Трехфазные цепи
Автор: anuta2008 • Март 15, 2023 • Контрольная работа • 817 Слов (4 Страниц) • 417 Просмотры
Найдем комплексные сопротивления фаз приемника при полном наборе параметров:
Фаза а-х:
Za = + = + r1 + j ⋅ xL1 – j ⋅ xc1 = [pic 1][pic 2][pic 3]
= + 16 + j ⋅ 4 – j ⋅ 20 = + 16 – j ⋅ 16 = [pic 4][pic 5]
= + 16 – j ⋅16 = 10 – j ⋅ 10 + 16 – j ⋅ 16 = 26 – j ⋅ 26[pic 6]
ϕa = arctg = arctg = arctg (-1) = - 45°[pic 7][pic 8]
[pic 9][pic 10]
Za = √ + = √262 + 262 = 36,8 Ом[pic 11][pic 12]
Za = 36,8 ⋅ [pic 13]
Фаза b – y:
Zb = r2 + j ⋅ xL2 – j ⋅ xc2 = 25 + j ⋅ 50 – j ⋅ 25 = 25 + j ⋅ 25
ϕb = arctg = arctg = arctg 1 = 45°[pic 14][pic 15]
[pic 16]
Zb = √ + = √252 + 252 = 35,4 Ом[pic 19][pic 17][pic 18]
Zb = 35,4 ⋅ [pic 20]
Фаза c – z:
Zc = = = = = = =[pic 21][pic 22][pic 23][pic 24][pic 25]
= 19,5 – j ⋅ 24,4
ϕc = arctg = arctg = arctg (-1,2513) = - 51°[pic 26][pic 27]
[pic 28]
Zc = √ + = √19,52 + 24,42 = 31,2 Ом[pic 31][pic 29][pic 30]
Zc = 31,2 ⋅ [pic 32]
[pic 33]
Схема «звезда с нейтральным проводом»
Найдем фазные (линейные) токи в соответствии с законом Ома:
А = = = = 3,45 ⋅ = 2,44 + j ⋅ 2,44[pic 34][pic 35][pic 36][pic 37][pic 38]
В = = = 3,59 ⋅ = -3,47 - j ⋅ 0,93[pic 39][pic 40][pic 41][pic 42]
С = = = = 4,07 ⋅ = - 4,02 + j ⋅ 0,64[pic 43][pic 44][pic 45][pic 46][pic 47]
I1 = 3,45 A, I2 = 3,59 A, I3 = 4,07 A
В соответствии с первым законом Кирхгофа ток в нейтральном проводе равен:
= + + = - 5,05 + j ⋅ 2,15 = 5,5 ⋅ [pic 48][pic 49][pic 50][pic 51][pic 52]
I4 = 5,5 A
Найдем комплексные мощности фаз приемника:
= ⋅ = 127 ⋅ 3,45 ⋅ = 438 ⋅ = 310 - j ⋅ 310[pic 53][pic 54][pic 55][pic 56][pic 57]
PA = 310 Вт; QA = - 310 вар; SA = 438 B ⋅ A
= ⋅ = 127 ⋅ 3,59 ⋅ = 456 ⋅ = 322 + j ⋅ 322[pic 58][pic 59][pic 60][pic 61][pic 62][pic 63]
PB = 322 Вт; QB = 322 вар; SB = 456 B ⋅ A
= ⋅ = 127 ⋅ ⋅ 4,07 ⋅ = 517 ⋅ = 325 + j ⋅ 402[pic 64][pic 65][pic 66][pic 67][pic 68][pic 69]
PC = 325 Вт; QC = - 402 вар; SC = 517 B ⋅ A
Схема «звезда без нейтрального провода»
Напряжение смещения нейтрали найдем по формуле:
[pic 70]
= =[pic 71][pic 72]
= = =[pic 73][pic 74]
= = = = - 59,8 + j ⋅ 60,2[pic 75][pic 76][pic 77]
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