Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE) PDF Download

VOLTAGE RECULATION
It is defined as the rise in voltage expressed as a fraction f full load rated voltage, when full load (at specified pf) is removed while keeping input voltage constant.

Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

where full load voltage = Rated voltage.
V'2 = aV2

Approximate Voltage Regulation

Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

To find voltage regulation at leading pf replace ø by –ø.

Condition for Maximum Voltage Regulation

Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

• Maximum voltage regulation

Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

Note:
• Here tanø is positive, therefore, maximum voltage regulation occurs at a lagging load 

p.f. = req/Zeq 

Condition for Zero Voltage Regulation

  • Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

or Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

or Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

or ø = (90°– θeq) leading

• Negative value of tanø indicates a leading pf. Therefore zero voltage regulation occurs when load  Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

Remember:
• For leading pf greater than Xpu/Zpu the voltage regulation will be negative.

TRANSFORMER LOSSES
• There are mainly two kinds of losses in a transformer.
Core Loss
• These consist of hysteresis loss Ph and eddy current loss Pe.
• Hysteresis loss P= Kh fBmx

• Eddy current loss P= Ke f2Bm2

Where,
K= Proportionality constant depend upon the quality of core and volume.
Ke = Proportionality constant whose depends on the volume and resistiviy of the core material, thickness of laminations and the units employed.
Bm = maximum flux density in the core
f = frequency of the alternating flux

x = Steinmetz's constant varies from 1.5 to 2.5. it is also depend upon magnetic material

∴ Pc =  Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

• Losses in terms of applied voltage and frequency

Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

Ohmic loss
• Ohmic losses occurs in both the primary and secondary winding resistance.

Pcu = I2req 

Note:
• Generally student get confused related with iron loss and copper loss. Actually iron loss (Pi) is also called core loss (Pc) and copper loss (Pcu) is also called ohmic loss (Poh). So it must be clear iron loss is also called constant loss because it is independent to the load current and ohmic loss (I2req ) is called variable loss because it is totally dependent to the square of load current.

EFFICIENCY OF TRANSFORMER
• The efficiency is may be defined as the ratio of output power to input power.

Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

or  Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

Condition for Maximum Efficiency
• Pi = Pcu = I2 req
• Copper loss = Iron loss
• The maximum efficiency for a constant load current occurs at unity power factor.
• Current maximum efficiency

Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

• kVA rating at maximum efficiency

Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

Where
S(know load) = kVA at known load
Pcu(know load) = Copper loss at known load

AUTO TRANSFORMER
• A single-phase auto-transformer is a one-winding transformer in which a part of the winding is common to both high voltage and low voltages sides.
• It is not electrically isolated.

Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

Number of turns of primary winding AC = Nand number of turns of secondary windings BC = N2

• If applied voltage Vacross AC winding, then the Voltage across winding BC is  Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

• If ideal case, Input power = output power

V1I1 cos θ1 = V2I2 cos θ2

• If cos θ1 = cos θ2

then, V1I1 = V2I2

Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

Where a = turn ratio.

Advantages of Auto trasformer Over Two Winding Transformer
• Auto transformer ha higher efficiency than two winding of same output.
• An autotransformer has lower value of leakage impedance and has superior voltage regulation than two winding transformer of same output.
• An auto transformer is more economic.

Disadvantages of Autotransformer Over Two Winding Transformer
• If turn ratio (a) differs for from unity the economic advantage of autotransformer over two winding transformer decreases.
• The short circuit current in an auto transformer is higher than that in a corresponding two winding transformer.
• The main disadvantage of an auto transformer is due to the direct electric connection between low voltage and high voltage side. If primary is supplied at high voltage, then an open circuit in common winding, would result in the appearance of dangerously high voltage on low voltage side.

Comparison of Characteristic of Autotransformers and Two Winding Transformers

Copper Saving in Autotransformer

• Cu(auto) = Cu(2wdg)Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

• Percentage copper saving
% Cu saving = 1/a x 100

Ratings

Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

Losses

Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

Voltage Regulation

Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

Short Circuit Current

Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

Note:
• Single phase and 3 phase auto transformer are mainly employed.
• For interconnecting power systems having voltage ration, not differing from unity.
• For obtaining variable output voltages.

 PARALLEL OPERATION OF 1-Ø TRANSFORMER
Advantage of Parallel operation
There are following advantages of the parallel operation of single-phase transformer

  • With two or more transformers the power system become more reliable. If one transformer develops fault, it can be removed and the other transformers can maintain the flow of power, though at a reduced level.
  • Transformers can be switched-off or on depending upon the power demand. In this manner the transformer losses decreases and the system becomes more economical and efficient in operation.
  • The cost of a standby (or spare) unit is much less when two or more transformers are installed.

Condition for Parallel Operation
• Condition for the satisfactory parallel operation of two or more single-phase transformers are as follows.

Necessary Conditions
• The polarities of the transformers must be the same.
• The turn ratios of the transformers should be equal. i.e. with the primaries connected to the same voltage source, the secondary voltages of all transformers should be equal in magnitude.

Desirable Conditions
• The per unit leakage impedance of the transformers based on their own KVA ratings must be equal.
• The ratio of equivalent leakage reactance to equivalent resistance i.e. xeq/req should be equal for all the transformers.

• This condition ensures that both transformers operate at the same power factor, thus sharing active power and reactive volt-amperes according to their ratings.

parallel Operation at Same voltage Ratio

Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

Where EA and EB are no-load secondary voltages.

Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

or  Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

Similarly,  Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

For Proportional Load Sharing

Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

or ZA(pu) = ZB(pu)
Where the pu values are on their respective or own base.

Same Voltage Ratio and Different (x/r) Ratio

Let θA > θB
Equal S for two transformer with
SA = S with θA
SB = S with θB

Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

Then S= Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

Unequal Voltage Ratio

Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

• Following steps are followed to calculate load kVA.

Steps:

  • Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)
  • Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)
  • Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

where Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

and Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

THREE PHASE TRANSFORMER
• When three identical units of single-phase transformers are used, the arrangement is commonly called a bank of three transformers or a three- phase transformer bank.
• Three phase current in three primaries produce three-phase fluxes mutually time-displaced by 120°. These fluxes flow through their respective
yokes and then through the central limbs placed together. The resultant flux in the three central limbs must be zero.

Core Type Transformer

Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

Three-phase core-type transformer from three single-phase units
• The reluctance offered to the flux of central limb II is less than the reluctance offered to the outer two fluxes produced in legs I and III. Consequently, the exciting current for the phase winding on the central limb is less than it is for the outer two phase windings. Shell Type Transformer
• A three- phase shell type transformer is obtained if three single-phase shell type cores are placed side by side.

Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

Three-phase shell type transformer with three windings wound in the same direction
• In the magnetic circuits marked 2 and 3, the resultant flux is seen to be equal to the phasor difference of the component fluxes.

Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

• For the same flux density, the cross-sectional areas at 2 and 3 are 86% of the central core area.

parallel Operation of 3-ø Transformers
• The various conditions that must be fulfilled, for the successful parallel operation of 3-phae transformers, are as follows:
• The line voltage rations of the transformers must be the same.
• The transformers should have equal per unit leakage impedances.
• The ratio of equivalent leakage reactance to equivalent resistance should be same for all the transformers.

• The transformers should have the same polarity.
• In addition to these four conditions, two more essential conditions that must be fulfilled for the parallel operation of three-phase transformers are as follows:

 Relative phase displacement: The relative phase displacement between the secondary line voltage of all the transformers must be zero i.e. the transformers to be connected in parallel, must belong to the same group number.

Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

Note:
• Transformers for group numbers 3 and 4 can be successfully operated in parallel.
• Phase Sequence: An improper phase sequence as shown in figure (b) below, would give zero voltage across switch S1 and line voltages across switch S2 and S3. Consequently the parallel operations is not possible.

Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

The document Transformers - 3 | Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE) is a part of the Electrical Engineering (EE) Course Electrical Engineering SSC JE (Technical).
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FAQs on Transformers - 3 - Electrical Engineering SSC JE (Technical) - Electrical Engineering (EE)

1. What is the basic principle behind the operation of transformers?
Ans. Transformers work on the principle of electromagnetic induction. When an alternating current flows through the primary coil, it creates a changing magnetic field, which induces a voltage in the secondary coil.
2. How does the turns ratio affect the transformer's voltage and current?
Ans. The turns ratio of a transformer determines the ratio of voltage between the primary and secondary coils. If the turns ratio is higher, the voltage in the secondary coil will be higher than the primary coil, while the current will be lower. Conversely, a lower turns ratio will result in a lower secondary voltage and higher current.
3. What are the advantages of using transformers in electrical power transmission?
Ans. Transformers play a crucial role in electrical power transmission due to their ability to step up or step down voltages. This allows for long-distance transmission with reduced losses, as higher voltages minimize the current required. Additionally, transformers provide electrical isolation and improve power quality.
4. Can transformers be used to convert DC (direct current) to AC (alternating current)?
Ans. No, transformers only work with AC. DC cannot be transformed using traditional transformers due to the absence of a changing magnetic field required for induction. However, electronic devices like inverters can convert DC to AC by utilizing other techniques.
5. How can the efficiency of a transformer be improved?
Ans. The efficiency of a transformer can be improved by reducing its copper and iron losses. Copper losses can be minimized by using thicker conductors with lower resistance, while iron losses can be reduced by using high-quality magnetic materials and optimizing the design. Additionally, operating the transformer at its rated voltage and current can also enhance efficiency.
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