Transformer Formulas and Equations

Electrical Technology

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.

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EMF Induced In Primary & Secondary Windings:

Where

E₁= 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
φ_m = Maximum Flux in Core
B_m = Maximum flux density
A = Area of Core

Related Post: EMF Equation of a Transformer

Voltage Transformation Ratio:

Where

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

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:

Where

X₁ = Primary leakage Reactance
X₂ = Secondary leakage Reactance
e_L1 = Self-Induced EMF in primary
e_L2 = Self-Induced EMF in Secondary

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:

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.

Losses In Transformer:

Core / Iron Losses

The losses that occur inside the core;

Hysteresis Loss

Due to magnetization and demagnetization of the core

Eddy Current Loss

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

Where

W_h = Hysteresis loss
W_e = Eddy current loss
η = Steinmetz Hysteresis coefficient
K_e = Eddy current constant
B_max = 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

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.

₀V₂= 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 Down

Regulation “Down” is commonly referred as regulation

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:

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 Reactance 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.