Fundamental Theory Of A Transformer: Mark Antony M. Pon-an, Pee, Mba

FUNDAMENTAL THEORY OF A TRANSFORMER MARK ANTONY M. PON-AN, PEE, MBA DEPED ECOTECH, CEBU CITY, AUG 30-31, 2019

OUTLINE • • • • • •

Definition of a transformer Fundamental Theory of a transformer Electromagnetic Induction Equivalent Circuits Parts of a transformer Construction of a transformer

What is a Transformer? According to IEC 60076-1 Transformer is defined as: “A static piece of apparatus with two or more windings which, by electromagnetic induction, transforms a system of alternating voltage and current into another system of voltage and current usually of different values and at the same frequency for the purpose of transmitting electrical power”

According to IEEE C57.12.80-2002 Transformer is defined as: A static device consisting of a winding, or two or more coupled windings with or without a magnetic core for introducing mutual coupling between electrical circuits.

Fundamental Theory of a Transformer •

Transformers are simple static electrical devices, involving no continuously moving parts used in electric power system to transfer energy (or power) from one circuit to another by linking circuits magnetically through a magnetic steel core.

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This magnetic steel core provides the path for the common magnetic field produced by a coil or winding excited by an alternating current source.

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In the common 2-winding transformer, there is no electrical connection from input to output

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Transformer change voltage in direct proportion to the ratio of input to output winding turns

Figure shows an alternating current flowing in a wire creating a magnetic field around the wire.

Fundamental Theory of a Transformer •

Lines can be step-up, that is, going from lower voltage to higher voltage; or step down, that is going from higher voltage to lower voltage.

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The terms primary and secondary refer to the input and output windings respectively.

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Generally, primary side is connected to the SOURCE. Secondary side is connected to the LOAD.

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Input side is always the primary side regardless of relative voltage values, that is, it can be of a lower voltage or higher voltage value than the output side.

Fundamental Theory of a Transformer •

As the current varies in magnitude with respect to time, so does the magnetic field.

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The magnetic field also reverses its direction each half cycle.

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The building up and collapsing of the magnetic field tend to have the stationary wire cutting the magnetic field, thus inducing a voltage in the wire which is also of varying magnitude having a voltage waveform similar to the alternating current waveform.

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The magnetic field exists in air which is a poor conducting path for the magnetic (or magnetic flux)

ELECTROMAGNETICS •

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If the conductor is wound into a coil, the magnetic lines of flux add to produce a stronger magnetic field. A coil with 10 turns of wire produces a magnetic field that is 10 times as strong as the magnetic field around a single conductor. The two factors that determine the number of flux lines produced by an electromagnet are the number of turns of wire and the amount of current flow through the wire.

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The strength of an electromagnet is proportional to its ampere-turns. Ampere-turns are determined by multiplying the number of turns of wire by the current flow.

ELECTROMAGNETICS •

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When a coil is wound around a non magnetic material such as wood or plastic, it is known as an air-core magnet. When a coil is wound around a magnetic material such as iron or soft steel, it is known as an ironcore magnet. The addition of magnetic material to the center of the coil can greatly increase the strength of the magnet.

ELECTROMAGNETIC INDUCTION • Electromagnetic Induction, which states that whenever a conductor cuts through magnetic lines of flux, a voltage is induced into the conductor. • It can be concluded that the polarity of the induced voltage is determined by the polarity of the magnetic field in relation to the direction of movement.

Fundamental Theory of a Transformer •

Lines can be step-up, that is, going from lower voltage to higher voltage; or step-down, that is going from higher voltage to lower voltage.

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The terms primary and secondary refer to the input and output windings, respectively.

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Input side is always the primary side regardless of relative voltage values, that is, it can be of a lower voltage or higher voltage value than the output side.

Fundamental Theory of a Transformer •

According to Faraday’s law of induction, the magnetic flux Φ, in the core induces an emf, e1 in the primary winding that opposes the applied voltage, v1.

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The magnetic field exists in air which is a poor conducting path for the magnetic field (or magnetic flux).

Fundamental Theory of a Transformer

Above shows the conditions when another wire is placed in the magnetic field.

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The two wires shown have only one turn each. The building up and collapsing of the magnetic field produced by the wire with an alternating current flows into it as earlier discussed.

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If another wire is placed in the varying magnetic field an alternating voltage will be induced in the second wire.

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But since air is a poor conducting (or high reluctance) path for the magnetic flux, less amount of magnetic flux from the first wire will link the second wire.

Fundamental Theory of a Transformer

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The voltage induced in the second wire will be small compared to the first wire. The number of turns in the second wire can be increased to increase the voltage output, but this will be a high added cost.

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The best option, which is of lesser cost is to increase the amount of flux from the first wire to link with the second wire.

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In actual practice, there will be larger number of turns for both primary and secondary coils or windings. A magnetic steel core is a good conducting path for the magnetic flux compared to air.

Fundamental Theory of a Transformer •

In magnetic circuit, the ability of magnetic steel or iron to carry magnetic flux is called permeability. 

Iron is an element while steel is an alloy. Steel is a derivative of iron. Steel can rust, and is magnetic. Metals are anti corrosive and nonmagnetic, and are high thermal and electrical conductors. Steel is magnetic, and stainless steel is nonmagnetic, except some grades of stainless steel that are magnetic.

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Air has a permeability of 1.0 which is used as reference.

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Modern magnetic iron or steel core have permeabilities in the order of 1,500.

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The core is made of thin steel sheets designed to reduce eddy current of the transformer.

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These sheets are insulated from each other by thin coat of varnish or an oxide film.

Fundamental Theory of a Transformer The input winding is insulated from and wrapped around laminated core. The input or primary winding is impressed with an A.C. voltage source, thus there will be varying amount of magnetic flux in the steel core. This magnetic flux in the steel core induces voltage back into the primary coil. This induced counter voltage in the primary opposes the main impressed voltage from the source.

The induced counter voltage is almost equal to the main impressed voltage from the source, thus, the resulting primary current is kept down low!

Fundamental Theory of a Transformer

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A secondary or output winding is added in the core.

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The same flux called mutual flux which is produced by the primary induces a voltage in the secondary winding.

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For both primary and secondary windings, there will be the same voltage per turn induced.

Fundamental Theory of a Transformer •

With transformer loaded, that is, a load is connected to the secondary, the current in the secondary winding produces new magnetic flux that opposes the mutual flux in the core.

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This mutual flux was produced by the primary winding before the loading of the secondary.

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The secondary flux tends to weaken momentarily the mutual flux in the core.

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Please note the opposing directions of the magnetic fluxes.

Fundamental Theory of a Transformer

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When the mutual flux tries to drop off or reduced, the induced counter voltage in the primary decreases.

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With the decrease in the induced counter voltage in the primary there will be for a moment, an increase of the difference between the main impressed voltage (from the source) and the induced counter voltage in the primary.

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Thus the increase in net voltage (main impressed voltage and induced counter voltage) will increase, pushing more current through the transformer primary to produce additional flux, compensating the secondary bucking flux and to maintain the original value of the mutual flux.

Fundamental Theory of a Transformer

The operation sequences of the magnetic flux flow in the core for changes of load in the secondary are shown Figure 7(a, b, c and d).

Fundamental Theory of a Transformer

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Since the iron core is subjected to alternating flux, there occurs eddy current and hysteresis loss in it.

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These two losses together are known as iron losses or core losses.

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The iron losses depend upon the supply frequency, maximum flux density in the core, volume of the core etc.

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It may be noted that magnitude of iron losses is quite small in a practical transformer. RNMILITAR

Fundamental Theory of a Transformer Practical Transformer has winding resistance and leakage reactance on the primary and secondary windings. Winding resistance is due to the resistance of the total turns of conductors in the winding. The leakage reactance is due to magnetic leakage in the respective winding.

Figure 8 shows the complete series impedance of the transformer consisting of winding resistance and leakage reactance on the primary and secondary winding.

Fundamental Theory of a Transformer

Shown in Figure 9 is the flux paths (main flux and leakage fluxes) of a two-winding transformer.

When the primary winding is excited so that a flux is built up through the iron core, not all the flux goes around the magnetic core. •That is, not all the flux cutting through the primary winding links up with the secondary winding.

•The flux that links with both primary and secondary is the mutual flux and its maximum value is termed Øm.

Fundamental Theory of a Transformer The flux that cuts only the primary turns is called the primary leakage flux Øl1.

When the secondary winding is connected to a load, the ampere turns of the secondary produce a leakage flux around the secondary turns which does not link with the primary. These leakage flux Øl1 and Øl2 are proportional to the current producing them.

There are three fluxes, namely mutual flux Øm linking both primary and secondary.

Fundamental Theory of a Transformer

The primary leakage flux Øl1, linking only the primary turns and varying with I1. The secondary leakage flux Øl2, linking only the secondary turns and varying with I2.

It should be noted that not all turns are interlinked with the same leakage flux. In the situation, the values of leakage fluxes Øl1 & Øl2 are equivalent values.

Fundamental Theory of a Transformer The effect of these leakage fluxes can be accounted for by an inductance called leakage inductance. Series leakage reactance X1 represents the leakage flux in the input winding.

Likewise, series leakage reactance X2 represents the leakage flux in the output winding. The equivalent circuit is shown in Figure 1. For purposes of computation, visualizing and understanding, it is better to replace the actual transformer by an equivalent circuit that has similar properties.

Fundamental Theory of a Transformer Also, it will have the same losses with same magnetizing and core-loss currents, the same percent impedance drops on the primary and secondary, and the same electromotive forces. The same equations and vector diagrams apply to the transformer and its equivalent circuit.

That is, when delivering a given secondary current at a given secondary terminal voltage and power factor, it will draw the same primary input current at the same input voltage and power factor as the actual transformer.

Fundamental Theory of a Transformer

The exact equivalent circuit Figure 2. Is a I2(h+e) and rc represents the core loss (hysteresis circuit shown as the exact equivalent of and eddy current loss) of the transformer, and Xm (magnetizing reactance) is equal to E1/IØ. the circuit shown in Figure 1. The core loss of the transformer is practically constant from no-load to full-load.

Fundamental Theory of a Transformer THE APPROXIMATE EQUIVALENT CIRCUIT

In as much as the no-load current of transformers is small, it causes very little voltage drop through r1 and x1. The exact equivalent circuit then can be simplified by connecting the noload network across V1. This is shown in Figure 3 above.

Fundamental Theory of a Transformer THE APPROXIMATE EQUIVALENT CIRCUIT In as much as the no-load current of transformers is small, it causes very little voltage drop through r1 and x1. The exact equivalent circuit then can be simplified by connecting the no-load network across V1. This is shown in Figure 3.

In this circuit the equivalent load impedance Za2 is replace d by its components a2R and a2X This circuit assumes that the only voltage drops in the primary and secondary are those caused by the primary current required to balance the load current of the secondary.

TRANSFORMER VOLTAGES AND THE GENERAL TRANSFORMER EQUATION

𝑉𝑃 = 4.44𝑓𝑁𝑃 𝜙𝑚

Ø m

𝑉𝑆 = 4.44𝑓𝑁𝑆 𝜙𝑚

1 4𝑓 1 𝑓

𝑉𝑎𝑣𝑒 = 𝑁𝑥 𝑉𝑎𝑣𝑒 = 𝑁𝑥

𝜙𝑚 𝑡

𝑉 = 1.11𝑉𝑎𝑣𝑒

𝜙𝑚 1Τ4 𝑓

𝑉 = 4.44𝑓𝑁𝜙𝑚

𝑉𝑎𝑣𝑒 = 4𝑓𝑁𝜙𝑚

In a Sine wave: Effective Voltage, V is equal to 1.11 times the Average Voltage, Vave

Mathematically: V = 1.11 Vave

Fundamental Theory of a Transformer

Fundamental Theory of a Transformer

Parts of a Transformer

TRANSFORMER CONSTRUCTION

1) Winding Works

4) Coil Insertion Works

2) Core lamination

3) View of Core Structure (After Completion of Core Lamination)

5) View of Core and Coil Assembly Works

7) Completion of Core & Coil Assembly

6) Drying Works in Vacuum Vaporization Facility 8) Factory Test

THANKS A LOT FOR LISTENING FUNDAMENTAL THEORY OF TRANSFORMER

DEPED ECOTECH, CEBU CITY, AUG 30-31, 2019