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Transformer Formulas and Equations

Electrical Transformer Formulas & Equations

The following parameters can be calculated by using the basic electrical transformer formulas, equation and functions while designing and analyzing transformers related circuits and networks.

EMF Induced In Primary & Secondary Windings:

EMF induced in Primary & Secondary Windings of transformer

Where

  • E= EMF induced in primary winding
  • E2 = EMF induced in Secondary winding
  • N1 = Number of Turns in Primary winding
  • N2 = Number of Turns in Secondary winding
  • f  = Line frequency
  • φm = Maximum Flux in Core
  • Bm = Maximum flux density
  • A = Area of Core

Related Post: EMF Equation of a Transformer

Voltage Transformation Ratio:

Voltage Transformation ratio of transformer

Where

  • K = voltage transformation ratio of transformer
  • V1I1 = Primary voltage & current Respectively
  • V2I2 = Secondary voltage & current Respectively

Electrical Transformer Formulas and Equations

Equivalent Resistance of Transformer Windings:       

Equivalent resistance of transformer windings

Where

  • R1 = Resistance of Primary winding in Secondary
  • R2 = Resistance of Secondary winding in primary
  • R01 = Equivalent resistance of transformer from primary side
  • R02 = Equivalent resistance of transformer from Secondary side
  • R1 = Primary winding Resistance
  • R2 = Secondary Winding Resistance

Leakage Reactance:

Leakage Reactance of transformer

Where

  • X1 = Primary leakage Reactance
  • X2 = Secondary leakage Reactance
  • eL1 = Self-Induced EMF in primary
  • eL2 = Self-Induced EMF in Secondary

Equivalent Reactance Of Transformer Windings:                    

Equivalent reactance of transformer windings

Where

  • X1 = Reactance of Primary winding in Secondary
  • X2 = Reactance of Secondary winding in primary
  • X01 = Equivalent reactance of transformer from primary side
  • X02 = Equivalent reactance of transformer from Secondary side

Total Impedance of Transformer Winding:

Total Impedance of Transformer winding

Where

  • Z1 = Impedance of primary winding
  • Z2 = Impedance of Secondary winding
  • Z01 = Equivalent Impedance of transformer from primary side
  • Z02 = Equivalent Impedance of transformer from Secondary side

Input & Output Voltage Equations

Input and output voltage of a transformer can be found by the following equations.

Input & Output Voltage equations of transformer

Losses In Transformer:

Core / Iron Losses

The losses that occur inside the core;

  • Hysteresis Loss

Due to magnetization and demagnetization of the core

Hysteresis loss in transformer

  • Eddy Current Loss

Due to the induced EMF produced inside the core causes the flow of eddy current.

Eddy Current Loss in transformer

Where

  • Wh = Hysteresis loss
  • We = Eddy current loss
  • η = Steinmetz Hysteresis coefficient
  • Ke = Eddy current constant
  • Bmax  = Maximum magnetic flux
  • f = frequency of flux
  • V = Volume of the core
  • t = thickness of the lamination

Copper Loss:

The loss due to the resistance of the winding

Copper Loss in transformer

Voltage Regulation Of Transformer:

When the input voltage to the transformer primary is kept constant and a load is connected to the secondary terminal, the secondary voltage decreases due to internal impedance.

The comparison of no load secondary voltage to the full load secondary voltage is called voltage regulation of the transformer.

Voltage Regulation of transformer

  • 0V= No load Secondary voltage
  • V2 = Full load Secondary voltage
  • V1 = No load Primary voltage
  • V2’ = V2/K = Full load Secondary voltage from primary side
  • Regulation Up

Regulation Up

  • Regulation Down

Regulation Down

Regulation “Down” is commonly referred as regulation

  • Regulation in Primary Voltage Terms:

Regulation in primary voltage terms

  • Regulation When Secondary Voltage Supposed to be Constant

After connecting load, the primary voltage needs to be increased from V1 to V1, where the voltage regulation is given by:

Regulation when secondary voltage supposed to be constant

Percentage Resistance, Reactance & Impedance:

These quantities are measured at full load current with the voltage drop, and expressed as the percentage of normal voltage.

  • Percentage Resistance at Full Load:

Percentage resistance at full load

  • Percentage Reactance at Full Load:

  • Percentage Impedance at Full Load:

Percentage Impedance at Full Load

Transformer Efficiency:

The efficiency of the transformer is given by the output power divide by the input power. Some of the input power is wasted in internal losses of the transformer.

Transformer Efficiency

Total losses = Cu loss + Iron Loss

Efficiency At Any Load:

The efficiency of the transformer at an actual load can be given by;

transformer Efficiency at any load

Where

x = Ratio of Actual load to full load kVA

All Day Efficiency:

The ratio of energy delivered in Kilo Watt-Hour (kWh) to the energy input in kWh of the transformer for 24 hours is called all day efficiency.

All Day Efficiency of transformer

Condition For Maximum Efficiency:

The copper lost must be equal to the iron loss, which the combination of hysteresis loss and eddy current loss.

Cu Loss = Iron Loss

Wcu = Wi

Where

  • Wi = Wh­ + We
  • Wcu = I12 R01 = I22 R02

Load Current For Maximum Efficiency:

The load current required for the maximum efficiency of the transformer is;

Load Current for Maximum Efficiency

Related Formulas and Equations Posts:

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