# Analysis of magnetic circuits of Transformer

**Transformers**

Transformers are commonly used in applications which require the conversion of AC voltage from one voltage level to another. There are two broad categories of transformers: electronic transformers, which operate at very low power levels, and power transformers, which process thousands of watts of power. Electronic transformers are used in consumer electronic equipment like television sets, VCRs, CD players, personal computers, and many other devices, to reduce the level of voltage from 220V (available from the AC mains) to the desired level at which the device operates. Power transformers are used in power generation, transmission and distribution systems to raise or lower the level of voltage to the desired levels. The basic principle of operation of both types of transformers is the same.

**Magnetic Field**

Magnetic fields are created due to movement of electrical charge, and are present around permanent magnets and wires carrying current (electromagnet).

-In permanent magnets, spinning electrons produce a net external field.

-If a current carrying wire is wound in the form of a coil of many turns, the net magnetic field is stronger than that of a single wire. This field of the electromagnet is further intensified if this coil is wound on an iron core.

In many applications, we need to vary the strength of magnetic fields. Electromagnets are very commonly used in such applications.

-The magnetic field is represented by “lines of flux”.

-These lines of flux help us to visualize the magnetic field of any magnet even though they only represent an invisible phenomena.

-Magnetic field forms an essential link between transfer of energy from mechanical to electrical form and vice-versa

Magnetic fields form the basis for the operation of transformers, generators, and motors.

The direction of this magnetic field can be determined using the right hand rule.

-This rule states that if you point the thumb of your right hand in the direction of the current, your fingers will point in the direction of the magnetic field.

**Magnetic Flux**

Magnetic field can be visualized as lines of magnetic flux that form closed paths (see Figure 1). Magnetic

flux emanates from the north pole and returns through the south pole.

-Magnetic flux describes the total amount of magnetic field in a given region.

-Magnetic flux is imperceptible to the five senses and thus hard to describe.

-Flux is known only through its effects.

-It is measured in Weber (Wb)

**Magnetic Flux density**

If we examine the cross-sectional area of the magnet shown in Figure 1(a) and assume that the flux is uniformly

distributed over the area, the magnetic flux density is defined as the magnetic Flux per cross-sectional area.

i.e.,

B=Flux Density/Area

where A is the cross sectional area.

-Flux density is a vector quantity

-Its units are Weber per sq meter or Tesla (T).

**Real Transformers**

The ideal model neglects the following basic linear aspects in real transformers:

Core losses collectively called magnetizing current losses consisting of:

•Hysteresis losses due to nonlinear application of the voltage applied in the transformer core

•Eddy current losses due to joule heating in core proportional to the square of the transformer’s applied voltage.

Whereas the ideal winding have no impedance, the winding in a real transformer have finite non-zero impedance in the form of:

•Joule losses due to resistance in the primary and secondary windings[15]
•Leakage flux that escapes from the core and passes through one winding only resulting in primary and secondary reactive impedance.

Linkage Flux

The ideal transformer model assumes that all flux generated by the primary winding links all the turns of every winding, including itself. In practice, some flux traverses paths that take it outside the winding. Such flux is termed leakage flux, and results in leakage inductance in series with the mutually coupled transformer winding.Leakage flux results in energy being alternately stored in and discharged from the magnetic fields with each cycle of the power supply. It is not directly a power loss, but results in inferior voltage regulation, causing the secondary voltage to not be directly proportional to the primary voltage, particularly under heavy load.Transformers are therefore normally designed to have very low leakage inductance. Nevertheless, it is impossible to eliminate all leakage flux because it plays an essential part in the operation of the transformer. The combined effect of the leakage flux and the electric field around the winding is what transfers energy from the primary to the secondary.

In some applications increased leakage is desired, and long magnetic paths, air gaps, or magnetic bypass shunts may deliberately be introduced in a transformer design to limit the short-circuit current it will supply.Leaky transformers may be used to supply loads that exhibit negative resistance, such as electric arcs, mercury vapor lamps, and neon signs or for safely handling loads that become periodically short-circuited such as electric arc welders.

Air gaps are also used to keep a transformer from saturating, especially audio-frequency transformers in circuits that have a DC component flowing through the winding.

Knowledge of leakage inductance is for example useful when transformers are operated in parallel. It can be shown that if the percent impedance (Z) and associated winding leakage reactance-to-resistance (X/R) ratio of two transformers were hypothetically exactly the same, the transformers would share power in proportion to their respective volt-ampere ratings (e.g. 500 kVA unit in parallel with 1,000 kVA unit, the larger unit would carry twice the current). However, the impedance tolerances of commercial transformers are significant. Also, the Z impedance and X/R ratio of different capacity transformers tends to vary, corresponding 1,000 kVA and 500 kVA units’ values being, to illustrate, respectively, Z ~ 5.75%, X/R ~ 3.75 and Z ~ 5%, X/R ~ 4.75.

Questions

1.What are the meanings of these ratings?

The voltage ratio indicates that the transformer has two winding, the high-voltage winding is rated for 1100 Volts and the low-voltage winding for 110 volts.

These voltages are proportional to their respective number of turns. Therefore, the voltage ratio also represents

the turns ratio a. (e.g., a = 10)

The kVA rating (i.e., apparent power) means that each winding is designed for 10 kVA.

Therefore the current rating for the high-voltage winding = 10000/1100 = 9.09A

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### One Response to Analysis of magnetic circuits of Transformer

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Thanks for explaining the in-depth analysis of the magnetic circuits that work on the transformers. Transformers are of great use that help to maintain the voltage levels and to offer a steady current flow across the electrical units. There are various types of transformers available these days, from which one can choose based on their needs.