1. Testing of transformers

2. Transformer Tests
The performance of a transformer can be calculated on the basis of equivalent circuit.The four main parameters of equivalent circuit are:
- R01 as referred to primary (or secondary R02)
- the equivalent leakage reactance X01 as referred to primary (or secondary X02)
- Magnetising susceptance B0 ( or reactance X0)
- core loss conductance G0 (or resistance R0)
The above constants can be easily determined by two tests
- Oper circuit test (O.C test / No load test)
- Short circuit test (S.C test/Impedance test)

3. Open-circuit Test
In Open Circuit Test the transformer’s secondary winding is open-circuited, and its primary winding is connected to a full-rated line voltage.
Usually conducted on H.V side
To find
(i) No load loss or core loss
(ii) No load current Io which is helpful in finding Go(or Ro ) and Bo (or Xo )

4. Circuit diagram

5. Model caluclations

6. Short-circuit Test
In Short Circuit Test the secondary terminals are short circuited, and the primary terminals are connected to a fairly low-voltage source
The input voltage is adjusted until the current in the short circuited windings is equal to its rated value. The input voltage, current and power is measured.
Usually conducted on L.V side
To find
(i) Full load copper loss – to pre determine the efficiency
(ii) Z01 or Z02; X01 or X02; R01 or R02 - to predetermine the voltage regulation

7. Circuit diagram

8. Model calculations &eqivalent circuit

9. Voltage regulation of a transformer
recall
Secondary voltage on no-load
V2 is a secondary terminal voltage on full load
Substitute we have

10. Transformer equivalent circuit
To determine the voltage regulation of a transformer, it is necessary understand the voltage drops within it.

11. Cont..
Ignoring the excitation of the branch (since the current flow through the branch is considered to be small), more consideration is given to the series impedances (Req +jXeq).
Voltage Regulation depends on magnitude of the series impedance and the phase angle of the current flowing through the transformer.
Phasor diagrams will determine the effects of these factors on the voltage regulation. A phasor diagram consist of current and voltage vectors.

12. Cont..
Assume that the reference phasor is the secondary voltage, VS. Therefore the reference phasor will have 0 degrees in terms of angle.
Based upon the equivalent circuit, apply Kirchoff Voltage Law,

13. Transformer Phasor Diagram
When the power factor is unity, VS is lower than VP so VR > 0.

14. Transformer Phasor Diagram
With a leading power factor, VS is higher than the referred VP so VR < 0

15. Transformer Phasor Diagram
For lagging loads, the vertical components of Req and Xeq will partially cancel each other. Due to that, the angle of VP/a will be very small
hence we can assume that VP/k is horizontal. Therefore the approximation will be as follows:

16. voltage regulation

17. Transformer Efficiency
The Efficiency of the transformer is defined as the ratio of useful power output to the input power.
The input and the output power are measured in the same unit. Its unit is either in Watts (W) or KW. Transformer efficiency is denoted by Ƞ.

18. seperation of losses test in a transformer

19. PROCEDURE:
Start the alternator with the help of prime mover (DC Motor).
Adjust the speed of the prime mover so that the alternator voltage frequency should be 50 Hz.
Vary the excitation of the alternator so that the required voltage builds across the armature (Say 230 V between line and neutral).
Note down all meter readings.
Repeat the above steps for different frequencies by changing the speed of the prime mover (With Speed control of DC Shunt motor by Armature control or Field Control).
Repeat step 6 for different frequencies of the alternator say 46 Hz, 48 Hz, 50 Hz, and 54 Hz keeping V/f ratio constant.
Plot the graph between V/f and core losses of the transformer.

20. Model graph

21. Parallel operation of transformers

22. Necessity Of Parallel Operation Of Transformers
Why parallel operation of transformers is needed?
Increased Load:
Non-availability of large transformer:
Increased reliability:
Transportation is easier for small transformers:

23. Conditions For Parallel Operation
Voltage ratio of all connected transformers must be same.
The per unit (pu) impedance of each transformer on its own base must be same.
The polarity of all connected transformers must be same
The phase sequence must be identical of all parallel transformers.
The short-circuit impedances should be approximately equal

24. Parallel operation of two transformers
the transformers are connected in parallel when the load is more than the rating of the individual transformers.
several smaller units are operated in parallel which share a common load.
in the fig. we can see that the primary windings are connected to the supply bus bars while the secondary are connected to load bus bars

25. OF TWO IDEAL TRANSFORMER
PARALLEL OPERATION
OF TWO IDEAL TRANSFORMER

26. Parallel operation of two ideal transformers

27. phasor diagram
now we will consider ideal case of two transformers having the same voltage ratio and their voltage triangles are equal in size and shape.
as seen the impedance voltage triangles of both the transformers is same .

28. Current through two t/f’s

29. Parallel operation oftwo t/f’s with equal voltage ratio

30. theory this is represented in the shown circuit.
let us now consider the case of two transformers connected in parallel having equal voltage ratios. the two transformers are having no load secondary voltage same .
these voltages are in phase with each other.
this is possible if the magnetizing currents of the two transformers are not much different .
this is represented in the shown circuit.

31. The phasor diagram under this condition is shown .
The two impedances Z1 and Z2 are in parallel.
The values of Z1 and Z2 are with respect to secondary.

32. Parallel
Operation of
Transformers
With unequal
Voltage ratios

33. Parallel Operation of Transformers with Unequal Voltage Ratios
Now we will consider the case of two transformers working in parallel and having unequal voltage ratio. This is shown in the Fig. 1.
   The voltage ratios of the two transformers are not equal. The parallel operation under this case is still possible. But as seen previously there would be a circulating current under no load condition.

34. Derivation for currents
Let us consider voltage ratio of transformer 1 is slightly more than 2. So that induced e.m.f.. E1 is greater than E2. Thus the resultant terminal voltage will be E1 - E2 which will cause a circulating current under no load condition. Ic = (E1 - E2)/(Z1 + Z2 ) From the circuit diagram we have, E1 = V2 + I1 Z1 E2 = V2 + I2 Z2 Also, IL = I1 + I2 V2 = IL ZL = ( II + I2 ) ZL E1 =(I1 + I2) ZL + II Z (a) E2 =(I1 + I2 ) ZL + I2 Z (b) Subtracting equations (a) and (b) we have, E1 - E2 = I1 Z1 - I2 Z2 I1 = ((E1 - E2) + I2 Z2) /Z1

35. Cont.. Subtracting this value in equation (b),
...                       I2 = (E2 Z1 - (E1 - E2)ZL) / (Z1 Z2 + ZL (Z1 + Z2))
Similarly,             I1 = (E1 Z2 + (E1 - E2)ZL)/ (Z1 Z2 + ZL (Z1 + Z2))
Adding the above equations,
                   I1 + I2 = (E1 Z2 + E2 Z1) / (Z1 Z2 + ZL (Z1 + Z2))           (c)
But                     IL = I1 + I2
Load voltage,     V2 = IL ZL
       Dividing both numerator and denominator of equation (c) by Z1 Z2,

36. Cont..

37. AUTO
TRANSFORMERS

38. CONSTRUCTION:
In an autotransformer , only one winding is wound on a laminating magnetic core while in 2 winding , two windings are wound. the single winding of the autot/f are used as primary and secondary. the part of the winding is common to both primary and secondary. the voltage can be stepped down or up using an autotransformer. accordingly they are classified as
step up autotransformers
step down autotransformers

39. in the fig the convectional two winding t/f and the step up and down t/f are shown .
in step down t/f the entire winding acts as a primary while the part of the winding is used common to both primary and secondary.
thus ab forms the primary having n1 turns while bc forms secondary with n2 turns.

40. transfprmation ratio of a.t/f:
THE CURRENT DISTRIBUTION IN STEP UP AND STEP DOWN AUTO T/F ARE SHOWN AS BELOW :
transfprmation ratio of a.t/f:
neglecting the losses the leakage reactance and the magnetizing current,the transformation ratio of an auto t/f can be obtained as ,
k=v2/v1
=i1/i2
=N2/N1

41. k is greater than unity for step up auto t/f while k is less than unity for step down auto t/f.
due to the use of single winding compared to the normal two winding t/f for the same cpacity and voltage ratio,
there is substantial saving in copper in case of auto t/f.
COPPER SAVING IN AUTO T/F:
for any winding the cross section o winding is proportional to the current i.
while the total length of the winding is proportional to the number of turns n .
hence the weight of copper is proportional to the product og n and i.
while i=current of winding
n=number of turns of winding

42. CONSIDER A TWO WINDING T/F AND A STEP DOWN T/F AS SHOWN IN FIG .
TWO WINDING TRASFORMER
then let
Wtw= total weight of copper in two winding t/f
Wat=weight of copper in auto t/f
Saving of copper=KWtwv for step down transformer
Saving of copper=1/K *Wtwv for step up transformer

43. POWER TRANSFER IN AUTO T/F :
it is mentioned earlier that the power input to an autotransformer gets transferred to the scondary by two ways , i.e,
by electromagnetic induction
by conduction
consider a loaded auto t/f as shown .
the current drawn form the supply is i1 while the input voltage is v1.
input power = v1i1
while the load current id i2 at a load voltage v2
output power=v2i2

44. PT=(1-K)V1 I1 = (1-K)INPUT POWER
now bc portion has n2 turns and acts as secondary. the current induced in this scondary due to transformer action is i2-i1 while secondary induced voltage is v2.
pt=power transferred inductively
=(i2-i1)v2=v2i2-v2i1
k=v2/v1 = i1/i2
pt=k.v1(i1/k - k.v1.i1)
=v1 i1- k v1 i1
while the remaining power gets transffered directly that is, conductively as windings are electrically connected.
PT=(1-K)V1 I1 = (1-K)INPUT POWER

45. VA RATING OF AYTO TRANSFORMERS:
let us compare the VA rating of two winding transformer and the VA rating of two winding transformer when connected as an auto t/f. for step down transformer
For step up transformer K is replaced by 1/K

46. CONVERSION OF TWO WINDING T/F TO AN AUTO T/F :
consider a two winding t/f with the polarities as shown . the t/f turns ratio is 1:1 and v2=v1=400v.
this t/f can be converted to an auto t/f in two ways
additive polarity
subtractive polarity
the primary and secondary windings can be connected in series with additive polarity as ashown .

47. the common point a which is common to input and output can be taken as the top of an auto t/f.
the corresponding auto t/f is as shown .
thus if input is v1 then the output is v1+v2 due to additive polarities
with common point a at the bottom auto t/f can be shown .

48. SUBTRACTIVE POLARITY :
the primary and secindary windings can be connected in series opposition as shown in fig.
the common point a which is common to input and output can be taken as the top of the auto t/f as shown in fig.
thus if the input is v1 then the output voltage is v1-v2 due to subtractive polarities.

49. ADVANTAGES OF AUTO TRANSFORMERS :
copper requried is very less.
the efficiency is higher compared to two winding t/f.
the size and cost is less compared to two winding transformer.
the resistance and leakage reactance is less compared to two winding t/f.
the copper losses are less.
due to less resistance and leakage resistance the voltage regulation is supirior than the two winding t/f.
va rating is more compared to two winding.
a smooth and continious variation of voltage is possible.

50. LIMITATIONS OF AUTO TRANSFORMERS :
low impedance hence high short circuit currents for short circuits on secondary side.
if a section of winding common to primary and secondary is opened full primary voltage appears across the secondary resulting in higher voltages on secondary and danger of accidents.
no elecrical seperation between primary and secondary which is risky in case of high voltage levels .
economical only where the voltage ratio is less than 2 .

51. APPLICATIONS OF AUTO TRANSFORMER :
for safely starting the machines like induction motors, synchronous motors as a stators.
to give a small boost to a distribution cable to compensate for a voltage drop i.e as a booster.
as a furnace t/f to supply power to the furnace as the requried supply voltage.
for interconnecting the systems which are operating roughly at same voltage level.
it can be used to vary the voltage to the load, smoothly from zero to the rated voltage. such a device giving smooth and continuous supply using an ayto t/f is called variac. a single phase auto t/f used as a variac is as shown….

52. POLY PHASE transformers

53. Definition of polyphase
Poly phase is essentically acombination of two or more than single phase volage having same magnitude and frequent but displaced from one another by equal eletrical degrees or angle

54. Terminology
Phase Sequence : The phase sequence is the order in which the voltage in the three phase attain their maximum value is called phase sequence or phase order. Phase voltage : The voltage between one of the phase and the neutral terminal is known as the phase voltage and it is represented as the Vph. Phase Current : The current flowing through any phase of the winding is called as the phase current and it is denoted by Iph.

55. Line voltage : The voltage between any two phases of the supply system is called line voltage and it is represented by VL. Line Current : The current flowing through any two phases is termed as a line current and it is denoted by IL.

56. Three Phase Voltages and Currents

57. the primary and secondary windings of a transformer can be connected in different configuration as shown to meet practically any requirement. in the case of three phase transformer windings, three forms of connection are possible: “star” (wye), “delta” (mesh) and “interconnected-star” (zig-zag).
the combinations of the three windings may be with the primary delta-connected and the secondary star-connected, or star-delta, star- star or delta-delta, depending on the transformers use. when transformers are used to provide three or more phases they are generally referred to as a polyphase transformer.

58. THREE PHASE TRASFORMER CONNECTION

59. TRANSFROMER STAR AND DELTA CONFIGURATIONS

60. symbols are generally used on a three phase transformer to indicate the type or types of connections used with upper case y for star connected, d for delta connected and z for interconnected star primary windings, with lower case y, d and z for their respective secondaries. then, star- star would be labelled yy, delta-delta would be labelled dd and interconnected star to interconnected star would be zz for the same types of connected transformers.

61. Transformer winding identification

62. we now know that there are four different ways in which three single-phase transformers may be connected together between their primary and secondary three-phase circuits. these four standard configurations are given as: delta-delta (dd), star-star (yy), star-delta (yd), and delta-star (dy).
transformers for high voltage operation with the star connections has the advantage of reducing the voltage on an individual transformer, reducing the number of turns required and an increase in the size of the conductors, making the coil windings easier and cheaper to insulate than delta transformers.
the delta-delta connection nevertheless has one big advantage over the star- delta configuration, in that if one transformer of a group of three should become faulty or disabled, the two remaining ones will continue to deliver three-phase power with a capacity equal to approximately two thirds of the original output from the transformer unit.a

63. Trasfromer delta and delta connection

64. Cont..
in a delta connected ( dd ) group of transformers, the line voltage, vl is equal to the supply voltage, vl = vs. but the current in each phase winding is given as: 1/√3 × il of the line current, where il is the line current.
one disadvantage of delta connected three phase transformers is that each transformer must be wound for the full-line voltage, (in our example above 100v) and for 57.7 per cent, line current. the greater number of turns in the winding, together with the insulation between turns, necessitate a larger and more expensive coil than the star connection. another disadvantage with delta connected three phase transformers is that there is no “neutral” or common connection.

65. Trasfromer star and star connection

66. Cont....
The voltage between any line of the three-phase transformer is called the “line voltage”, VL, while the voltage between any line and the neutral point of a star connected transformer is called the “phase voltage”, VP. This phase voltage between the neutral point and any one of the line connections is 1/√3 × VL of the line voltage. Then above, the primary side phase voltage, VP is given as.
The secondary current in each phase of a star-connected group of transformers is the same as that for the line current of the supply, then IL = IS.

67. Three phase voltage and current

68. Star – delta turns ratio
likewise, for a delta–star ( dy ) connected transformer, with a 1:1 turns ratio, the transformer will provide a 1:√3 step-up line-voltage ratio. then for a delta-star connected transformer the turns ratio becomes:

69. Delta-star turns ratio
then for the four basic configurations of a three-phase transformer, we can list the transformers secondary voltages and currents with respect to the primary line voltage, vland its primary line current il as shown in the following table.

70. Three phase trasfromer line voltage and current
where:  n equals the transformers “turns ratio” (t.r.) of the number of secondary windings ns, divided by the number of primary windings np. ( ns/np ) and vl is the line-to-line voltage with vp being the phase-to-neutral voltage.

71. Detla – Star trasfromer
the replacement of delta or mesh by equivalent star connection is known as delta - star transformation. the two connections are equivalent or identical to each other if the impedance is measured between any pair of lines. that means, the value of impedance will be the same if it is measured between any pair of lines irrespective of whether the delta is connected between the lines or its equivalent star is connected between that lines.

72. Advantages of star connection
In a star connection, phase voltage Vph = VL/ (3)1/2. Since the induced emf in the primary winding of an alternator is directly proportional to the number of turns, a star connected alternator will require less number of turns than a delta connected alternator for the same voltage.
For the same line voltage, a star connected alternator requires less insulation than a delta connected alternator. Due to the above reasons three phase alternators are generally star connected.

73. Cont..
In star connection, we get 3-phase and 4-wire system. This permits the use of two voltages (phase voltages as well as line voltages). Single phase loads can be connected between any one lie and neutral wire while the 3-phase loads can be put across the three lines. Such a flexibility is not available in delta connection
In star connection, the neutral point can be earthed. Such a measure offers many advantages. For example, in case of line to earth fault (L-G fault), the insulators have to bear 1/31/2 (57.7%) times the line voltage. Earthing of neutral also permits the use of protective devices (relays) to protect the system in the case of ground faults

74. Advantages of delta connection
This type of connection is most suitable for rotatory conveyersMost of the three phase loads are delta connected than star connected.
One reason for this, atleast for the case of unbalanced load, is the flexibility with which loads may be added or removed on a single phase.
This is difficult to do with star connected 3-wire loadMost of the3-phase induction motors are delta connected

75. The end!!