Equivalent Circuit of Transformer
No load Components
The no-load primary current Io has two components, namely Im and Iw.
Where Im = magnetizing component = Io sin φo
and Iw = core-loss component = Io cos φo.
- Iw supplies for the no-load losses and is assumed to flow through the no-load resistance which is also known as core-loss resistance (Ro).
- The magnetizing component, Im is assumed to be flowing through a reactance which is known as magnetizing reactance, Xo.
- The parallel combination of Ro and Xo is also known as the exciting circuit.
From the equivalent circuit of transformer,
Ro = V1/Iw and Xo = V1/Im.
- The core-loss resistance (Ro) and the magnetizing reactance (Xo) of a transformer are determined by the open circuit test of transformer.
- The resistance R1 and reactance X1 correspond to the winding resistance (DC resistance) and leakage reactance of the primary winding.
- The total current I1 on the primary side is equal to the phasor sum of Io and I2’.
- I2’ = KI2 is the additional primary current which flows due to the load connected on the secondary side of the transformer.
- The resistance R2 and reactance X2 correspond to the winding resistance and leakage reactance of the secondary winding.
- Load impedance ZL can be resistive, inductive or capacitive.
- The equivalent circuit of single phase transformer is further simplified by transferring all the quantities to either primary or secondary side.
- This is done in order to make the calculations easy.
Equivalent Circuit of Transformer Referred to Primary
- R2’, X2’ and ZL’ are the values of R2, X2 and ZL referred to primary respectively.
- The values of these components are obtained as follows:
R2’ = R2/K2 , X2’ = X2/K2 and ZL’ = ZL/K2
where K = N2/N1 (transformation ratio).
- The current I2 and voltage E2 are also transferred to the primary side as I2’ and E2’ respectively. The expressions for I2’ and E2’ are as follows:
E2’ = E2/K and I2’ = KI2
Equivalent Circuit of Transformer Referred to Secondary
- Components R1’, X1’, Ro’ and Xo’ are the primary components referred to secondary. The expressions for these components are as follows:
R1’ = K2R1 , X1’ = K2X1
Ro’ = K2Ro , Xo’ = K2Xo
- The primary voltages and currents also get transferred to the secondary side as I1’, V1’, Io’, E1’ respectively and are given by:
I1’ = I1/K , E1’ = KE1 , Io’ = Io/K
where K = N2/N1 (transformation ratio).
Approximate Transformer Equivalent Circuit
An approximate equivalent circuit is one which is obtained by shifting the exciting circuit to the left of R1 and X1 as shown in the figure.
Although this shifting creates an error in the voltage drop across R1 and X1 yet it greatly simplifies the calculation work and gives much simplified equivalent circuit.
- Now it is possible to combine the resistances R1 with R2’ and X1 with X2’. So R1 and R2’ are combined to obtain the equivalent resistance of transformer referred to the primary R01.
Therefore, R01 = R1 + R2’ = R1 + R2/K2
- Similarly X1 and X2’ can be combined to obtain the equivalent reactance of transformer referred to primary X01.
Therefore, X01 = R1 + R2’ = R1 + R2/K2
Now the impedance of the transformer referred to the primary is given by,
Z01 = R01 + jX01
Transformer — 6 | Objective Type Question Answers
#1 The voltage transformation ratio of a transformer is equal to the ratio of
secondary induced em.f. to primary induced e.m.f.
#2 Part of the transformer which is most subject to damage from overheating is
#3 If a transformer is switched on to a voltage more than the rated voltage
#4 Auto-transformer makes effective saving on copper and copper losses, when its transformation ratio is
approximately equal to one
#5 Minimum voltage regulation occurs when the power factor of the load is
#6 In a step-down transformer, there is a change of 15 A in the load current. This results In change of supply current of
less than 15 A
#7 The efficiencies of transformers compared with that of electric motors of the same power are
#8 The short circuit voltage of a transformer mainly depends on the
magnitude of leakage flux
#9 In an ideal transformer, on no-load, the primary voltage is balanced by
the secondary induced e.m.f.
#10 As per the nameplate of a transformer, the secondary normal voltage is 220 V. Which of the following statements about it is correct ?
The no-load voltage is more than 220 V
#11 A transformer is working at its maximum efficiency. Its iron loss is 1 kW. Its copper loss will be
#12 A transformer is working at full load and its efficiency is also maximum. Its iron loss is 1 kW, its copper loss at half load will be
#13 In some transformers the tappings are provided on
#14 In case of transformers using cold rolled grain oriented steel, the area of yoke is taken
equal to that of core
#15 The distribution transformers are designed to keep the iron-losses minimum because
the primary of distribution transformer is energized for all the twenty four hours
#16 Which of the following materials is suitable for the manufacture of trans-former and large turbo alternator ?
Cold rolled grain oriented steel
#17 Which of the following statements is correct ?
transformer operates at a power actor depending on the power factor of the load
#18 A transformer, as compared to an amplifier, cannot increase
the output power
#19 A transformer having a turn ratio 1: 5 and a resistance of 1000 ohm is connected across the secondary terminals, the resistance offered to a current flowing in the primary will be
#20 Which of the following statements about a transformer having a small short-circuit voltage is true?
A high short-circuit current flows through the transformer
#21 Helical coils arc very well suited for
low voltage winding of large rating transformers
Do not forget to click the “finish” button to see the correct answers and result.
- Single Phase Transformer Working Principle
- Ideal Transformer on No Load
- Construction of Three Phase Transformer
- Types of Transformers
- Equivalent Resistance and Reactance of Transformer
- Power Loss in a Transformer
- Open Circuit Test of Single Phase Transformer
- Short Circuit Test on Single Phase Transformer
- Transformer Efficiency
- Regulation of Transformer
- Instrument Transformers
- Polarity of Transformer Windings
- Significance of Vector Group of Transformer
- Buchholz Relay Construction | Working
- Why current transformer secondary should not be opened