Figure 4.2 – Distribution of compressing forces for our case

4.3.8 The time of heating of windings up to extreme allowable temperature (aluminium – 200^оC):

t_SC200.1 = 0.79· ,

where U_sc – voltage of short circuit, %;

Δ – density of current, А/m².

t_SC200.1 = 0.79· = 5.838 > 4.

t_SC200.2 = 0.79· = 4.45 > 4..

5 Calculation of transformer magnetis system

5.1 Design of magnetic system

5.1.1 Design of circuit is plane with laminated magnetic system, which construct is from cold-rolled grain-oriented roll steel of the trademark 3405 with width 30 mm under fig. 8.14.

5.1.2 The sizes of bundle are chosen from the table. 8.3 [1] for the rod with calculated diameter d_n=0.16 m. The number of steps in the cross section of the rod are 6, the number of steps in the cross section of the yoke are 5.

5.1.3 The area of cross section of rods’ and yokes’ step figure under the tabl. 8.7, р. 365 [1]:

A_leg =0.01835 m²;

A_yoke = 0.01885 m²;

V_cms = 0.002470 m³.

5.1.4 The active cross section of the rod:

A_L = К_filling · A_leg = 0.97· 0. 01835 = 0.018 m²,

Where К_filing = 0.97 – under the table. 2.2, р. 77 [1].

5.1.5 The active cross section of the yoke:

A_Y = К_filling · A_yoke = 0.97·0. 01885 = 0.018284m².

5.1.6 The volume of steel of a corner of magnetic system:

V_stcms = К_filling · V_cms = 0.97·0.002470 = 0.0023959 m³.

Figure 5.1 – The definition of scales of the plane magnetic system

The base sizes of magnetic system and cross section of rod and yoke are shown on fig.5.1

Figure 5.2 – Magnetic system of transformer

а) – cross section of rod and yoke ; b) – base scales of magnetic system .

The sizes of bundles in the cross section of rod and yoke under the

table. 8.3, р. 358 [1]:

№ Of bundle The rod, mm The yoke (in one-half

of cross section ), mm

1 155×20 155×20

2 135×25 135×25

3 120×13 120×13

4 105×8 105×8

5 85×9 85×9

6 55×8 ---

5.1.7 The length of rod:

l = l + (l^´_O + l^´´_O),

where l^´_O =30 mm, l^´´_O = 30 mm – from tabl. 4.5, 184 [1].

l = 0.5+ (30 + 30)·10^-3 = 0.545m.

5.1.8 The distance between axes of rods:

С = D^´´₂ + a₂₂ = 0.283 + 0.01 = 0.293 m.

5.1.9 Weight of yoke parts, stacked between axes of extreme rods (fig.5.1):

G^´_yoke = 2·(c –1)·C·A_Y·γ_st = 2·(3 – 1)·0.293· 0.018·7650 =164.13 kg,

Where γ_st – density of transformer steel 7650 kg/m³.

5.1.10 Weight of steel corner of the multi step form of the cross section:

G_corner = К_filling·V_cms·γ_st = 0.97·0.00247 ·7650 =18.32 kg.

5.1.11 Weight of steel in the yoke parts, which are shown on the

fig. 5.1:

G^´´_yoke = 2·G_corner = 2·18.32= 36.657 kg.

5.1.12 Weight of steel yoke’s:

G_yoke = G^´_yoke + G^´´_yoke = 164.13+ 36.657= 200.787 kg.

5.1.13 Weight of steel rods’ within the limits of a magnetic systems’ window:

G^´_st = c·A_L·L_Leg·γ_st = 3·0.018·0.545·7650 =222.637kg.

5.1.14 Weight of steel in the places of a joint of rod’s and yoke’s bundles:

G^´´_st = 3·(A_L·a_1yoke·γ_st – G_corner) = 3·(0.018·0.155·7650 –18.32) =-230.968 kg,

Where a_1yoke – jointing yoke’s width a_1yoke = 0.155m.

5.1.15 Weight of rods’ steel:

G_st = G^´_st + G^´´_st =222.637-230.968 = 230.968 kg.

5.1.16 Common weight of steel:

G_steel = G_yoke + G_st = 200.787+ 230.968 = 431.755 kg.

5.2 Determination of the idling losses

5.2.1 The real induction in the rod:

В_steel = = 1.499T.

5.2.2 The real induction in the yoke:

В_yoke = = 1.459T.

5.2.3 Induction in the area of skew joint:

В_skew = = 1.06T.

5.2.4 The area of cross section of the area of skew joint:

A_skew = = 0.018 = 0.025172m².

Specific losses for rods, yokes, area of joint are determine under the tabl. 8.10, р. 376 [1].

For В_leg = 1.499T: P_Сleg = 0.965Wt/kg; P_zlegС=565 Wt/m².

For В_yoke = 1.459T: P_yoke = 0.9Wt/kg; P_zyoke=535 Wt/m².

For В_skew = 1.06T: P_skew = 275 Wt/m².

5.2.5 The losses of idling:

Р_0s= [К_Рr·K_pz·(P_leg·G_st+P_yoke·G^´_yoke-6·P_yoke·G_corner + ) + ΣnЗAsPЗ]·К_pa·К_pp·К_ph where К_pr=1.11 p.380[1];

K_pr=1.02 p.380[1];

К_pa=1 p.379[1];

К_pp=1.02 tabl. 8.12, р. 380 [1];

К_ph=1.01 р. 380 [1];

К_PУ=8.58 tabl. 8.13, р. 382 [1].

Σp_Зп_ЗП_З = 6·р_КОС·П_кос .

ΣnЗAsPЗ =6·0.025·275 = 41.534 Wt

Р₀=[1.11·1.02·(0.965·230.968+ 0.9·200.787- 6·0.9·18.329+

+ ·8.58·18.329) +53.651]· 1.0·1.02·1.01 = 569/1000=0.569 Wt,

5.2.6 Deviation of real idling losses to prescribed (Р_ОЗ):

ΔР_О = = 5.396% < 7.5%.

5.3 Determination of idling current

5.3.1 under the table. 8.17, p. 390 [1] finds specific power of magnetizing:

For В_leg = 1.4999Tl q_leg = 1.2; VA/kg; q_ZLeg = 13500 ВА/м²;

For В_yoke = 1.459Tl: q_yoke = 1.15 VA/kg; q_ZYoke = 11500 ВА/м²;

For В_skew = 1.06Tl q_skew =2000ВА/м².

5.3.2 Idling magnetizing power:

Q_X = [K_tr·K_tz· (q_leg·G_st + q_yoke·G^´_yoke - 6·q_yoke·G_corner + ·K_tУ·К_trl·G_corner) +6·q_skew·A_skew+

+ 1·q_ZLeg·A_L + 2·q_ZYoke·A_Y] ·K_tyoke·К_tp·К_th,

Where K_tr = 1.49 p.393 [1];

K_tz = 1.01 p.393 [1];

К_trl = 1.65 table. 8.21, р. 396 [1];

K_tY = 1 p.394 [1];

К_tp = 1.04 table. 8.12, р. 380 [1];

К_th = 1.01 p.394[1];

K_ty = 27.95 table. 8.20, p.395 [1]

Q_X = [1.49·1.01· (1.2·230.968+ 1.15·164.13– 6·1.15·18.329 +

+ ·27.95·1.65·18.329) + 6·2000·0.025 +

+13500·0.018+2^. 11500·0.018]·1·1.04·1.01 = 3118 ВА.

5.3.3 Reactive component of idling current:

I_Or = = 1.949%.

5.3.4 Active component of idling current:

I_OA = = 3.557*10^-4%.

5.3.5 Total idling current:

I_O = = 1.949%.

5.3.6 Deviation of real idling current value to prescribed:

ΔI_O = = 18.802%< 30%.