# Chapter 36: Single-Phase Motors¶

## Example Number 36.1, Page Number:1374¶

In [9]:
import math

#variable declaration
R1=1.86
X1=2.56
R2=3.56
X2=2.56
Xm=53.5
r1=R1/2
x1=X1/2
r2=R2/2
x2=X2/2
xm=Xm/2
v=110
f=60
s=0.05

#calculations
xo=xm+x2

zf=(((r2/s)*xm)/(((r2/s)*(r2/s))+(xo*xo)))*xm
jf=(((r2/s)*(r2/s)+(x2*xo))/(((r2/s)*(r2/s))+(xo*xo)))*xm
Jf=math.degrees(math.atan(jf/zf))

zb=(((r2/(2-s))*xm)/(((r2/s)*(r2/(2-s)))+(xo*xo)))*xm
jb=(((r2/(2-s))*(r2/(2-s))+(x2*xo))/(((r2/(2-s))*(r2/(2-s)))+(xo*xo)))*xm
Jb=math.degrees(math.atan(jb/zb))

Z1=R1
J1=X1
z01=Z1+zf+zb
j01=jf+jb+J1
J01=math.degrees(math.atan(j01/z01))

i1=v/z01
vf=i1*zf
vb=i1*zb
z3=math.sqrt(((r2/s)*(r2/s))+(x2*x2))
z5=math.sqrt(((r2/(2-s))*(r2/(2-s)))+(x2*x2))

i3=vf/z3
i5=vb/z5
tf=(i3*i3*r2)/s
tb=t5=(i5*i5*r2)/(2-s)
t=tf-tb
output=t*(1-s)

#result
print "output = ",output

output =  206.798750547


# Example Number 36.2, Page Number:1375¶

In [4]:
import math

#variable declaration
p=185
v=110
f=50
s=0.05
R1=1.86
X1=2.56
Xo=53.5
R2=3.56
X2=2.56
Xm=53.5
cl=3.5#core loss
fl=13.5#friction loss
vf=(82.5/100)*v
ic=(cl*100)/vf
r1=R1/2
x1=X1/2
r2=R2/2
x2=X2/2
xm=Xm/2
rc=vf/ic

#calculations

#motor 1
c=1/rc #conductance of corebranch
s=-(1/xm)#susceptance
yf=c+a1
yfj=s+a1j
zf=(yf*yf)+(yfj*yfj)
zfr=yf/zf
zfj=yfj/zf

#motor 2
a2=(r2/2-s)/(((r2/(2-s))*(r2/(2-s)))+(x2*x2))
a2j=-x2/(((r2/(2-s))*(r2/(2-s)))+(x2*x2))
Z1=R1
J1=X1
yb=yf+a2
ybj=yfj+a2j
zb1=(yb*yb)+(ybj*ybj)
zbr=yb/zb1
zbj=ybj/zb1
z01=Z1+zf+zbr
z01j=J1+zfj+zbj

i1=v/z01
vf=i1*zf
vb=i1*zbr
z3=math.sqrt(((r2/s)*(r2/s))+(x2*x2))
z5=math.sqrt(((r2/(2-s))*(r2/(2-s)))+(x2*x2))

i3=vf/z3
i5=vb/z5
tf=(i3*i3*r2)/s
tb=t5=(i5*i5*r2)/(2-s)
t=tf-tb
watt=t*(1-s)
net_output=watt-fl

#result
print "Net output = ",net_output

Net output =  -446.423232085


## Example Number 36.3, Page Number:1376¶

In [25]:
import math

#variable declaration
w=250
v=230
f=50
zm=4.5
zmj=3.7
za=9.5
zaj=3.5

#calculations
zma=math.degrees(math.atan(zmj/zm))
xc=x+zaj
c=1000000/(xc*2*50*3.14)

#result
print "C= ",c," uf"

C=  211.551875951  uf


## Example Number 36.4, Page Number:1393¶

In [30]:
#variable declaration

p=250
f=50
v=220
ndc=2000
ia=1
ra=20
la=0.4

#calculations
ebdc=v-(ia*ra)
#ac
xa=2*3.14*f*la
ebac=-(ia*ra)+math.sqrt((v*v)-((ia*xa)*(ia*xa)))
nac=(ebac*ndc)/ebdc
cos_phi=(ebac+(ia*ra))/v
pmech=ebac*ia
T=(pmech*9.55)/nac

#result
print "Speed= ",nac," rpm"
print "Torque= ",T," N-m"
print "Power Factor= ",cos_phi," lag"

Speed=  1606.22922133  rpm
Torque=  0.955  N-m
Power Factor=  0.821013282424  lag


## Example Number 36.5, Page Number:1394¶

In [36]:
import math

#variable declaration
r=30
l=0.5
v=250
idc=0.8
ndc=2000
f=50
ia=0.8

#calculations

xa=2*3.14*f*l
ra=r
ebac=-(ia*ra)+math.sqrt((v*v)-((ia*xa)*(ia*xa)))
ebdc=v-(r*idc)
nac=(ndc*ebac)/ebdc
cos_phi=(ebac+(ia*ra))/v

#result
print "Speed= ",nac," rpm"
print "Power Factor= ",cos_phi," lag"

Speed=  1700.52062383  rpm
Power Factor=  0.864635321971  lag


## Example Number 36.6, Page Number:1396¶

In [38]:
import math

#variable declaration
f=50
a=30
w=8
v=220
v2=205
pole=4

#calculations

ns=(120*f)/pole
tsh=(9.55*w*1000)/ns

Torque angle if voltage drops to 205 V =  42.9327261097  degrees