Module 3. Transformers

Lesson 10

TRANSFORMER THEORY-I

10.1  Introduction

Transformer is used to increase or decrease the voltage. Transformer is an important electrical machine in a power system (Fig. 10.1). A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductors—the transformer's coils. A varying current in the first or primary winding creates a varying magnetic flux in the transformer's core and thus a varying magnetic field through the secondary winding. This varying magnetic field induces a varying electromotive force (EMF), or "voltage", in the secondary winding. This effect is called inductive coupling.

Fig. 10.1 A pole mount transformer

Electrical power is generated at power plant (Thermal/Hydel/Nuclear) generally at 11 kV. The voltage is stepped up to 220 kV or 400 kV for transmission to long distances. It is done to reduce loss and increase distribution efficiency. Transformer can be broadly classified as:

10.1.1  Step up transformer

When output voltage is greater than input voltage (V₂>V₁).

Fig. 10.2 Step up transformer

10.1.2  Step down transformer

When output voltage is less than input voltage (V₂<V₁).

Fig. 10.3 Step down transformer

10.2  Principle of Operation

Transformer works on the principle of electromagnetic induction. The basic elements of a transformer are (Fig. 10.3):

1. Steel core: on which primary and secondary winding are done.

2. Primary winding: a.c. supply is connected.

3. Secondary winding: Load is connected.

When primary winding is connected to a.c. voltage V₁, an alternating flux is set up in the core. This alternating flux links with the secondary winding through the steel core. An e.m.f. is induced in the secondary winding known as mutually induced e.m.f. According to Lenz’s law the direction of induced e.m.f. V₂ is opposite to the applied voltage V₁ (Fig.10.4).

Fig. 10.4 Direction of induced emf in secondary coil is opposite to applied voltage

The primary and secondary windings are not connected but due to mutual flux emf is induced in the secondary coils.

10.3 E.m.f. Equation of a Transformer

Consider a transformer having

N₁ number of turns in primary side

N₂ number of turns in secondary side

The transfer is updated by a.c input of frequency f. Let Φ_m be the maximum flux in the transfer core.

Φ_m  = B_m × A

Where

Φ_m = Maximum flux in core , Wb

B_m= Maximum flux density

A = area of core

Fig. 10.5 Wave form of alternating flux

From above figure it is evident that flux increase from zero to the maximum value Φ_m in T/4 seconds.

......... (1)  [Since T = 1/f]

 We know,

Form factor = r.m.s. value/average value = 1.11

Or,   r.m.s value = 1.11 × average value ......... (2)

From eqn (1) & (2)

r.m.s value of e.m.f/ turn = 1.11 × 4 f Φ_m volts

= 4.44 f Φ_m volts/turn

r.m.s value of induced emf in primary winding having N₁ turns

E₁ =4.44 f Φ_m N₁ volts ......... (3)

r.m.s value of induced emf in secondary winding having N₂ turns

E₂ = 4.44 f Φ_m N₂ volts ......... (4)

Dividing equation (4) & (5)

Or   
......... (5)

The ratio of secondary voltage (E₂) to primary voltage (E₁) is known as transformation ratio (K).

· Step up transformer        N₂ > N₁ or K > 1

· Step down transformer    N₁ > N₂ or K < 1

 In case of an ideal transformer

Input power = output power

or

......... (6)

From (5) & (6)

10.3.1  Turn ratio

The ratio of secondary to primary turns is called turn ratio,

turn ratio= N₂/N₁.

If N₂>N₁ transformer is step-up transformer

            If N₂<N₁ transformer is step-down transformer.

The relationship between transformation ratio and turn ratio is given as:

10.4  Working

When an alternating voltage V₁ is applied to the primary, an alternating flux  is set up in the core. The alternating flux links both the windings and induces e.m.f.s E₁ and E₂ in them according to Faraday’s laws of electromagnetic induction. The e.m.f. E₁ is termed as primary e.m.f. and e.m.f. E₂ is termed as secondary e.m.f.

Note that magnitude of E₂ and E₁ depend upon the number of turns on the secondary and primary respectively. If N₂>N₁, then E₂>E₁ (or V₂>V₁) and we get a step-up transformer. On the other hand, if N₂<N₁, then E₂<E₁ (or V₂<V₁) and we get a step-down transformer. If load is connected across the secondary winding, the secondary e.m.f. E₂ will cause a current I₂ to flow through the load. Thus, a transformer enables us to transfer a.c. power from one circuit to another with a change in voltage level. The following points may be noted carefully:

· The transformer action is based on the laws of electromagnetic induction.

· There is no electrical connection between the primary and secondary. The a.c. power is transferred from primary to secondary through magnetic flux.

· The transformer cannot work on d.c. power.

· There is no change in frequency i.e. output power has the same frequency as the input power.

· The losses that occur in a transformer are:

a) Core losses-eddy current and hysteresis.

b) Copper losses-in the resistance of the windings.

In practice, these losses are very small so that output power is nearly equal to the input primary power. In other words, a transformer has very high efficiency.

10.5  Application of Transformer

10.5.1  Power distribution

Big generating stations are located at hundreds or more km away from the load center (where the power will be actually consumed). Long transmission lines carry the power to the load centre from the generating stations. Generator is a rotating machines and the level of voltage at which it generates power is limited to several kilo volts only a typical value is 11 kV. To transmit large amount of power (several thousands of mega watts) at this voltage level means large amount of current has to flow through the transmission lines. The cross sectional area of the conductor of the lines accordingly should be large. Hence cost involved in transmitting a given amount of power raises many folds. Not only has that, the transmission lines had their own resistances. This huge amount of current will cause tremendous amount of power loss or I²R loss in the lines. This loss will simply heat the lines and becomes a wasteful energy. In other words, efficiency of transmission becomes poor and cost involved is high. The above problems may address if we could transmit power at a very high voltage say, at 200 kV or 400 kV or even higher at 800 kV. But as pointed out earlier, a generator is incapable of generating voltage at these levels due to its own practical limitation. The solution to this problem is to use an appropriate step-up transformer at the generating station to bring the transmission voltage level at the desired value as depicted in figure 10.6 where for simplicity single phase system is shown to understand the basic idea.

Fig. 10.6 Power transmission system

Obviously when power reaches the load centre, one has to step down the voltage to suitable and safe values by using transformers. Thus transformers are an integral part in any modern power system. Transformers are located in places called substations. In cities or towns you must have noticed transformers are installed on poles – these are called pole mounted distribution transformers. These type of transformers change voltage level typically from 3-phase, 6 kV to 3-phase 440 V line and then to 220 V line.

10.5.2  Domestic use

Small transformers are used in the mobile charger, emergency light etc to bring 220 V domestic supply to low voltage may be 4.5 V or 6 V.  

10.6  Construction of Transformer

1. Steel core: Silicon steel in the form of thin laminations is used for the core material. The core is laminated to minimize the eddy current loss. These laminations are coated with a thin layer of insulating varnish, oxide or phosphate. The thickness of laminations ranges from 0.35 mm to 0.5 mm. The construction can be core type or shell type:

a) Core type: In a core type construction the winding surrounds the core. The laminations are cut in L shape and are assembled in form of rectangular frame (Fig. 10.7). To prevent flux leakage primary and secondary windings are placed overlapping on the limbs of core.

Fig. 10.7 Core type transformer

b)  Shell type: In case of shell-type transformer, individual laminations are cut in the form of long strips of E’s and I’s as shown in fig 10.8. In order to avoid high reluctance at the joints where the laminations are butted against each other, the alternate layers are stacked differently to eliminate continuous joints.

Fig. 10.8 Shell type transformer

In a shell-type transformer, the core has three limbs, the central limb carries whole of the flux, where as the side limbs carry half of the flux. Therefore, the width of the central limb as about double to that of the other limbs.  Both of the primary and secondary windings are placed on the central limb side by side or concentrically. The low voltage winding is placed nearer the core and the high voltage winding is placed outside the low voltage winding to reduce the cost of insulation placed between core and low voltage winding. In this case also the windings are form-wound in cylindrical shape and the core laminations are inserted later on.

2. Windings: Windings form another important part of transformers. In a two winding transformer two windings would be present. The one which is connected to a voltage source and creates the flux is called primary winding. The second winding where the voltage is induced by induction is called a secondary. If the secondary voltage is less than that of the primary the transformer is called a step down transformer. If the secondary voltage is more then it is a step up transformer. A step down transformer can be made a step up transformer by making the low voltage winding as its primary. Hence it may be more appropriate to designate the windings as High Voltage (HV) and Low Voltage (LV) windings. The winding with more number of turns will be a HV winding. The current on the HV side will be lower as V-I product is a constant and given as the VA rating of the machines. Also the HV winding needs to be insulated more to withstand the higher voltage across it. HV also needs more clearance to the core, yoke or the body. These aspects influence the type of the winding used for the HV or LV windings.

a. Primary winding: a.c. supply is connected.

b. Secondary winding: Load is connected.

3. Container/tank: It forms the outer covering and body of the transformer. It is filled with oil in case of oil cooled transformers.

4. Bushings: Are required for connecting the ends of the winding to the external circuit. Bushings are made of porcelain and it insulate the terminals from the transformer body. Two separate bushings are provided for High Voltage (HV) and Low Voltage (LV) connections (Fig. 10.9).

Fig. 10.9 Outer construction of a transformer

5. Cooling arrangement: Heat is produced in a transformer by the iron losses in the core and I²R loss in the windings. To prevent undue temperature rise, this heat is removed by cooling. Type of cooling methods used are:

· Dry type transformer: Natural air circulation, air blast

· Liquid (oil) immersed: self-cooled, forced air cooled, forced water cooled, forced oil cooled

a) In small transformers (below 50 kVA), natural air cooling is employed i.e. the heat produced is carried away by the surrounding air.

b) Medium size power or distribution transformers are generally cooled by housing them in tanks filled with oil. The oil serves a double purpose, carrying the heat from the windings to the surface of the tank and insulating the primary from the secondary. Self oil cooled transformer have cooling tubes on the outer body. Due to heat dissipation from the winding convective circulation of oil occurs in the cooling tubes.

c) For large transformers, external radiators are added to increase the cooling surface of the oil filled tank. The oil circulates around the transformer and moves through the radiators where the heat is released to surrounding air. Sometimes cooling fans blow air over the radiators to accelerate the cooling process (Fig. 10.10).

Fig. 10.10 Oil cooled transformer

Numericals

1.  Calculate transformation ratio if the voltage in the primary and secondary coil are 11000 and 440 volts respectively.

transformation ratio

=

 2. Calculate the number of turns in the secondary coils of a transformer if transformation ratio is 10 and number of turns in primary side is 2500.

Given

K = 10

N₁ = 2500

K = N₁ / N₂

N₂ = 10 × 2500

     = 25000 turns.

3.  If the number of turns in the primary and secondary windings of the transformer is 500 and 1000 respectively. Find the voltage in the secondary side of transformer. The primary side voltage is 220 V.

transformation ratio K = N₁ / N₂ = 500/1000 =0.5

E₂ = 110 V