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Трехобмоточные трансформаторы
Схема замещения трехобмоточного трансформатора

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Трехобмоточные трансформаторы

Основные уравнения для трехобмоточного трансформатора

У многообмоточных трансформаторов на каждом стержне размещается не две, а большее число обмоток с разным числом витков. Это позволяет от одного трансформатора получить несколько напряжений и, следовательно, уменьшить количество трансформаторов. Такие трансформаторы выпускаются как в однофазном, так и в трехфазном исполнении.

Многообмоточные трансформаторы небольшой мощности широкое распространение находят в радиотехнике и автоматике. В качестве силовых применяются главным образом трехобмоточные трансформаторы.

В общем случае обмотки многообмоточных трансформаторов могут иметь разные номинальные мощности (все они указываются на табличке трансформатора). За номинальную мощность такого трансформатора принимается мощность наиболее мощной обмотки. При анализе работы многообмоточного трансформатора токи, напряжения и сопротивления остальных обмоток приводят к числу витков этой обмотки.

Рабочий процесс многообмоточного трансформатора рассмотрим на примере трехобмоточного трансформатора с одной первичной и двумя вторичными обмотками (рис. 1), причем наибольшую мощность имеет первичная обмотка. Такие трансформаторы наиболее распространены в энергосистемах.

Рабочий магнитный поток трехобмоточного трансформатора создается результирующей МДС F0, равной геометрической сумме МДС всех обмоток, т.е.

 

  

F1 + F2+ F3= I1ω1+ I2ω2+ I3ω3= F0.

(1)

При изменении режима работы трансформатора от холостого хода до нагрузок, несколько превышающих номинальную, и постоянстве напряжения, подводимого к первичной обмотке (U1=const), магнитный поток и, следовательно, МДС F0 практически остаются постоянными. Поэтому намагничивающий ток можно принять равным току холостого хода I0, а МДС

F0 = I0ω1 =const.

(2)

 

Разжелив левую и правую части (1) на ω1 с учетом (2) получим

I1+ I΄2+ I΄3= I0.

(3)

или

I1= I0. - ( I΄2+ I΄3)

(4)

 

где I΄2= I2·(ω2/ ω1) и I΄3= I3·(ω3/ ω1) - приведенные к числу витков первичной обмотки токи второй и третьей обмоток.

Первичный ток I1 имеет три составляющие; одна из них создает магнитный поток (составляющая I0), а две другие компенсируют размагничивающее действие токов вторичных обмоток [составляющие - ( I΄2+ I΄3)] Ток I0 составляет 0,3-10 % номинального тока, поэтому им можно пренебречь. Тогда

I1= - ( I΄2+ I΄3)

(5)

Как следует из (5), при росте тока во вторичных обмотках увеличивается ток первичной обмотки. Так как ток I1 равен геометрической сумме токов I΄2 и I΄3то арифметическая сумма последних может быть больше первичного тока. Соответственно этому сумма полных мощностей вторичных обмоток также может превышать полную мощность первичной обмотки. Однако при этом баланс активных и реактивных мощностей в трансформаторе должен выполняться.

С учетом сказанного, а также того, что полная загрузка вторичных обмоток может не совпадать во времени, первичная обмотка трехобмоточных трансформаторов рассчитывается на мощность, меньшую арифметической суммы номинальных мощностей вторичных обмоток. Стандартом предусматривается следующее соотношение номинальных мощностей обмоток (в долях номинальной мощности первичной обмотки):

 

Вариант

Обмотка 1

Обмотка 2

Обмотка 3

1

 

1

1

1

2

 

1

1

2/3

3

 

1

2/3

2/3

 

Основные уравнения для разных обмоток имеют тот же вид, что и для двухобмоточного трансформатора:

для первичной обмотки

U1= - E1 + I1Z1,

(6)

для вторичных обмоток

U΄2= E΄2 - I΄2Z΄2,

(7)

U΄3= E΄3 - I΄3Z΄3,

(8)

 

где Z1=r1+jx1 - комплексное сопротивление первичной обмотки; Z'2 = r'2 + jx'2; Z'3 = 3+jx'3 -комплексные сопротивления вторичных обмоток, приведенные к числу витков первичной обмотки.

Активные сопротивления r1, 2 и 3 представляют реальные (с учетом приведения) сопротивления соответствующих обмоток, а индуктивные сопротивления x1, 2, и 3 следует рассматривать как эквивалентные сопротивления, при которых уравнения (6) - (8) дают правильные количественные связи между токами и напряжениями, имеющими место в реальном трехобмоточном трансформаторе.

Для трехобмоточного трансформатора справедливо равенство

- E1= - E΄2 = - E΄3.

(9)

Определив из (6) - (8) ЭДС и подставив их в ;(9), получим

U1- I1Z1= - (U΄2 + I΄2Z΄2)= - (U΄3 + I΄3Z΄3),

(10)



 

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