Working Principle of Transformer

Ideal Transformer

EMF Equation of Transformer

Theory of Transformer

Leakage Reactance of Transformer

Equivalent Circuit of Transformer

Voltage Regulation of Transformer

Losses in Transformer

Open and Short Circuit Test on Transformer

Tertiary Winding of Transformer

Parallel operation of Transformers

Core of Transformer

Transformer Insulating Oil

Dissolved Gas Analysis of Transformer Oil

Transformer Cooling System

Transformer Accessories

• Conservator Tank of Transformer

• Buchholz Relay in Transformer

• Silica Gel Breather

• Radiator of Transformer

• Magnetic Oil Gauge or MOG

• Temperature Indicators of Transformer

• On and No Load Tap Changer

Auto Transformer

Three phase transformer

Current Transformer

Voltage Transformer

• Accuracy Limit & Instrument Security Factor

• Knee Point Voltage of Current Transformer

More.........

Equivalent Circuit of Transformer Referred to Primary

Approximate Equivalent Circuit of Transformer

Equivalent Circuit of Transformer Referred to Secondary

## Equivalent Circuit of Transformer

Equivalent **impedance of Transformer** is essential to be calculated as because the electrical power transformer is an electrical power system equipment so for estimating different parameters of electrical power system it may be required to calculate total internal impedance of an electrical power transformer viewing from primary side or secondary side as per requirement. This calculation requires **equivalent circuit of transformer referred to primary** or **equivalent circuit of transformer referred to secondary** sides respectively. Percentage impedance is also very essential parameter of transformer. Special attention is to be given to this parameter during installing a transformer in an existing electrical power system. Percentage impedance of different power transformers should be properly matched during parallel operation of power transformers. The percentage impedance can be derived from equivalent **impedance of transformer** so it can be said that **equivalent circuit of transformer** is also required during calculation of % impedance.

## Equivalent Circuit of Transformer Referred to Primary

For drawing **equivalent circuit of transformer referred to primary**, first we have to establish general **equivalent circuit of transformer** then we will modify it for referring from primary side. For doing this we first recall the complete vector diagram of a transformer which is shown in the figure below.

Let us consider the transformation ratio be,

In the figure right,

the applied voltage to the primary is V_{1} and voltage across the the primary winding is E_{1}. Total electric current supplied to primary is I_{1}. So the voltage V_{1} applied to the primary, is partly dropped by I_{1}Z_{1} or I_{1}R_{1} + j.I_{1}X_{1} before it appears across primary winding. The voltage appeared across winding is countered by primary induced emf E_{1}. So voltage equation of this portion of the transformer can be written as

The equivalent circuit for that equation can be drawn as below,

From the vector diagram above it is found that total primary current I_{1} has two components one is no - load component I_{o} and other is load component I_{2}′. As this primary current has two components or branches so there must be a parallel path with primary winding of transformer. This parallel path of electric current is known as excitation branch of equivalent circuit of transformer. The resistive and reactive branches of the excitation circuit can be represented as

The load component I_{2}′ flows through the primary winding of transformer and induced voltage across the winding is E_{1} as shown in the figure right. This induced voltage E_{1} transforms to secondary and it is E_{2} and load component of primary current I_{2}′ is transformed to secondary as secondary current I_{2}. Current of secondary is I_{2}. So the voltage E_{2} across secondary winding, is partly dropped by I_{2}Z_{2} or I_{2}R_{2} + j.I_{2}X_{2} before it appears across load. The load voltage is V_{2}.

The complete equivalent circuit of transformer is shown below.

Now if we see the voltage drop in secondary from primary side then it would be ′K′ times greater and would be written as K.Z_{2}.I_{2}.

Again I_{2}′.N_{1} = I_{2}.N_{2}

Therefore,

From above equation,

Secondary impedance of transformer referred to primary is,

So The complete equivalent circuit of transformer referred to primary is shown in the figure below,

### Approximate Equivalent Circuit of Transformer

Since I_{o} is very small compared to I_{1}, it is less than 5% of full load primary current, I_{o} changes the voltage drop insignificantly. Hence, it is good approximation to ignore the excitation circuit in approximate equivalent circuit of transformer. The winding resistance and reactance being in series can now be combined into equivalent resistance and reactance of transformer referred to any particular side. In this case it is side 1 or primary side.

## Equivalent Circuit of Transformer Referred to Secondary

In similar way approximate equivalent circuit of transformer referred to secondary can be drawn.

Where, equivalent impedance of transformer referred to secondary, can be derived as

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