939:
and core losses. These shunt components can be referenced to the primary or secondary side. For simplified transformer analysis, admittance from shunt elements can be neglected. When shunt components have non-negligible effects on system operation, the shunt admittance must be considered. In the diagram below, all shunt admittances are referred to the primary side. The real and imaginary components of the shunt admittance, conductance and susceptance, are represented by
893:
938:
In the context of electrical modeling of transformers and transmission lines, shunt components that provide paths of least resistance in certain models are generally specified in terms of their admittance. Each side of most transformer models contains shunt components which model magnetizing current
962:
Transmission lines can span hundreds of kilometers, over which the line's capacitance can affect voltage levels. For short length transmission line analysis, which applies to lines shorter than 80 kilometres (50 mi), this capacitance can be ignored and shunt components are not necessary in the
716:
707:
472:
548:
888:{\displaystyle {\begin{aligned}\left|Y\right|&={\sqrt {G^{2}+B^{2}}}={\frac {1}{\sqrt {R^{2}+X^{2}}}}\\\angle Y&=\arctan \left({\frac {B}{G}}\right)=\arctan \left(-{\frac {X}{R}}\right)\,,\end{aligned}}}
721:
553:
352:
148:
1009:
930:
Note that (as shown above) the signs of reactances become reversed in the admittance domain; i.e. capacitive susceptance is positive and inductive susceptance is negative.
159:). Likewise, admittance is not only a measure of the ease with which a steady current can flow, but also the dynamic effects of the material's susceptance to polarization:
155:
is a measure of the opposition of a circuit to the flow of a steady current, while impedance takes into account not only the resistance but also dynamic effects (known as
531:
323:
198:
1082:
Ushida, Jun; Tokushima, Masatoshi; Shirane, Masayuki; Gomyo, Akiko; Yamada, Hirohito (2003). "Immittance matching for multidimensional open-system photonic crystals".
963:
model. Lines from 80 to about 250 kilometres (50 to about 155 mi), generally considered to be in the medium-line category, contain a shunt admittance governed by
1227:
702:{\displaystyle {\begin{aligned}G&=\mathrm {Re} (Y)={\frac {R}{R^{2}+X^{2}}}\,,\\B&=\mathrm {Im} (Y)=-{\frac {X}{R^{2}+X^{2}}}\,.\end{aligned}}}
1041:
1179:
54:
956:
81:
to represent the magnitude of admittance, but it quickly became the conventional symbol for admittance itself through the publications of
1143:
120:
1196:
247:
1222:
966:
31:
1058:
82:
497:
289:
164:
1053:
905:
216:
46:
38:
333:
152:
250:, the power law scaling of a system's admittance with frequency under alternating current conditions.
1101:
343:
261:
156:
105:
50:
45:
is a measure of how easily a circuit or device will allow a current to flow. It is defined as the
1117:
1091:
467:{\displaystyle Y=Z^{-1}={\frac {1}{R+jX}}=\left({\frac {1}{R^{2}+X^{2}}}\right)\left(R-jX\right)}
1040:
1175:
1139:
1109:
485:
273:
70:
1105:
923:
909:
239:
101:
62:
1216:
1121:
17:
955:
919:
477:
226:
1113:
260:
Parts of this article or section rely on the reader's knowledge of the complex
1063:
112:
265:
1096:
269:
1039:
476:
Admittance, just like impedance, is a complex number, made up of a
954:
30:
This article is about electrical engineering. For other uses, see
246:
The dynamic effects of the material's susceptance relate to the
66:
58:
69:, and its symbol is ℧ (an upside-down uppercase omega Ω).
711:
The magnitude and phase of the admittance are given by:
93:
in the alphabet, the conventional symbol for impedance.
969:
934:
Shunt admittance in electrical power systems modeling
719:
551:
500:
355:
292:
167:
123:
1003:
887:
701:
525:
466:
317:
192:
142:
1156:Grainger, John J.; Stevenson, William D. (1994).
1172:Power System Analysis and Design, Fifth Edition
1138:, p. 88, Johns Hopkins University Press, 1992
1197:"Equivalent- π Representation of a Long Line"
8:
1030:is the length of the transmission line; and
286:, is composed of real and imaginary parts,
1184:Transmission Lines: Steady-State Operation
65:(symbol S); the older, synonymous unit is
1095:
997:
968:
877:
862:
831:
795:
782:
772:
761:
748:
742:
720:
718:
691:
682:
669:
659:
636:
618:
609:
596:
586:
566:
552:
550:
519:
499:
429:
416:
406:
378:
366:
354:
311:
291:
186:
166:
130:
122:
1024:is the shunt admittance per unit length;
1174:, Cengage Learning, Connecticut, 2012,
1074:
254:Conversion from impedance to admittance
143:{\displaystyle Y\equiv {\frac {1}{Z}}}
1228:Electrical resistance and conductance
1170:J. Glover, M. Sarma, and T. Overbye,
7:
1004:{\displaystyle Y=yl=j\omega Cl\,,}
808:
640:
637:
570:
567:
25:
1136:Steinmetz: Engineer and Socialist
77:in December 1887. Heaviside used
1036:is the capacitance of the line.
104:, is defined as the inverse of
27:Ease of electrical current flow
1018:is the total shunt admittance;
650:
644:
580:
574:
1:
248:universal dielectric response
89:simply because it is next to
543:(susceptance) are given by:
209:is the admittance (siemens);
85:. Heaviside probably chose
32:Admittance (disambiguation)
1244:
1114:10.1103/PhysRevB.68.155115
61:unit of admittance is the
55:conductance and resistance
29:
1059:SI electromagnetism units
526:{\displaystyle Y=G+jB\,,}
318:{\displaystyle Z=R+jX\,,}
276:representation of signals
193:{\displaystyle Y=G+jB\,,}
83:Charles Proteus Steinmetz
1160:. New York: McGraw-Hill.
272:and on knowledge of the
1054:Nodal admittance matrix
488:part (the susceptance,
480:part (the conductance,
1044:
1005:
959:
889:
703:
527:
468:
319:
194:
144:
39:electrical engineering
1158:Power System Analysis
1043:
1006:
958:
890:
704:
528:
469:
320:
195:
145:
18:Electrical admittance
967:
717:
549:
498:
353:
290:
165:
121:
1223:Physical quantities
1106:2003PhRvB..68o5115U
922:, also measured in
53:, analogous to how
1045:
1001:
960:
885:
883:
699:
697:
539:(conductance) and
523:
464:
315:
264:representation of
190:
140:
1180:978-1-111-42577-7
1134:Ronald R. Kline,
1084:Physical Review B
870:
839:
802:
801:
767:
689:
616:
436:
397:
138:
57:are defined. The
16:(Redirected from
1235:
1208:
1207:
1205:
1203:
1195:Ghosh, Arindam.
1192:
1186:
1168:
1162:
1161:
1153:
1147:
1132:
1126:
1125:
1099:
1097:cond-mat/0306260
1079:
1035:
1029:
1023:
1017:
1010:
1008:
1007:
1002:
952:, respectively.
951:
947:
917:
903:
894:
892:
891:
886:
884:
876:
872:
871:
863:
844:
840:
832:
803:
800:
799:
787:
786:
777:
773:
768:
766:
765:
753:
752:
743:
734:
708:
706:
705:
700:
698:
690:
688:
687:
686:
674:
673:
660:
643:
617:
615:
614:
613:
601:
600:
587:
573:
542:
538:
532:
530:
529:
524:
491:
483:
473:
471:
470:
465:
463:
459:
441:
437:
435:
434:
433:
421:
420:
407:
398:
396:
379:
374:
373:
341:
331:
324:
322:
321:
316:
285:
274:frequency domain
237:
224:
214:
208:
199:
197:
196:
191:
149:
147:
146:
141:
139:
131:
110:
99:
92:
88:
80:
73:coined the term
71:Oliver Heaviside
21:
1243:
1242:
1238:
1237:
1236:
1234:
1233:
1232:
1213:
1212:
1211:
1201:
1199:
1194:
1193:
1189:
1169:
1165:
1155:
1154:
1150:
1133:
1129:
1081:
1080:
1076:
1072:
1050:
1033:
1027:
1021:
1015:
965:
964:
949:
946:
940:
936:
915:
901:
882:
881:
858:
854:
827:
814:
805:
804:
791:
778:
757:
744:
735:
724:
715:
714:
696:
695:
678:
665:
664:
629:
623:
622:
605:
592:
591:
559:
547:
546:
540:
536:
496:
495:
489:
481:
446:
442:
425:
412:
411:
402:
383:
362:
351:
350:
339:
329:
288:
287:
283:
282:The impedance,
256:
232:
222:
212:
206:
163:
162:
119:
118:
108:
97:
90:
86:
78:
35:
28:
23:
22:
15:
12:
11:
5:
1241:
1239:
1231:
1230:
1225:
1215:
1214:
1210:
1209:
1187:
1163:
1148:
1127:
1090:(15): 155115.
1073:
1071:
1068:
1067:
1066:
1061:
1056:
1049:
1046:
1038:
1037:
1031:
1025:
1019:
1000:
996:
993:
990:
987:
984:
981:
978:
975:
972:
944:
935:
932:
928:
927:
913:
908:, measured in
880:
875:
869:
866:
861:
857:
853:
850:
847:
843:
838:
835:
830:
826:
823:
820:
817:
815:
813:
810:
807:
806:
798:
794:
790:
785:
781:
776:
771:
764:
760:
756:
751:
747:
741:
738:
736:
733:
730:
727:
723:
722:
694:
685:
681:
677:
672:
668:
663:
658:
655:
652:
649:
646:
642:
639:
635:
632:
630:
628:
625:
624:
621:
612:
608:
604:
599:
595:
590:
585:
582:
579:
576:
572:
569:
565:
562:
560:
558:
555:
554:
522:
518:
515:
512:
509:
506:
503:
462:
458:
455:
452:
449:
445:
440:
432:
428:
424:
419:
415:
410:
405:
401:
395:
392:
389:
386:
382:
377:
372:
369:
365:
361:
358:
348:
347:
337:
314:
310:
307:
304:
301:
298:
295:
280:
279:
255:
252:
244:
243:
240:imaginary unit
230:
229:(siemens); and
220:
210:
189:
185:
182:
179:
176:
173:
170:
137:
134:
129:
126:
111:, measured in
100:, measured in
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
1240:
1229:
1226:
1224:
1221:
1220:
1218:
1198:
1191:
1188:
1185:
1181:
1177:
1173:
1167:
1164:
1159:
1152:
1149:
1145:
1141:
1137:
1131:
1128:
1123:
1119:
1115:
1111:
1107:
1103:
1098:
1093:
1089:
1085:
1078:
1075:
1069:
1065:
1062:
1060:
1057:
1055:
1052:
1051:
1047:
1042:
1032:
1026:
1020:
1014:
1013:
1012:
998:
994:
991:
988:
985:
982:
979:
976:
973:
970:
957:
953:
943:
933:
931:
925:
921:
914:
911:
907:
900:
899:
898:
895:
878:
873:
867:
864:
859:
855:
851:
848:
845:
841:
836:
833:
828:
824:
821:
818:
816:
811:
796:
792:
788:
783:
779:
774:
769:
762:
758:
754:
749:
745:
739:
737:
731:
728:
725:
712:
709:
692:
683:
679:
675:
670:
666:
661:
656:
653:
647:
633:
631:
626:
619:
610:
606:
602:
597:
593:
588:
583:
577:
563:
561:
556:
544:
533:
520:
516:
513:
510:
507:
504:
501:
493:
487:
479:
474:
460:
456:
453:
450:
447:
443:
438:
430:
426:
422:
417:
413:
408:
403:
399:
393:
390:
387:
384:
380:
375:
370:
367:
363:
359:
356:
345:
338:
335:
328:
327:
326:
312:
308:
305:
302:
299:
296:
293:
277:
275:
271:
267:
263:
258:
257:
253:
251:
249:
241:
235:
231:
228:
221:
218:
211:
205:
204:
203:
200:
187:
183:
180:
177:
174:
171:
168:
160:
158:
154:
150:
135:
132:
127:
124:
116:
114:
107:
103:
94:
84:
76:
72:
68:
64:
60:
56:
52:
48:
44:
40:
33:
19:
1200:. Retrieved
1190:
1183:
1182:, Chapter 5
1171:
1166:
1157:
1151:
1135:
1130:
1087:
1083:
1077:
961:
941:
937:
929:
896:
713:
710:
545:
534:
494:
475:
349:
281:
259:
245:
233:
201:
161:
151:
117:
95:
74:
42:
36:
920:susceptance
906:conductance
336:(ohms); and
227:susceptance
217:conductance
96:Admittance
1217:Categories
1144:0801842980
1070:References
1064:Immittance
484:), and an
334:resistance
266:capacitors
219:(siemens);
153:Resistance
75:admittance
47:reciprocal
43:admittance
1122:119500762
989:ω
860:−
852:
825:
809:∠
657:−
492:), thus:
486:imaginary
451:−
368:−
344:reactance
270:inductors
262:impedance
157:reactance
128:≡
106:impedance
51:impedance
1048:See also
1102:Bibcode
924:siemens
918:is the
910:siemens
904:is the
897:where
346:(ohms).
342:is the
332:is the
225:is the
215:is the
202:where
102:siemens
63:siemens
1202:30 Apr
1178:
1142:
1120:
1011:where
849:arctan
822:arctan
535:where
325:where
238:, the
1118:S2CID
1092:arXiv
912:; and
1204:2018
1176:ISBN
1140:ISBN
948:and
478:real
268:and
236:= −1
113:ohms
1110:doi
67:mho
49:of
37:In
1219::
1116:.
1108:.
1100:.
1088:68
1086:.
115::
59:SI
41:,
1206:.
1146:.
1124:.
1112::
1104::
1094::
1034:C
1028:l
1022:y
1016:Y
999:,
995:l
992:C
986:j
983:=
980:l
977:y
974:=
971:Y
950:B
945:c
942:G
926:.
916:B
902:G
879:,
874:)
868:R
865:X
856:(
846:=
842:)
837:G
834:B
829:(
819:=
812:Y
797:2
793:X
789:+
784:2
780:R
775:1
770:=
763:2
759:B
755:+
750:2
746:G
740:=
732:|
729:Y
726:|
693:.
684:2
680:X
676:+
671:2
667:R
662:X
654:=
651:)
648:Y
645:(
641:m
638:I
634:=
627:B
620:,
611:2
607:X
603:+
598:2
594:R
589:R
584:=
581:)
578:Y
575:(
571:e
568:R
564:=
557:G
541:B
537:G
521:,
517:B
514:j
511:+
508:G
505:=
502:Y
490:B
482:G
461:)
457:X
454:j
448:R
444:(
439:)
431:2
427:X
423:+
418:2
414:R
409:1
404:(
400:=
394:X
391:j
388:+
385:R
381:1
376:=
371:1
364:Z
360:=
357:Y
340:X
330:R
313:,
309:X
306:j
303:+
300:R
297:=
294:Z
284:Z
278:.
242:.
234:j
223:B
213:G
207:Y
188:,
184:B
181:j
178:+
175:G
172:=
169:Y
136:Z
133:1
125:Y
109:Z
98:Y
91:Z
87:Y
79:Y
34:.
20:)
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