This document contains design calculations for a single-phase distribution transformer. It specifies design parameters such as a rated output of 50 kVA, primary voltage of 13800V, secondary voltage of 460/230V, and an efficiency of at least 0.96 at full load. The document then shows calculations for transformer components like winding dimensions and currents, core size, flux density, losses, and temperature rise. Design goals are to have losses lower than specified guarantees and a temperature rise under 55°C at full load.

1. Republic of the Philippines
JOSE RIZAL MEMORIAL STATE UNIVERSITY
The Premier University in Zamboanga del Norte
Main Campus, Dapitan City
ELECTRICALMACHINE DESIGN 1
EE-55
TRANSFORMER DESIGN
SUBMITTED BY:
MARK ANTHONY B. ENOY
BS EE-V
SUBMITTED TO:
ENGR. URSINO P. TABILIRAN
INSTRUCTOR

2. DESIGN SHEET FOR TRANSFORMER
Single-phase Distribution Core Type with Cruciform Section
Guaranteed losses (watts):
 COPPER (FULL LOAD)………………………………………………
 IRON…………………………………………….……………...…..…...
ITEM NO.
1
SUMMARY OF CALCULATION
Volts per turn: from formula
WIN
DIN
GS
H.T.
2
Total number of turns
3
Number of coils
4
Turns per coil
5
11
Full-load current,
Amp
Current density, Amp
per sq. in.
Cross section of each
conductor, sq. in.
Dimension of
conductors
Number of turns per
layer per coil
Number of layers per
coil
Taps
12
Volts per coil
13
Volts between layers
14
Length of winding
layer including
insulation, in.
6
7
8
9
10
L.T
2880
96
4
4
720
24
3.623
108.696
0.00407
0.0644
No. 13
0.204x0.325
72
24
11
1
None
None
3450
115
627.273
6.157
13.72

3. 15
.045
16
Insulation between
layers, in.
Insulation on wire
dcc
dcc
17
Length per turn, in.
30.096
23.025
18
Total length, all turns
in series, ft
Weight of copper, lb.
7223.04
184.2
112.887
45.552
Resistance at 75°Call coils in series,
ohms
IR drop, volts
17.672
0.028
64.026
3.043
19
20
21
22
2
3
2
4
2
5
2
6
2
7
2
8
2
9
3
0
Full-load copper loss
231.966
(compare with
guarantee)
THE MAGNETIC CIRCUIT
330.762
Dimensions of “windows”, in.
5.769x14.423
Total flux, maxwells
1798673.674
Flux density in core under windings, lines per sq. in.
83000
Cross section of iron in core under windings, gross
24.079
Widths of ribbon strips in cruciform section, in.
3.28 and 5.311
Total weight of iron in core, lb
353.219
Watts lost in iron (compare with guarantee)
286.107
Total full-load losses, watts
848.835
EFFICIENCY AND EXCITING CURRENT
31
Efficiency at unity factor
At 1 ¼ full load
0.9817
At full load
0.9833
At ¾ full load
0.9842

4. At ½ full load
At ¼ full load
3
2
3
3
0.9832
0.9749
All-day efficiency (4- hr full load)
0.9564
Primary exciting current, amp
0.2237
REGULATION
34
Total Equivalent IR drop, percent
1.125
35
Total reactive drop, percent
1.829
36
Regulation at unity power factor, percent
1.142
37
Regulation At 0.8 power factor, percent
2.001
DESIGN OF TANK-TEMPERATURE RISE
38
Effective cooling surface of tank, sq. in.
39
Watts per sq. in. of tank surface
0.2532
40
Approximate temperature rise of oil, °C
44.427
DESIGN OF DISTRIBUTION TTRANSFORMER
3352

5. TRANSFORMER DESIGN SPECIFICATIONS
OUTPUT IN KILOVOLT-AMPERES
50
PRIMARY (HIGH TENSION) VOLTS
13800
SECONDARY (LOW TENSION) VOLTS
460/230
FREQUENCY, HERTZ
60
At full load = 0.96
EFFICIENCY AT UNITY POWER FACTOR
ALLOWABLE TEMPERATURE RISE
At ¼ full load = 0.95
55°
DESIGN ITEMS: FROM 1-40 WITH CALCULATIONS
ITEM 1:
It is proposed to design a core-type distribution transformer with circular coils. The core
is to have one step cruciform section and is to be constructed w/ ribbon-oriented steel, U.S.S.
Transformer 58 grade, 29 gauge, the core-loss curve is given in engineering Manual No.3 (U.S.S.
Electrical steel sheets) on page 30. It is to be oil-immersed and self-cooling, without taps for
voltage adjustments.
Insulation test (in tank with oil); voltage applied for one minute; high tension winding to
low tension winding and core, 10,000 volts; low tension winding to core, 4,000 volts.
The specified temperature rise of 55° implies that the winding temperature, as measured
by the resistance method, after the transformer has been operating continuously at full load, will
not be more than 55°C above the ambient temperature.
CALCULATIONS
Guaranteed losses:
Total losses at full load
Total losses at ¼ full load
Full load copper loss
Core loss = 2083.333-1520.467 = 562.866 W

6. After several preliminary trials of approximate calculations of losses, the value c= 46.9
was selected. Thus,
Vtper turn
ITEM 2 TO 4: PRIMARY AND SECONDARY TURNS
It will be desirable to use four primary and secondary coils in this design, which means
that the total number of turns on both primary and secondary must be multiple of four. Thus,
Total secondary turns
Total primary turns
Turns per secondary coils
Turns per primary coilsx24=720
ITEMS 5: FULL-LOAD CURRENT
Ip
Is
ITEM 6 TO 16: DESIGN OF THE WINDOW OPENING
The window opening, to accommodate the primary and secondary windings, will next be
determined, but before doing this, it will be necessary to assume an approximate winding space
factor and current density. Using formula (134), sf, but this will be arbitrary reduced to about
0.228, because with circular coils, there will be some loss of winding space between the flat
sides of the core and the low tension windings, and also because of the extra insulation required
between the low tension coils on each leg. A current density of 1100 will be selected, subject to
later modification should space requirements, copper losses, and need for selecting standard wire
sizes for primary and secondary make this necessary. Thus,
HXD
Making H equal to about 2.5D,
D=
H=2.5D
Also H=14.423 in.
Before proceeding further, it will be advisable to estimate the core dimensions and the
iron loss. The maximum flux in the core is

7. Φ
Assuming a core density B’’= 83,000 lines per sq. in., and a stacking factor of 0.9, the gross
section of the iron will be
Agross
Referring to article 133 and figs. 158 and 157, A gross=2WL-W2, W=0.618L, W=0.525C and
L=0.85C, so that;
From which
C=6.248 in., W=3.28 in.
L=5.311 in.
Since the core is wound through the coils with ribbon of two windings, one of them W=3.28 in.,
and the other L=5.311 in., proper allowances must be made as indicated in fig.1.
The length of the mean magnetic flux path is, therefore,
The total weight of the iron core is
Referring next to the curves from U.S.S. Manual previously mentioned, or appendix 2, the watts
per lb at 83,000 lines per sq. in., for oriented steel strips sheared parallel to the grain of rolling, is
0.81; whence the core loss is watts which is lesser than the guaranteed loss of 562.866 watts.

8.  Approximate copper Losses.
In making calculations for the approximate copper losses in both primary and secondary it
will be assumed that the current densities in the two windings are the same, although this is
generally not the case when standard wire sizes must be selected.

9. Fig. 1 Sketch showing core dimensions, window
opening, and mean magnetic path of the design.
Neglecting the small separation between the outer coils in the window opening (see figure 3),
the average mean length turn (m.l.t) of the circular coils will be the average of the inner
circumference πC and the outer circumference π(D+L);
By formula (131) the watts loss per pound is 2.5∆2/106, whence
 Size for wire and winding particular
Figure 2 shows the general arrangement of the core and its surrounding windings. Note
particularly the cruciform corner molds, and the tube forms around which the windings are
placed and properly insulated before the transformer is assembled. Another sketch illustrating the
manner in which the windings are arranged in window opening is given in fig. 3.

10. Fig. 2. Sketch showing the coil and insulation arrangement over the cruciform core of the design.
The four secondary coils, two on each leg, will be wound directly over the insulating tube
forms; each of the latter will be 1/8 in. thick, and will be covered a 45-mil tape before the
winding is stated.
The size of a suitable conductor of rectangular section may be calculated as follows.
For a current density of about 1100 ampere per sq. in. the cross section will be sq. in.
Assuming a winding layer of about 13.72 in. with 40 conductors to the layer, each
conductor should have a total width including insulation of 0.343 in. The cotton covering will
account for 18 mils, leaving 0.325 in. for copper. Consulting table III, Appendix 1 of page 435, it
is found that an area of 0.0644 sq. in. would be suitable. The thickness of the wire, including
insulation, will, therefore, be 0.228 in.
Thus, the active secondary current density will be Finally, the radial width of both
secondary coils, allowing 45-mil paper between coils, will be )=0.501 in. (see Fig. 3)
Fig. 3 cross section of the winding and
insulation in the window opening of the
design
Continuing radially, suitable insulating
materials are placed over the outer low-tension
coil; this will be about the same as that given in the table on page 377 for the illustrative
Example of Art. 145, so that g=0.188 in. .There will be four primary oils as shown in Fig.3, each
one containing 720 turns.
For a current density of about 1100 amp per sq. in., the conductor area should be The
size of the standard wire that would be suitable in No.13 (see Table 1 page 431), which has an
area of 0.00407 sq. in., this is again slightly larger than that indicated above, so that the actual
primary current density will be
Allowing a 13.017 in. in height for both coils on each leg, and 0.703 in. between coils to
properly insulate them from each other, each coil will be high. Since No. 13 dcc winds 11.8
wires to the inch, there will be wires in each layer.s

11. With 720 turns per coil there would, therefore, be 10 layers of 730 conductors and a final
layer of 10 conductors;
Using 45-mil paper between layers, the total radial width of the primary coil will be:
The greatest difference of the potential between layers will be twice the volts per layer.
With volts per coil in the high tension winding; this will be , which is satisfactory; note
particularly that the volts between layers would have been twice this value if two primary coils
had been used.
It will next be desirable to determine if there is sufficient clearance between the high tension
coils at the center of the window; if not it is generally customary to widen the dimension D
sufficiently without increasing the iron loss perceptibly. Referring to fig. 3, which shows the coil
and insulation arrangement in the window, the following radial dimension may be noted.
6.248-5.311
0.125x2
1.002
1.374x2
2.748
0.188x2
Secondary
winding
plus
insulation, s x 2
Primary
winding
plus
insulation, p x 2
Insulating between primary
and secondary, g x 2
0.08
0.501x2
Insulating tape on tube x 2
0.25
0.04x2
Insulting tube x 2
0.25
0.125x2
Corner mold x 2
0.937
.0376
TOTAL
5.305
Subtracting 5.305 in. from the dimension D=5.769 in. leaves 0.464 in., which is ample for the
separation of the primary coils at the center of the window.
ITEM 17 TO 22: VOLTAGE DROP AND COPPER LOSSES

12. Since the magnetizing component of the primary current is small it may be neglected in
these calculations. Referring to Fig. 3, the mean length of the turns of the windings, as design,
are:
The total lengths of the windings are:
Secondary lengths=
Primary length=
The weights of the windings are:
The resistance of the winding at 75°C is:
Secondary resistance=
Primary resistance=

13. Where the number ## is the resistance per 1,000 ft of the secondary conductors at 75°C, at the
number ## is the resistance per 1,000 of the primary conductors at 60°C
The voltage drops in the windings are:
The copper losses are:
The total copper loss , which is less than the guaranteed loss of 1520.467W.
ITEM 23-30:

14. The core dimension and other data concerned with the core are given in Fig. 3 and item 6
to 16.
The total full load losses, item 30, are:
ITEM 31: EFFICIENCIES
The efficiency occurs when
=
ITEM 32: ALL-DAY EFFICIENCY
On the basic of 4-hours full load and 20 hours no load, the all day efficiency is
ITEM 33: PRIMARY EXITING CURRENT
Referring again to appendix 2, it is found out that the magnetizing force, for the density
of 83,000 lines per sq. in. is 14.5 ampere turns per in. also consulting Fig. 162, the number of
ampere turns per joint at the same density is about 63. ( there is only one joint in the magnetic
circuit of a ribbon-wound core). The maximum value of the total number of ampere- turns
required to magnetize the core will, therefore, be
Where the 58.211 is the m.m.p. as determined on items 6-16.
The magnetizing component of the primary current- the rms value- thus becomes

15. The “enegy” component is
So that the exciting current is
ITEM 34 TO 37: REGULATION
The percentage IR drop in the two winding is the total copper loss, item 22, expressed as
a percentage of the rated KVA output.
Thus,
Percent IR drop
The numeral values of the quantities in formula (135) required for the calculation of the percent
leakage reactance drop are as follows: f=60, TS=96, IS=108.696A, n=2. The length l may be
taken as the average of the mean length per turn of the high and low tension windings.
The remaining dimensions are taken from Fig. 3, where H=14.423 in, g=0.188 in,
p=1.374 in, s=0.501 in.
This is equivalent to a reactive drop of in the primary winding.
 TEMPERATURE RISE
In designing a tank for the transformer, it is important to bear in mind that the oil
temperature near the top must be somewhat less than the specified temperature rise of the

16. windings. It is, moreover, desirable to have a reasonable clearance between the outside surface of
the coils and the inside surface of the tank. For an average temperature rise of 50°C, for a which
the cooling coefficient, , the total effective outside area of the tank should be about
Remembering that the surface to be considered is the area of the vertical sides plus one-half the
area of the lid, a rectangular tank having dimensions and a height of 46 in. should be suitable.
The cooling surface will; therefore, be
Whence the probable maximum temperature rise of the oil is