Transformer Definition
Transformers are electrical devices consisting of two or more coils of wire used to transfer electrical energy by means of a changing magnetic field.
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A device consisting of two or more windings coupled by a magnetic core that is used to transform a balanced set of three-phase voltages from one voltage level to another without changing the frequency.
or
A Transformer is a static electrical device that transfers electrical energy between two or more circuits through electromagnetic induction.
The transformer is an essential element of an electrical power system. It is among the primary reasons for the far-flung utilization of AC power systems. It makes power generation possible at the most efficient voltage, transmission system and distribution at the most economic voltage levels, and electric power usage at the most appropriate voltage. The electric transformer is also extensively applied to measure very high voltages using voltage or potential transformers and very large currents using a current transformer). Additional salient uses of transformers include impedance matching, Insulating one electric circuit from another.
Transformer Working Principle
A single-phase transformer fundamentally comprises two main windings coupled up by a magnetic core. When one of the windings (common refer as primary) is linked to an AC power source, a time-varying flux is generated in the core which links the second winding(commonly referred as secondary winding). Consequently, a voltage is induced in the secondary winding. When an electrical load is connected to the secondary winding, a secondary current starts flowing.
A single-phase transformer unit is exemplified in Fig 1. The primary and secondary windings have N1 and N2 turns respectively. The voltages and currents associated with each winding are stated in the Pharos form.
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| Fig-1 Transformer Circuit |
Transformer Construction (single-phase)
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| Fig-2 Transformer Construction |
Where:
V – is the Primary Voltage
V – is the Secondary Voltage
N – is the Number of Primary Windings
N – is the Number of Secondary Windings
Φ (phi) – is the Flux Linkage
Notice that the two coil windings are not electrically connected but are only linked magnetically. A single-phase transformer can operate to either increase or decrease the voltage applied to the primary winding. When a transformer is used to “increase” the
voltage on its secondary winding with respect to the primary, it is called a Step-up transformer. When it is used to “decrease” the voltage on the secondary winding with respect to the primary it is called a Step-down transformer.
However, a third condition exists in which a transformer produces the same voltage on its secondary as is applied to its primary winding. In other words, its output is identical with respect to voltage, current and power transferred. This type of transformer is
called an “Impedance Transformer” and is mainly used for impedance matching or the isolation of adjoining electrical circuits.
The difference in voltage between the primary and the secondary windings is achieved by changing the number of coil turns in the primary winding ( N ) compared to the number of coil turns on the secondary winding ( N ).
As the transformer is basically a linear device, a ratio now exists between the number of turns of the primary coil divided by the number of turns of the secondary coil. This ratio, called the ratio of transformation, more commonly known as a transformers “turns ratio”, ( TR ). This turns ratio value dictates the operation of the transformer and the corresponding voltage available on the secondary winding.
It is necessary to know the ratio of the number of turns of wire on the primary winding compared to the secondary winding. The turns ratio, which has no units, compares the two windings in order and is written with a colon, such as 3:1 (3-to-1). This means in this
example, that if there are 3 volts on the primary winding there will be 1 volt on the secondary winding, 3 volts-to-1 volt. Then we can see that if the ratio between the number of turns changes the resulting voltages must also change by the same ratio, and this is true.
Transformers are all about “ratios”. The ratio of the primary to the secondary, the ratio of the input to the output, and the turns ratio of any given transformer will be the same as its voltage ratio. In other words for a transformer: “turns ratio = voltage ratio”. The actual number of turns of wire on any winding is generally not important, just the turns ratio and this relationship is given as:
A Transformers Turns Ratio
Assuming an ideal transformer and the phase angles: Φ ≡ Φ
Note that the order of the numbers when expressing a transformers turns ratio value is very important as the turns ratio 3:1 expresses a very different transformer relationship and output voltage than one in which the turns ratio is given as: 1:3.
E.M.F Equation of Transformer
The primary winding draws a current when it is connected to an alternating voltage source this sinusoidal current produces a sinusoidal flux Φ that can be expressed as:
ɸ=ɸ𝒎𝒔𝒊𝒏𝒘𝒕 ……..(1)
Instantaneous emf induced in the primary winding is:
𝒆𝟏= −𝑵𝟏𝒅ɸ𝒅𝒕 ……..(2)
Similarly, instantaneous emf induced in the secondary winding is:
𝒆𝟐= −𝑵𝟐𝒅ɸ𝒅𝒕 ……..(3)
Substituting eq.(1) in (2) yields ,
𝒆𝟏= −𝑵𝟏𝒅𝒅𝒕 (ɸ𝒎𝒔𝒊𝒏𝒘𝒕) ……..(4)
𝒆𝟏= −𝑵𝟏𝒘ɸ𝒎 𝒄𝒐𝒔𝒘𝒕 ……..(5)
𝒆𝟏= −𝑵𝟏𝒘ɸ𝒎𝐬𝐢𝐧(𝒘𝒕−𝟗𝟎) ……..(6)
The maximum value of 𝑒1 is:
𝑬𝒎𝟏=𝑵𝟏𝒘ɸ𝒎 ……..(7)
The rms value of the primary emf is:
𝑬𝟏=𝑬𝒎𝟏√𝟐 ……..(8)
Substituting eq.(7) into eq.(8) yields,
𝑬𝟏=𝑵𝟏 𝟐л𝒇ɸ𝒎√𝟐 ……..(9)
𝑬𝟏=𝟒.𝟒𝟒ɸ𝒎𝑵𝟏 ……..(10)
Similarly the expression of the secondary emf is:
𝑬𝟐=𝟒.𝟒𝟒ɸ𝒎𝑵𝟐 ……..(11)
The primary and secondary voltage can be determined from eq. (10) and (11) if other parameters are known.
Where:
ƒ – is the flux frequency in Hertz, = ω/2π
Ν – is the number of coil windings.
Φ – is the amount of flux in Weber's
This is known as the Transformer EMF Equation. For the primary winding emf, N will be the number of primary turns, ( N ) and for the secondary winding emf, N will be the number of secondary turns, ( N ).
Also please note that as transformers require an alternating magnetic flux to operate correctly, transformers cannot therefore be used to transform or supply DC voltages or currents, since the magnetic field must be changing to induce a voltage in the secondary
winding. In other words, transformers DO NOT operate on steady state DC voltages, only alternating or pulsating voltages.
If a transformers primary winding was connected to a DC supply, the inductive reactance of the winding would be zero as DC has no frequency, so the effective impedance of the winding will therefore be very low and equal only to the resistance of the copper used.
Thus the winding will draw a very high current from the DC supply causing it to overheat and eventually burn out, because as we know I = V/R.
Thank You !!!