# Chapter 35: Computations and Circle Diagrams¶

## Example Number 35.1, Page Number:1316¶

In [1]:
import math
#variable declaration
i=10#A
p=450#W
v=110#V
r=0.05#ohm
loss=135#w

#calculations
cu_loss=3*i**2*r
core_loss=p-loss-cu_loss
volt=v/math.sqrt(3)
g=core_loss/(3*(v/math.sqrt(3))**2)
y=i*math.sqrt(3)/v
b=math.sqrt(y**2-g**2)

#result
print "exciting conductance=",g,"seimens/phase"
print "susceptance/phase=",b,"seimens/phase"

exciting conductance= 0.0247933884298 seimens/phase
susceptance/phase= 0.155494939853 seimens/phase


## Example Number 35.2, Page Number:1317¶

In [8]:
import math
#variable declaration
v=110.0#V
i=25.0#A
v2=30.0#V
inpt=440.0#W
loss=40.0#W
r=0.1#ohm
ratio=1.6

#calculations
vs=v2/math.sqrt(3)
z01=vs/i
losses=inpt-loss
r01=losses/(3*i**2)
x01=math.sqrt(z01**2-r01**2)
dc_r=r/2.0
ac_r=dc_r*ratio
effective_r=r01-ac_r

#result
print "x01=",x01,"ohm"
print "r1=",ac_r,"ohm"
print "r2=",effective_r,"ohm"

x01= 0.659157711696 ohm
r1= 0.08 ohm
r2= 0.133333333333 ohm


## Example Number 35.10, Page Number:1333¶

In [18]:
import math
#variable declaration
ratio=1/4.0
slip=3.0
ratio2=4.0

#calculations
K=math.sqrt(ratio/((ratio2**2)*0.01*slip))

#result
print "Percentage Tapping=",K*100,"%"

Percentage Tapping= 72.1687836487 %


## Example Number 35.11, Page Number:1333¶

In [22]:
import math
#variable declaration
v1=400#V
n=950#rpm
f=50.0#Hz
v2=400#V
ratio=1.8
i=30#A

#calculations
v=v1/math.sqrt(ratio)
If=6*v*i/v1
K=v/v1
kisc=K**2*6*i
ts_tf=(1/6.0)*6**2*(f/1000.0)

#result
print "a)voltage=",v,"V"
print "b)current=",If,"A"
print "c)line current=",kisc,"A"
print "d)percentage=",ts_tf*100,"%"

a)voltage= 298.142397 V
b)current= 134.16407865 A
c)line current= 100.0 A
d)percentage= 30.0 %


## Example Number 35.12, Page Number:1334¶

In [29]:
import math
#variable declaration
ratio=5.0
per=5

#calculations
k=math.sqrt(ratio/3)
tst_tf=(3.0/5)*5**2*0.01*per*100

#result
print "auto-transformation ratio=",tst_tf,"%"

auto-transformation ratio= 75.0 %


## Example Number 35.13, Page Number:1334¶

In [31]:
import math
#variable declaration
v=400.0#V
per=3.5
v2=92.0#V

#calculations
k=math.sqrt(2/(v/v2))
ts_tf=k**2*(v/v2)**2*0.01*per

#result
print "auto-transformation ratio=",ts_tf*100,"%"

auto-transformation ratio= 30.4347826087 %


## Example Number 35.14, Page Number:1336¶

In [34]:
import math
#variable declaration
v=440.0#V
efficiency=0.85
pf=0.8
i=45.0#A
v2=220.0#V

#calculations
isc=i*v/v2
ist=isc/math.sqrt(3)
ratio=ist/if_

#result
print "ratio=",ratio

ratio= 2.244


## Example Number 35.15, Page Number:1336¶

In [37]:
import math
#variable declaration
i=60.0#A
n1=940.0#rpm
t=150.0#N-m
i2=300.0#A

#calculations
sf=(1000-n1)/1000
tst=t*(i2/i)**2*sf
s_i=i2/3
sd_tst=tst/3

#result
print "Starting torque=",tst,"N-m"
print"when star/delta is used:"
print "starting current=",s_i,"A"
print "starting torque=",sd_tst,"N-m"

Starting torque= 225.0 N-m
when star/delta is used:
starting current= 100.0 A
starting torque= 75.0 N-m


## Example Number 35.16, Page Number:1336¶

In [48]:
import math
#variable declaration
tapping=70.7
ratio=6.0
slip=4.0

#calculation
tst_tf=(1.0/3.0)*ratio**2.0*slip*0.01
tst_tf2=(1.0/2)*ratio**2.0*slip*0.01

#result
print "star-delta switch:starting torque=",tst_tf*100,"%"
print "auto-transformer switch:starting torque=",tst_tf2*100,"%"

star-delta switch:starting torque= 48.0 %
auto-transformer switch:starting torque= 72.0 %


## Example Number 35.17, Page Number:1337¶

In [49]:
import math
#variable declaration
f=50.0#Hz
v=400.0#V
n=960.0#rpm
i=86.4#A
efficiency=0.88
pf=0.85

#calculations
isc=i/math.sqrt(3)
ist=isc/math.sqrt(3)
iph=il/math.sqrt(3)
tst_tf=(ist*math.sqrt(3)/il)**2*0.05

#result
print "starting torque=",tst_tf*100,"%"

starting torque= 26.6369577796 %


## Example Number 35.18, Page Number:1337¶

In [53]:
import math
#variable declaration
output=10.0#kW
v=400.0#V
pf=0.85
efficiency=0.88
v2=200.0#V
i=40.0#A

#calculations
isc=i*v/v2
iscp=isc/math.sqrt(3)
ist=iscp/math.sqrt(3)
ratio=ist/il

#result
print "ratio=",ratio

ratio= 1.23388000387


## Example Number 35.19, Page Number:1337¶

In [55]:
#variable declaration
v=400.0#V
f=50.0#Hz
slip=4.5
t=250.0
i=650.0
tap=60.0

#calculation
il=i/3
im=i/3
tst=t/3
ilm=(tap/100)**2*i
imk=(tap/100)*i
tstk=(tap/100)**2*t

#result
print "star/delta:"
print "line current=",il,"%"
print "motor current=",im,"%"
print "starting torque=",tst,"%"
print "60% taps:"
print "line current=",ilm,"%"
print "motor current=",imk,"%"
print "starting torque=",tstk,"%"

 star/delta:
line current= 216.666666667 %
motor current= 216.666666667 %
starting torque= 83.3333333333 %
60% taps:
line current= 234.0 %
motor current= 390.0 %
starting torque= 90.0 %


## Example Number 35.20, Page Number:1338¶

In [68]:
#variable declaration
flt=35.0
tap=75.0

#calculations
isck=tap**2*isc/100
sf=flt*3
tst_tf=tap**2*sf/100
#result
print "starting current=",isck,"%"
print "starting torque=",tst_tf/100,"%"

starting current= 303.75 %
starting torque= 59.0625 %


## Example Number 35.21, Page Number:1338¶

In [71]:
#variable declaration
w=7.46#kW
ic=1.7
t=35.0
ratio=60.0

#calculations
sf=t*3/100
il1=ic*3
tst=(ratio/1000)**2*sf*10000
il2=(ratio/100)*3*ic

#results
print "auto-starter:"
print "line-current=",il1,"%"
print "torque=",tst,"%"
print "voltage decreased to 60%"
print "line-current",il2,"%"
print "torque=",tst,"%"

auto-starter:
line-current= 5.1 %
torque= 37.8 %
voltage decreased to 60%
line-current 3.06 %
torque= 37.8 %


## Example Number 35.22, Page Number:1342¶

In [107]:
import math

#variable declaration
slip=2.0
r=0.02#ohm
n=6.0
#calculations
smax=r2=slip/100.0
R1=r2/smax
K=math.pow(smax,1.0/5)
R2=K*R1
R3=K*R2
R4=K*R3
R5=K*R4
p1=R1-R2
p2=R2-R3
p3=R3-R4
p4=R4-R5
p5=R5-r2

#result
print "resistances of various starter sections:"
print "p1=",p1,"ohm"
print "p2=",p2,"ohm"
print "p3=",p3,"ohm"
print "p4=",p4,"ohm"
print "p5=",p5,"ohm"

resistances of various starter sections:
p1= 0.542694948073 ohm
p2= 0.248177141409 ohm
p3= 0.113492660539 ohm
p4= 0.0519007670213 ohm
p5= 0.0237344829577 ohm


## Example Number 35.23, Page Number:1345¶

In [11]:
import math
#variable declaration
primary=complex(1,3)
outer=complex(3,1)
inner=complex(0.6,5)
s=4
outer2=complex(3/(s*0.01),1)
inner2=complex(0.6/(s*0.01),5)
v=440#V

#calculations
#s=1
z01=primary+1/((1/outer)+(1/inner))
current_per_phase=v/abs(z01)
torque=3*current_per_phase**2*(z01.real-1)

print "s=1: torque=",torque,"synch watt"

#s=4
z01=primary+1/((1/outer2)+(1/inner2))
current_per_phase=v/abs(z01)
torque=3*current_per_phase**2*(z01.real-1)

print "s=4: torque=",torque,"synch watt"

s=1: torque= 35065.3642462 synch watt
s=4: torque= 32129.9449695 synch watt


## Example Number 35.24, Page Number:1346¶

In [37]:
import math
#variable declaration
inner=complex(0.4,2)
outer=complex(2,0.4)
s=5
inner2=complex(0.4/(s*0.01),2)
outer2=complex(2/(s*0.01),0.4)
print
#calculations
#s=1
zi=abs(inner)
zo=abs(outer)
r_ratio=inner.imag/outer.imag
to_ti=r_ratio*(zo/zi)**2
print "Ratio of torques when s=1:",to_ti

#s=5
zi=abs(inner2)
zo=abs(outer2)
print zi
r_ratio=inner2.imag/outer2.imag
to_ti=r_ratio*(zi/zo)**2

print "Ratio of torques when s=5:",to_ti

Ratio of torques when s=1: 5.0
8.24621125124
Ratio of torques when s=5: 0.212478752125


## Example Number 35.25, Page Number:1346¶

In [43]:
import math
#variable declaration
s=5
zi=complex(0.05,0.4)
zo=complex(0.5,0.1)
v=100#V

#calculations
#s=1
z=zo*zi/(zo+zi)
r2=z.real
z=abs(z)
i2=v/z
t=i2**2*r2
print "s=1:torque=",t,"synch watts"

#s=0.01
zi=complex(0.05/(s*0.01),0.4)
zo=complex(0.5/(s*0.01),0.1)
z=zo*zi/(zo+zi)
r2=z.real
z=abs(z)
i2=v/z
t=i2**2*r2
print "s=5:torque=",t,"synch watts"

s=1:torque= 22307.6923077 synch watts
s=5:torque= 9620.58966517 synch watts


## Example Number 35.26, Page Number:1348¶

In [6]:
import math
from sympy.solvers import solve
from sympy import Symbol
#variable declaration
s=Symbol('s')
z2=complex(2,1.2)
z1=complex(0.5,3.5)
#Z1=((2/s)^2+1.2^2)^0.5
#Z2=((0.5/s)^2+3.5^2)^0.5
#T1=T2
ans=solve([(((2**2)/(s**2))+1.2**2)-((((0.5**2)/(s**2))+3.5**2)*4)],[s])
print "slip=",round(ans[1][0]*100,1),"%"

slip= 25.1 %


## Example Number 35.27, Page Number:1347¶

In [49]:
import math
#variable declaration
zo=complex(1,0)
zi=complex(0.15,3)
v=250#V
n=1000#rpm

#calculations
z2=zo*zi/(zo+zi)
stator=complex(0.25,3.5)
z01=z2+stator
i=complex(v,0)/z01
i=abs(i)
cu_loss=i**2*z01.real
T=cu_loss*3/(2*math.pi*(n/60))
#result
print "torque=",T,"N-m"

torque= 135.560320318 N-m


## Example Number 35.28, Page Number:1348¶

In [58]:
import math
#variable declaration
z1=complex(1,2.8)
zo=complex(3,1)
zi=complex(0.5,5)
v=440#V
s=0.04

#calculations
#s=1
z2=zo*zi/(zo+zi)
z01=z1+z2
i2=v/z01
r2=z2.real
t=abs(i2)**2*r2

print "s=1:torque=",t,"synch. watt"

#s=0.04
zo=complex(3.0/s,1.0)
zi=complex(0.5/s,5.0)
z2=zo*zi/(zo+zi)
z01=z1+z2
i2=v/z01
r2=z2.real
t=abs(i2)**2*r2
print "s=4:torque=",t,"synch. watt"

s=1:torque= 12388.3258184 synch. watt
s=4:torque= 11489.1141244 synch. watt


## Example Number 35.29, Page Number:1351¶

In [60]:
#variable declaration
f=50.0#Hz
r=0.30#ohm
n1=1440.0#rpm
n2=1320.0#rpm
ns=120.0*f/4.0
#calculations
s1=(ns-n1)/ns
s2=(ns-n2)/ns
r=s2*r/s1-r

#result
print "external resistance=",r,"ohm"

external resistance= 0.6 ohm


## Example Number 35.30, Page Number:1348¶

In [61]:
#variable declaration
f=50.0#Hz
s=0.03
ratio=10.0
r=0.2

#calculations
ns=120*f/6
s1=s
n1=ns*(1-s1)
n2=n1-10*n1/100
s2=(ns-n2)/ns
r=s2*r/s1-r

#result
print "external resistance=",r,"ohm"

external resistance= 0.646666666667 ohm


## Example Number 35.31, Page Number:1354¶

In [69]:
#Variable declaration
f=50#Hz
s=0.02

#calculations
nsc=120*f/10
n=(1-s)*nsc
nsa=120*f/6
sa=(nsa-n)/nsa
f_=sa*f
n_=(120*f_)/4
sb=(n_-n)/n_
f__=sb*f_

#resu;t
print "f_=",f_,"Hz"
print "f_ _=",f__,"Hz"

f_= 20.6 Hz
f_ _= 1.0 Hz


## Example Number 35.32, Page Number:1354¶

In [75]:
#variable declaration
f=50.0#Hz
f2=1.0#Hz

#calculations
nsc=120*f/10
s=f2/f
n=nsc-s*nsc
nsa=120*f/4
sa=(nsa-n)/nsa
f1=sa*f
n2=120*f1/6
sb=(n2-n)/n2

#result
print "sa=",sa*100,"%"
print "sb=",sb*100,"%"

sa= 60.8 %
sb= 3.28947368421 %


## Example Number 35.33, Page Number:1354¶

In [79]:
#variable declaration
f=50#Hz

#calculations
nsc=120*f/10

#result
print "speed of set=",nsc,"rpm"
print "electric power transferred=",output,"kW"

speed of set= 600 rpm
electric power transferred= 29.84 kW


## Example Number 35.34, Page Number:1355¶

In [78]:
#variable declaration
f=50#Hz

#calculations
nsc=120*f/10

speed of set= 600 rpm