Electrical Transformers

What is the transformer?
Every electrical network contains a lot of transformers but do you know what a transformer is or why we use a transformer?

In simple words, the transformer is a static device (they don’t have any moving parts) in which electric power in one circuit is transformed into electric power of the same frequency in another circuit with the physical basis of mutual induction between two circuits.

Also, an electrical transformer is a device that is used mainly for transforming electrical energy. It is able to change the voltage from high to a low one (and otherwise). This enables the transportation of electricity more easily and efficiently.
What is a transformer construction?
The transformer is generally composed of two circuits:

The electrical circuit
The magnetic circuit

The Electrical circuit

The electrical circuit consists of two winding. Firstly, the primary winding connects to the source. Secondly, the secondary winding connects the loads. Additionally, these winding may be copper  (common) or aluminum (rarely)

The magnetic circuit

It consists of metal sheets made of high-quality silicon steel, where both winding are wrapped.
Single-phase transformer core type transformer
The core is built of metal sheet steel lamination assembled to provide a continuous magnetic path with a minimum of air-gap included. The eddy current loss is minimized to reduce heat by laminating the core.

the core has two types:

Core-type:

The magnetic flux path is of one loop and this loop connects the primary and secondary winding together magnetically. It uses a small transformer because of its flux losses through the core.

Practically the primary winding and secondary winding are wrapped around each other.

Shell type:

The magnetic flux path has two loops and it uses a large transformer because of less of its flux losses through the core.
Mutual inductance
It consists of two inductive coils that are separated electrically but linked through the magnetic flux.

As I mentioned earlier that transformers contain two coils primary and secondary. If the number of primary coils is less than the number of secondary coils, that means this transformer is a step-up transformer.

This transformer can step up voltage according to the turns ratio between primary and secondary coils. Thus, the current is decreased at the secondary side as the relation between voltage and current.
The function of the transformer?
The main function of the transformer is to decrease currents through the transmission process of electricity from the production location to distribution locations.

It’s economical to decrease the current through the transmission process because as current decreases, the cross-section of transmission lines decreases losses, and transmitted power decrease  P = I² * R.

As power losses depend on a current-voltage drop in transmission lines decreases. In other words, the voltage drop depends on the current decrease size of power transmission towers.

Because transmission lines have a small cross-section area.

And after transmitting this power to distribution location, we use a step-down transformer to decrease voltage and distribute to customers
Types of transformers?
Transformers can be classified into many categories. These classifications based on:
Classifications according to function :

Step-up transformer
Step down transformer

Classifications according to Type :

Power Transformer
Distribution Transformer
Autotransformer
Instrument transformer

Classifications according to phases:

Single-phase transformer
Three-phase transformer

Classifications according to insulation :

Oil-immersed transformer
Dry-type transformer (depend on vans to move air)
SF6 (Stable gas) Transformer

Equation of ideal transformer:
What do we mean by the ideal transformer? We mean transformer at no losses condition and unfortunately it does not occur practically.
1. turns ratio of transformer

Assume that :

N1: number of primary winding turns

N2: number of secondary winding turns

V1: Voltage at the primary side (source side)

V2: voltage at the secondary side (load side)

In this case (single-phase ideal transformer)

V1/V2 = N1/N2 = k

Such as “k” called turns ratio.

From the above equation, we notice that:

If N2 > N1 … the transformer is a step-up transformer that voltage at primary less than secondary side

If N1 > N2 … the transformer is step down transformer that voltage at primary greater than secondary side

Also for the ideal transformer (that means no losses).

Input Power = Output power

P1(input power) = V1 * I1 , P2(output power) = V2*I2

So V1 *I1 = V2*I2

From above equations we notice that

V1/V2 = N1/N2 = I2/I1 = K

Let’s try an example:

So if the number of primary turns = 1000 turn and secondary turns = 50 turns, primary voltage = 100 volts. Let us calculate secondary voltage and indicate the type of transformer (step up or step down) …

Solution:

V1/V2 = N1/N2 = k

100/V2 = 1000/50 then V2 = 5 volt ..

This transformer is a step-down transformer because of the voltage at the primary side greater than the secondary side.
2. EMF of transformer equation
A flux increases from zero to its maximum value in the first quarter of the cycle (because it follows the AC current motion)

Equation of the transformer is the rate of change of flux per turns is called EMF (Electromotive force)

As flux varies sinusoidal, then r.m.s value of induced EMF is obtained from

Now, r.m.s. value of the induced e.m.f. in the whole of primary winding = (induced e.m.f/turn) × No. of primary turns

From two-equation above (i) and (ii) we conclude that at ideal transformer V1/V2 = N1/N2 = E1/E2 this is an ideal no-load condition.
Transformer equivalent circuit
Firstly, we assumed that ideal transformer windings have only reactance and have no physical resistance. Secondly, this assumption is to obtain the conversion rate of voltages, currents, and impedance of the load.

But in fact, there is a resistance to both primary and secondary windings since they are made of copper.
Real transformer
Our interest now is to obtain the true values of currents and transmitted power by obtaining the transformer equivalent circuit.

Based on this, we will take into consideration winding resistance where the primary winding resistance is symbolized by R1 and secondary winding resistance is symbolized by R2 .

We assumed that in the ideal transformer there is no magnetic leakage. But in fact, the magnetic flux resulting from the flow of a current in the primary windings is not completely linked with the secondary winding.

But a small part of magnetic flux (ɸ1) leaks around the primary windings and completes its magnetic circuit through the air.

So, this leaking flux is linked with the primary winding and produces self-induced Electro-Motive force (EMF) which results in leakage reactance of the primary winding X1.. such that X1=2πfL1

Also, when the transformer is loaded and a current is passed in the secondary winding, this causes a magnetic flux (ɸ2). Also generated, this flux causes a part of the secondary winding to leaks out.

Thus, this leaking flux linked with the secondary winding produces an Electromotive force (EMF) results in leakage reactance of the Secondary winding X2 … such that X2=2πfL2
Types of losses
Previously we assumed that, in the ideal transformer there is no loss of electrical power. But actually the transformer has two types of losses-iron core losses and copper winding losses.

Xo: Magnetic reactance of the iron core

Ro: Magnetic resistance of the iron core

They represented iron core losses impedance …

Io: Current at no-load condition

Ia: core loss of effective current

Im : magnetizing current

We can simplify and abbreviate the equivalent circuit referred to primary windings:
equivalent circuit of transformer referred to primary
All the parameters in the secondary windings are moved to the primary windings and take different values.

These values differ from their first position So, we can calculate the new values from the following equations :

such that:

Vʼ2 = (N1/N2) * V2

Iʼ2 = (N2/N1) * I2

Rʼ2 = R2 * (N1/N2)²

Xʼ2 = X2 * (N1/N2)²

By moving the parallel branch either to the primary windings or to the secondary windings

However, we can also ignore the parallel branch (magnetism) to obtain the approximate equivalent circuit of the transformer

We can calculate Equivalent Resistance Req1 and equivalent Reactance Xeq1 values Referred to primary windings from the following equations :

Req1 = R1 + Rʼ2

Xeq1 = X1 + Xʼ2

ZʼL = ZL * (N1/N2)²
equivalent circuit of transformer referred to Secondary winding
Also, Equivalent Resistance Req2 and equivalent Reactance Xeq2 values Referred to secondary windings are calculated from the following equations :

approximate transformer equivalent circuit referred to secondary, such that:

Req2 = Rʼ1 + R2

Xeq2 = Xʼ1 + X2

Vʼ1 = (N2/N1) * V1

Iʼ1 = (N1/N2) * I1

Rʼ1 = R1 * (N2/N1)²

Xʼ1= X1 * (N2/N1)²