ESO 210

Introduction to Electrical Engineering Lecture-23

Three Phase Transformers

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A conceptual three phase transformer A practical core type three phase transformer

Instead of using three number of single phase transformers, a three phase transformer can be constructed as a single unit.

The advantage of a single unit of 3-phase transformer is that the cost is much less compared to a bank of single phase transformers.

In fact all large capacity transformers are a single unit of three phase transformer.

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Here three, single phase transformers are so placed that they share a common central limb.

If the primary windings are connected to a balanced 3-phase supply (after connecting the windings in say star), the fluxes φA(t), φB(t) and φC(t) will be produced in the cores differing in time phase mutually by 120°.

The return path of these fluxes are through the central limb of the core structure. In other words the central limb carries sum of these three fluxes. Since instantaneous sum of the fluxes, φA(t)+ φB(t)+ φC(t) = 0, no flux lines will exist in the central limb at any time.

As such the central common core material can be totally removed without affecting the working of the transformer.

Immediately we see that considerable saving of the core material takes place if a 3-phase transformer is constructed as a single unit. The structure however requires more floor area as the three outer limbs protrudes outwardly in three different directions.

A further simplification of the structure can be obtained by bringing the limbs in the same plane as shown in the figure for a practical core type three phase transformer.

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But what do we sacrifice when we go for this simplified structure?

In core structure of figure for conceptual three phase transformer, we note that the reluctance seen by the three fluxes are same, Hence magnetizing current will be equal in all the three phases.

In the simplified core structure of figure, reluctance encountered by the flux φB is different from the reluctance encountered by fluxes φA and φC, Hence the magnetizing currents or the no load currents drawn will remain slightly unbalanced.

This degree of unbalanced for no load current has practically no influence on the performance of the loaded transformer. Transformer having this type of core structure is called the core type transformer.

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Magnetostriction:

Magnetic flux in a ferromagnetic material, such as the core, causes it to physically expand

and contract slightly with each cycle of the magnetic field, an effect known

as magnetostriction. This produces the buzzing sound commonly associated with

transformers and can cause losses due to frictional heating.

Mechanical losses:

In addition to magnetostriction, the alternating magnetic field causes fluctuating forces

between the primary and secondary windings. These incite vibrations within nearby

metalwork, adding to the buzzing noise, and consuming a small amount of power.

Stray losses:

Leakage inductance is by itself largely lossless, since energy supplied to its magnetic fields

is returned to the supply with the next half-cycle. However, any leakage flux that intercepts

nearby conductive materials such as the transformer's support structure will give rise to

eddy currents and be converted to heat. There are also radiative losses due to the

oscillating magnetic field, but these are usually small.

Some additional minor losses:

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Problem: A 2400 V/400 V single-phase transformer takes a no-load current of 0.5 A and the core loss is 400 W. Determine the values of the magnetizing and core loss components of the no-load current. Draw to scale the no-load phasor diagram for the transformer.

Solution:

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Transformer Construction

There are broadly two types of single-phase double-wound transformer constructions—the core type and the shell type, as shown in Figure below. The low and high voltage windings are wound as shown to reduce leakage flux.

Core type Shell type

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•For power transformers, rated possibly at several MVA and operating at a frequency of 50 Hz in India, the core material used is usually laminated silicon steel or stalloy, the laminations reducing eddy currents and the silicon steel keeping hysteresis loss to a minimum. •Large power transformers are used in the main distribution system and in industrial supply circuits. Small power transformers have many applications, examples including welding and rectifier supplies, domestic bell circuits, imported washing machines and so on.

For audio frequency (a.f.) transformers, rated from a few mVA and operating at frequencies up to about 15 kHz, the small core is also made of laminated silicon steel. A typical application of a.f. transformers is in an audio amplifier.

Radio frequency (r.f.) transformers, operating in the MHz frequency region have either an air core, a ferrite core or a dust core. Ferrite is a ceramic material having magnetic properties similar to silicon steel, but having a high resistivity. Dust cores consist of fine particles of carbonyl iron or permalloy (i.e. nickel and iron), each particle of which is insulated from its neighbour. Applications of r.f. transformers are found in radio and television receivers.

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Transformer windings are usually of enamel-insulated copper or aluminium.

Cooling is achieved by air in small transformers and oil in large transformers.

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Problem: A 200 kVA rated transformer has a full-load copper loss of 1.5 kW and an iron loss of 1 kW. Determine the transformer efficiency at full load and 0.85 power factor.

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Solution:

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Problem: Determine the efficiency of the transformer in previous Problem at half full-load and 0.85 power factor.

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A 400 kVA transformer has a primary winding resistance of 0.5 and a secondary winding resistance of 0.001 . The iron loss is 2.5 kW and the primary and secondary voltages are 5 kV and 320 V respectively. If the power factor of the load is 0.85, determine the efficiency of the transformer (a) on full load, and (b) on half load.

Problem:

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Solution:

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Equivalent circuit of a Practical Transformer

R1 and R2 represent the resistances of the primary and secondary windings and X1 and X2 represent the reactances of the primary and secondary windings, due to leakage flux.

The core losses due to hysteresis and eddy currents are allowed for by resistance R which takes a current Ic, the core loss component of the primary current. Reactance X takes the magnetizing component IM.

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R and X are omitted since the no-load current I0 is normally only about 3–5% of the full load primary current.

Transformer on no-load

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It is often convenient to assume that all of the resistance and reactance as being on one side of the transformer.

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Maximum Efficiency:

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Major Quiz-2: Oct 8, 2014 on Transformers Lectures on DC machines: Oct 13,15,17 and Oct 18, 2014 by Prof. Sandeep Anand