**Parallel operation of transformers**, the *purpose of parallel operation, single-phase transformer parallel operation, three-phase transformer parallel operation, polarity, power-sharing, and various related issues are highlighted.*

**Objectives of parallel operation: -**

1. It is more dependent to operate two transformers in parallel than one large transformer. Because, even if there is a problem with the same transformer, the supply can be ensured with another.2. To provide a three-phase supply with the help of a few single-phase transformers.

3.Load to guarantee to share.

4. To supply power at a load greater than the rated load of a transformer.

5. To facilitate the rest of each transformer.

6. Transformers often have to be maintained and repaired during operation, if there are two or more transformers, one of them can be switched off and the supply can be continued with the other.

7. Transformer efficiency is more available.

**parallel operation of single-phase transformer (**condition for parallel operation of the transformer**)**

**parallel operation of the three-phase transformer ****(Conditions of Parallel Operation)**

### 3 phase polarity test/3 phase transformer test

### what is the polarity test?

*The purpose of the polarity test:-*

**If the parallel operation is performed without knowing the polarity, the following problems will occur: -**

**Subtractive polarity**

**Additive polarity**

### Importance of polarity test of transformer

*Description of the test required to determine the polarity of the transformer*

**Parallel operation of equal voltage ratio transformer**

`\Rightarrow\frac{V_P}a=V_S+I_1Z_{e1}`

`\Rightarrow\frac{V_P}a=V_S+I_2Z_{e2}`

`I_1Z_{e1}=I_2Z_{e2}`

`\frac{I_1}{I_2}=\frac{Z_{e2}}{Z_{e1}}`----------(1)

**Parallel operation at a voltage equal to the ideal condition of the transformer**

`\Rightarrow\frac1{Z_{AB}}=\frac1{Z_A}+\frac1{Z_B}`

`\Rightarrow\frac1{Z_{AB}}=\frac{Z_A+Z_B}{Z_AZ_B}`

`\Rightarrow Z_{AB}=\frac{Z_AZ_B}{Z_A+Z_B}`---------(1)

Again,

`\Rightarrow I_AZ_A=I_BZ_B=IZ_{AB}`

`\Rightarrow I_A=I\frac{Z_{AB}}{Z_A}`-----------(2)

`\Rightarrow I_B=I\frac{Z_{AB}}{Z_B}`---------(3)

`\Rightarrow I_A=I\times\frac{Z_AZ_B}{Z_A+Z_B}\times\frac1{Z_A}`

`\Rightarrow I_A=I\times\frac{Z_B}{Z_A+Z_B}`-------(4)

`\Rightarrow I_B=I\times\frac{Z_A}{Z_A+Z_B}`-------(5)

**Power-sharing **

`\Rightarrow I_A\times\frac V{1000}=I\times\frac{Z_B}{Z_A+Z_B}\times\frac V{1000}`

`\Rightarrow\frac{VI_A}{1000}=\frac{VI}{1000}\times\frac{Z_B}{Z_A+Z_B}`

`\Rightarrow Q_A(KVA)=Q\times\frac{Z_B}{Z_A+Z_B}`[Q Total power KVA ]

Similarly

`\Rightarrow Q_B(KVA)=Q\times\frac{Z_A}{Z_A+Z_B}`

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