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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.
where full load voltage = Rated voltage.
V'_{2} = aV_{2}
Approximate Voltage Regulation
To find voltage regulation at leading pf replace ø by –ø.
Condition for Maximum Voltage Regulation
• Maximum voltage regulation
Note:
• Here tanø is positive, therefore, maximum voltage regulation occurs at a lagging load
p.f. = r_{eq}/Z_{eq}
Condition for Zero Voltage Regulation
or
or
or ø = (90°– θ_{eq}) leading
• Negative value of tanø indicates a leading pf. Therefore zero voltage regulation occurs when load
Remember:
• For leading pf greater than X_{pu}/Z_{pu} 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 P_{h} and eddy current loss P_{e}.
• Hysteresis loss P_{h }= K_{h} fB_{m}^{x}
• Eddy current loss P_{e }= K_{e} f^{2}B_{m}^{2}
Where,
K_{h }= Proportionality constant depend upon the quality of core and volume.
K_{e} = Proportionality constant whose depends on the volume and resistiviy of the core material, thickness of laminations and the units employed.
B_{m} = 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
∴ P_{c} =
• Losses in terms of applied voltage and frequency
Ohmic loss
• Ohmic losses occurs in both the primary and secondary winding resistance.
P_{cu} = I^{2r}_{eq}
Note:
• Generally student get confused related with iron loss and copper loss. Actually iron loss (P_{i}) is also called core loss (P_{c}) and copper loss (P_{cu}) is also called ohmic loss (P_{oh}). So it must be clear iron loss is also called constant loss because it is independent to the load current and ohmic loss (I^{2}r_{eq} ) 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.
or
Condition for Maximum Efficiency
• P_{i} = P_{cu} = I_{2 req}
• Copper loss = Iron loss
• The maximum efficiency for a constant load current occurs at unity power factor.
• Current maximum efficiency
• kVA rating at maximum efficiency
Where
S_{(know load)} = kVA at known load
P_{cu(know load)} = Copper loss at known load
AUTO TRANSFORMER
• A singlephase autotransformer is a onewinding transformer in which a part of the winding is common to both high voltage and low voltages sides.
• It is not electrically isolated.
Number of turns of primary winding AC = N_{1 }and number of turns of secondary windings BC = N_{2}
• If applied voltage V_{1 }across AC winding, then the Voltage across winding BC is
• If ideal case, Input power = output power
V_{1}I_{1} cos θ_{1} = V_{2}I_{2} cos θ_{2}
• If cos θ_{1} = cos θ_{2}
then, V_{1}I_{1} = V_{2}I_{2}
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)}
• Percentage copper saving
% Cu saving = 1/a x 100
Ratings
Losses
Voltage Regulation
Short Circuit Current
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 1Ø TRANSFORMER
Advantage of Parallel operation
There are following advantages of the parallel operation of singlephase transformer
Condition for Parallel Operation
• Condition for the satisfactory parallel operation of two or more singlephase 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. x_{eq}/r_{eq} 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 voltamperes according to their ratings.
parallel Operation at Same voltage Ratio
Where EA and EB are noload secondary voltages.
or
Similarly,
For Proportional Load Sharing
or Z_{A(pu)} = Z_{B(pu})
Where the pu values are on their respective or own base.
Same Voltage Ratio and Different (x/r) Ratio
Let θ_{A} > θ_{B}
Equal S for two transformer with
S_{A} = S with θ_{A}
S_{B} = S with θ_{B}
Then S_{L }=
Unequal Voltage Ratio
• Following steps are followed to calculate load kVA.
Steps:
where
and
THREE PHASE TRANSFORMER
• When three identical units of singlephase 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 threephase fluxes mutually timedisplaced 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
Threephase coretype transformer from three singlephase 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 singlephase shell type cores are placed side by side.
Threephase 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.
• For the same flux density, the crosssectional areas at 2 and 3 are 86% of the central core area.
parallel Operation of 3ø Transformers
• The various conditions that must be fulfilled, for the successful parallel operation of 3phae 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 threephase 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.
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 S_{1} and line voltages across switch S_{2} and S_{3}. Consequently the parallel operations is not possible.
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