# Equivalent Circuit of Transformer referred to Primary and Secondary

## Equivalent Circuit of Transformer

Equivalent**impedance of transformer**is essential to be calculated because the electrical power transformer is an electrical power system equipment for estimating different parameters of electrical power system which 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, first we need to 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 above, the applied voltage to the primary is V

_{1}and voltage across the primary winding is E

_{1}. Total 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 the total primary current I

_{1}has two components, one is no - load component I

_{o}and the 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 current is known as excitation branch of equivalent circuit of transformer. The resistive and reactive branches of the excitation circuit can be represented as

_{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

**Comments/Feedbacks**

Closely Related Articles What is transformer? Definition and Working Principle of TransformerEMF Equation of Transformer | Turns Voltage Transformation Ratio of TransformerIdeal TransformerTheory of Transformer on Load and No Load OperationResistance and Leakage Reactance or Impedance of TransformerHysteresis Eddy Current Iron or Core Losses and Copper Loss in TransformerVoltage Regulation of TransformerSingle Three Phase Transformer vs Bank of Three Single Phase TransformersParallel operation of TransformersMagnetizing Inrush Current in Power TransformerMore Related Articles Instrument TransformersCurrent Transformer CT class Ratio Error Phase Angle Error in Current TransformerVoltage Transformer or Potential Transformer TheoryKnee Point Voltage of Current Transformer PS ClassAccuracy Limit Factor and Instrument Security Factor of Current TransformerIsolation TransformerTransformer Insulating Oil and Types of Transformer OilCauses of Insulating Oil DeteriorationCollecting Oil Sample from Oil Immersed Electrical EquipmentAcidity Test of Transformer Insulating OilDGA or Dissolved Gas Analysis of Transformer Oil | Furfural or Furfuraldehyde AnalysisPrinciple of Water Content Test of Insulating OilTransformer Accessories | Breather and Conservator Tank | RadiatorSilica Gel Breather of TransformerConservator Tank of TransformerRadiator of Transformer | Function of RadiatorMagnetic Oil Gauge or MOG | Magnetic Oil Level Indicator of TransformerOil Winding and Remote Temperature Indicator of TransformerTransformer Cooling System and MethodsOn Load and No Load Tap Changer of Transformer | OLTC and NLTCTertiary Winding of Transformer | Three Winding TransformerCore of Transformer and Design of Transformer CoreRestricted Earth Fault Protection of Transformer | REF ProtectionBuchholz Relay in Transformer | Buchholz Relay Operation and PrincipleWhat is Earthing Transformer or Grounding TransformerDifferential Protection of Transformer | Differential RelaysOver Fluxing in TransformerTransformer Testing | Type Test and Routine Test of TransformerTransformer Winding Resistance MeasurementVoltage and Turn Ratio Test of TransformerVector Group Test of Power TransformerOpen and Short Circuit Test on TransformerInsulation Dielectric Test of TransformerTransformer Oil and Winding Temperature Rise TestImpulse Test of TransformerMaintenance of TransformerSweep Frequency Response Analysis Test | SFRA TestInstallation of Power TransformerCommissioning of Power TransformerElectrical Power Transformer | Definition and Types of TransformerStep Up TransformerStep Down TransformerWhat is Auto Transformer ?High Voltage TransformerDistribution Transformer | All Day Efficiency of Distribution TransformerDry Type TransformerAir Core TransformerDesign of Inductor in Switched Mode Power Supply SystemsDesign of High Frequency Pulse TransformerSingle Phase TransformerToroidal TransformerNew Articles Measurement of Insulation ResistanceAmpere's Circuital LawMechanical Equivalent of HeatTrees and Cotrees of Electric NetworkDifferentiatorIntegrator