# Chapter 38: Synchronous Motor¶

## Example Number 38.1, Page Number:1495¶

In [1]:
import math
#variable declaration
p=75#kW
f=50#Hz
v=440#V
pf=0.8
loss=0.95
xs=2.5#ohm

#calculations
ns=120*f/4
pm=p*1000/loss
ia=pm/(math.sqrt(3)*v*pf)
vol_phase=v/math.sqrt(3)

#calculations
print "mechanical power=",pm,"W"
print "armature current=",ia,"A"

mechanical power= 78947.3684211 W
armature current= 129.489444346 A


## Example Number 38.2, Page Number:1498¶

In [2]:
import cmath
#variable declaration
p=20
vl=693#V
r=10#ohm
lag=0.5#degrees

#calculations
#lag=0.5
alpha=p*lag/2
eb=vp=vl/math.sqrt(3)
zs=complex(0,10)
ia=er/zs
print "displacement:0.5%"
print "alpha=",alpha,"degrees"
print "armature emf/phase=",eb,"V"
print "armature current/phase=",ia,"A"
print "power drawn=",power_input,"W"
print ""

#lag=5
lag=5
alpha=p*lag/2
eb=vp=vl/math.sqrt(3)
zs=complex(0,10)
ia=er/zs

print "displacement:5%"
print "alpha=",alpha,"degrees"
print "armature emf/phase=",eb,"V"
print "armature current/phase=",ia,"A"
print "power drawn=",power_input,"W"

displacement:0.5%
alpha= 5.0 degrees
armature emf/phase= 400.103736548 V
armature current/phase= (3.4871338335-0.152251551219j) A
power drawn= 4189.63221768 W

displacement:5%
alpha= 50 degrees
armature emf/phase= 400.103736548 V
armature current/phase= (30.6497244054-14.2922012106j) A
power drawn= 40591.222447 W


## Example Number 38.3, Page Number:1499¶

In [15]:
import math
#variable declaration
v=400.0#V/ph
i=32.0#A/ph
xs=10.0#ohm

#calculations
e=math.sqrt(v**2+(i*xs)**2)
delta=math.atan((i*xs)/v)
power=3*v*i
power_other=3*(v*e/10)*math.sin(delta)*0.001

#result
print "E=",e,"V"
print "delta=",math.degrees(delta),"degrees"

E= 512.249938995 V
delta= 38.6598082541 degrees


## Example Number 38.4, Page Number:1506¶

In [27]:
import math
#variable declaration
w=150#kW
f=50#Hz
v=2300#V
n=1000#rpm
xd=32#ohm
xq=20#ohm
alpha=16#degrees

#calculations
vp=v/math.sqrt(3)
eb=2*vp
pm=3*(ex_power+rel_power)
tg=9.55*pm/1000

#result
print "torque=",tg,"N-m"

torque= 1121.29686485 N-m


## Example Number 38.5, Page Number:1506¶

In [27]:
import math
from sympy.solvers import solve
from sympy import Symbol
#variable declaration
x=Symbol('x')
v=3300.0#V
P=1.5#MW
phi=3.0
xd=4.0#ohm per phase
xq=3.0#ohm per phase
sin_phi=0
cos_phi=1
phi=0
#calculations
v1=v/math.sqrt(3)
ia=P*math.pow(10,6)/(math.sqrt(3)*v*cos_phi)
tan_sigma=(v1*sin_phi-ia*xq)/(v1*cos_phi)
sigma=math.atan(tan_sigma)
alpha=phi-sigma
i_d=ia*math.sin(sigma)
iq=ia*math.cos(sigma)
eb=v1*math.cos(alpha)-i_d*xd
#eb=1029sin(alpha)+151sin(2*alpha)
#dPm/d(alpha)=1029sin(alpha)+151sin(2*alpha)=0
ans=solve([(604.0*x**2+1029.0*x-302.0)],[x])
Pm=1029*math.sin(alpha2)+151*math.sin(alpha2)
max_P=Pm*3

#result
print "Maximum mechanical power which the motor would develop=",round(max_P),"kW"

Maximum mechanical power which the motor would develop= 3540.0 kW


## Example Number 38.6, Page Number:1506¶

In [1]:
import math
#variable declaration
v=11000#V
ia=60#A
r=1#ohm
x=30#ohm
pf=0.8

#calculations
p2=math.sqrt(3)*v*ia*pf
cu_loss=ia**2*3
pm=p2-cu_loss
vp=v/math.sqrt(3)
phi=math.acos(pf)
theta=math.atan(x/r)
zs=x
z_drop=ia*zs
eb=math.sqrt((vp**2+z_drop**2-(2*vp*z_drop*math.cos(theta+phi))))*math.sqrt(3)

#result
print "power supplied=",p2/1000,"kW"
print "mechanical power=",pm/1000,"KW"
print "induced emf=",eb,"V"


power supplied= 914.522826396 kW
mechanical power= 903.722826396 KW
induced emf= 13039.2734763 V


## Example Number 38.7, Page Number:1507¶

In [60]:
import math
#variable declaration
v=400#V
i=32#A
pf=1
xd=10#ohm
xq=6.5#ohm

#calculations
e=math.sqrt(v**2+(i*xq)**2)+((xd-xq)*14.8)
delta=math.atan((i*xq)/v)
power=3*v*i
power_other=3*(v*e/10)*math.sin(delta)*0.001

#result
print "E=",e,"V"
print "delta=",math.degrees(delta),"degrees"

E= 502.648089715 V
delta= 27.4744316263 degrees


## Example Number 38.8, Page Number:1508¶

In [3]:
import math
#variable declaration
v=500#V
output=7.46#kW
pf=0.9
r=0.8#ohm
loss=500#W
ex_loss=800#W

#calculations
pm=output*1000+loss+ex_loss
ia=(v*pf-math.sqrt(v**2*pf**2-4*r*pm))/(2*r)
m_input=loss*ia*pf
efficiency=output*1000/m_input

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

commercial efficiency= 82.1029269497 %


## Example Number 38.9, Page Number:1509¶

In [12]:
import math
#variable declaration
v=2300#V
r=0.2#ohm
x=2.2#ohm
pf=0.5
il=200#A

#calculations
phi=math.acos(pf)
theta=math.atan(x//r)
v=v/math.sqrt(3)
zs=math.sqrt(r**2+x**2)
eb=math.sqrt(v**2+(il*zs)**2-(2*v*il*zs*math.cos(phi+theta)))

#result
print "Eb=",eb,"volt/phase"

Eb= 1708.04482042 volt/phase


## Example Number 38.10, Page Number:1509¶

In [18]:
import math
#variable declaration
vl=6600#V
f=50#Hz
il=50#A
r=1#ohm
x=20#ohm
pf=0.8

#calculations
#0.8 lagging
power_i=math.sqrt(3)*v*f*pf
v=vl/math.sqrt(3)
phi=math.acos(pf)
theta=math.atan(x/r)
zs=math.sqrt(x**2+r**2)
eb=math.sqrt(v**2+(il*zs)**2-(2*v*il*zs*math.cos(phi-theta)))*math.sqrt(3)

print "0.8 lag: Eb=",eb

power_i=math.sqrt(3)*v*f*pf
v=vl/math.sqrt(3)
phi=math.acos(pf)
theta=math.atan(x/r)
zs=math.sqrt(x**2+r**2)
eb=math.sqrt(v**2+(il*zs)**2-(2*v*il*zs*math.cos(phi+theta)))*math.sqrt(3)


0.8 lag: Eb= 5651.1180113


## Example Number 38.11, Page Number:1510¶

In [25]:
import math
#variable declaration
x=0.4
pf=0.8
v=100#V
phi=math.acos(pf)
#calculations
#pf=1
eb=math.sqrt(v**2+(x*v)**2)
#pf=0.8 lag
#result
print "pf=1: Eb=",eb,"V"
print "pf=0.8 lag:Eb=",eb2,"V"

pf=1: Eb= 107.703296143 V
pf=0.8 lag:Eb= 82.4621125124 V


## Example Number 38.12, Page Number:1510¶

In [56]:
import math
#variable declaraion
v=11000#V
r=3.5#ohm
x=40#ohm
pf=0.8

#calculations
vp=v/math.sqrt(3)
phi=math.acos(pf)
ra=ia*r
xa=ia*x
za=math.sqrt(ra**2+xa**2)
theta=math.atan(x/r)

#pf=1
eb1=math.sqrt(vp**2+za**2-(2*vp*za*math.cos(theta)))
alpha1=math.asin(xa*math.sin(theta)/eb1)

#pf=0.8 lag
eb2=math.sqrt(vp**2+xa**2-(2*vp*xa*math.cos(theta-phi)))*math.sqrt(3)
alpha2=math.asin(xa*math.sin(theta-phi)/eb2)
#pf=1
eb3=math.sqrt(vp**2+xa**2-(2*vp*xa*math.cos(theta+phi)))*math.sqrt(3)
alpha3=math.asin(xa*math.sin(theta+phi)/eb3)

#result
print "at pf=1"
print "Eb=",eb1*math.sqrt(3),"V"
print "alpha=",math.degrees(alpha1),"degrees"
print "at pf=0.8 lagging"
print "Eb=",eb2,"V"
print "alpha=",math.degrees(alpha2),"degrees"
print "Eb=",eb3,"V"
print "alpha=",math.degrees(alpha3),"degrees"

at pf=1
Eb= 11283.8105339 V
alpha= 18.7256601694 degrees
at pf=0.8 lagging
Eb= 8990.39249633 V
alpha= 10.0142654731 degrees
Eb= 13283.8907748 V
alpha= 7.71356041367 degrees


## Example Number 38.14, Page Number:1513¶

In [65]:
import math
#variable declaration
z=complex(0.5,0.866)
v=200#V
output=6000#W
loss=500#W
i=50#A

#calculations
cu_loss=i**2*z.real
motor_intake=output+loss+cu_loss
phi=math.acos(motor_intake/(v*i))
theta=math.atan(z.imag/z.real)
zs=abs(z)*i
#result
print "lag:eb=",eb1,"V"
print "lag:eb=",eb2,"V"

lag:eb= 154.286783862 V
lag:eb= 213.765547573 V


## Example Number 38.15, Page Number:1513¶

In [72]:
import math
#variable declaration
v=2200#V
f=50#Hz
z=complex(0.4,6)
lag=3#degrees

#calculations
eb=v/math.sqrt(3)
alpha=lag*8/2
zs=abs(z)
ia=er/zs
theta=math.atan(z.imag/z.real)
pf=math.cos(phi)
total_input=3*eb*ia*pf
cu_loss=3*ia**2*z.real
pm=total_input-cu_loss
pm_max=(eb*eb/zs)-(eb**2*z.real/(zs**2))
#result
print "armature current=",ia,"A"
print "power factor=",pf
print "power of the motor=",pm/1000,"kW"
print "max power of motor=",pm_max/1000,"kW"

armature current= 44.1583059199 A
power factor= 0.99927231631
power of the motor= 165.803353329 kW
max power of motor= 250.446734776 kW


## Example Number 38.16, Page Number:1514¶

In [73]:
import math
#variable declaration
eb=250#V
v=200#V
x=2.5#times resistance
#calculations
theta=math.atan(x)
pf=math.cos(phi)

#results
print "pf at which the motor is operating=",pf

pf at which the motor is operating= 0.928476690885


## Example Number 38.17, Page Number:1514¶

In [82]:
import math
#variable declaration
v=6600#V
r=10#ohm
inpt=900#kW
e=8900#V

#calculations
vp=v/math.sqrt(3)
eb=e/math.sqrt(3)
icos=inpt*1000/(math.sqrt(3)*v)
bc=r*icos
ac=math.sqrt(eb**2-bc**2)
oc=ac-vp
phi=math.atan(oc/bc)
i=icos/math.cos(phi)

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

Line current= 149.188331836 A


## Example Number 38.18, Page Number:1515¶

In [97]:
import math
#variable declaration
v=6600#V
x=20#ohm
inpt=1000#kW
pf=0.8
inpt2=1500#kW

#variable declaration
va=v/math.sqrt(3)
ia1=inpt*1000/(math.sqrt(3)*v*pf)
zs=x
phi=math.acos(pf)
ia1zs=ia1*zs
ia2cosphi2=inpt2*1000/(math.sqrt(3)*v)
cosphi2=x*ia2cosphi2
ac=math.sqrt(eb**2-cosphi2*2)
phi2=math.atan(ac/cosphi2)
pf=math.cos(phi2)
alpha2=math.atan(cosphi2/ac)

#results
print "new power angle=",math.degrees(alpha2),"degrees"
print "new power factor=",pf

new power angle= 25.8661450552 degrees
new power factor= 0.436270181217


## Example Number 38.19, Page Number:1515¶

In [2]:
import math
#variable declaration
v=400#V
inpt=5472#W
x=10#ohm

#calculations
va=v/math.sqrt(3)
iacosphi=inpt/(math.sqrt(3)*v)
zs=x
iazs=iacosphi*zs
ac=math.sqrt(va**2-iazs**2)
oc=va-ac
bc=iazs
phi=math.atan(oc/iazs)
pf=math.cos(phi)
ia=iacosphi/pf
alpha=math.atan(bc/ac)
#result
print "power factor=",pf
print "armature current=",ia,"A"

load angle= 19.9987718079 degrees
power factor= 0.984809614116
armature current= 8.01997824686 A


## Example Number 38.20, Page Number:1515¶

In [152]:
import math
import scipy
from sympy.solvers import solve
from sympy import Symbol
#variable declaration
i2=Symbol('i2')
v=2000.0#V
r=0.2#ohm
xs=2.2#ohm
inpt=800.0#kW
e=2500.0#V

#calculations
i1=inpt*1000/(math.sqrt(3)*v)
vp=v/math.sqrt(3)
ep=e/math.sqrt(3)
theta=math.atan(xs/r)
i2=solve(((i1*xs+r*i2)**2+(vp+i1*r-xs*i2)**2)-ep**2,i2)
i=math.sqrt(i1**2+i2[0]**2)
pf=i1/i

#result
print "line currrent=",i,"A"
print "power factor=",pf

line currrent= 241.492937915 A
power factor= 0.956301702525


## Example Number 38.21, Page Number:1516¶

In [156]:
import math
#variable declaration
v=440#V
f=50#Hz
inpt=7.46#kW
r=0.5#ohm
pf=0.75
loss=500#W
ex_loss=650#W

#calculations
ia=inpt*1000/(math.sqrt(3)*v*pf)
cu_loss=3*ia**2*r
power=inpt*1000+ex_loss
output=inpt*1000-cu_loss-loss
efficiency=output/power

#result
print "armature current=",ia,"A"
print "power=",power,"W"
print "efficiency=",efficiency*100,"%"

armature current= 13.0516151762 A
power= 8110.0 W
efficiency= 82.6693343026 %


## Example Number 38.22, Page Number:1517¶

In [157]:
import math
v=3300#V
x=18#ohm
pf=0.707
inpt=800#kW

#calculations
ia=inpt*1000/(math.sqrt(3)*v*pf)
ip=ia/math.sqrt(3)
zs=x
iazs=ip*zs
phi=math.acos(pf)
eb=math.sqrt(v**2+iazs**2-(2*v*iazs*(-1)*pf))
alpha=math.asin(iazs*math.sin(theta+phi)/eb)

#result
print "excitation emf=",eb,"V"
print "rotor angle=",math.degrees(alpha),"degrees"

excitation emf= 4972.19098879 V
rotor angle= 17.0098509277 degrees


## Example Number 38.23, Page Number:1517¶

In [158]:
import math
#variable declaration
inpt=75#kW
v=400#V
r=0.04#ohm
x=0.4#ohm
pf=0.8
efficiency=0.925

#calculations
input_m=inpt*1000/efficiency
ia=input_m/(math.sqrt(3)*v)
zs=math.sqrt(r**2+x**2)
iazs=ia*zs
phi=math.atan(x/r)
vp=v/math.sqrt(3)
eb=math.sqrt(vp**2+iazs**2-(2*vp*iazs*math.cos(theta+phi)))
cu_loss=3*ia**2*r
ns=120*50/40
pm=input_m-cu_loss
tg=9.55*pm/ns

#result
print "emf=",eb,"eb"
print "mechanical power=",pm,"W"

emf= 235.683320812 eb
mechanical power= 79437.5456538 W


## Example Number 38.24, Page Number:1517¶

In [161]:
import math
#variable declaration
v=400#V
f=50#Hz
r=0.5#ohm
zs=x=4#ohm
i=15#A
i2=60#A

#calculations
vp=v/math.sqrt(3)
iazs=i*zs
xs=math.sqrt(x**2-r**2)
theta=math.atan(xs/r)
eb=math.sqrt(vp**2+iazs**2-(2*vp*iazs*math.cos(theta)))
iazs2=i2*zs
phi=theta-math.acos(vp**2-vp**2+iazs2**2/(2*vp*iazs2))
pf=math.cos(phi)
input_m=math.sqrt(3)*v*i2*pf
cu_loss=3*i2**2*r
pm=input_m-cu_loss
ns=120*50/6
tg=9.55*pm/ns

#result
print "gross torque developed=",tg,"N-m"
print "new power factor=",pf

gross torque developed= 310.739709828 N-m
new power factor= 0.912650996943


## Example Number 38.25, Page Number:1518¶

In [164]:
import math
#variable declaration
v=400#V
inpt=7.46#kW
xs=10#W/phase
efficiency=0.85

#calculations
input_m=inpt*1000/efficiency
il=input_m/(math.sqrt(3)*v)
zs=il*xs
vp=v/math.sqrt(3)
eb=math.sqrt(vp**2+zs**2)

#result
print "minimum current=",il,"A"
print "inducedemf=",eb,"V"

minimum current= 12.6677441416 A
inducedemf= 263.401798584 V


## Example Number 38.26, Page Number:1518¶

In [206]:
import math
#variable declaration
v=400#V
f=50#Hz
inpt=37.5#kW
efficiency=0.88
zs=complex(0.2,1.6)
pf=0.9

#calculations
input_m=inpt/efficiency
ia=input_m*1000/(math.sqrt(3)*v*pf)
vp=v/math.sqrt(3)
er=ia*abs(zs)
phi=math.acos(pf)
theta=math.atan(zs.imag/zs.real)
eb=math.sqrt(vp**2+er**2-(2*vp*er*math.cos(theta+phi)))
alpha=math.asin(math.sin(theta+phi)*er/eb)
pm=3*eb*vp*math.sin(alpha)/abs(zs)
#result
print "excitation emf=",eb*math.sqrt(3),"V"
print "total mechanical power developed=",pm,"W"

excitation emf= 495.407915636 V
total mechanical power developed= 44844.4875189 W


## Example Number 38.27, Page Number:1519¶

In [228]:
import math
import scipy
from sympy.solvers import solve
from sympy import Symbol
#variable declaration
v=6600.0#V
xs=20.0#ohm
inpt=1000.0#kW
pf=0.8
inpt2=1500.0#kW
phi2=Symbol('phi2')
#calculations
vp=v/math.sqrt(3)
ia=inpt*1000/(math.sqrt(3)*v*pf)
er=ia*xs
zs=xs
phi=math.acos(pf)
eb=math.sqrt(vp**2+er**2-(2*vp*er*math.cos(theta+phi)))
alpha=math.asin(inpt2*1000*zs/(3*eb*vp))
#vp/eb=cos(alpha+phi2)/cos(phi2)
#solving we get
pf=math.cos(phi2)
#result
print "new power factor=",pf

new power factor= 0.943280616635


## Example Number 38.28, Page Number:1519¶

In [229]:
import math
#variable declaration
v=400#V
x=4#ohms/phase
r=0.5#ohms/phase
ia=60#A
pf=0.866
loss=2#kW

#calculations
vp=v/math.sqrt(3)
zs=abs(complex(r,x))
phi=math.acos(pf)
iazs=ia*zs
theta=math.atan(x/r)
eb=math.sqrt(vp**2+iazs**2-(2*vp*iazs*math.cos(theta+phi)))
pm_max=(eb*vp/zs)-(eb**2*r/zs**2)
pm=3*pm_max
output=pm-loss*1000

#result
print "maximum power output=",output/1000,"kW"

maximum power output= 51.3898913442 kW


## Example Number 38.29, Page Number:1519¶

In [231]:
import math
#variable declaration
z=10#ohm
x=0.5#ohm
v=2000#V
f=25#Hz
eb=1600#V

#calculations
pf=x/z
pm_max=(eb*v/z)-(eb**2*pf/zs)
ns=120*f/6
tg_max=9.55*pm_max/ns

#result
print "maximum total torque=",tg_max,"N-m"

maximum total torque= 5505.51976175 N-m


## Example Number 38.30, Page Number:1520¶

In [234]:
import math
#variabke declaration
v=2000#V
n=1500#rpm
x=3#ohm/phase
ia=200#A

#calculations
eb=vp=v/math.sqrt(3)
zs=ia*x
sinphi=(eb**2-vp**2-zs**2)/(2*zs*vp)
phi=math.asin(sinphi)
pf=math.cos(phi)
pi=math.sqrt(3)*v*ia*pf/1000
tg=9.55*pi*1000/n

#result
print "power input=",pi,"kW"
print "power factor=",pf
print "torque=",tg,"N-m"

power input= 669.029147347 kW
power factor= 0.965660395791
torque= 4259.48557144 N-m


## Example Number 38.31, Page Number:1520¶

In [235]:
import math
#variable declaration
v=3300#V
r=2#ohm
x=18#ohm
e=3800#V

#calculations
theta=math.atan(x/r)
vp=v/math.sqrt(3)
eb=e/math.sqrt(3)
alpha=theta
er=math.sqrt(vp**2+eb**2-(2*vp*eb*math.cos(theta)))
zs=math.sqrt(r**2+x**2)
ia=er/zs
pm_max=((eb*vp/zs)-(eb**2*r/zs**2))*3
cu_loss=3*ia**2*r
input_m=pm_max+cu_loss
pf=input_m/(math.sqrt(3)*v*ia)

#result
print "maximum total mechanical power=",pm_max,"W"
print "current=",ia,"A"
print "pf=",pf

maximum total mechanical power= 604356.888001 W
current= 151.417346198 A
pf= 0.857248980398


## Example Number 38.32, Page Number:1521¶

In [240]:
import math
#variable declaration
v=415#V
e=520#V
z=complex(0.5,4)
loss=1000#W

#calculations
theta=math.atan(z.imag/z.real)
er=math.sqrt(v**2+e**2-(2*v*e*math.cos(theta)))
zs=abs(z)
i=er/zs
il=math.sqrt(3)*i
pm_max=((e*v/zs)-(e**2*z.real/zs**2))*3
output=pm_max-loss
cu_loss=3*i**2*z.real
input_m=pm_max+cu_loss
pf=input_m/(math.sqrt(3)*il*v)
efficiency=output/input_m

#result
print "power output=",output/1000,"kW"
print "line current=",il,"A"
print "power factor=",pf
print "efficiency=",efficiency*100,"%"

power output= 134.640174346 kW
line current= 268.015478962 A
power factor= 0.890508620247
efficiency= 78.4816159071 %


## Example Number 38.33, Page Number:1524¶

In [243]:
import math
#variable declaration
v=400#V
inpt=37.3#kW
efficiency=0.88
z=complex(0.2,1.6)
pf=0.9

#calculations
vp=v/math.sqrt(3)
zs=abs(z)
il=inpt*1000/(math.sqrt(3)*v*efficiency*pf)
izs=zs*il
theta=math.atan(z.imag/z.real)
phi=math.acos(pf)
eb=math.sqrt(vp**2+izs**2-(2*vp*izs*math.cos(theta+phi)))
input_m=inpt*1000/efficiency
cu_loss=3*il**2*z.real
pm=input_m-cu_loss

#result
print "induced emf=",eb*math.sqrt(3),"V"
print "total mechanical power=",pm/1000,"kW"

induced emf= 494.75258624 V
total mechanical power= 39.6138268735 kW


## Example Number 38.34, Page Number:1525¶

In [251]:
import math
#variable declaration
inpt=48#kW
v=693#V
pf=0.8
ratio=0.3
x=2#W/phase

#calculations
il=inpt*1000/(math.sqrt(3)*v*pf)
vp=v/math.sqrt(3)
zs=x
izs=zs*il
theta=math.atan(float("inf"))
phi=math.acos(pf)
eb=math.sqrt(vp**2+izs**2-(2*vp*izs*math.cos(theta-phi)))
i_cosphi=pf*il
bc=i_cosphi*x
eb=eb+(ratio*eb)
ac=math.sqrt(eb**2-bc**2)
oc=ac-vp
phi2=math.atan(oc/bc)
pf=math.cos(phi2)
i2=i_cosphi/pf

#result
print "current=",i2,"A"
print "pf=",pf

current= 46.3871111945 A
pf= 0.862084919821


## Example Number 38.35, Page Number:1526¶

In [253]:
import math
#variable declaration
inpt=240.0#kW
pf=0.8
pf2=0.9

#calculations
phi=math.acos(pf2)
phil=math.acos(pf)
kVAR=inpt*math.tan(phil)
kVA=inpt/pf
#synchronous motor

leading kVAR supplied by the motor= 60.0