2 The calculation of base scales of transformer

The base scales of transformer are shown on the fig. 2.1, the main insulation of windings is shown on the fig. 2.2.

Figure 2.1 – Base scales of transformer

Figure 2.2 – The main isolation of HV and LV windings

2.1 The sum approximate reduced radial scale of HV and LV windings:

,

Where S_ph – the power of one phase (kVА);

К = 0.63*1.25 (tabl. 3.3, p. 121 [1]).

For windings of aluminum assume К = 1.25·0.64 = 0.8m

= 0.0213 m.

2.2 The primary width of reduced dissipation channel of transformer:

a_r = a₁₂ + ,

where a₁₂ – insulation length between HV and LV windings, it is:

a₁₂ = а^´₁₂·10^-3 m, а^´₁₂ =27 mm – for cylindrical windings without electrostatic screen (tabl. 4.5, p. 184 [1]), then:

а_r = 27·10^-3 + 0.0213 = 0.048 m.

2.3 The coefficient of filling of a circle by steel.

According to instructions § 2.3 [1] is chosen three-phase rod with laminated magnetic system with slanting joints at extreme rods and with combined joints on an average rod. Pressing of tire rods is by fiberglass tape and the yoke – by steel beams. Material of magnetic system is cold-rolled roll steel of the trademark 3405 with width 0.3 mm. Induction in the rod (tabl. 2.4, p. 78 [1]) В_leg = 1,55 – 1,6 Т (assume В_leg = 1.55 Т).

К_steel = К_kr·К_filling,

where К_kr – ratio the area of cross section of a rod of a step figure to the area of

the circle with a diameter d.

К_filling – ratio of the area of active cross section of rod (clean steel) to the area of the cross section of a rod of a step figure.

К_kr = 0.918 – (table. 2.5, р. 83 [1]);

К_filling = 0.96 (table. 2.2, р. 77 for steel trademark 3405 with with 0,3 mm [1]).

К_steel = 0.913·0.96 = 0.876.

The value of coefficient β, which connect average length of a circle of the channel of dispersion between windings of transformer and height of the winding choose from the table. 3.12, р. 159 [1]. At the given capacity of the transformer for aluminum windings coefficient β is recommended β = 1.5 Assume β = 1.5

2.4 The primary diameter of the rod:

d = 0.507· = 0.158 m,

where К_Р = 0,95 coefficient of reduction of an ideal field of dispersion to real (coefficient of Rogovsky).

The final diameter of the rod is accepted on the normalized scale d_n. Assume d_n = 0,16 m.

2.5 I determine value β_n, which corresponds to the normalized diameter:

β_n = = 1.566

2.6 Radial scale LV windings а1 primary determine under the formula:

а₁ = К₁· ,

Where К₁ = 1,1 – coefficient, which choose from the tabl. 2.3, р. 78 [2], then:

а₁ = К₁· 1.1·0.0213 = 0,023 m.

2.7 The average primary diameter between windings:

d₁₂ = dn + 2·a₀₁ + 2·a₁ + a₁₂ =0.16 + 2·4·10^-3 + 2·0.026 + 27·10^-3

=0.24182m,

Where а₀₁ = 4·10^-3 m – under the table. 4.4, р. 183 [1];

а₁₂ = 27·10^-3 m – under the table. 4.5, р. 184 [1].

2.8 The height of the winding of transformer:

L = = 0.485 m.

2.9 The active (clean) cross section of steel of the rod:

S_steel = К_steel· = 0.018 m².

2.10 The voltage of the coil:

V_turn = 4, 44·f₁·B_leg·S_steel = 4.44·50·1.55·0.018= 6.064 V.

2.11 Quantity of coils HV and LV windings on the phase:

W₁ = = 38.084 turns, assumed W₁ = 39turns.

W₂ = = 571.26037 turns, assume W₂ = 571 turns.

2.12 The average density of current in the windings (for aluminium windings):

Δ_avd = 0.463·K_al· = 1.846 MА/m²,

Where К_al = 0.95 – coefficient of additional losses in windings, taps, walls of a tank and etc. (tabl. 3.6, р. 131 [1]).

2.13 From the tabl. 5.7, р. 257 [1] the average density of current in the windings for the modern transformer with aluminum windings is in limits 1.2 –2.5 MА/m²

2.14 The primary cross section of wire HV and LV windings:

S_w1 = = 124.099·10^-6 m²;

S_w2 = =8.34·10^-6 m².

From the table. 5.8, р. 258 [1] and in accordance with the task choose cylindrical multilayer windings with rectangular wire and with concentric inside (closer to a rod) arrangement winding of the low voltage. On the high voltage choose cylindrical windings with rectangular wire.