  Electrical Machines - Basic vocational knowledge (Institut f�r Berufliche Entwicklung, 144 p.)  8. Transformer  8.1. Transformer principle  8.1.1. Operating principle of a transformer 8.1.2. Voltage transformation 8.1.3. Current transformation

### 8.1.1. Operating principle of a transformer

Transformers are stationary electrical machines which transmit energy from systems with certain current and voltage values into systems with generally different current and voltage values but with identical frequency.

Two separate windings are on the same iron core.

Following connection to alternating voltage U1 there is a standstill current I0. The magnetomotive force Q = I0 · N1 generates a magnetic alternating flow (F1) in the iron core.

The input and output winding of an alternating voltage are induced in accordance with the induction law. A self-induction voltage U10 arises in the input winding. It is counter-positioned in accordance with Lenz’s law on applied voltage. During idling operation - because of mutual induction - there arises the output voltage U20 which is simultaneously the terminal voltage U2.

U1~ ® I0~ ® Q0~ ® F1~ ® U20~

The value of the induced voltage is derived from the following equation:  max. flow density AFe limb cross-section U0 induction voltage f frequency N number of turns

The induction voltage increases along with the number of turns, the magnetic flow density in the iron core, the iron cross-section and the frequency.

Example:

Which maximum flow density occurs in an iron core of 16 cm2 cross-section when a voltage of 380 V (50 Hz) is applied to the primary coil with 980 turns?

Given: AFe = 16 cm2; N1 = 980; U1 = 380 V; f = 50 Hz

Sought: Solution:     » 1.09 V · s · m-2 » 1.09 T

The iron core evidences a maximum flow density of 1.09 T.

### 8.1.2. Voltage transformation

A few field lines already close before reaching the output coil (Figure 125) so that flow F1 can be divided into a maximum flow FK which saturates both coils and a leakage flow FS.

The leakage flow may be ignored in regard to the unloaded transformer (idling). Therefore the following applies: According to the transformer equation and .

If we relate both equation then Shortening gives us During idling no current flows into the output winding, thus there is no voltage decrease. Consequently the induced voltage U20 equal to the terminal voltage U2 (Cp Figure 125): Figure 125 - Transformer principle

1 Input winding/upper voltage winding/primary winding, 2 Output winding/under voltage winding/secondary winding

U20 = U2

In the event of minimal idling current I voltage decrease in the input winding is negligibly minimal. We therefore have

U10 = U1

which results in The voltages behave like the numbers of turns.

The interrelationship of the numbers of turns is known as the transformation ratio We have: The rated voltages U1n and U2n are indicated on the rating plate of the transformer.

Example:

What secondary terminal voltage arises in a transformer where 380 V is applied to the primary winding of 980 turns and the secondary winding has 594 turns?

Given: U1 = 380 V; N1 = 980; N2 = 594

Sought: U2

Solution:   U2 » 230 V

### 8.1.3. Current transformation

If the transformer is output-loaded, current I2 flows into coil N2. Current I2 generates the magnetic flow F2K. According to Lenz’s Law this magnetic flow is counter-positioned to the cause (F1K). In this manner the magnet flow F1K is weakened and induction voltage U10 decreases. Given uniform rated voltage, the difference increases between the two voltages U10 and U1.

Consequently, a greater input current I1 flows whereby the magnetic flow F1K is increased. The magnetic flow F in the iron core thus remains virtually constant:

F = F1K - F2K = constant

This also applies to the output voltage of the transformer.

The input current I1 increases as the load current I2 becomes greater.

Transformation ratio

Without heeded the losses of the transformer, the following applies according to the energy conservation law:

s1 = s2

U1 · I1 = U2 · I2

If we arrange the equation so that the voltage and current values appears on respective sides, then .

The following relationships may be cited for current ratio: Conversely the currents are proportional to the voltages or numbers of turns. A transformer converts high currents into low ones or low currents into higher ones.

Example:

A welding transformer takes up 220 (current being 10A). The output voltage is 20V. How great is the welding current?

Solution:  I2 » 110A