528" vert-adv-y="528"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,12.137,3.132)"><path d="M390 111C344 68 312 56 269 56C212 56 118 102 118 241C118 346 175 401 241 401C277 401 312 388 342 360C350 352 355 349 361 349C372 349 394 371 394 392C394 403 391 411 378 422C362 436 329 449 288 449H287C250 449 190 432 138 392C71 341 37 274 37 197C37 90 112 -12 238 -12C297 -12 363 32 407 90L390 111Z" id="g190-100"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="423" vert-adv-y="423"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,16.018,3.132)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z" id="g50-51"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg>, and (d) neutral point voltage deviation (<svg height="11.9087pt" id="M150" style="vertical-align:-3.2728pt" version="1.1" viewbox="-0.0498162 -8.6359 55.5551 11.9087" width="55.5551pt" 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="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(.0091,0,0,-0.0091,7.332,3.132)"><path d="M517 51L485 54C448 58 441 63 441 115V712C404 700 337 684 285 678V653C357 648 362 645 362 580V437C339 446 309 449 295 449C159 449 38 340 38 201C38 61 143 -12 223 -12C234 -12 261 -6 301 17L362 53V-12C420 9 495 22 517 26V51ZM362 85C338 67 301 51 266 51C201 51 128 109 128 228C128 373 212 411 259 411C296 411 338 395 362 360V85Z" id="g190-101"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="528" vert-adv-y="528"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,12.137,3.132)"><path d="M390 111C344 68 312 56 269 56C212 56 118 102 118 241C118 346 175 401 241 401C277 401 312 388 342 360C350 352 355 349 361 349C372 349 394 371 394 392C394 403 391 411 378 422C362 436 329 449 288 449H287C250 449 190 432 138 392C71 341 37 274 37 197C37 90 112 -12 238 -12C297 -12 363 32 407 90L390 111Z" id="g190-100"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="423" vert-adv-y="423"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,16.018,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,23.87,0)"><path d="M535 230V280H52V230H535Z" id="g117-33"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,34.407,0)"><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(.0091,0,0,-0.0091,41.739,3.132)"><path d="M517 51L485 54C448 58 441 63 441 115V712C404 700 337 684 285 678V653C357 648 362 645 362 580V437C339 446 309 449 295 449C159 449 38 340 38 201C38 61 143 -12 223 -12C234 -12 261 -6 301 17L362 53V-12C420 9 495 22 517 26V51ZM362 85C338 67 301 51 266 51C201 51 128 109 128 228C128 373 212 411 259 411C296 411 338 395 362 360V85Z" id="g190-101"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="528" vert-adv-y="528"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,46.544,3.132)"><path d="M390 111C344 68 312 56 269 56C212 56 118 102 118 241C118 346 175 401 241 401C277 401 312 388 342 360C350 352 355 349 361 349C372 349 394 371 394 392C394 403 391 411 378 422C362 436 329 449 288 449H287C250 449 190 432 138 392C71 341 37 274 37 197C37 90 112 -12 238 -12C297 -12 363 32 407 90L390 111Z" id="g190-100"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="423" vert-adv-y="423"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,50.426,3.132)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z" id="g50-51"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg>), for dynamic state condition of inductive to capacitive load.</div>

Mathematical Problems in Engineering

fig14

Figure 14

Figure 14: Enhanced Instantaneous Power Theory with Average Algorithm for Indirect Current Controlled Three-Level Inverter-Based Shunt Active Power Filter under Dynamic State Conditions 

Figure 14 | Enhanced Instantaneous Power Theory with Average Algorithm for Indirect Current Controlled Three-Level Inverter-Based Shunt Active Power Filter under Dynamic State Conditions 