# Chapter 32: Transformer¶

## Example Number 32.1, Page Number:1123¶

In [1]:
#variable declaration
v1=250.0#V
v2=3000.0#V
f=50.0#Hz
phi=1.2#Wb-m2
e=8.0#V

#calculations
n1=v1/e
n2=v2/e
a=v2/(4.44*f*n2*phi)

#result
print "primary turns=",n1
print "secondary turns=",n2
print "area of core=",round(a,2),"m2"

primary turns= 31.25
secondary turns= 375.0
area of core= 0.03 m2


## Example Number 32.2, Page Number:1123¶

In [4]:
#variable declaration
v1=11000#V
v2=550#V
f=50#Hz
bm=1.3#Tesla
sf=0.9
per=10#%
a=20*20*sf/10000#m2

#calculation
n1=v1/(4.44*f*bm*a)
n2=v2/(4.44*f*bm*a)
e_per_turn=v1/n1

#result
print "HV TURNS=",round(n1)
print "LV TURNS=",round(n2)
print "EMF per turns=",round(e_per_turn,1),"V"

HV TURNS= 1059.0
LV TURNS= 53.0
EMF per turns= 10.4 V


## Example Number 32.3, Page Number:1123¶

In [7]:
#variable declaration
n1=400.0
n2=1000.0
a=60.0/10000.0#cm2
f=50.0#Hz
e1=520.0#V

#calculations
k=n2/n1
e2=k*e1
bm=e1/(4.44*f*n1*a)

#result
print "peak value of flux density=",bm,"WB/m2"
print "voltage induced in the secondary winding=",e2,"V"

peak value of flux density= 0.975975975976 WB/m2
voltage induced in the secondary winding= 1300.0 V


## Example Number 32.4, Page Number:1124¶

In [11]:
#variable declaration
n1=500.0
n2=50.0
v=3000.0#V
f=50.0#Hz

#calculations
k=n2/n1
i2=i1/k
e1=v/n1
e2=e1*n2
phim=v/(4.44*f*n1)

#result
print "primary and secondary currents=",i1,"A", i2,"A"
print "secondary emf=",e2,"V"
print "flux=",phim*1000,"mWB"

primary and secondary currents= 8.33333333333 A 83.3333333333 A
secondary emf= 300.0 V
flux= 27.027027027 mWB


## Example Number 32.5, Page Number:1123¶

In [12]:
#variable declaration
f=50#Hz
v1=11000#V
v2=550#V
phim=0.05#Wb

#calculation
e=4.44*f*phim
e2=v2/1.732
t1=v1/e
t2=e2/e
HV=100*1000/v1
LV=100*1000/e2

#result
print "HV turns=",t1
print "LV turns=",t2
print "emf per turn=",e2

HV turns= 990.990990991
LV turns= 28.6082849593
emf per turn= 317.551963048


## Example Number 32.6, Page Number:1124¶

In [15]:
#variable declaration
n1=500.0
n2=1200.0
a=80.0/10000.0#m2
f=50.0#Hz
v=500.0#V

#calculation
phim=n1/(4.44*f*n1)
bm=phim/a
v2=n2*v/n1

#result
print "peak flux-density=",bm,"Wb"
print "voltage induced in the secondary=",v2,"V"

peak flux-density= 0.563063063063 Wb
voltage induced in the secondary= 1200.0 V


## Example Number 32.7, Page Number:1125¶

In [18]:
#varible declaration
n1=250.0
n2=40.0
v=1500.0#V
f=50.0#Hz

#calculation
v2=n2*v/n1
phim=v/(4.44*f*n1)

#result
print "i)primary current an secondary current=",i1,"A",i2,"A"
print "ii)seconary emf=",v2,"V"
print "iii)maximum flux=",phim*1000,"mWb"

i)primary current an secondary current= 16.6666666667 A 104.166666667 A
ii)seconary emf= 240.0 V
iii)maximum flux= 27.027027027 mWb


## Example Number 32.8, Page Number:1125¶

In [22]:
#variable declaration
f=50.0#Hz
a=20.0*20.0/10000#m2
phim=1.0#Wbm2
v1=3000.0#V
v2=220.0#V

#calculation
t2=v2/(4.44*f*phim*a)
t1=t2*v1/v2
n1=t1/2
n2=t2/2

#result
print "HV turns=",n1
print "LV turns=",n2

HV turns= 168.918918919
LV turns= 12.3873873874


## Example Number 32.9, Page Number:1126¶

In [24]:
#variable declaration
v1=2200.0#V
v2=200.0#V
i1=0.6#A
p=400.0#W
v3=250.0#V
i0=0.5#A
pf=0.3

#calculation
il=p/v1
imu=(i1**2-il**2)**0.5
iw=i0*pf
imu2=(i0**2-iw**2)**0.5

#result
print "magnetising currents=",imu,"A"
print "iron loss current=",il,"A"
print "magnetising components of no load primary current=",imu2,"A"
print "working components of no-load primary current=",iw,"A"

magnetising currents= 0.571788552492 A
iron loss current= 0.181818181818 A
magnetising components of no load primary current= 0.476969600708 A
working components of no-load primary current= 0.15 A


## Example Number 32.10, Page Number:1127¶

In [42]:
#variable declaration
n1=500.0
n2=40.0
l=150.0#cm
airgap=0.1#mm
e1=3000.0#V
phim=1.2#Wb/m2
f=50.0#Hz
d=7.8#grma/cm3
loss=2.0#watt/kg

#calculation
a=e1/(4.44*f*n1*phim)
k=n2/n1
v2=k*e1
iron=l*5
air=phim*airgap/(1000*4*3.14*10**(-7))
bmax=iron+air
imu=bmax/(n1*2**0.5)
volume=l*a
im=volume*d*10
total_i=im*2
iw=total_i/(e1)
i0=(imu**2+iw**2)**0.5
pf=iw/i0

#result
print "a)cross sectional area=",a*10000,"cm2"
print "d)power factor=",pf

a)cross sectional area= 225.225225225 cm2
b)no load secondary voltage= 240.0 V
d)power factor= 0.145353269536


## Example Number 32.11, Page Number:1127¶

In [51]:
import math
#variable declaration
n1=1000
n2=200
i=3#A
pf=0.2
i2=280#A
pf2=0.8

#calculations
phi1=math.acos(pf2)
i2_=i2/5
phi2=math.acos(pf)
sinphi=math.sin(phi2)
sinphi2=math.sin(math.acos(phi1))
i1=i*complex(pf,-sinphi)+i2_*complex(pf2,-sinphi2)

#result
print "primary current=",abs(i1),"/_",math.degrees(phi1),"degrees"

primary current= 64.4918252531 /_ 36.8698976458 degrees


## Example Number 32.12, Page Number:1130¶

In [53]:
#variable declaration
v1=440.0#v
v2=110.0#V
i0=5.0#A
pf=0.2
i2=120.0#A
pf2=0.8

#calculation
phi2=math.acos(pf2)
phi0=math.acos(pf)
k=v2/v1
i2_=k*i2
angle=phi2-phi0
i1=(i0**2+i2_**2+(2*i0*i2_*math.cos(angle)))**0.5

#result
print "current taken by the primary=",i1,"A"

current taken by the primary= 33.9022604184 A


## Example Number 32.13, Page Number:1130¶

In [59]:
#variable declaration
n1=800.0
n2=200.0
pf=0.8
i1=25.0#A
pf2=0.707
i2=80.0#A
#calculations
k=n2/n1
i2_=i2*k
phi2=math.acos(pf)
phi1=math.acos(pf2)
i0pf2=i1*pf2-i2_*pf
i0sinphi=i1*pf2-i2_*math.sin(math.acos(pf))
phi0=math.atan(i0sinphi/i0pf2)
i0=i0sinphi/math.sin(phi0)

#result

no load current= 5.91703050525 A


## Example Number 32.14, Page Number:1131¶

In [60]:
#variable declaration
i=10#A
pf=0.2
ratio=4
i2=200#A
pf=0.85

#calculations
phi0=math.acos(pf)
phil=math.acos(pf)
i0=complex(2,-9.8)
i2_=complex(42.5,-26.35)
i1=i0+i2_
phi=math.acos(i1.real/57.333)

#result
print "primary current=",i1,"A"
print "power factor=",math.degrees(phi),"degrees"

primary current= (44.5-36.15j) A
power factor= 39.0890154959 degrees


## Example Number 32.15, Page Number:1136¶

In [64]:
#variable decaration
v1=2400.0#V
v2=120.0#V
f=50.0#Hz
r1=0.1#ohm
x1=0.22#ohm
r2=0.034#ohm
x2=0.012#ohm

#calculations
k=v2/v1
r01=r1+r2/k**2
x01=x1+x2/k**2
z01=(r01**2+x01**2)**0.5
r02=r2+r1*k**2
x02=x2+x1*k**2
z02=(r02**2+x02**2)**0.5

#result
print "high voltage side:"
print "equivalent winding resistance=",r01,"ohm"
print "reactance=",x01,"ohm"
print "impedence=",z01,"ohm"
print "low voltage side:"
print "equivalent winding resistance=",r02,"ohm"
print "reactance=",x02,"ohm"
print "impedence=",z02,"ohm"

high voltage side:
equivalent winding resistance= 13.7 ohm
reactance= 5.02 ohm
impedence= 14.5907642021 ohm
low voltage side:
equivalent winding resistance= 0.03425 ohm
reactance= 0.01255 ohm
impedence= 0.0364769105051 ohm


## Example Number 32.16, Page Number:1136¶

In [68]:
#variable declaration
v1=4400.0#V
v2=220.0#V
r1=3.45#ohm
r2=0.009#ohm
x1=5.2#ohm
x2=0.015#ohm

#calculations
k=v2/v1
r01=r1+r2/k**2
r02=r2+k**2*r1
x01=x1+x2/k**2
x02=x2+x1*k**2
z01=(r01**2+x01**2)**0.5
z02=(r02**2+x02**2)**0.5
cu_loss=i1**2*r01

#result
print "i)resistance="
print "primary=",r01,"ohm"
print "secondary=",r02,"ohm"
print "iii)reactance="
print "primary=",x01,"ohm"
print "secondary=",x02,"ohm"
print "iv)impedence="
print "primary=",z01,"ohm"
print "secondary=",z02,"ohm"
print "v)copper loss=",cu_loss,"W"

resistance=
primary= 7.05 ohm
secondary= 0.017625 ohm
reactance=
primary= 11.2 ohm
secondary= 0.028 ohm
impedence=
primary= 13.2341414531 ohm
secondary= 0.0330853536327 ohm
copper loss= 910.382231405 W


## Example Number 32.17, Page Number:1137¶

In [70]:
#variable declaration
ratio=10.0
v1=2400.0#V
v2=240.0#V
f=50.0#Hz
v=240.0#V

#calculation
z2=v/(i2)
k=v2/v1
z2_=z2/k**2
i2_=k*i2

#result
print "b)impedence referred to high tension side=",z2_,"ohm"
print "c)the value of current referred to the high tension side=",i2_,"A"

a)load impedence= 1.152 ohm
b)impedence referred to high tension side= 115.2 ohm
c)the value of current referred to the high tension side= 20.8333333333 A


## Example Number 32.18, Page Number:1137¶

In [76]:
#variable declaration
v1=11000.0#V
v2=317.0#V

#calculations
k=v1/v2
r2_=r2*k**2
x01=4*v1/(i1*100)
x2_=x01*r2_/(r1+r2_)
x1=x01-x2_
x2=x2_*10/k**2

#result
print "i)r1=",r1,"ohm"
print "r2=",r2,"ohm"
print "r2_=",r2_,"ohm"
print "ii)reactance=",x01,"ohm"
print "x1=",x1,"ohm"
print "x2=",x2,"ohm"
print "x2_=",x2_,"ohm"

i)r1= 7.502 ohm
r2= 0.004823472 ohm
r2_= 5.808 ohm
ii)reactance= 48.4 ohm
x1= 27.28 ohm
x2= 0.175398981818 ohm
x2_= 21.12 ohm


## Example Number 32.19, Page Number:1137¶

In [94]:
#variable declarations
k=19.5
r1=25.0#ohm
x1=100.0#ohm
r2=0.06#ohm
x2=0.25#ohm
i=1.25#A
angle=30#degrees
i2=200#A
v=50#V
pf2=0.8

#calculations
v2=complex(500,0)
i2=i2*complex(0.8,-0.6)
z2=complex(r2,x2)
e2=v2+i2*z2
beta=math.atan(e2.imag/e2.real)
e1=e2*k
i2_=i2/k
i0=i*complex(math.cos(angle),math.sin(angle))
i1=-i2_+i0
v2=-e1+i1*complex(r1,x1)
phi=math.atan(v2.imag/v2.real)-math.atan(i1.imag/i1.real)
pf=math.cos(phi)
r02=r2+r1/k**2
cu_loss=abs(i2)**2*r02
output=500*abs(i2)*pf2
loss=cu_loss+power
inpt=output+loss
efficiency=output*100/inpt

#result
print "primary applied voltage=",v2,"V"
print "primary pf=",pf
print "efficiency=",efficiency,"%"

primary applied voltage= (-11464.2126901-1349.15424294j) V
primary pf= 0.698572087114
efficiency= 86.7261056254 %


## Example Number 32.20, Page Number:1138¶

In [96]:
#variable description
v1=1100#V
v2=220#V
f=50#Hz
zh=complex(0.1,0.4)
zl=complex(0.006,0.015)

#calculations
k=v1/v2
#HV
r1=zh.real+zl.real*k**2
x1=zh.imag+zl.imag*k**2
z1=(r1**2+x1**2)**0.5
#LV
r2=r1/k**2
x2=x1/k**2
z2=z1/k**2

#result
print "HV:"
print "resistance=",r1,"ohm"
print "reactance=",x1,"ohm"
print "impedence=",z1,"ohm"
print "LV:"
print "resistance=",r2,"ohm"
print "reactance=",x2,"ohm"
print "impedence=",z2,"ohm"

HV:
resistance= 0.25 ohm
reactance= 0.775 ohm
impedence= 0.814324873745 ohm
LV:
resistance= 0.01 ohm
reactance= 0.031 ohm
impedence= 0.0325729949498 ohm


## Example Number 32.21, Page Number:1141¶

In [97]:
#variable declaration
v1=230#V
v2=460#V
r1=0.2#ohm
x1=0.5#ohm
r2=0.75#ohm
x2=1.8#ohm
i=10#A
pf=0.8

#calculation
k=v2/v1
r02=r2+k**2*r1
x02=x2+k**2*x1
vd=i*(r02*pf+x02*math.sin(math.acos(pf)))
vt2=v2-vd

#result
print "secondary terminal voltage=",vt2,"V"

secondary terminal voltage= 424.8 V


## Example Number 32.22, Page Number:1141¶

In [98]:
#variable declaration
r=1.0#%
x=5.0#%
pf=0.8

#calculation
mu=r*pf+x*math.sin(math.acos(pf))
mu2=r**2+x*0
mu3=r*pf-x*math.sin(math.acos(pf))

#result
print "regulation at pf=0.8 lag:",mu,"%"
print "regulation at pf=1:",mu2,"%"

regulation at pf=0.8 lag: 3.8 %
regulation at pf=1: 1.0 %
regulation at pf=0.8 lead: -2.2 %


## Example Number 32.23, Page Number:1141¶

In [100]:
#variable declaration
x=5#%
r=2.5#%

#calculation
phi=math.atan(x/r)
cosphi=math.cos(phi)
sinphi=math.sin(phi)
regn=r*cosphi+x*sinphi

#result
print "regulation=",regn,"%"
print "pf=",cosphi

regulation= 5.59016994375 %
pf= 0.4472135955


## Example Number 32.24, Page Number:1142¶

In [102]:
#variable declaration
r=2.5#%
x=5#%
pf=0.8

#calculations

#result
print "percentage voltage drop=",drop,"%"

percentage voltage drop= 4.0 %


## Example Number 32.25, Page Number:1144¶

In [42]:
import math
#variable declaration
f=50.0#Hz
v1=2300.0#V
v2=230.0#V
r1=0.286#ohm
r2_=0.319#ohm
ro=250.0#ohm
x1=0.73#ohm
x2_=0.73#ohm
xo=1250.0#ohm
z1=complex(r1,x1)
z2_=complex(r2_,x2_)
zl=complex(0.387,0.29)
ym=complex(0.004,-0.0008)

#calculations
k=v2/v1
zl_=zl/(k**2)
zm=1/ym
x=zm+zl_+z2_
i1=v1/(z1+(zm*(z2_+zl_))/(zm+z2_+zl_))
i2_=i1*zm/(zm+z2_+zl_)
io=i1*(z2_+zl_)/(zm+z2_+zl_)
pf=i1.real/abs(i1)
pi=v1*abs(i1)*pf/1000
po=abs(i2_)**2*zl_.real/1000
cu_loss=abs(i1)**2*r1
cu_loss2=abs(i2_)**2*r2_
core_loss=io.real**2*240
e=po*100/pi
v2_=i2_*zl_
reg=(v1-v2_.real)*100/v2_.real

#result
print "Power input=",round(pi.real,1),"kW"
print "Power output=",round(po,1),"kW"
print "Primary Cu loss=",round(cu_loss),"W"
print "Secondary Cu loss=",round(cu_loss2),"W"
print "Efficiency=",round(e.real,2),"%"
print "Regulation=",round(reg.real),"%"

Power input= 104.6 kW
Power output= 82.5 kW
Primary Cu loss= 854.0 W
Secondary Cu loss= 680.0 W
Efficiency= 78.91 %
Regulation= 3.0 %


## Example Number 32.26, Page Number:1145¶

In [103]:
import math
#variable declaration
v1=600#V
v2=1080#V
v=720#V

#calculation
ir2_=ir2*v2/v1
il2_=il2*v/v1
ir2=math.sqrt(ir2_**2+il2_**2)
s=abs(s)

#result
print "primary current=",i,"A"
print "power factor=",pf

primary current= 21.3437474581 A
power factor= 0.624695047554


## Example Number 32.27, Page Number:1046¶

In [104]:
import math
#variable declaration
v=220#V
v1=110#V
i=0.5#A
p=30#W
r=0.6#ohm

#calculation
ratio=v/v1
pf=p/(i*v)
sinphi=math.sqrt(1-pf**2)
ip=i*sinphi
iw=i*pf
cu_loss=i**2*r
iron_loss=p-cu_loss

#result
print "i)turns ratio=",ratio
print "ii)magnetising component of no-load current=",ip,"A"
print "iii)working component of no-load current=",iw,"A"
print "iv)the iron loss=",iron_loss,"W"

i)turns ratio= 2
ii)magnetising component of no-load current= 0.481045692921 A
iii)working component of no-load current= 0.136363636364 A
iv)the iron loss= 29.85 W


## Example Number 32.28, Page Number:1047¶

In [105]:
#variable declaration
v1=200.0#V
v2=1000.0#V
f=50.0#Hz
vo=2000.0#V
io=1.2#A
po=90.0#W
vs=50.0#V
i_s=5.0#A
ps=110.0#W
p=3.0#kW
pf=0.8
v=200.0#V

#calculation
r0=v**2/po
ia0=v/r0
ip=math.sqrt(io**2-ia0**2)
xm=v/ip
z=vs/i_s
r=ps/25
x=math.sqrt(z**2-r**2)
r1=r*(v1/v2)**2
x1=x*(v1/v2)**2
i_lv=(p*1000/pf)/v
sinphi=math.sin(math.acos(pf))
reg=i_lv*(r1*pf+x1*sinphi)/v
vt=v2-reg*1000/v

#result
print "LV crrent at rated load=",i_lv1,"A"
print "LV current at 3kW at 0.8 lagging pf",i_lv,"A"
print "output secondary voltage=",vt,"V"
print "percentage regulation=",reg*100,"%"

LV crrent at rated load= 25.0 A
LV current at 3kW at 0.8 lagging pf 18.75 A
output secondary voltage= 999.832975251 V
percentage regulation= 3.34049498886 %


## Example Number 32.29, Page Number:1048¶

In [107]:
import math
from sympy.solvers import solve
from sympy import Symbol
#variable declaration
A=Symbol('A')
B=Symbol('B')
loss1=52.0#W
f1=40.0#Hz
loss2=90.0#W
f2=60.0#Hz
f=50.0#Hz

#calculation
ans=solve([(loss1/f1)-(A+f1*B),(loss2/f2)-(A+f2*B)],[A,B])
wh=ans[A]*f
we=ans[B]*f**2

#result
print "hysteresis=",round(wh),"W"
print "eddy current=",round(we),"W"

hysteresis= 45.0 W
eddy current= 25.0 W


## Example Number 32.30, Page Number:1048¶

In [1]:
%matplotlib inline
import matplotlib.pyplot as plt
import math
from sympy.solvers import solve
from sympy import Symbol
#variable declaration
A=Symbol('A')
B=Symbol('B')
m=10#kg
f=50.0#Hz
f1=25.0
f2=40.0
f3=50.0
f4=60.0
f5=80.0
l1=18.5/f1
l2=36.0/f2
l3=50.0/f3
l4=66.0/f4
l5=104.0/f5
#calculation
ans=solve([l1/f1-(A+f1*B),l2/f2-(A+f2*B)],[A,B])
eddy_loss_per_kg=ans[B]*f**2/m

#result
print"eddy current loss per kg at 50 Hz=",eddy_loss_per_kg,"W"

#plot
F=[f1,f2,f3,f4,f5]
L=[l1,l2,l3,l4,l5]
plt.plot(F,L)
plt.xlabel("f -->")
plt.ylabel("Wi/f")
plt.xlim((0,100))
plt.ylim((0.74,2))
plt.show()

eddy current loss per kg at 50 Hz= -0.118333333333333 W


## Example Number 32.31, Page Number:1148¶

In [8]:
import math
from sympy.solvers import solve
from sympy import Symbol
#variable declaration
A=Symbol('A')
B=Symbol('B')
v1=440#V
f1=50#Hz
p1=2500#W
v2=220#V
f2=25#Hz
p2=850#z

#calculation
ans=solve([(p1/f1)-(A+f1*B),(p2/f2)-(A+f2*B)],[A,B])
wh=ans[A]*f
we=ans[B]*f**2

#result
print "hysteresis=",round(wh),"W"
print "eddy current=",round(we),"W"

hysteresis= 900.0 W
eddy current= 1600.0 W


## Example Number 32.32, Page Number:1149¶

In [111]:
#variable declaration
v1=1000.0#V
f1=50.0#Hz
core=1000.0#W
wh=650.0#W
we=350.0#W
v2=2000.0#V
f2=100.0#Hz

#calculation
a=wh/f1
b=we/f1**2
wh=a*f2
we=b*f2**2
new_core=wh+we

#result
print "new core loss=",new_core,"W"

 new core loss= 2700.0 W


## Example Number 32.33, Page Number:1149¶

In [119]:
#variable declaration
phi=1.4#Wb/m2
we=1000.0#W
wh=3000.0#W
per=10.0#%

#calculation
wh1=wh*1.1**1.6
we1=we*1.1**2
wh2=wh*0.9**(-0.6)
wh3=wh*1.1**1.6*1.1**(-0.6)
#result
print "a)wh and we when applied voltage is increased by 10%=",wh1,"W","and",we1,"W"
print "b)wh when frequency is reduced by 10%=",wh2,"W"
print "c)wh and we when both voltage and frequency are increased y 10%=",wh3,"W","and",we1,"W"

a)wh and we when applied voltage is increased by 10%= 3494.21441464 W and 1210.0 W
b)wh when frequency is reduced by 10%= 3195.77171838 W
c)wh and we when both voltage and frequency are increased y 10%= 3300.0 W and 1210.0 W


## Example Number 32.34, Page Number:1150¶

In [122]:
#variable declaration
v=2200.0#V
f=40.0#Hz
loss=800.0#W
wh=600.0#W
we=loss-wh
v2=3300.0#V
f2=60.0#Hz

#calculations
a=wh/f
b=we/f**2
core_loss=a*f2+b*f2**2

#result
print "core loss at 60 Hz=",core_loss,"W"

core loss at 60 Hz= 1350.0 W


## Example Number 32.35, Page Number:1151¶

In [124]:
#variable declaration
v1=6000.0#V
v2=230.0#V
r1=10.0#ohm
r2=0.016#ohm
x01=34.0#ohm

#calculations
k=v2/v1
r01=r1+r2/k**2
z01=(r01**2+x01**2)**0.5
vsc=i1*z01
pf=r01/z01

#result
print "primary voltage=",vsc,"V"
print "pf=",pf

primary voltage= 199.519931911 V
pf= 0.523468222173


## Example Number 32.36, Page Number:1152¶

In [130]:
#variable declaration
v1=200.0#V
v2=400.0#V
f=50.0#Hz
vo=200.0#V
io=0.7#A
po=70.0#W
vs=15.0#v
i_s=10.0#A
ps=85.0#W
pf=0.8

#calculations
cosphi0=po/(vo*io)
sinphi0=math.sin(math.acos(cosphi0))
iw=io*cosphi0
imu=io*sinphi0
r0=v1/iw
x0=v1/imu
z02=vs/i_s
k=v2/v1
z01=z02/k**2
r02=ps/i_s**2
r01=r02/k**2
x01=(z01**2-r01**2)**0.5
i2=output*1000/v2
x02=(z02**2-r02**2)**0.5
drop=i2*(r02*pf+x02*math.sin(math.acos(pf)))
v2=v2-drop
print z02
#result
print "secondary voltage=",v2,"V"

1.5
secondary voltage= 377.788243349 V


## Example Number 32.37, Page Number:1152¶

In [132]:
#variable declaration
k=1.0/6
r1=0.9#ohm
x1=5.0#ohm
r2=0.03#ohm
x2=0.13#ohm
vsc=330.0#V
f=50.0#Hz

#calculations
r01=r1+r2/k**2
x01=x1+x2/k**2
z01=(r01**2+x01**2)**0.5
i1=vsc/z01
i2=i1/k
cosphisc=i1**2*r01/(vsc*i1)

#result
print "current in low voltage winding=",i2,"A"
print "pf=",round(cosphisc,1)

current in low voltage winding= 200.396236149 A
pf= 0.2


## Example Number 32.38, Page Number:1153¶

In [140]:
#variable declaration
v1=500.0#V
v2=250.0#V
f=50.0#Hz
r1=0.2#ohm
x1=0.4#ohm
r2=0.5#ohm
x2=0.1#ohm
r0=1500.0#ohm
x0=750.0#ohm

#calculation
k=v2/v1
imu=v1/x0
iw=v1/r0
i0=(iw**2+imu**2)**0.5
pi=v1*iw
r01=r1+r2/k**2
x01=x1+x2/k**2
z01=(r01**2+x01**2)**0.5
vsc=i1*z01
power=i1**2*r01

#result

reading of instruments= 46.8187996429 V, 20.0 A, 880.0 W


## Example Number 32.39, Page Number:1153¶

In [148]:
import math
from sympy.solvers import solve
from sympy import Symbol
#variable declaration
x=Symbol('x')
y=Symbol('y')
v1=110#V
v2=220#V
f=50#Hz
per1=98.5#%
pf=0.8
per2=98.8#%

#calculaions
inpt=output*100/per2
loss=inpt-output
loss2=inpt_half-400
ans=solve([x+y-loss,(x/4)+y-loss2],[x,y])
output=kva*1
cu_loss=ans[y]
total_loss=2*cu_loss
efficiency=output/(output+total_loss)
#result
print "maximum efficiency=",efficiency,"%"

full load copper loss= 4.07324441521606 kW
maximum efficiency= 0.968720013059872 %


## Example Number 32.40, Page Number:1154¶

In [149]:
#variable declaration
v1=200.0#v
v2=400.0#V
r01=0.15#ohm
x01=0.37#ohm
r0=600.0#ohm
x0=300.0#ohm
i2=10.0#A
pf=0.8

#calculations
imu=v1/x0
iw=v1/r0
i0=(imu**2+iw**2)**0.5
tantheta=iw/imu
theta=math.atan(tantheta)
angle=theta0-math.acos(pf)
k=v2/v1
i2_=i2*k
i1=(i0**2+i2_**2+2*i0*i2_*math.cos(angle))**0.5
r02=k**2*r01
x02=x01*k**2
vd=i2*(r02*pf+x02*math.sin(math.acos(pf)))
v2=v2-vd

#result
print "i)primary current=",i1,"A"
print "ii)secondary terminal voltage=",v2,"V"

i)primary current= 20.6693546639 A
ii)secondary terminal voltage= 386.32 V


## Example Number 32.43, Page Number:1158¶

In [158]:
#variable declaration
n1=400.0
n2=80.0
r1=0.3#ohm
r2=0.01#ohm
x1=1.1#ohm
x2=0.035#ohm
v1=2200.0#V
pf=0.8

#calculations
k=n2/n1
r01=r1+r2/k**2
x01=x1+x2/k**2
z01=complex(r01,x01)
z02=k**2*z01
v2=k*v1
vd=i2*(z02.real*pf-z02.imag*math.sin(math.acos(pf)))
regn=vd*100/v2
v2=v2-vd

#result
print "i)equivalent impedence=",z02,"ohm"
print "ii)voltage regulation=",regn,"%"
print "secondary terminal voltage=",v2,"V"

i)equivalent impedence= (0.022+0.079j) ohm
ii)voltage regulation= -1.53925619835 %
secondary terminal voltage= 446.772727273 V


## Example Number 32.44, Page Number:1158¶

In [162]:
#variable declaration
va=450.0#V
vb=120.0#V
v1=120.0#V
i1=4.2#A
w1=80.0#W
v2=9.65#V
i2=22.2#A
w2=120.0#W
pf=0.8

#calculations
k=vb/va
i0=i1*k
cosphi0=w1/(va*i0)
phi0=math.acos(cosphi0)
sinphi0=math.sin(phi0)
iw=i0*cosphi0
imu=i0*sinphi0
r0=va/iw
x0=va/imu
z01=v2/i2
r01=vb/i2**2
x01=(z01**2-r01**2)**0.5
drop=i1*(r01*pf+x01*math.sin(math.acos(pf)))
regn=drop*100/va
loss=w1+w2
efficiency=output/(output+loss)
iron_loss=w1
cu_loss=(0.5**2)*w2
total_loss=iron_loss+cu_loss
efficiency2=output/(output+total_loss)

#result
print "i)equivalent circuit constants="
print "z01=",z01,"ohm"
print "x01=",x01,"ohm"
print "r01=",r01,"ohm"
print "ii)efficiency and voltage regulation at pf=0.8=",efficiency*100,"%",regn,"%"
print "iii)efficiency at half load and pf=0.8=",efficiency2*100,"%"

i)equivalent circuit constants=
z01= 0.434684684685 ohm
x01= 0.360090249002 ohm
r01= 0.243486729973 ohm
ii)efficiency and voltage regulation at pf=0.8= 97.5609756098 % 2.02885695496 %
iii)efficiency at half load and pf=0.8= 97.3236009732 %


## Example Number 32.45, Page Number:1159¶

In [172]:
#variable declaration
va=2200.0#V
vb=220.0#V
f=50.0#Hz
v1=220.0#V
i1=4.2#A
w1=148.0#W
v2=86.0#V
i2=10.5#A
w2=360.0#W
pf=0.8

#calculations
z01=v2/i2
r01=w2/i2**2
x01=(z01**2-r01**2)**0.5
drop=i1*(r01*pf+x01*math.sin(math.acos(pf)))
regn=drop*100/va
pf=r01/z01

#result
print "regulation=",regn,"%"
print "pf=",round(pf,1),"lag"

regulation= 2.94177963326 %
pf= 0.4 lag


## Example Number 32.46, Page Number:1159¶

In [182]:
#variable declaration
v1=2000.0#V
v2=400.0#V
v=60.0#V
i=4.0#A
w=100.0#W
pf=0.8
v_=400.0#V

#calculations
z01=v/i
r01=w/i**2
x01=(z01**2-r01**2)**0.5
vd=i1*(r01*pf+x01*math.sin(math.acos(pf)))

#result
print "voltage applied to hv side=",v1+vd,"V"

voltage applied to hv side= 2065.90767043 V


## Example Number 32.47, Page Number:1159¶

In [190]:
#variable declaration
v1=250.0#V
v2=500.0#V
vs=20.0#V
i_s=12.0#A
ws=100.0#W
vo=250.0#V
io=1.0#A
wo=80.0#W
i2=10#A
v2=500#V
pg=0.8

#calculation
cosphi0=wo/(vo*io)
iw=io*cosphi0
imu=(1-iw**2)**0.5
r0=v1/iw
x0=v1/imu
r02=ws/i_s**2
z02=vs/i_s
x02=(z02**2-r02**2)**0.5
k=v2/v1
r01=r02/k**2
x01=x02/k**2
z01=z02/k**2
cu_loss=i2**2*r02
iron_loss=wo
total_loss=iron_loss+cu_loss
efficiency=i2*v2*pf/(i2*v2*pf+total_loss)
v1_=((vo*pf+x01)**2+(vo*math.sin(math.acos(pf))+i1*x01)**2)**0.5

#result
print "applied voltage=",v1_,"V"
print "efficiency=",efficiency*100,"%"

applied voltage= 251.442641983 V
efficiency= 96.3984469139 %


## Example Number 32.48, Page Number:1160¶

In [194]:
#variable declaration
v1=230.0#V
v2=230.0#V
vo=230.0#V
io=2.0#A
wo=100.0#W
vs=15.0#V
i_s=13.0#A
ws=120.0#W
pf=0.8

#calculations
cu_loss=ws
core_loss=wo
efficiency=output*100/(output+cu_loss+core_loss)
z=vs/i_s
r=ws/(vs**2)
x=(z**2-r**2)**0.5
regn=i*(r*pf+x*math.sin(math.acos(pf)))*100/v1

#result
print "regulation=",regn,"%"
print "efficiency=",efficiency,"%"

regulation= 5.90121149256 %
efficiency= 91.6030534351 %


## Example Number 32.49, Page Number:1161¶

In [196]:
#variable declaration
v1=500.0#V
v2=250.0#V
efficiency=0.94
per=0.90
pf=0.8

#calculation
inpt=output/efficiency
loss=inpt-output
core_loss=loss/2
pc=core_loss/per**2
cu_loss=pc
efficiency=output/(output+cu_loss+core_loss)

#result
print "efficiency=",efficiency*100,"%"

efficiency= 92.5728354534 %


## Example Number 32.50, Page Number:1161¶

In [199]:
#variable declaration
f=50.0#Hz
v1=2300.0#V
v2=230.0#V
r1=3.96#ohm
r2=0.0396#ohm
x1=15.8#ohm
x2=0.158#ohm
pf=0.8
v=230.0#V

#calculations
r=r2+r1*(v2/v1)**2
x=x1*(v2/v1)**2+x2
v1_=v2+i*(r*pf+x*math.sin(math.acos(pf)))
v1=v1_*(v1/v2)
phi=math.atan(r/x)
pf=math.cos(phi)
#result
print "a)HV side voltage necessary=",v1,"V"
print "b)pf=",round(pf,2)

a)HV side voltage necessary= 2409.9826087 V
b)pf= 0.97


## Example Number 32.51, Page Number:1162¶

In [200]:
#variable declaration
v1=2200.0#V
v2=220.0#v
r1=3.4#ohm
x1=7.2#ohm
r2=0.028#ohm
x2=0.060#ohm
pf=0.8

#calculations
r=r1*(v2/v1)**2+r2
x=x1*(v2/v1)**2+x2
dc=i*x*math.sin(math.acos(pf))
bd=i*r*math.sin(math.acos(pf))
b_f=x*pf
cf=b_f-bd
v1_=(oc**2+cf**2)**0.5
v1=v1_*(v1/v2)

#result
print "terminal voltage on hv side=",v1,"V"

terminal voltage on hv side= 2229.28500444 V


## Example Number 32.52, Page Number:1163¶

In [209]:
#variable declaration
v1=200.0#V
v2=400.0#V
i1=0.7#A
w1=65.0#W
v=15.0#V
i2=10.0#A
w2=75.0#W
pf=0.80
#calculation
cu_loss=w2
constant_loss=w1
z=v/i2
r=w2/i2**2
x=(z**2-r**2)**0.5
regn=i2*(r*pf+x*math.sin(math.acos(pf)))

#result

full load efficiency= 96.6183574879 %


## Example Number 32.53, Page Number:1164¶

In [214]:
#variable declaration
v1=3300.0#V
v2=230.0#V
z=4
cu_loss=1.8

#calculations
x=(z**2-cu_loss**2)**0.5
r01=cu_loss*v1/(100*i1)
x01=x*v1/(100*i1)
z01=z*v1/(100*i1)
isc=i1*100/z
print
#result
print "%x=",x,"%"
print "resistance=",r01,"ohm"
print "reactance=",x01,"ohm"
print "impedence=",z01,"ohm"
print "primary sc current=",isc,"A"

%x= 3.5721142199 %
resistance= 3.9204 ohm
reactance= 7.78006477094 ohm
impedence= 8.712 ohm
primary sc current= 378.787878788 A


## Example Number 32.54, Page Number:1164¶

In [222]:
#variable declaration
v1=2200.0#V
v2=220.0#V
f=50.0#Hz
vo=220.0#V
i_o=4.2#A
wo=148.0#W
vs=86.0#V
i_s=10.5#A
ws=360.0#W
pf=0.8

#calculations
k=v2/v1
r01=ws/i_s**2
r02=k**2*r01
z10=vs/i_s
x01=(z10**2-r01**2)**0.5
x02=k**2*x01
v1_=((v1*pf+i1*r01)**2+(v1*math.sin(math.acos(pf))+i1*x01)**2)**0.5
regn1=(v1_-v1)/v1
i2=i1/k
core_loss=wo
cu_loss=i1**2*r01
cu_loss_half=(i1/2)**2*r01
print v1_
#result
print "a)core loss=",wo,"W"
print "b)equivalent resistance primary=",r01,"ohm"
print "c)equivalent resistance secondary=",r02,"ohm"
print "d)equivalent reactance primary=",x01,"ohm"
print "e)equivalent reactance secondary=",x02,"ohm"
print "f)regulation=",regn1*100,"%"

2265.01840886
a)core loss= 148.0 W
b)equivalent resistance primary= 3.26530612245 ohm
c)equivalent resistance secondary= 0.0326530612245 ohm
d)equivalent reactance primary= 7.51143635755 ohm
e)equivalent reactance secondary= 0.0751143635755 ohm
f)regulation= 2.95538222101 %
g)efficiency at full load= 97.4548448466 %
h)efficiency at half load= 95.0360304208 %


## Example Number 32.55, Page Number:1165¶

In [223]:
#variable declaration
er=1.0/100
ex=5.0/100
pf=0.8

#calculation
regn=er*pf+ex*math.sin(math.acos(pf))
regn2=er*1
regn3=er*pf-ex*math.sin(math.acos(pf))

#result
print "i)regulation with pf=0.8 lag=",regn*100,"%"
print "ii)regulation with pf=1=",regn2*100,"%"

i)regulation with pf=0.8 lag= 3.8 %
ii)regulation with pf=1= 1.0 %
iii)regulation with pf=0.8 lead= -2.2 %


## Example Number 32.56, Page Number:1165¶

In [225]:
#variable declaration
v1=3300#V
v2=500#V
f=50#Hz
per=0.97
ratio=3.0/4
zper=0.10
pf=0.8

#calculation
x=0.75
pi=0.5*(output*(1/per-1))
pc=pi/x**2
r=pc*1000/i1**2
er=i1*r/v1
ez=zper
ex=(ez**2-er**2)**0.5
regn=er*pf+ex*math.sin(math.acos(pf))

#result
print "regulation=",regn*100,"%"

regulation= 7.52529846012 %


## Example Number 32.57, Page Number:1166¶

In [226]:
#variable declaration
cu_loss=1.5#%
xdrop=3.5#%
pf=0.8

#calculation
pur=cu_loss/100
pux=xdrop/100
regn2=pur*pf+pux*math.sin(math.acos(pf))
regn1=pur*1
regn3=pur*pf-pux*math.sin(math.acos(pf))

#result
print "i)regulation at unity pf=",regn1*100,"%"
print "ii)regulation at 0.8 lag=",regn2*100,"%"

i)regulation at unity pf= 1.5 %
ii)regulation at 0.8 lag= 3.3 %
iii)regulation at 0.8 lead= -0.9 %


## Example Number 32.58, Page Number:1168¶

In [229]:
#variable declaration
w1=5.0#kW
w2=7.5#kW
efficiency=0.75
pf=0.8

#calculation
total_loss=w1+w2
loss=total_loss/2
cu_loss=efficiency**2*w2/2
efficiency=output*100/(output+cu_loss+2.5)

#result
print "efficiency=",efficiency,"%"

efficiency= 97.0186963113 %


## Example Number 32.59, Page Number:1170¶

In [232]:
#variable declaration
v1=2000.0#V
v2=200.0#V
w1=350.0#W
w2=400.0#W

#calculation
total_loss=w1+w2
efficiency=output/(output+total_loss)
cu_loss=w2*(0.5)**2
total_loss=cu_loss+w1

#result

i)efficiency at full load= 97.0873786408 %
ii)efficiency at half load= 96.5250965251 %


## Example Number 32.60, Page Number:1170¶

In [233]:
#variable declaration
efficiency=0.75

#calculation
ratio=efficiency**2

#result
print "ratio of P1 and P2=",ratio

ratio of P1 and P2= 0.5625


## Example Number 32.61, Page Number:1170¶

In [237]:
#variable declaration
v1=11000.0#V
v2=230.0#V
f=50.0#Hz
loss=1.4#kW
cu_loss=1.6#kW
pf=0.8

#calculation
total_loss=loss*2
efficiency=output/(output+total_loss)
cu_loss=cu_loss*(0.5)**2
total_loss=total_loss+cu_loss
efficiency2=output2/(output2+total_loss)

#result
print "max efficiency=",efficiency*100,"%"

i)kVA load for max efficiency= 150.0 kVA
max efficiency= 98.283858876 %
ii)efficiency at half load= 95.2481856352 %


## Example Number 32.62, Page Number:1171¶

In [2]:
%matplotlib inline
import matplotlib.pyplot as plt
#variable declaration
v1=2300#V
v2=230#V
f=50#Hz
iron_loss=40#W
cu_loss=112#W
pf=0.8
#calculations
def e(k):
e=k*pf*1000*100/(k*pf*1000+(cu_loss*(k/5)**2+40))
return(e)

e1=e(1.25)
e2=e(2.5)
e3=e(3.75)
e4=e(5.0)
e5=e(6.25)
e6=e(7.5)

K=[1.25,2.5,3.75,5.0,6.25,7.5]
E=[e1,e2,e3,e4,e5,e6]
plt.plot(K,E)
plt.ylabel("Efficiency")
plt.xlim((0,8))
plt.ylim((92,98))
plt.show()


## Example Number 32.63, Page Number:1171¶

In [3]:
#variable declaration
efficiency=0.98
pf=0.8

#calculations
inpt=output/efficiency
loss=inpt-output
x=loss*1000/(1+9.0/16)
y=(9.0/16)*x
cu_loss=x*(1.0/2)**2
total_loss=cu_loss+y
efficiency=output/(output+total_loss/1000)

#result

efficiency at hald load= 97.9216626699 %


## Example Number 32.64, Page Number:1172¶

In [5]:
#variable declaration
v1=2200.0#V
v2=220.0#V
r1=1.0#ohm
r2=0.01#ohm
pf=0.8
loss=0.80

#calculations
k=v2/v1
r02=r2+k**2*r1
cu_loss=i2**2*r02
iron_loss=loss*cu_loss
total_loss=cu_loss+iron_loss
efficiency=output/(output+total_loss)

#result
print "secondary resistance=",r02,"ohm"
print "efficiency=",efficiency*100,"%"

secondary resistance= 0.02 ohm
efficiency= 97.7284199899 %


## Example Number 32.65, Page Number:1172¶

In [14]:
#variable declaration
v1=200.0#V
v2=400.0#V
r01=0.5#ohm
x01=1.5#ohm
ratio=3.0/4
pf=0.8
v=220.0#V
loss=100.0#W

#calculations
k=v2/v1
r02=k**2*r01
x02=k**2*x01
drop=i2*(r02*pf+x02*math.sin(math.acos(pf)))
v2=v2-drop
cu_loss=i2**2*r02
total_loss=loss+cu_loss
inpt=output*1000+total_loss
efficiency=output*1000/(inpt)
#result
print "output=",output,"w"
print "efficiency=",efficiency*100,"%"

output= 2.4 w
efficiency= 91.8660287081 %


## Example Number 32.66, Page Number:1172¶

In [3]:
#variable declaration
v1=440.0#V
v2=220.0#V
f=50.0#Hz
loss=324.0#W
cu_loss=100.0#W
pf=0.8
#calculations
cu_loss=4*cu_loss
per=(loss/cu_loss)**0.5

#result
print "i)efficiency=",efficiency*100,"%"

i)efficiency= 95.6708921311 %


## Example Number 32.67, Page Number:1173¶

In [9]:
import math
#variable declaration
v1=200.0#V
v2=400.0#V
pf=0.8
vo=200.0#V
io=0.8#A
wo=70.0#W
vs=20.0#V
i_s=10.0#A
ws=60.0#W

#calculation
loss=ws+wo
efficiency=output/(output+loss/1000)
z02=vs/i_s
r02=ws/i2**2
x02=(z02**2-r02**2)**0.5
drop=i2*(r02*pf+x02*math.sin(math.acos(pf)))
v2=v2-drop

#result
print "efficiency=",efficiency*100,"%"
print "secondary voltage=",v2,"V"
print "current=",i1,"A"

efficiency= 96.0960960961 %
secondary voltage= 383.752729583 V
current= 20.0 A
load at unity pf= 4.32049379894 kW


## Example Number 32.68, Page Number:1173¶

In [8]:
import math
from sympy.solvers import solve
from sympy import Symbol
#variable declaration
Wi=Symbol('Wi')
Wcu=Symbol('Wcu')
P=600.0#kVA
e=0.92#efficiency
pf=0.8
x=0.6

#calculations
ans=solve([(e*(1*P*1+Wi+1**2*Wcu))-(1*P*1),(e*(0.5*P*1+Wi+0.5*0.5*Wcu))-(0.5*P*1)],[Wi,Wcu])
e2=(x*P*pf*100)/((x*P*pf)+ans[Wi]+(x**2*ans[Wcu]))

#result
print "Efficiency=",round(e2,1),"%"

Efficiency= 90.6 %


## Example Number 32.69, Page Number:1174¶

In [21]:
import math
from sympy.solvers import solve
from sympy import Symbol
#variable declaration
x=Symbol('x')
y=Symbol('y')
efficiency=0.92
per=0.60

#calculation
ans=solve([x+y-loss1,x+y/4-loss2],[x,y])
cu_loss=ans[y]*0.36
loss=cu_loss+ans[x]
efficiency=output/(output+loss)

#result
print "efficiency=",efficiency*100,"%"

389.913043478261
efficiency= 92.3282783229260 %


## Example Number 32.70, Page Number:1174¶

In [37]:
#variable declaration
e1=0.98
e2=0.80
pf=8
z=0.05
pf1=0.8

#calculations
inpt=output/e1
loss=-output+inpt
cu_loss=loss/2
cu_loss_full=cu_loss/pf1**2
sin=math.sin(math.acos(pf1))
regn=(r*pf1+5*sin)+(1.0/200)*(5*pf1-r*sin)**2
#result
print "voltage regulation=",regn,"%"

voltage regulation= 3.8578 %


## Example Number 32.71, Page Number:1174¶

In [47]:
#variable declaration
v1=5000.0#V
v2=440.0#V
f=25.0#Hz
cu_loss=1.5
we=0.5
wh=0.6
v2=10000.0
#calculations
cu_loss2=cu_loss1
we2=(we1*(50.0/25.0)**2)
wh2=(wh1*(50.0/25))

#result
print "full load efficiency in first case=",e1,"%"
print "full load efficiency in second case=",e2,"%"

20.47 0.06 0.05
full load efficiency in first case= 97.4658869396 %
full load efficiency in second case= 97.7039570103 %


## Example Number 32.72, Page Number:1175¶

In [53]:
#variable declaration
r=1.5#%
pf=0.8

#calculations
total_loss=cu_loss+iron_loss

#result
print "efficiency=",efficiency,"%"

efficiency= 97.5610105096 %


## Example Number 32.73, Page Number:1175¶

In [58]:
#variable declaration
v1=2300#V
v2=230.0#V
f=50#Hz
phim=1.2#Wb/m2
a=0.04#m2
l=2.5#m
bm=1200
inpt=1200#W
pi=400#W
efficiency=0.75
pf=0.8
f2=100#Hz

#calculation
n1=v1/(4.44*f*phim*a)
k=v2/v1
n2=k*n1
i=1989/n1
cu_loss=efficiency**2*inpt
total_loss=pi+cu_loss
efficiency=output*100/(output+total_loss/1000)

#result
print "a)n1=",round(n1)
print "  n2=",round(n2)
print "b)magnetising current=",i,"A"
print "c)efficiency=",efficiency,"%"

0.00643416423287
a)n1= 216.0
n2= 22.0
b)magnetising current= 9.21512347826 A
c)efficiency= 98.2398690135 %


## Example Number 32.74, Page Number:1176¶

In [60]:
#variable declaration
r=1.8
x=5.4

#calculation
pf=r/x
phi=math.atan(pf)
phi2=math.atan(x/r)
regn=r*math.cos(phi2)+x*math.sin(phi2)
efficiency=100/(100+r*2)

#result
print "a)i)phi=",math.degrees(phi),"degrees"
print "  ii)regulation=",regn,"%"
print "b)efficiency=",efficiency*100,"%"

a)i)phi= 18.4349488229 degrees
ii)regulation= 5.6920997883 %
b)efficiency= 96.5250965251 %


## Example Number 32.75, Page Number:1176¶

In [64]:
#variable declaration
f=50.0#Hz
v1=500.0#V
v2=250.0#V
vo=250.0#V
io=3.0#A
wo=200.0#W
vsc=15.0#V
isc=30.0#A
wsc=300.0#W
pf=0.8

#calculations
cu_loss=(i/isc)**2*wsc
efficiency=output*100/(output+cu_loss+wo)
z=vsc/isc
r=wsc/isc**2
x=(z**2-r**2)**0.5
regn=(i/v2)*(r*pf-x*math.sin(math.acos(pf)))*v2

#result
print "efficiency=",efficiency,"%"
print "regulation=",regn,"%"

efficiency= 91.6030534351 %
regulation= 1.72239475667 %


## Example Number 32.76, Page Number:1177¶

In [71]:
#variable declaration
loss=400.0#W
cu_loss=800.0#W

#calculation
x=(loss/cu_loss)**0.5

#result
print "efficiency=",efficiency*100,"%"

efficiency= 97.2493723732 %


## Example Number 32.77, Page Number:1178¶

In [75]:
#variable declaration
v1=500#V
v2=250#V
vsc=60#V
isc=20#A
wsc=150#W
per=1.2
pf=0.8

#calculation
cu_loss=per**2*wsc
efficiency=output*100/(output+cu_loss*2/1000)
e2=output*100/(output+cu_loss+wsc)

#result
print "maximum efficiency=",efficiency,"%"

maximum efficiency= 96.5250965251 %


## Example Number 32.78, Page Number:1181¶

In [86]:
#variable declaration
cu_loss=4.5#kW
iron_loss=3.5#kW
t1=6.0#hrs
t2=10.0#hrs
t3=4.0#hrs
t4=4.0#hrs
pf1=0.8
pf2=0.75
pf3=0.8

#calculations
wc1=cu_loss
twc=(t1*wc1)+(t2*wc2)+(t3*wc3)+(t4*0)
iron_loss=24*iron_loss
total_loss=twc+iron_loss
efficiency=output*100/(output+total_loss)

#result
print "efficiency=",round(efficiency,1),"%"

efficiency= 97.6 %


## Example Number 32.79, Page Number:1182¶

In [89]:
#variable declaration
loss=3.0#kW
tf=3.0#hrs
th=4.0#hrs

#calculation
iron_loss=loss*24/2
wcf=loss*tf/2
wch=loss/8
wch=wch*4
total_loss=iron_loss+wch+wcf
efficiency=output*100/(output+total_loss)

#result
print "efficiency=",efficiency,"%"

efficiency= 92.2509225092 %


## Example Number 32.80, Page Number:1182¶

In [96]:
#variable declaration
efficiency=0.98
tf=4.0#hrs
th=6.0#hrs
t10=14.0#hrs

#calculations
#1st transformer
y=tloss/2
x=y
iron_loss=x*24
cu_loss=x*tf+th*(x/2**2)+t10*(x/10**2)
loss=iron_loss+cu_loss
e1=output/(output+loss)
#2nd transformer
y=tloss/(1+1.0/4)
x=(tloss-y)
iron_loss=x*24
wc=tf*y+th*(y/2**2)+t10*(y/10**2)
loss=iron_loss+wc
e2=output/(output+loss)

#result
print "efficiency of forst transformer=",e1*100,"%"
print "efficiency ofsecond transformer=",e2*100,"%"

0.408163265306 1.63265306122
efficiency of forst transformer= 96.5245532574 %
efficiency ofsecond transformer= 97.7876610788 %


## Example Number 32.81, Page Number:1183¶

In [115]:
#variable declaration
efficiency=0.95
nl=10.0#hrs
ql=7.0#hrs
hl=5.0#hrs
fl=2.0#hrs

#calculations
wc_fl=loss/2
iron_loss=loss/2
wc_fl_4=(1.0/4)**2*wc_fl
wc_fl_2=(1.0/2)**2*wc_fl
wc_ql=ql*wc_fl_4
wc_hl=hl*wc_fl_2
wc_fl_2=fl*wc_fl
wc=wc_ql+wc_hl+wc_fl_2
wh=wc
loss=wh+24*iron_loss
half_output=(output/2)
e=output*100/(output+loss)

#result
print "efficiency=",e,"%"

efficiency= 89.5592740985 %


## Example Number 32.82, Page Number:1183¶

In [120]:
#variable declaration
efficiency=0.98
t1=12.0#hrs
t2=6.0#hrs
t3=6.0#hrs
pf1=0.5
pf2=0.8
k1=2#kW
k2=12#kW

#calculations
inpt=output/efficiency
loss=inpt-output
wc=loss/2
wi=loss/2
w1=k1/pf1
w2=k2/pf2
wc2=wc
wc12=t1*wc1
wc6=t2*wc2
wc=(wc12+wc6)
wi=24*wi
output=(k1*t1)+(t2*k2)
inpt=output+wc+wi
e=output*100/inpt

#result
print "efficiency=",e,"%"

0.918367346939 3.67346938776
efficiency= 95.4351795496 %


## Example Number 32.83, Page Number:1184¶

In [127]:
#variable declaration
l1_=100.0#kVA
t=3.0#hrs
loss=1.0#KW

#calculations
l1=l1_/2
l2=l1_
loss=loss*2
e1=output/(output+loss)
wc1=t*(1.0/3)**2*1
wc2=8*(2.0/3)**2*1
wc=wc1+wc2
wi=24*1
loss=wc+wi
output=3*(l1*1)+8*(l2*1)
e2=(output*100)/(output+loss)

#result
print "ordinary efficiency=",e1*100,"%"
print "all day efficiency=",e2,"%"

ordinary efficiency= 98.6842105263 %
all day efficiency= 97.1480513578 %


## Example Number 32.84, Page Number:1184¶

In [129]:
#variable declaration
efficiency=0.94#%
nl=10
hl=5.0
ql=6.0
fl=3.0

#calculations
wch=(0.5)**2*pi
eh=wch*hl/1000
wcq=(0.25)**2*pi
eq=ql*wcq/1000
e3=pi*3/1000
e2=pi*24/1000
e=25*hl+12.5*ql+50*fl
efficiency=e/(e+e2+eh+eq+e3)

#result
print "efficiency=",efficiency*100,"%"

efficiency= 88.4557217274 %


## Example Number 32.85, Page Number:1185¶

In [142]:
#variable declaration
t1=7.0#hrs
t2=4.0#hrs
t3=8.0#hrs
t4=5.0#hrs
k1=3.0#kW
k2=8.0#kW
pf1=0.6
pf2=0.8

#calculations
pc1=(0.5)**2*0.1
pc2=pc3=0.10
o1=k1*t1
o2=k2*t2
output=o1+o2+o3
wc1=pc1*t1
wc2=pc2*t2
wc3=pc3*t3
cu_loss=wc1+wc2+wc3
loss=400.0*24/10000
efficiency=output/(output+loss+cu_loss)

#result
print "efficency=",efficiency*100,"%"

efficency= 98.27465179 %


## Example Number 32.86, Page Number:1185¶

In [143]:
#variable declaration
efficiency=.98
t1=12.0
t2=6.0
t3=6.0
pf1=0.8
pf2=0.8
pf3=0.9
k1=2.0
k2=12.0
k3=18.0
#calculations
inpt=output/efficiency
loss=inpt-output
cu_loss=loss/2
wc1=0.131
wc2=0.918
wc3=1.632
o1=t1*k1
o2=t2*k2
o3=t3*k3
output=o1+o2+o3
loss=wc1+wc2+wc3+0.153*24
efficiency=(output*100)/(output+loss)

#result
print "efficiency=",efficiency,"%"

efficiency= 96.9798386522 %


## Example Number 32.87, Page Number:1188¶

In [145]:
#variable declaration
v1=115.0#V
v2=230.0#V

#calculation
k=v1/v2

#result
print "a)power transferred inductively=",power,"kW"
print "b)power transferred conductively=",power2,"kW"

a)power transferred inductively= 1.5 kW
b)power transferred conductively= 1.5 kW


## Example Number 32.88, Page Number:1188¶

In [147]:
#variable declaration
v1=500.0#V
v2=400.0#V
i=100.0#A

#calculations
k=v2/v1
i1=k*i
saving=k*100

#result
print "economy of cu=",saving

economy of cu= 80.0


## Example Number 32.89, Page Number:1188¶

In [150]:
#variable declaration
f=50.0#Hz
v1=6600.0#V
v2=5000.0#V
e=8.0#V
phim1=1.3#Wb/m2

#calculations
phim=e/(4.44*f)
area=phim/phim1
n1=v1/e
n2=v2/e

#result
print "core area=",area*10000,"m2"
print "number of turns on the hv side=",n1
print "number of turns on the lv side=",n2

core area= 277.2002772 m2
number of turns on the hv side= 825.0
number of turns on the lv side= 625.0


## Example Number 32.90, Page Number:1189¶

In [159]:
#variable declaration
v1=2400.0#V
v2=240.0#V

#calculation
k=v2/v1
i2=i1/k
kva=2640*i2*0.001
i1_=kva*1000/v1
ic=i1_-i2
over=ic*100/i1

#result
print "i)i1=",i1,"A"
print "ii)i2=",i2,"A"
print "iii)kVA rating=",kva,"kVA"
print "iv)per cent increase in kVA=",kva_per,"%"
print "v)I1=",i1_,"A"
print "  Ic=",ic,"A"

i)i1= 8.3 A
ii)i2= 83.0 A
iii)kVA rating= 219.12 kVA
iv)per cent increase in kVA= 1095.6 %
v)I1= 91.3 A
Ic= 8.3 A


## Example Number 32.91, Page Number:1190¶

In [160]:
#variable declaration
v1=2400.0#V
v2=240.0#V

#calculation
k=v2/v1
i2=i1/k
kva=2160*i2*0.001
i1_=kva*1000/v1
ic=i2-i1_
over=ic*100/i1

#result
print "i)i1=",i1,"A"
print "ii)i2=",i2,"A"
print "iii)kVA rating=",kva,"kVA"
print "iv)per cent increase in kVA=",kva_per,"%"
print "v)I1=",i1_,"A"
print "  Ic=",ic,"A"

i)i1= 8.3 A
ii)i2= 83.0 A
iii)kVA rating= 179.28 kVA
iv)per cent increase in kVA= 896.4 %
v)I1= 74.7 A
Ic= 8.3 A


## Example Number 32.92, Page Number:1190¶

In [163]:
#variable declaration
v1=110.0#V
v2=110.0#V
f=50.0#Hz
efficiency=0.95
iron_loss=50.0#W
v=220.0#V

#calculations

#result
print "efficiency=",efficiency*100,"%"
print "current drawn on hv side=",i2,"A"

efficiency= 97.9760216579 %
current drawn on hv side= 23.1967703349 A


## Example Number 32.93, Page Number:1191¶

In [164]:
#variable declaration
v1=11500#V
v2=2300#V

#calculations
kva=(v1+v2)*50*0.001

#result
print "voltage output=",v1+v2,"V"
print "kVA rating of auto transformer=",kva,"kVA"

voltage output= 13800 V
kVA rating of auto transformer= 690.0 kVA


## Example Number 32.94, Page Number:1191¶

In [167]:
#variable declaration
v1=11500.0#V
v2=2300.0#V

#calculations
kva1=(v1+v2)*i1/(100)
kva2=(v1+v2)*i2/(100)
#result
print "voltage ratios=",(v1+v2)/v1,"or",(v1+v2)/v2
print "kVA rating in first case=",kva1
print "kVA rating in second case=",kva2

voltage ratios= 1.2 or 6.0
kVA rating in first case= 120.0
kVA rating in second case= 600.0


## Example Number 32.95, Page Number:1192¶

In [169]:
#variable declaration
v1=2400.0#v
v2=240.0#V

#calculations
output=2640*i2
i=i2*2640/v1
k=2640/v1
poweri=v1*i1*0.001
power=output/1000-poweri

#result
print "rating of the auto-transformer=",output/1000,"kVA"
print "inductively transferred powers=",poweri,"kW"
print "conductively transferred powers=",power,"kW"

rating of the auto-transformer= 550.0 kVA
inductively transferred powers= 50.0 kW
conductively transferred powers= 500.0 kW


## Example Number 32.96, Page Number:1196¶

In [174]:
#variable declaration
za=complex(0.5,3)
zb=complex(0.,10)
pf=0.8

#calculations
sa=s*zb/(za+zb)
sb=s*za/(za+zb)

#result
print "SA=",abs(sa)*math.cos(math.atan(sa.imag/sa.real)),"kW"
print "SB=",abs(sb)*math.cos(math.atan(sb.imag/sb.real)),"kW"

96.082805253
SA= 74.5937961595 kW
SB= 25.4062038405 kW


## Example Number 32.97, Page Number:1197¶

In [202]:
#variable declaration
r1=0.005#ohm
r2=0.01#ohm
x1=0.05#ohm
x2=0.04#ohm
pf=0.8

#calculation
za=complex(r1,x1)
zb=complex(r2,x2)
pf=math.cos(math.degrees((-1)*math.acos(pf))*math.degrees(math.atan((za/zb).imag/(za/zb).real)))

#result
print "pf of B=",pf

load of B= 1.21872643265
pf of B= 0.613584256393


## Example Number 32.98, Page Number:1197¶

In [205]:
#variable declaration
za=complex(1,6)
zb=complex(1.2,4.8)
pf=0.8

#calculations
sa=s*zb/(za+zb)
sb=s*za/(za+zb)

#result
print "SA=",abs(sa),math.degrees(math.atan(sa.imag/sa.real)),"degrees"
print "SB=",abs(sb),math.degrees(math.atan(sb.imag/sb.real)),"degrees"

SA= 224.451917244 -39.3923099293
SB= 275.942423833 -34.8183886694


## Example Number 32.99, Page Number:1197¶

In [214]:
#variabledeclaration
r1=0.5
x1=8.0
r2=0.75
x2=4.0
pf=0.9

#calculations
z1=complex(r1,x1)
z2=complex(r2,x2)
s1=s*z2/(z1+z2)
s2=s*z1/(z1+z2)
kw1=abs(s1)*math.cos(math.atan(s1.imag/s1.real))
kw2=abs(s2)*math.cos(math.atan(s2.imag/s2.real))

#result
print "kW1=",kw1,"kW"
print "kW2=",kw2,"kW"

(1.25+12j)
kW1= 58.119626171 kW
kW2= 121.880373829 kW


## Example Number 32.100, Page Number:1197¶

In [216]:
#variable declaration
pf=0.85
za=complex(1,5)
zb=complex(2,6)

#calculations
sa=s*zb/(za+zb)
sb=s*za/(za+zb)

#result
print "kVA for A=",abs(sa),math.cos(math.atan(sa.imag/sa.real)),"lag"
print "kVA for B=",abs(sb),math.cos(math.atan(sb.imag/sb.real)),"lag"

kVA for A= 130.53263665 0.819364787986 lag
kVA for B= 105.238776124 0.884143252833 lag


## Example Number 32.101, Page Number:1198¶

In [218]:
#variable declaration
v1=2200.0#V
v2=110.0#V
pf=0.8
za=complex(0.9,10)
zb=(100/50)*complex(1.0,5)

#calculation
sa=s*zb/(za+zb)
sb=s*za/(za+zb)

#result
print "SA=",abs(sa),math.degrees(math.atan(sa.imag/sa.real)),"degrees"
print "SB=",abs(sb),math.degrees(math.atan(sb.imag/sb.real)),"degrees"

SA= 63.0780848499 -39.929442891 degrees
SB= 62.1031510961 -33.7622749748 degrees


## Example Number 32.102, Page Number:1199¶

In [219]:
#variable declaration
za=complex(1,5)
zb=complex(1.5,4)
v2=400#V
pf=0.8

#calculation
sa=s*zb/(za+zb)
sb=s*za/(za+zb)

#result
print "SA=",abs(sa),math.degrees(math.atan(sa.imag/sa.real)),"degrees"
print "SB=",abs(sb),math.degrees(math.atan(sb.imag/sb.real)),"degrees"

SA= 471.125736359 -40.3232138964 degrees
SB= 281.165527855 -31.0771011508 degrees


## Example Number 32.103, Page Number:1199¶

In [220]:
#variable declaration
i=1000#A
pf=0.8
za=complex(2,3)
zb=complex(2.5,5)

#calculations
i=i*complex(pf,-math.sin(math.acos(pf)))
ratio=zb/za
ib=i/(1+ratio)
ia=i-ib
ratio=ia.real/ib.real

#result
print "IA=",ia
print "IB=",ib
print "ratio of output=",ratio

IA= (504.451038576-341.246290801j)
IB= (295.548961424-258.753709199j)
ratio of output= 1.70682730924


## Example Number 32.104, Page Number:1200¶

In [223]:
#variable declaration
v1=1000.0#V
v2=500.0#V
za=complex(1.0,5.0)
zb=complex(2.0,2.0)
pf=0.8

#calculations
zb=(100.0/250)*zb
sa=s*zb/(za+zb)
sb=s*za/(za+zb)
zab=za*zb/(za+zb)
drop=zab.real*240/100+zab.imag*180/100
v2=v2-v2*drop/100

#result
print "SA=",abs(sa),math.degrees(math.atan(sa.imag/sa.real)),"degrees"
print "SB=",abs(sb),math.degrees(math.atan(sb.imag/sb.real)),"degrees"
print "secondary voltage=",v2,"V"

SA= 55.8895719399 -64.6284382469 degrees
SB= 251.890896741 -30.9383707209 degrees
secondary voltage= 486.177874187 V


## Example Number 32.105, Page Number:1200¶

In [225]:
#variable declaration
n11=5000.0
n12=440.0
n21=5000.0
n22=480.0
x=3.5

#calculation
x1=x*n12/(100*i1)
x2=x*n22/(100*i2)
ic=(n22-n12)/0.057

#result
print "no-load circulation current=",ic/i1,"times the normal current of 200 kVA unit"

no-load circulation current= 1.54385964912 times the normal current of 200 kVA unit


## Example Number 32.106, Page Number:1203¶

In [227]:
#variabe declaration
ea=6600#V
eb=6400#V
za=complex(0.3,3)
zb=complex(0.2,1)
zl=complex(8.0,6.0)
ia=(ea*zb+(ea-eb)*zl)/(za*zb+zl*(za+zb))
ib=(eb*za-(ea-eb)*zl)/(za*zb+zl*(za+zb))

#result
print "IA=",abs(ia),"A"
print "IB=",abs(ib),"A"

IA= 195.492387533 A
IB= 422.567795916 A


## Example Number 32.107, Page Number:1204¶

In [231]:
#variable declaration
v1=1000.0#V
v2=950.0#V
r1=2.0
r2=2.5
x1=8.0
x2=6.0

#calculations
ra=v1*r1/(100*ia)
xa=v1*x1/(100*ia)
rb=v2*r2/(100*ib)
xb=v2*x2/(100*ib)
z=((ra+rb)**2+(xa+xb)**2)**0.5
ic=(v1-v2)/z
alpha=math.atan((xa+xb)/(ra+rb))

#result

no load circulating current= 25.0948635944 A


# Example Number 32.108, Page Number:1204¶

In [233]:
#variable declaration
v1=500.0#V
v2=510.0#V
z1=3.0
z2=5.0
r=0.4

#calculation
za=z1*v1/(100*ia)
zb=z2*v2/(100*ib)
ic=(v2-v1)/(za+zb)

#result
print "cross current=",ic,"A"

cross current= 315.656565657 A


## Example Number 32.109, Page Number:1204¶

In [243]:
#variable declaration
pf=0.8
v1=405.0#V
v2=415.0#V
ra=1.0
rb=1.5
xa=5.0
xb=4.0

#calculations
ra=400/(100*ia)
xa=xa*400/(100*ia)
rb=rb*400/(100*ib)
xb=xb*400/(100*ib)
za=complex(ra,xa)
zb=complex(rb,xb)
ic=(v1-v2)/(za+zb)
ia=(v1*zb+(v1-v2)*zl)/(za*zb+zl*(za+zb))
ib=(v2*za-(v1-v2)*zl)/(za*zb+zl*(za+zb))
sa=400*ia/1000
sb=400*ib/1000
pf1=math.cos(math.atan(sa.imag/sa.real))
pf2=math.cos(math.atan(sb.imag/sb.real))

#result
print "a)cross current=",-abs(ic),math.degrees(math.atan(ic.imag/ic.real))
print "b)SA=",abs(sa),pf1,"lag"
print "  SB=",abs(sb),pf2,"lag"

a)cross current= -229.754569404 -72.8972710309
b)SA= 387.844943528 0.820048560714 lag
SB= 351.964386212 0.738709225528 lag


## Example Number 32.110, Page Number:1205¶

In [248]:
#variable declaration
zl=complex(2.0,1.5)
za=complex(0.15,0.5)
zb=complex(0.1,0.6)
ea=207#V
eb=205#V

#calculations
ia=(ea*zb+(ea-eb)*zl)/(za*zb+zl*(za+zb))
ib=(eb*za-(ea-eb)*zl)/(za*zb+zl*(za+zb))
v2_=(ia+ib)*zl
angle=math.atan(v2_.imag/v2_.real)-math.atan(ia.imag/ia.real)
pfa=math.cos(angle)
angle=math.atan(v2_.imag/v2_.real)-math.atan(ib.imag/ib.real)
pfb=math.cos(angle)
pa=abs(v2_)*abs(ia)*pfa
pb=abs(v2_)*abs(ib)*pfb

#result
print "power output:"
print " A:",pa,"W"
print " B:",pb,"W"
print "power factor:"
print " A:",pfa
print " B:",pfb

power output:
A: 6535.37583042 W
B: 4925.36941503 W
power factor:
A: 0.818428780129
B: 0.775705655277


## Example Number 32.111, Page Number:1206¶

In [251]:
#variable declaration
ia=200.0#A
ib=600.0#A
ra=0.02#ohm
rb=0.025#ohm
xa=0.05#ohm
xb=0.06#ohm
ea=245.0#V
eb=240.0#V
zl=complex(0.25,0.1)

#calculation
za=(ea/ia)*complex(ra,xa)
zb=(eb/ib)*complex(rb,xb)
i=(ea*zb+eb*za)/(za*zb+zl*(za+zb))
v2=i*zl

#result
print "terminal voltage=",round(abs(v2)),round(math.degrees(math.atan(v2.imag/v2.real))),"degrees"

terminal voltage= 230.0 -3.0 degrees

In [ ]: