TRANSFORMER DESIGN : CALCULATIONS SHEET:
SPECIFICATIONS AND DESIGN DATA:
KVA= 1000 connection= Delta-Star
Vp(line)= 11000 KV Type: Core type, Distribution
Vs(line)= 430 V
frequency= 50 Hz Tappings: 2.5% - 5%
phases= 3 Temperature rise: <=40 deg
%impedance= < 5%
CALCULATIONS:
Taking value of k, for k= 0.45
distribution transformers as:
Voltage per turn : Et= 14.2302495 V
therefore flux in core is: fm= 0.06410022 Wb
Taking the flux density as: Bm= 1.6 Wb/m^2
Thus the iron area required is: Ai= 0.04006264 m^2
Take stacking factor (for cold ks= 0.97
rolled grain oriented steel)
Gross iron Area available is: Ag= 0.04130169 m^2
CORE DESIGN:
Per phase primary: Voltage: V(H.V)ph= 11000 KV
Current: I(H.V)ph= 30.3030303 A
Per phasesecondary: Voltage: V(L.V)ph= 248.260616 KV
Current: I(L.V)ph= 1342.67504 A
Taking a 6 step core : k1= 0.92
Actual Taken
Diameter of circumscribing circle: d= 0.23908072 m 240 mm
a= 0.22951749 m 230 mm
b= 0.21158643 m 212 mm
c= 0.18528756 m 186 mm
d= 0.15085993 m 151 mm
e= 0.11117253 m 112 mm
f= 0.05977018 m 60 mm
Modified values of iron area: Ai '= 0.04037132 m^2
flux density: Bm'= 1.58776636
WINDOW AND YOKE DESIGN:
Take Window space Factor as: Kw= 0.3
Selecting Current Density: d= 2.75 A/mm^2
Window area required by Output Equation: Aw= 0.11357226 m^2
Selecting Height to Width Ratio as: Hw/Ww= 2.5
Window Height: Hw= 0.53285144 m @ 530 mm
Window Width: Ww= 0.21314057 m @ 215 mm
Distance Between Limbs; D= 455 mm
Taking the Yoke also to be 6 stepped:
Height of yoke: Hy= 230 mm
Depth Of Yoke: Dpth= 230 mm
Overall Height: H= 990 mm
Overall Width W= 1150 mm
WINDING DESIGN:
Actual 5% tap Integral value Taken
Total Primary turns Required= T(H.V)= 773.001206 811.6513 819
Total Secondary turns Required= T(L.V)= 17.4459778 18
Area of conductors: H.V: ah= 11.0192837 mm^2
L.V: al= 488.245471 mm^2
L.V WINDING DESIGN:
Taking Stranded Conductors: Strands= 15
Area per Strand is: a= 32.5496981 mm^2
Selecting a Double Helical Winding , Taking the distribution of each L.V Conductor as:
5 Vertical and 3 horizontal,(Rectangular Conductor) From the Conductor Size data sheet:
Dimensions of each Strand is h= 6 mm
w= 5.5 mm
the per strand area is 32.1mm^2,thus
modified value of current density: d'= 2.78852553 A/mm^2
Taking 0.25mm insulation all over h'= 6.5 mm
Dimension of each strand is: w'= 6 mm
Therefore Conductor Size is: Hc= 32.5 mm
Wc= 18 mm
Thus the L.V Winding comprises of 2 Layers Helicaly Positioned and,
9 conductors per layer for a total of 18 conductors, taking 2mm for duct between the 2 layers:
Taking space between conductors for cooling asp= 20 mm
Total Winding Height:= H= 452.5 mm
Total Winding Width:= W= 38 mm
Taking 5mm clearance for bakelite former between lv and the core:
inner diameter of L.V Winding: din= 250 mm
outer diameter of L.V Winding: dout= 326 mm
Length of mean turn is Lmt(h.v)= 904.7808 mm
H.V WINDING DESIGN:
The H.V Winding design is done using the cross over winding using rectangular conductors.
A total of 819 turns are accomodated using 13 coils and 7 coils per layer.
Each coil consists of 9 horizontal winding turns.Thus total turns=7*13*9=819.
voltage per coil is: V/coil= 846.153846 V
the area of each conductor is 10.9mm^2
thus, modified value of current density: d'= 2.78009452 A/mm^2
Dimensions for each conductor h= 3.8 mm
w= 3 mm
including the 0.25mm insulation all over: h'= 4.3 mm
w'= 3.5 mm
Thus, Coil Height hc= 30.1 mm
coil width ; wc= 31.5 mm
using inter coil spacing of 5.5mm and inter layer(horizontal)spacing of 1mm
Winding Height= H= 457.3 mm
W= 39.5 mm
Taking the clearance between H.V and L.V as: a= 12 mm
inner diameter of H.V Winding: din= 350 mm
outer diameter of H.V Winding: dout= 429 mm
Length of mean turn is Lmt(h.v)= 1223.6532 mm
OPERATING CHARACTERISTICS:
RESISTANCE;
Resistivity of copper is= r= 0.021 W-mm^2/m
Resistance of: H.V: r(H.V)= 1.8026211 W
Resistance of: L.V: r(L.V)= 0.00070048 W
Equivalent Resistance refered to H.V: Req= 3.17782364 W
p.u value of resitance= Rp.u= 0.00875434
REACTANCE:
Average mean turn is: Lmt(avg) 1064.217 mm
Average Height of Winding: Lc= 454.9 mm
Ratio of Lmt/Lc is Ratio= 2.33945263
value of reactance is: X= 20.8789598 W
p.u value of reactance: Xp.u= 0.0575178
Net impedance is: Z= 20.9028936 W
p.u value of impedance is: Z(p.u)= 0.05758373
REGULATION:
at 0.8 pf full load regulation is: Reg(p.u)= 0.04151415
at upf full load the regulation is: Reg(p.u)= 0.00875434
LOSSES AND EFFICIENCY:
IRON LOSSES:
From the loss graph of the crgo grade 56 loss curves,
Loss per unit volume is Loss/vol= 1.42 W/kg
now total fluxpath length is: L= 4120 mm
volume of the iron parts: volume= 0.16632984 m^3
Taking density of grade 56 crgo is: s= 7650 kg/m^3
Total mass of the iron parts is: M= 1272.42324 kgs
thus total iron loss is: Pi= 1806.841 W
Total copper Losses is= Pc= 8754.3351 W
thus %full load at max efficiency is x= 0.45430591
and efficiency at 0.8pf is: h= 0.98697054
upf is: h= 0.9895492
MAGNETIZATION CHARACTERISTICS:
Total iron losses= Pi= 1806.841 W
Thus the loss component of no load current is: Il= 0.05475276
now the mmf/meter for iron is: Ati/m= 110 AT
Total mmf required is Ati= 453.2 AT
taking atotal of 0.05mm air gap per joint
Total airgap length is: La/g= 0.3 mm
mmf required for the air gap is: Ata/g= 381.063927 AT
Total mmf Required is AT0= 834.263927 AT
the magnetizing current per phase is: Im= 0.25438239
thus the no load current is: I0= 0.26020812 0.858687 % of full load current.
OVERALL TANK DIMENSIONS AND VOLUME:
Taking the basic clearances of: b= 50 mm
l= 80 mm
h= 300 mm
Width of the tank is= W= 1439 mm 1450 mm
L= 589 mm 600 mm
H= 1290 mm 1300 mm
thus total volume of tank is: V= 1.131 m^3
for calculation of copper volume:
volume of lv winding: V(lv)= 0.01555771 m^3
volume of hv winding: V(hv)= 0.02210328 m^3
Thus total copper volume is V= 0.11298295 m^3
total iron volume is V= 0.16632984 m^3
thus volume of oil in transformer V(oil)= 1.34667402 m^3
(including radiators is:)
CONSERVATOR DESIGN:
Volume of conservator is taken . V(cons)= 0.1346674 m^3
as 10% of oil in tank and radiators
thus taking length to diameter ratio as: R= 2.5
D= 0.40933341 m
L= 1.02333352 m
DESIGN OF COOLING ARRANGEMENTS (RADIATORS):
Value of thermal coefficient at 75 deg c is C= 12.5 W/(m^2-degC)
Temperature rise limits specified: q= 40 degC
Total Watts dissipating from surface W/m^2= 500 W/m^2
for the requisite temperature rise is:
Surface Area of Tank is: St= 5.33 m^2
Total Watts that are dissipated
from the tank walls naturaly is= Diss= 2665 W
Thus the total watts required to be Rdwats= 7896.1761 W
dissipated by radiators is
Taking height of radiators as: Hrad= 1200 mm
thus the watts per section for this height
and temperature is: W/sectn= 167
thus no of section required is sections= 47.2824916
now the values of spacing constants are: c= 0.955
b= 0.93
d= 1
Modified value of no of sections required sections= 53.2370564 56
Thus we select 56 elliptical Radiator sections in total of 6 Radiators,with 7 sections per radiator.
Thus Radiator section dimensions are: h= 1200 mm
w= 300 mm
l= 25 mm
Horizontal distance between each Section is: 50 mm
vertical surface area of each radiator is: A= 0.00736588 m^2
Volume of each radiator= V= 0.00883905 m^3
Net Volume of all Radiators Vnet= 0.4949868 m^3
TRANSFORMER DESIGN
KVA= 25000 KVA connection= Star-Delta
Vp(line)= 33 KV type= power transformer
Vs(line)= 6.9 KV temp= 75
frequency= 50 Hz tappings= 10.00%
phase= 3
transportation height=3.5m
load loss= 20 KW
no load loss= 110 KW
load loss capitalization= 1 lakh/KW
load loss capitalization= 5 lakh
Bmax= 1.7 tesla
current density= 3 A/mm2
width of conductor= 17<x<6 thickness of conductor= 4<x<1.5
ratio= 2>y>7 stacking factor= 0.9
specific loss= 1.2 KW/Kg
copper rate= 425 Rs./Kg
iron rate= 180 Rs./Kg
CALCULATIONS
HV side voltage: Vhv= 19.052558883 KV
LV side voltage: Vlv= 6.9 KV
Current in HV & LV
Current in HV: Iph(hv)= 437.38656757
current in LV: Iph(lv)= 1207.7294686
Core area
assuming diameter: D= 440 mm
core area: A= 136847.77599 mm2
No. of turns in HV & LV
HV no. of turns: N(hv)= 133.60092072 134
LV no.of turns N(lv)= 368.90426216 369
min.HV turns(90%): N(hv min)= 332.1 333
max. HV turns(110%) N(hv max) 405.9 406
Height of core structure
assuming height of core structure 2500 mm.
H= 2500 mm
height of core window:H(window) 1620 mm
height of winding: H(wdg)= 1470 mm
Design of HV winding
using Disc winding.
assuming No. of turns/disc= 3
HV no.of turns: T(hv)= 369
No. of discs: Discs= 123 123
actual No. of discs: 128
width of HV conductor:w(hv)= 8.184375
assuming current density: 2.5
area of conductor: a(hv)= 174.95462703
assuming thickness: 3.47
No. of parallel paths: paths= 6.1604216415 6
Design of LV conductor
area of conductor: a(lv)= 483.09178744
width of LV conuctor: w(lv)= 7.6701492537
assuming thickness: 2.5
No. of parallel paths: paths= 25.193344821 26
Design of Tapping winding
winding turns: T(tap)= 73
assuming no. of turns per discs: 3
No. of discs: Discs= 24.333333333 25
actual no. of discs: Discs= 28
ht of tapping winding: ht(tap)= 964.6875
Calculation of %Z
width of air gap btwn core & LV: Tg= 15 mm
width of air gap btwn LV & HV: Tg1= 15 mm
width of air gap btwn HV & tap: Tg2= 10 mm
width of LV winding: T1= 78
Inner Dia for LV: ID(lv)= 470
mean dia of LV: D1= 587
width of HV winding: T2= 71.46
Inner Dia of HV: ID(hv)= 656
mean dia of HV: D2= 763.19
width of Tapping wdg T3= 23.82
Inner Dia of Tapping: ID(tap): 818.92
mean dia of Tapping: D3= 854.65
ID for air gap btwn HV-LV: 626
mean diameter Dg1= 661.73
ID for air gap btwn HV-Tap: 798.92
mean diameter: Dg2= 813.92
summation ATD: ATD= 45516.097448 mm2
455.16097448
Rogowski Factor: Kr= 0.9643882695
Heq= 1524.2823316 mm
152.42823316 cm
Ampere turns: AT= 161395.64343
Volts/turns: V/T= 52.177581393
% impedance: %Z= 11.453260837 %
Width of core
width of transformer: W(core)= 2536.76
Volume of core
volume of 3 limbs: vlm(limb)= 738977990.35
volume of 2 yokes: vlm(yoke)= 736777185.31
total volume of core: total= 1475755176
Core loss
Weight of core: wt= 11289.527094
No load loss: core loss= 18.06324335 KW
Copper loss
mean dia of LV: d(lv)= 548 mm
mean dia of HV: d(hv)= 727.46 mm
mean dia of Tap: d(tap)= 842.74 mm
mean length turn LV: Lmt(lv)= 1721.5927742
mean length turn HV: Lmt(hv)= 2285.3829918
mean length turn Tap: Lmt(tap)= 2647.5457929
area of conductor LV: a(lv)= 483.09178744 mm2
area of conductor HV: a(hv)= 174.95462703 mm2
length of LV: l(lv)= 230693.43174 mm2
length of HV: l(hv)= 843306.32397 mm2
length of Tap: l(tap)= 74131.282201 mm2
resistance LV: Rlv= 0.0095507081
resistance HV: Rhv= 0.0964028604
resistance Tap: Rtap= 0.0084743437
Copper loss in LV: loss(lv)= 41.792288358 KW
Copper loss in HV(normal tap)= 56.947208919 KW
Total loss
total loss: 116.80274063
