# Chapter 33: Transformer:Three Phase¶

## Example Number 33.1, Page Number:1216¶

In [14]:
import math
#variable declaration
p=3
f=50.0#Hz
vd=22000.0#V
vs=400.0#V
phi=0.8
i=5.0#A

#calcuations
v_phase_secondary=vs/math.sqrt(3)
K=(vs/vd)/math.sqrt(3)
i_primary=i/math.sqrt(3)
i_secondary=i_primary/K
il=i_secondary
output=math.sqrt(3)*il*vs*phi

#result
print "Output=",output/10000,"kW"

Output= 15.2420471066 kW


## Example Number 33.2, Page Number:1217¶

In [1]:
import math
#variable declaration
w=500.0#kVA
f=50.0#Hz
vls=11.0#kV
vld=33.0#kV
rh=35.0#ohm
rl=0.876#ohm
iron_loss=3050.0#W
phi1=1.0
phi2=0.8

#calculations

K=(vls*1000)/(math.sqrt(3)*vld*1000)
r02=rl+K**2*rh
i_Secondary=(w*1000)/(math.sqrt(3)*vls*1000)
fl_culoss=3*((w/(vls*math.sqrt(3)))**2)*r02
fl_totalloss=fl_culoss+iron_loss
fl_efficiency1=w*1000/(w*1000+fl_totalloss)
fl_efficiency2=(phi2*w*1000)/(w*phi2*1000+fl_totalloss)
cu_loss=.5**2*fl_culoss
totalloss=cu_loss+iron_loss
efficiency1=(w*1000/2)/((w*1000/2)+totalloss)
efficiency2=(w*1000*phi2/2)/((phi2*w*1000/2)+totalloss)
#result
print "full load efficiency at p.f. 1=",fl_efficiency1*100,"%"
print "full load efficiency at p.f. 0.8=",fl_efficiency2*100,"%"
print "half load efficiency at p.f. 1=",efficiency1*100,"%"
print "half load efficiency at p.f. 0.8=",round(efficiency2*100),"%"

full load efficiency at p.f. 1= 98.5147491838 %
full load efficiency at p.f. 0.8= 98.1503046336 %
half load efficiency at p.f. 1= 98.3585709725 %
half load efficiency at p.f. 0.8= 98.0 %


## Example Number 33.3, Page Number:1218¶

In [39]:
#variable declaration
r=0.02
va=2000
reactance=0.1
pf=0.8
phi=math.acos(pf)
#calculation
cu_loss=r*100*va/100
regn=r*100*math.cos(phi)+reactance*100*math.sin(phi)

#result
print "Cu loss=",cu_loss,"kW"
print "Regulation=",regn,"%"

Cu loss= 40.0 kW
Regulation= 7.6 %


## Example Number 33.4, Page Number:1218¶

In [46]:
#variable declaration
w=120.0#kVA
v1=6000.0
v2=400.0
f=50.0#Hz
iron_loss=1600.0#W
pf=0.8

#calculations
cu_loss_fl=iron_loss*((4/3)**2)
fl_output=w*pf*1000
total_loss=iron_loss+cu_loss_fl
efficiency1=fl_output/(fl_output+total_loss)
cu_loss_hl=0.5**2*cu_loss_fl
total_loss2=cu_loss_hl+iron_loss
efficiency2=(w*1000/2)/((w*1000/2)+total_loss2)
total_loss3=2*iron_loss
output=(3.0/4)*w*1000
inpt=output+total_loss3
efficiency=output/inpt

#result

full load efficiency= 96.7741935484 %


## Example Number 33.5, Page Number:1218¶

In [59]:
import math
#variable declaration
rp=8.0#ohm
rs=0.08#ohm
z=0.07
pf=0.75
v1=33.0
v2=6.6
w=2*10.0**6
phi=math.acos(pf)
#calculations
fl_i=w/(math.sqrt(3)*v2*10**3)
K=v2/(math.sqrt(3)*v1)
r02=rs+(rp*(K*K))
z_drop=z*v2*1000/math.sqrt(3)
z02=z_drop/fl_i
x02=math.sqrt((z02*z02)-(r02*r02))
drop=fl_i*(r02*math.cos(phi)+x02*math.sin(phi))
secondary_v=v2*1000/math.sqrt(3)
V2=secondary_v-drop
line_v=V2*math.sqrt(3)
regn=drop*100/secondary_v

#result
print "secondary voltage",line_v,"V"
print "regulation=",regn,"%"

secondary voltage 6254.29059005 V
regulation= 5.23802136291 %


## Example Number 33.6, Page Number:1219¶

In [75]:
import math
#variable declaration
w=100.0#kWA
f=50.0#Hz
v1=3300.0#V
v2=400.0#V
rh=3.5#ohm
rl=0.02#ohm
pf=0.8
efficiency=0.958

#calculations
output=0.8*100
inpt=output/efficiency
total_loss=(inpt-output)*1000
K=v2/(math.sqrt(3)*v1)
r02=rl+K**2*rh
i2=((w*1000)/math.sqrt(3))/v2
cu_loss=3*i2**2*r02
iron_loss=total_loss-cu_loss
#result
print "ironloss=",iron_loss,"W"

0.0371411080502
2321.31925314
ironloss= 1185.98763622 W


## Example Number 33.7, Page Number:1219¶

In [95]:
import math
#variable declaration
w=5000.0#kVA
v1=6.6#kV
v2=33.0#kV
nl=15.0#kW
fl=50.0#kW
drop=0.07
pf=0.8
phi=math.acos(pf)
#calculations
i2=w*1000/(math.sqrt(3)*v2*1000)
impedence_drop=drop*(v2/math.sqrt(3))*1000
z02=impedence_drop/i2
cu_loss=fl-nl
r02=cu_loss*1000/(3*i2**2)
x02=math.sqrt(z02**2-r02**2)

drop_=drop*1000*(r02*math.cos(phi)+z02*math.sin(phi))
regn=(drop_*100)/(v2*1000/math.sqrt(3))
vp=v1+regn/100*v1
print "Primary voltage=",vp*1000,"V"

full-load x02: 15.1695784661
Primary voltage= 6851.39317975 V


## Example Number 33.8, Page Number:1219¶

In [96]:
import math
#variable declaration
r=1
x=6
v=6600#V
v2=4800#V
pf=0.8
phi=math.acos(pf)
#calculations
regn=(r*math.cos(phi)+z*math.sin(phi))
secondary_v=v2+regn/100*v2
secondary_vp=secondary_v/math.sqrt(3)
K=secondary_vp/v

#result
print "Transformation Ratio=",K

Transformation Ratio= 0.423426587968


## Example Number 33.9, Page Number:1220¶

In [109]:
import math
#variable declaration
w=2000#kVA
v1=6600#V
v2=400#V
pf=0.8
scv=400#V
sci=175#A
scw=17#kW
ocv=400#V
oci=150#A
ocw=15#kW
phi=math.acos(pf)
#calculations
i1=sci/math.sqrt(3)
z01=scv/i1
r01=scw*1000/(3*i1*i1)
x01=math.sqrt(z01**2-r01**2)
r=i1*r01*100/v1
x=i1*x01*100/v1
regn=(r*math.cos(phi)-x*math.sin(phi))
I1=w*1000/(math.sqrt(3)*v1)
total_loss=scw+ocw
fl_output=w*pf
efficiency=fl_output/(fl_output+total_loss)

#result
print "% resistance=",r,"%"
print "% reactance=",x,"%"
print "% efficiency=",efficiency*100,"%"
print "%regulation=",regn,"%"

% resistance= 0.849779616989 %
% reactance= 6.00073499035 %
% efficiency= 98.0392156863 %
%regulation= -2.92061730062 %


## Example Number 33.10, Page Number:1220¶

In [116]:
import math
#variable declaration
v1=11000.0#V
v2=440.0#V
i=5.0#A
pf=0.8

#calculations
secondary_rating=v2/math.sqrt(3)
primary_i=i/math.sqrt(3)
voltsamps=v1*5/math.sqrt(3)
i2=voltsamps/secondary_rating
output=pf*voltsamps/1000

#result
print "Each coil current=",i2,"A"
print "Total output=",output,"kW"

Each coil current= 125.0 A
Total output= 25.4034118443 kW


## Example Number 33.12, Page Number:1224¶

In [126]:
#variable declaration

#calculations
delta_delta_rating=kVA_per_transformer*3

#result
print "increase=",increase,"%"

increase= 72.5 %


## Example Number 33.13, Page Number:1224¶

In [130]:
import math
#variable declaration
w=20#kVA
v1=2300#v
v2=230#V

#calculations
kvarating_vv=2*w*0.866
vv_delta=kvarating_vv*100/60

#result
print "ii)per cent of rated load carried by each transformer=",percent_rated,"%"
print "iii)total kVA rating of the V-V bank",kvarating_vv,"kVA"
print "iv)ratio of the v-v bank to delta-delta bank",vv_delta,"%"

i)kVA load of each transformer= 23.0940107676 kVA
ii)per cent of rated load carried by each transformer= 115.470053838 %
iii)total kVA rating of the V-V bank 34.64 kVA
iv)ratio of the v-v bank to delta-delta bank 57.7333333333 %
v)percent increase in load= 177.646236674 %


## Example Number 33.14, Page Number:1225¶

In [133]:
import math
#variable declaration
v1=1000.0#V
pf=0.866
v=2000.0#V

#calculations
ip=il/math.sqrt(3)
ratio=v1/v
ip=ip*ratio
I=il
Ip=I*ratio
pf=86.6/100*pf

#result
print "delta-delta:current in the windings=",ip,"A"
print "v-v:current in the windings=",Ip,"A"
print "Power factor",pf

delta-delta:current in the windings= 28.8683602771 A
v-v:current in the windings= 50.0014667312 A
Power factor 0.749956


## Example Number 33.15, Page Number:1225¶

In [134]:
import math
#variable declaration
v=11#kV
pf=0.8

#calculations
transformer_pf=86.6/100*pf

#result
print "Il=",il,"A"
print "phase current=",il/math.sqrt(3),"A"

Il= 339.521323075 A
phase current= 196.022727273 A


## Example Number 33.16, Page Number:1225¶

In [136]:
import math
#variable declaration
pf=0.866
v=440#V

#calculations
phi=math.acos(pf)
p=p1+p2

#result
print "kVA supplied by each transformer=",kVA_each,"kVA"
print "kW supplied by each transformer=",p,"kW"

kVA supplied by each transformer= 230.946882217 kVA
kW supplied by each transformer= 399.995027715 kW


## Example Number 33.17, Page Number:1228¶

In [139]:
import math
#variable declaration
v=400.0#V
v2=3300.0#V

#calculations
vl=0.866*v2
ils=ilp/(440/v2)
main_kva=v2*ilp*0.001
teaser_kva=0.866*main_kva

#result
print "voltage rating of each coil=",vl
print "current rating of each coil=",ils
print "main kVA=",main_kva,"kVA"
print "teaser kVA=",teaser_kva,"kVA"

voltage rating of each coil= 2857.8
current rating of each coil= 43.3012701892
main kVA= 19.0525588833 kVA
teaser kVA= 16.4995159929 kVA


## Example Number 33.18, Page Number:1231¶

In [2]:
#variable declaration
v=440.0#V
v2=200.0#V
output=150.0#kVA

#calculations
ratio=v2/v
i2=output*1000/(2*v2)
i1=i2*ratio
primary_volts=(math.sqrt(3)*v)/2
ratio=v2/primary_volts

#result
print "primary current=",i1,"A"
print "turns ratio",ratio

primary current= 170.454545455 A
turns ratio 0.524863881081


## Example Number 33.19, Page Number:1231¶

In [150]:
#variable declaration
v=100.0#V
v2=3300.0#V
p=400.0#kW
pf=0.8

#calculations
K=v/v2
i2=p*1000/(pf*v)
ip=1.15*K*i2
I2m=K*i2
i2=ip/2
i1m=math.sqrt(I2m**2+i2**2)

#reslult
print "Current=",i1m,"A"

Current= 174.77684841 A


## Example Number 33.20, Page Number:1232¶

In [163]:
#variable declaration
w1=300#kW
w2=450#kW
v1=100#V
pf=0.707
v2=3300#V

#calculations
K=v/v2
i2t=(w2*1000)/(100*pf)
i1t=1.15*K*i2t
I2m=(K*w1*1000)/(100*pf)
i2=i1t/2
i1m=math.sqrt(I2m**2+i2**2)

#result
print "Current=",i1m,"A"

Current= 169.804606659 A


## Example Number 33.21, Page Number:1233¶

In [171]:
import math
#variable declaration
v1=80.0#V
v2=11000.0#V
w1=500.0#kW
w2=800.0#kW
pf=0.5

#calculations
K=v1/v2
#unity pf
i2t=w1*1000/v1
i1t=1.15*K*i2t
i2m=K*w2*1000/v1
i1t_half=i1t/2
ip=math.sqrt(i2m**2+i1t_half**2)

print "unity pf"
print "one 3 phase line carries",i1t,"A whereas the other 2 carry",ip,"A each"
#0.5 pf
i2t=w1*1000/(v1*pf)
i1t=1.15*K*i2t
i2m=K*w2*1000/(v1*pf)
i1t_half=i1t/2
ip=math.sqrt(i2m**2+i1t_half**2)
print "0.5 pf"
print "one 3 phase line carries",i1t,"A whereas the other 2 carry",ip,"A each"

unity pf
one 3 phase line carries 52.2727272727 A whereas the other 2 carry 77.281082436 A each
0.5 pf
one 3 phase line carries 104.545454545 A whereas the other 2 carry 154.562164872 A each


## Example Number 33.22, Page Number:1234¶

In [173]:
import math
#variable declaration
v1=50#V
v2=4.6*1000#V
w=200#kW
pf=0.8

#calculation
K=v1/v2
i2t=w*1000/(v1*pf)
i1t=1.15*K*i2t
Ki2m=K*i2m
i1t_half=i1t/2
i1m=math.sqrt(Ki2m**2+i1t_half**2)

#result
print "current in line A=",i1t
print "current in line B=",i1m
print "current in line C=",i1m

current in line A= 62.5
current in line B= 100.11107076
current in line C= 100.11107076


## Example Number 33.23, Page Number:1234¶

In [176]:
import math
#variable declaration
v=231#V
v2=6600#v
volt_induced=8#v

#calculations
hv=v2/volt_induced
vl=v*math.sqrt(3)
n_lv1=vl/volt_induced
n_lv2=math.sqrt(3)*n_lv1/2
n=2*n_lv2/3

#result
print "neutral point is located on the",math.ceil(n),"th turn from A downwards"

neutral point is located on the 29.0 th turn from A downwards


## Example Number 33.24, Page Number:1235¶

In [183]:
import math
#variable declaration
v=6000.0#V
v2=440.0#V
f=50.0#Hz
area=300.0#cm2
flux=1.2#Wb/m2

#calculations
n1=v/(4.44*f*flux*area*0.0001*0.9)
K=v2/v
n2=n1*K
n_lv=math.sqrt(3)*n2/2
turns=n_lv*2/3

#result
print "NUmber of turns in AN=",math.floor(turns)

 NUmber of turns in AN= 35.0


## Example Number 33.25, Page Number:1235¶

In [185]:
import math
#variable declaration
v=250.0#V
v2=250.0#V

#calculations
vl=0.866*v2
kva=il*vl*(0.001)

#result
print "Voltage=",vl,"V"
print "kVA rating",kva,"kVA"

Voltage= 216.5 V
kVA rating 14.9995599935 kVA


## Example Number 33.26, Page Number:1237¶

In [5]:
import cmath
#vaiable declaration
pf=0.8
za=complex(2,6)
zb=complex(2,5)
phi=math.acos(pf)
#calculations
z1=za/zb
z2=zb/za
sa=s/(1+z1)
sb=s/(1+z2)
pfa=cmath.phase(sa)
pfb=cmath.phase(sb)
#result
print "sa=",abs(sa)
print "sb=",abs(sb)
print "cos phi_a=",pfa
print "cos phi_b=",pfb

sa= 230.042839552
sb= 270.171613479
cos phi_a= 0.611765735265
cos phi_b= 0.670521557981


## Example Number 33.27, Page Number:1237¶

In [211]:
import cmath
#variable declaration
w=2000#kVA
w1=4000#kVA
w2=5000#kVA
pf=0.8
za=complex(2,8)
zb=complex(1.6,3)

#calculations
za_per=(w1/w)*za
zb_per=zb
z=za_per+zb_per
s=complex(w1,w-w2)
sb=s*(za/z)
sa=s-sb

#result
print "sa=",sa
print "sb=",sb

sa= (2284.2287695-1821.49046794j)
sb= (1715.7712305-1178.50953206j)


## Example Number 33.28, Page Number:1237¶

In [240]:
import cmath
#variable declaration
pf=0.866
w1=1000#kVA
w2=500#kVA
v1=6600
v2=400
za=complex(0.001,0.003)
zb=complex(0.0028,0.005)
phi=math.acos(pf)
#calculations
zb=(w1/w2)*zb
z=za/(za+zb)
x=math.cos(-phi)
y=math.sin(-phi)*1j
sb=s*z
sa=s-sb

#result
print "sa=",sa
print "sb=",sb

sa= (929.911014012-588.664867724j)
sb= (282.488985988-111.396729565j)


## Example Number 33.29, Page Number:1238¶

In [242]:
import cmath
#variable declaration
pf=0.707
w1=500#kVA
w2=250#kVA
v1=3300
v2=400
za=complex(2,3)
zb=complex(1.5,4)
phi=math.acos(pf)
#calculations
zb=(w1/w2)*zb
z=za/(za+zb)
x=math.cos(-phi)
y=math.sin(-phi)*1j
sb=s*z
sa=s-sb
per_r=za.real*(sa.real)/w1
per_x=(za.imag)*(sa.imag)/w1
total_per=per_r+per_x
vl=v2-(total_per*4)
#result
print "sa=",sa
print "sb=",sb

sa= (399.511103547-348.770523615j)
sb= (130.738896453-181.639636072j)


## Example Number 33.30, Page Number:1240¶

In [214]:
#variable declaration
ratio=100/5
i=5#A
i1=3.5#A

#calculations
il=i1*ratio

#result
print "Line current=",il,"A"

Line current= 70.0 A


## Example Number 33.31, Page Number:1240¶

In [216]:
#variable declaration
i1=2000#A
i2=2500#A
i=5#A

#calculations
ratio1=i1/i
ratio2=i2/i

#result
print "ratio in first case=",ratio1
print "ratio in second case=",ratio2

ratio in first case= 400
ratio in second case= 500

In [ ]: