Republic of the PhilippinesJOSE RIZAL MEMORIAL STATE UNIVERSITY

The Premier University in Zamboanga del NorteMain Campus, Dapitan City

ELECTRICALMACHINE DESIGN 1

EE-55

TRANSFORMER DESIGN

SUBMITTED BY:

MARK ANTHONY B. ENOYBS EE-V

SUBMITTED TO:

ENGR. URSINO P. TABILIRANINSTRUCTOR

DESIGN SHEET FOR TRANSFORMER

Single-phase Distribution Core Type with Cruciform Section

Guaranteed losses (watts): COPPER (FULL LOAD)………………………………………………

IRON…………………………………………….……………...…..…...

ITEM NO. SUMMARY OF CALCULATION

1 Volts per turn: from formula

WINDINGS

H.T. L.T

2 Total number of turns 2880 96

3 Number of coils 4 4

4 Turns per coil 720 24

5 Full-load current, Amp

3.623 108.696

6 Current density, Amp per sq. in.

7 Cross section of each conductor, sq. in.

0.00407 0.0644

8 Dimension of conductors

No. 13 0.204x0.325

9 Number of turns per layer per coil

72 24

10 Number of layers per coil

11 1

11 Taps None None

12 Volts per coil 3450 115

13 Volts between layers 627.273

14 Length of winding layer including insulation, in.

6.157 13.72

15 Insulation between layers, in.

.045

16 Insulation on wire dcc dcc

17 Length per turn, in. 30.096 23.025

18 Total length, all turns in series, ft

7223.04 184.2

19 Weight of copper, lb. 112.887 45.552

20 Resistance at 75°C- all coils in series, ohms

17.672 0.028

21 IR drop, volts 64.026 3.043

22 Full-load copper loss (compare with guarantee)

231.966 330.762

THE MAGNETIC CIRCUIT

23

Dimensions of “windows”, in. 5.769x14.423

24

Total flux, maxwells 1798673.674

25

Flux density in core under windings, lines per sq. in. 83000

26

Cross section of iron in core under windings, gross 24.079

27

Widths of ribbon strips in cruciform section, in. 3.28 and 5.311

28

Total weight of iron in core, lb 353.219

29

Watts lost in iron (compare with guarantee) 286.107

30

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

At ½ full load 0.9832

At ¼ full load 0.9749

32

All-day efficiency (4- hr full load) 0.9564

33

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. 3352

39 Watts per sq. in. of tank surface 0.2532

40 Approximate temperature rise of oil, °C 44.427

DESIGN OF DISTRIBUTION TTRANSFORMER

TRANSFORMER DESIGN SPECIFICATIONSOUTPUT IN KILOVOLT-AMPERES 50

PRIMARY (HIGH TENSION) VOLTS 13800

SECONDARY (LOW TENSION) VOLTS 460/230

FREQUENCY, HERTZ 60

EFFICIENCY AT UNITY POWER FACTOR

At full load = 0.96

At ¼ full load = 0.95

ALLOWABLE TEMPERATURE RISE 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

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 CURRENTIp

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,

H X D

Making H equal to about 2.5D,D=

H=2.5DAlso 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

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, Agross=2WL-W2, W=0.618L, W=0.525C and L=0.85C, so that;

From whichC=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.

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.

Fig. 1 Sketch showing core dimensions, windowopening, 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.

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

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 0.937

Corner mold x 2 0.125x2 0.25

Insulting tube x 2 0.125x2 0.25

Insulating tape on tube x 2 0.04x2 0.08

Secondary winding plus insulation, s x 2

0.501x2 1.002

Primary winding plus insulation, p x 2

1.374x2 2.748

Insulating between primary and secondary, g x 2

0.188x2 .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

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=

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:

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

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

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