The transformer is a key player in AC electrical power systems. It plays its role in stepping up right from generation again steps down the power on the other side while serving for primary and secondary distributions. For understanding the working of transformers you obviously need to understand the mathematics behind its working. Given below are the top ten formulas for transformers:

Turns ratio

Turns ratio is the ratio of primary turns to secondary turn. It is denoted by symbol ‘a’

Turns ratio Formula: a = Np / Ns

Related problem:

Problem 1: A certain transformer has 100 turns of wire on the primary side and 5 turns of wire on the secondary side. Find the turns ratio

Turns ratio = a = Np/Ns = 100/5 = 20

Voltage and turns ratio

The number of turns on the primary and secondary side is related to the turns ratio in the following manner:

Np/Ns = Vp(t)/Vs(t)

In simple terms a = Vp(t)/Vs(t)

where Vp(t) = AC voltage on primary side

Vs(t) = AC voltage on secondary side

Let’s solve a related problem

For problem 1, If 30 volts are applied on primary what will be the secondary voltage.

Solution: Np/Ns = Vp(t)/Vs(t);

100 / 5 = 30 / Vs(t)

Vs(t) = 30 * 5 / 100 = 1.5 volts

Current and turns ratio

The current and turns ration on a transformer are related by the following formula:

Np/Ns = Is(t)/Ip(t)

For problem 1, If we apply 1.5 amps on primary what will be the secondary current

Np/Ns = Is(t)/Ip(t);

100/5 = Is(t)/1.5

Is(t) = 30 amps

Transformer kVA Calculation Formula

Three phase kVA can be calculated using following formula:

kVA = (1.732 * Eline * Iline) / 1000

Efficiency

Generally, Efficiency is expressed as the ratio of output to input voltage.

Mathematically,

Efficiency (η) = Pout/Pin

%age Efficiency (η) = (Pout/Pin) * 100%

where Pin = Pout + Plosses

where Plosses = PCu + PCore

and Pout = Vs.IsCosθs

Putting above parameters in transformer efficiency formula we have:

Single phase full load current

Current flowing through the transformer can be calculated using kVA to amps calculation formula:

In case of known VA: Single phase full load current = VA/Voltage

In case of known kVA: Single phase full load current = kVA/Voltage

Three phase full load current

KVA to Amps in case of three phase

I = kVA * 1000 / 1.73 * Voltage

Primary and Secondary Line current

Ip (line) = (kVA*1000)/(1.73*E(line))

Is (line) = (kVA*1000)/(1.73*E(line))

Impedance transformation

A transformer can change the apparent impedance of the element. Using a transformer it is possible to match the load impedance to source impedance. The formula for impedance transformation on the transformer is:

Z’L = a2ZL

Where Z’L = Apparent impedance of primary circuit

Voltage regulation

Voltage regulation formula compares the output voltage of transformer at no load to the voltage transformer at full load.

where

Vs (nl) = Secondary voltage at no load

Vs (fl) = Secondary voltage at full load