A Stability Analysis of Thermostatically Controlled Loads for Power System Frequency Control

<div>Linearisation about the single group solution. (a) Single group solution <span class="nowrap"><svg height="12.4698pt" id="M290" style="vertical-align:-3.18147pt" version="1.1" viewbox="-0.0498162 -9.28833 26.0023 12.4698" width="26.0023pt" 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="M620 675H597C578 656 570 650 541 650H144C112 650 104 653 94 675H72C59 618 42 552 23 493L53 491C71 534 88 564 105 585C124 608 144 615 238 615H290L197 121C182 40 174 34 88 28L82 0H361L367 28C275 34 266 38 281 121L374 615H441C522 615 543 608 553 583C562 560 566 531 565 493L597 494C603 551 612 629 620 675Z" id="g113-85"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.176,3.132)"><path d="M493 498C488 549 483 613 482 650H43V617C122 611 130 603 130 521V129C130 47 122 39 42 33V0H319V33C226 39 217 47 217 129V580C217 609 221 611 250 611H324C386 611 407 605 422 585C438 567 447 539 458 494L493 498Z" id="g50-132"></path></g><g transform="matrix(.013,0,0,-0.013,12.396,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path></g><g transform="matrix(.013,0,0,-0.013,16.894,0)"><path d="M324 430H196L233 583L223 592L145 529L120 430H54L29 396L31 388H111L56 126C33 15 54 -12 77 -12C137 -12 214 57 250 95L233 119C208 92 155 59 138 59C126 59 120 70 131 125L186 390L298 394L324 430Z" id="g113-117"></path></g><g transform="matrix(.013,0,0,-0.013,21.328,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path></g></svg>.</span> (b) Temperature cycling of groups A and B close to the single group solution.</div>

Complexity

fig4

Figure 4

Figure 4: A Stability Analysis of Thermostatically Controlled Loads for Power System Frequency Control 