DONE BY MY COLLEAGUES IN COLLEGE BSEE-5

1. ALL-DAY EFFICIENCY
-> is defined as the ratio of the energy (kilowatt-hours) delivered
by the transformer in a 24-hour period to the energy input in the
same period of time.
-> to determine the all-day efficiency, it is necessary to know
how the load varies from hour to hour during the day.
Example:
The transformer of example 18 operates with the following loads
during a 24-hr period: 1 ½ times rated kva, power factor = 0.8,
1hr; 1 ¼ times rated kva, power factor = 0.8, 2hr; rated kva, power
factor = 0.9, 3hr; ½ rated kva, power factor = 1.0, 6hr; ¼ rated
kva, power factor = 0.8; no-load, 4hr. Calculate the all-day
efficiency.

2. Solution:
Energy output, kw-hr Energy losses, kw-hr
W1 = 1.5 x 5 x 0.8 x = 6.0 (1 ½)2
x 0.112 x 1 = 0.252
W2 = 1.25 x 0.8 x 2 = 10.0 (1 ½)2 x 0.112 x 2 = 0.350
W3 = 1 x 5 x 0.9 x 3 = 13.5 1 x 0.112 x 3 = 0.336
W6 = 0.5 x 5 x 1.0 x 6 = 15.0 (1/2)2 x 0.112 x 6 = 0.168
W8 = 0.25 x 5 x 1.0 x 8 = 10.0 (1/4)2 x 0.112 x 8 = 0.056
____
Total. . . . . . . . 54.5 Iron = 0.04 x 24 = 0.960
_____
Total. . . . . . . . .. . . . 2.122
All-day Efficiency = (1 – 2.122/54.5 + 2.122) x 100 = 96.25%

3. AUTOTRANSFORMERS
In principle and in general construction, the autotransformer
does not differ from the conventional two-winding transformer, but it
differ from the way in which the primary and the secondary are
interrelated. In conventional transformer, the primary and secondary
windings are completely insulated from each other but are magnetically
linked by a common core. In autotransformer, the two windings, primary
and secondary, are both electrically and magnetically interconnected: a
part of the single continuous winding is common to both primary and
secondary.
Two ways in constructing Autotransformer:
1.] in one arrangement, there is a single continuous winding with taps
brought out at a convenient points determined by the desired secondary
voltages.
2.] in other arrangement, there are two or more distinct coils which are
electrically connected to form a continuous winding.

4. Autotransformers are cheaper than conventional two-
winding transformers of similar rating. They also have a better
regulation, and operate at a higher efficiencies. However, they are
considered unsafe for use on ordinary distribution circuits
because the high-voltage primary circuit is directly connected to
the low-voltage secondary circuit.
They are frequently used in connection with the starting
of certain types of ca motors, so that lower than line voltage is
applied during the starting period.
INSTRUMENT TRANSFORMER
Instrument transformers are used to measure
comparatively high values of current or voltage.
Two kinds of Instrument Transformers:
1.] Current Transformer
-> is used with an ammeter to measure the current in an ac
circuit.
-> in practice, it is connected to ordinary 5-amp ammeters

5. -> it has a primary coil of one or more turns of heavy wire, which is
always connected in series in the circuit in which the current is to be
measured.
-> the secondary has many turns of comparatively fine wire, which
must always be connected across the ammeter terminals.
2.] Potential Transformers
-> is used with a voltmeter to measure the potential difference, or
voltage in an ac circuit.
-> are generally employed with standard 150-volt voltmeters.
Clamp-on or Clip-on Ammeter
-> a practical design of current transformer.
-> has a laminated core so arranged that it may be opened out at a
hinged section by pressing a trigger.
-> when the core is opened, it permits the admission of the current-
carrying conductor, whereupon the trigger is released and the core is
closed tight by a spring. The current-carrying conductor acts as a
single-turn primary, while the accurately wound secondary is
permanently connected to the ammeter conveniently mounted in the
handle.

6. Important Aspects of Current Transformer
-> is that its secondary must never be permitted to be open-circuited because,
unlike distribution and power transformers which are connected to constant-
potential sources, the voltage across the primary winding varies over a wide range as
the load changes.
Important Aspects of Potential Transformer
-> Potential Transformer are carefully designed, extremely accurate-ratio step-down
transformers. They are used with standard low-range voltmeters, the deflection of
which , when multiplied by the ratio of transformation, gives the true voltage on the
high side. They differ very little from the ordinary two-winding transformers, except
that they handle a very small amount of power.
TRANSFORMER POLARITY
Transformers are often connected in parallel to supply a common load, in much the
same way as are alternators and dc generators for the same purpose. Two or three
transformers are connected together so that they may be used in polyphase systems.
It is necessary that the polarity of the transformers be known before the connections
are made.

7. Polarity of a Transformers
-> refers to the relative directions of the induced voltages in the primary and
secondary windings with respect to the manner in which the terminal leads are
brought out and marked. Standard notations are additive polarity and subtractive
polarity.
PARALLEL OPERATION OF TRANSFORMERS
Several important conditions must be fulfilled if two or more transformer are to
operate successfully in parallel to deliver a common load.
These important conditions are:
1.] the voltage ratings of both primaries and secondaries must be identical. This
implies that the transformation ratios are the same.
2.] the transformers must be properly connected with regard to polarity.
3.] the equivalent impedances should be inversely proportional to the respective
kilovolt-ampere ratings.
4.] the ratio of the equivalent resistance to the equivalent reactance (Re:Xe) of all
transformers should be the same.
*The parallel operation of two or more transformers requires that the primaries be
joined to the same source and that the secondaries be connected to the same load.

8. No-load Operation
When the secondary load is removed, with switch S open, the primaries
will still be energized and secondaries will still remain connected in parallel. Since
the latter are in phase opposition with respect to each other, no current can circulate
in these windings if the induced voltages are exactly equal; this condition can exist
only if the ratio of transformation of the two transformers are exactly equal. If the
transformer 1 has a ratio of transformation a1 which is different that of transformer
2, which has a ratio of transformation a2, the circulating current in the secondary Ic
will be
Ic = (a1-a2)Vs / a1Ze1+a2Ze2
Where: Ze1 = equivalent impedance of transformer 1 in secondary terms
Ze2 = equivalent impedance of transformer 2 in secondary terms

9. Example 27:
The following information is given in connection with two transformers that are
connected in parallel:
Transformer 1 Transformer 2
rating = 25 kva rating = 35 kva
2,360/230 volts 2,300/230 volts
Ze = 0.08, in secondary terms Ze = 0.06, in secondary terms
Calculate the secondary circulating current at no load.
Solution:
a1 = 2,360/230 = 10.26 a2 = 2,300/230 = 10
Ic = (10.26 – 10) 230/ [(10.26 x 0.08) + (10 x 0.06)]
= 59.8 / (0.821 + 0.6)
= 42.1 A

10. Load Operation—Equal Ratios of Transformation
When two transformers having equal ratios of transformation are connected in
parallel, the total load current will divide between them in inversely as their
equivalent impedances.
Example:
The following information is given for two transformers connected in parallel and
delivering a total load of 300 kva:
Transformer 1 Transformer 2
Rating = 150 kva Rating = 250 kva
6,900/230 volts 6,900/230 volts
Ze = 9.4, in primary terms Ze = 5.8, in primary term
Calculate the load current and kilovolt-amperes delivered by each transformer.

11. Solution:
Total current IT = 300,00 / 6,900 = 43.5 amp
I1 / I2 = 5.8 / 9.4
I1 = (5.8 / 9.4) x I2
Also,
IT = I1 + I2
43.5 = [(5.8 / 9.4) x I2] + I2 = 1.617 I2
I2 = 26.9 amp
I1 = 43.5 – 26.9 = 16.6 amp
Therefore :
kva1 = 6.9 x 16.6 = 114.4
kva2 = 6.9 x 26.9 = 185.6
total = 300 kva

12. Load Operation—Unequal Ratios of Transformation
When two transformers having unequal ratios of transformation are
connected in parallel, the total load current will drive in accordance with the
following equations:
I1 = [(a2 – a1)Vs + (a2Ze2It)] / [(a1Ze1) + (a2Ze2)]
I2 = [(a1 – a2)Vs + (a1Ze1It)] / [(a1Ze1) + (a2Ze2)]
Example:
The transformer of example 27 deliver a total load of 46 kva. Calculate the
secondary currents and the kilovolt-ampere load of each one.
Solution:
a1 = 10.26 a2 = 10 Ze1 = 0.08 Ze2 = 0.06
It = 46,00 / 230 = 200 amp
I1 = [(10-10.26)230 + (10 x 0.06 x 200)] / [(10.26 x 0.08) + (10 x 0.06)]
= (-59.8 + 120) / 1.421 = 60.2 / 1.421 = 42.4
I2 = [(10.26 – 10)230 + (10.26 x 0.08 x 200)] / [(10.26 x 0.08) + (10 x 0.06)]
= (59.8 + 164) / 1.421 = 223.8 / 1.421 = 157.6
Kva1 = 42.4 x 0.23 = 9.75
Kva2 = 157.6 x x0.23 = 36.25

13. Three- phase Transformer Connections
Transformers that must handle a considerable amount of power are
generally grouped together in banks for polyphase service. In three-phase systems,
two or three identical transformers may be used in a bank for this purpose.
Four standard ways of connecting 3-phase transformer banks:
1.] wye-wye
2.] delta-delta
3.] delta-wye
4.] wye-delta
1.] WYE-WYE CONNECTIONS
If the ratio of transformation is a, the same ratio will exist between the line
voltages on the primary and secondary sides. This connection will give satisfactory
service only if the three-phase load is balanced. When the load is unbalanced, the
electrical neutral will shift from its exact centre to a point that will make the three
lone-to-neutral voltages unequal. The advantage of this system of connections is
that the insulation is stressed only to the extent of the line-to-neutral voltage, which
is 58% of the line-to-line voltage.

14. 2.]DELTA-DELTA CONNECTION
This arrangement is generally used in systems in which the
voltages are high and especially when continuity of service must be
maintained even though one of the transformers should fail. When
one of the transformers is removed from a delta-delta bank,
operation continues on what is known as open delta. The ratio of
transformation existing between primary and secondary line voltage
will be exactly the same as that of each transformer.
3.] WYE-DELTA CONNECTION
This scheme of connection, is generally employed where it is
necessary to step-up the voltage, for example, at the beginning of a
high-tension transmission system. On the high sides of transformer,
insulation is stressed only to the extent of 58% of the line-line
voltage.

15. 4.] WYE -DELTA CONNECTION
This connection is the reverse of the delta-wye connection. It
is used principally where the voltage is to be stepped down. It is also
employed in moderately low-voltage distribution circuits for
stepping down from transmission voltages of 4,000 – 8,000 volts to
230 and 115 volts. The points made concerning delta-wye
connections supply equally well here.
THE V-V CONNECTION
If one of the transformers of a delta-delta bank is removed
and a three-phase source is connected to the primaries, three equal
3-phase voltages will be measured at the secondary terminals at no
load. This method of transforming 3-phase power , using 2
transformers, is called open delta or V-V connection.

16. THE T-T CONNECTION
Another 2-transformer method
that can be used to transform 3-phase
power from one voltage to another is the
T-T connection. It was first proposed
by Charles F. Scott and is frequently
called the Scott connection.

17. MAIN TRANSFORMER
-must have at least two
primary and two secondary
coils so that a center tap
may be brought out from
each other.

18. TEASER TRANSFORMER
-must have primary and
secondary windings the
numbers of turns of w/c are
86.6% of the respective turns
of the main transformer.

19. FIG. 212
The kilovolt-ampere ratings of the MAIN
and TEASER TRANSFORMER will be exactly the
same, even thought the voltage across the latter
is only 886.6% of that across the former.
The reason for this is that kVA loads carried
by the TWO HALVES of the MAIN
TRANSFORMER are out of phase by 6O
electrical degrees; the result is that when these
are vectorially added, their sum equals the kVA
load on the teasier transforrmer.

20. THREE-PHASE TRANSFORMER
-more economical to use a three phase
transformer than, as previously discussed, a
bank of three single phase transformer.
Proper flux densities are maintained
because the three phase currents are
displaced 120 electrical degrees w/ respect to
each other.

21. TWO GENERAL ARRANGEMENT OF
THE WINDINGS AND THE CORE
 CORE TYPE, the three primary & secondary windings
surround a considerably part of the magnetic core.
FIG. 214a
 SHELL TYPE, the magnetic circuits surround a
considerable portion of the 3 phase primary &
secondary windings.
Advantage:
The former transformer can be operated in open
DELTA should one of the windings be damaged;