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Experiment4

Single Phase Transformer

Objectives:

- To study the characteristics of the single phase transformer.

- To study how transformers work.

- To study the voltages and currents curves when the operating single phase transformer.

Theory:

A transformer is an electrical device that transfers electrical energy between two or more circuits

through electromagnetic induction. Commonly, transformers are used to increase or decrease the

voltages of alternating current in electric power applications.

The coil to which the source supplies the power is called the primary winding. The coil that

delivers power to the load is called the secondary winding.

Since the induced emf in a coil is proportional to the number of turns in a coil, it is possible to

have a higher voltage across the secondary than the applied voltage to the primary. In this case,

the transformer is called a step-up transformer.

A step-up transformer is used to connect a relatively high-voltage transmission line to a

relatively low-voltage generator. On the other hand, a step-down transformer has a lower voltage

on the secondary side.

Figure 1: Single phase transformer

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Construction of a Transformer

In order to keep the core loss to a minimum, the core of a transformer is built up of thin

laminations of highly permeable ferromagnetic material such as silicon-sheet steel. Silicon steel

is used because of its properties and low magnetic losses.

In all types of transformer construction, the central iron core is constructed from of a highly

permeable material made from thin silicon steel laminations. These thin laminations are

assembled together to provide the required magnetic path with the minimum of magnetic losses.

The resistivity of the steel sheet itself is high, thus reducing any eddy current loss by making the

laminations very thin.

Figure 2: thin laminations from steel

Firstly// Ideal Transformer

A two-winding transformer with each winding acting as a part of a separate electric circuit. Let

N1, and N2 be the number of turns in the primary and secondary windings.

Figure 3: ideal transformer

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Let us first consider an idealized transformer in which there are no losses and no leakage flux. In

other words, we are postulating the following:

1- The core of the transformer is highly permeable.

2- The core does not exhibit any eddy-current or hysteresis loss.

3- All the flux is confined to circulate within the core.

4- The resistance of each winding is negligible.

A transformer turns ratio (a):

The total induced voltage in each winding is proportional to the number of turns in that winding

and the current is inversely proportional to both voltage and number of turns.

E1: primary voltage

I1: primary current

E2: secondary voltage

I2: secondary current

N1: primary turns

N2: secondary turns

a: turns ratio

Secondly//A Non-ideal Transformer

Practical transformers can be called non ideal transformer because not all of the magnetic flux

produced by the primary winding will link with the secondary winding can be losses induced within

transferring power from primary to secondary.

Winding Resistances

However small it may be, each winding has some resistance. Nonetheless, we can replace a non-ideal

transformer with an idealized transformer by including a lumped resistance equal to the winding

resistance of series with each winding. As shown in Figure 4, R1 and R2 are the winding resistances of

the primary and the secondary.

Figure 4: An ideal transformer with winding resistances

a = 𝑁1

𝑁2 =

𝑉1

𝑉2 =

𝐼2

𝐼1

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Leakage Fluxes

Not all of the flux created by a winding confines itself to the magnetic core on which the winding is

wound. Part of the flux, known as the leakage flux, does complete its path through air.

Figure 5: Transformer with leakage fluxes.

XI and X2 are the leakage reactances of the primary and secondary windings as shown in figure 6.

Figure 6: An ideal transformer with winding resistances and leakage fluxes

Finite Permeability

The core of a non-ideal transformer has finite permeability and core loss, known as the

excitation current from the source Iⱷ, is the sum of two currents: the core-loss current Ic and

the magnetizing current Im.

Iⱷ = Ic + Im

The core-loss component of the excitation current accounts for the magnetic loss (the

hysteresis loss and the eddy-current loss) in the core of a transformer, RC is the equivalent

core-loss resistance, Xm called magnetizing reactance can be represent the magnetizing

component of the excitation current.

Figure 7: Equivalent circuit of a transformer including winding resistances, leakage reactance,

core-loss resistance, magnetizing reactance, and an ideal transformer

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Exact equivalent circuit:

Figure 8The exact equivalent circuit as viewed from the primary side

Figure 9 The exact equivalent circuit as viewed from the secondary side

Approximate Equivalent Circuits:

Figure 10: Approximate equivalent circuit of a transformer as viewed from the primary side

Figure 11: Aapproximate equivalent circuit of a transformer as viewed from the secondary side

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Experimental Procedures:

You can find transformer turns ratio (a) by two methods: 1- Transformation voltage ratio

2- Transformation current ratio

Find the turn’s ratio between nodes 1, 2 primary side and nodes 3, 4 secondary side.

Part1 : Determine the turn’s ratio using voltage ratio

1- Connect the circuit as shown in figure below.

Figure 12 Determine the turn’s ratio using voltage ratio

2- Open data table window and record data step by 10% from 0% - 100%

Figure 13 Data table for voltage ratio

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3- Open graph window from data table to find slope of the line between E1 at Y-axis and E2

at X-axis.

Figure 14 Graph window for voltage ratio

4- Find slope of the line from figure above.

a = 1

2 =

1 12

3 2 = 0.55

Part2: Determine the turn’s ratio using current ratio

1- Connect the circuit as shown in figure below.

Figure 15 Determine the turn’s ratio using current ratio

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2- Open data table window and record data step by 10% from 0% - 100%

Figure 16 Data table for current ratio

3- Open graph window from data table to find slope of the line between I2 at Y-axis and I1

at X-axis.

Figure 17 Graph window for current ratio

4- Find slope of the line from figure above.

a = 2

1 =

1 1

2 1 = 0.55

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Exercise:

1- Repeat the above two methods to find transformer ratio (a) between:

a) Primary side 1,2 and secondary side 5,6

b) Primary side 7,8 and secondary side 5,6