# Example 5.1
# Computation of minimum value of (a) Locked rotor torque (b) Breakdown torque
# (c) Pull up torque
# Page No. 173
# Given data
f=60.; # Frequency in Hz
p=6.; # Number of poles
hp=10.; # Horsepower
n=1150.; # Rated speed of machine
ns=120.*f/p;
# (a) Locked rotor torque
Trated=hp*5252./n; # Rated torque
Tlockedrotor=2.25*Trated;
# (b) Breakdown torque
Tbreakdown=1.90*Trated;
# (c) Pull up torque
Tpullup=1.65*Trated;
# Display result on command window
print"Locked rotor torque =",Tlockedrotor,"lb-ft"
print"Breakdown torque =",Tbreakdown,"lb-ft"
print"Pull up torque =",Tpullup,"lb-ft"
# Example 5.2
# Determine (a) Slip (b) Line current (c) Apparent power, active power,
# reactive power and power factor of the motor (d) Equivalent rotor curret
# (e) Stator copper loss (f) Rotor copper loss (g) Core loss (h) Air-gap
# power (i) Mechanical power developed (j) Developed torque (k) Shaft
# horsepower (l) Shaft torque (m) Effiency
# Page No. 180
# Given data
from math import sqrt,pi,sin,cos
f=60.; # Frequency
P=6.; # Number of poles
nr=1185.;
R1=0.200; # Motor resistance
R2=0.250;
X1=1.20; # Motor reactance
X2=1.29;
Rfe=317.; # Field resistance
XM=42.; # Motor reactance
V=460.; # Voltage rating
PFPS=166.; # Stray loss
# (a) Slip
ns=(120.*f)/P;
s=(ns-nr)/ns; # Speed difference
# (b) Line current
Z2=20 + 1.29j;#(R2/s)+%i*X2;
# Complex to Polar form...
Z2_Mag=20.;#sqrt(real(Z2)**2+imag(Z2)**2); # Magnitude part
Z2_Ang =3.69;#atan(imag(Z2),real(Z2))*180/%pi; # Angle part
Z0_Num_Mag=Rfe*XM; # Z0 numerator
Z0_Num_Ang=0+90;
Z0_Den_R=Rfe; # Z0 denominator
Z0_Den_I=XM;
Z0_Den=317 + 42j;#Z0_Den_R+%i*Z0_Den_I;
# Complex to Polar form...
Z0_Den_Mag=320.;#sqrt(real(Z0_Den)**2+imag(Z0_Den)**2); # Magnitude part
Z0_Den_Ang =7.55;#atan(imag(Z0_Den),real(Z0_Den))*180/%pi; # Angle part
Z0_Mag=Z0_Num_Mag/Z0_Den_Mag; # Magnitude of Z0
Z0_Ang=Z0_Num_Ang-Z0_Den_Ang; # Angle of Z0
# Polar to Complex form
Z0_R=Z0_Mag*cos(-Z0_Ang*pi/180); # Real part of complex number
Z0_I=Z0_Mag*sin(Z0_Ang*pi/180); # Imaginary part of complex number
# ZP computation
ZP_Num_Mag=Z2_Mag*Z0_Mag; # ZP numerator magnitude
ZP_Num_Ang=Z2_Ang+Z0_Ang; # ZP numerator angle
ZP_Den_R=25.5;#real(Z2)+Z0_R; # Real part of ZP denominator
ZP_Den_I=42.6;#imag(Z2)+Z0_I;
ZP_Den=25.5 + 42.6j;#lZP_Den_R+%i*ZP_Den_I; # ZP in complex form
# Complex to Polar form...
ZP_Den_Mag=49.6;#sqrt(real(ZP_Den)**2+imag(ZP_Den)**2); # Magnitude part
ZP_Den_Ang =59.1;#atan(imag(ZP_Den),real(ZP_Den))*180/%pi; # Angle part
ZP_Mag=ZP_Num_Mag/ZP_Den_Mag; # Final vlaue of ZP in polar form
ZP_Ang=ZP_Num_Ang-ZP_Den_Ang;
# Polar to Complex form
ZP_R=ZP_Mag*cos(-ZP_Ang*pi/180); # Real part of complex number
ZP_I=ZP_Mag*sin(ZP_Ang*pi/180); # Imaginary part of complex number
# Zin computation
ZP=15 + 7.65j;#ZP_R+%i*ZP_I; # Parallel impedance
Z1=0.2 + 1.2j;#R1+%i*X1;
Zin=Z1+ZP; # Input impedance
# Complex to Polar form...
Zin_Mag=17.6;#sqrt(real(Zin)**2+imag(Zin)**2); # Magnitude part
Zin_Ang =30.2;#atan(imag(Zin),real(Zin))*180/%pi; # Angle part
# I1 computation
I1_Mag=(V/sqrt(3.))/Zin_Mag; # I1 magnitude
I1_Ang=0-Zin_Ang; # I1 angle
# (c) Apparent power, active power, reactive power and power factor of the motor
S_Mag=3.*(V/sqrt(3.))*I1_Mag; # S magnitude
S_Ang=0-(-Zin_Ang); # S angle
# Polar to Complex form
S_R=S_Mag*cos(-S_Ang*pi/180); # Real part of complex number
S_I=S_Mag*sin(S_Ang*pi/180); # Imaginary part of complex number
FP=0.864;#cosd(S_Ang); # Power factor
# (d) Equivalent rotor curret
E2_Mag=I1_Mag*ZP_Mag; # E2 magnitude
E2_Ang=I1_Ang+ZP_Ang; # E2 angle
I2_Mag=E2_Mag/Z2_Mag; # I2 magnitude
I2_Ang=E2_Ang-Z2_Ang; # I2 angle
# (e) Stator copper loss
Pscl=3.*I1_Mag**2.*R1;
# (f) Rotor copper loss
Prel=3.*I2_Mag**2.*R2;
# (g) Core loss
Pcore=3.*(E2_Mag**2./Rfe);
# (h) Air-gap power
Pgap=Prel/s;
# (i) Mechanical power developed
Pmech=Prel*(1.-s)/s;
# (j) Developed torque
TD=(21.12*I2_Mag**2*R2)/(s*ns);
# (k) Shaft horsepower
LOSS=Pscl+Prel+Pcore+PFPS;
Pshaft=(S_R-LOSS)/746.;
# (l) Shaft torque
T=5252.*Pshaft/nr;
# (m) Effiency
eta=Pshaft/S_R*746.;
# Display result on command window
print"\nSlip =",s
print"\nLine current magnitude =",I1_Mag,"A"
print"\nLine current angle =",I1_Ang,"deg"
print"\nApparent power =",S_R,"W"
print"\nActive power =",S_I,"var"
print"\nReactive power =",S_Mag,"VA"
print"\nPower factor of the motor =",FP
print"\nEquivalent rotor curret magnitude =",I2_Mag,"A"
print"\nEquivalent rotor curret angle =",I2_Ang,"deg"
print"\nStator copper loss =",Pscl,"W"
print"\nRotor copper loss =",Prel,"W"
print"\nCore loss =",Pcore,"W"
print"\nAir-gap power =",Pgap,"W"
print"\nMechanical power developed =",Pmech,"W"
print"\nDeveloped torque =",TD,"lb-ft"
print"\nShaft horsepower =",Pshaft,"hp"
print"\nShaft torque =",T,"lb-ft"
print"\nEffiency =",eta
# Example 5.3
# Computation of (a) Speed at which maximum torque is developed (b) Maximum
# torque that the machine can develop (c) Rated shaft torque (d) Which NEMA
# design fits this motor?
# Page No. 184
# Given data
from math import sqrt
f=60.; # Frequency in Hz
p=4.; # Number of poles
hp=40.; # Horsepower
n=1751.; # Rated speed of machine
v=460./sqrt(3.); # Voltage
s=0.1490; # Slip
R2=0.153; # Rotor resistance
R1=0.102;
X1=0.409; # Rotor reactance
X2=0.613;
# (a) Speed at which maximum torque is developed
STDmax=R2/(sqrt(R1**2.+(X1+X2)**2.));
ns=120.*f/p; #stator spped
nr=ns*(1.-s);
# (b) Maximum torque that the machine can develop
TDmax=(21.12*v**2.)/(2.*ns*(sqrt(R1**2.+(X1+X2)**2.)+R1));
# (c) Rated shaft torque
TDshaft=hp*5252./n;
# Display result on command window
print"\nSpeed at which maximum torque is developed =",nr,"r/min"
print"\nMaximum torque that the machine can develop =",TDmax,"lb-ft"
print"\nRated shaft torque =",TDshaft,"lb-ft"
print"\nMaximum torque is developed at slip of 0.1490 and \nhence machine is placed in design A category"
# Example 5.4
# Computation of (a) Amount of torque that must be removed from the motor
# shaft to maintain 1760r/min (b) Expected minimum startimg torque for the
# lower voltage (c) Percent change in developed torque caused by 10% drop in
# system voltage.
# Page No. 185
# Given data
hp=50.; # Horsepower
n=1760.; # Rated speed of machine
v1=460.;
# (a) Amount of torque that must be removed from the motor shaft to maintain
# 1760r/min
v2=v1*0.90;
Trated=hp*5252./n; #Rated torque
TD2=Trated*(v2/v1)**2.;
Treduction=Trated-TD2;
# (b) Expected minimum startimg torque for the lower voltage
Tlr=1.40*Trated;
Tlr2=Tlr*(v2/v1)**2;
# (c) Percent change in developed torque caused by 10% drop in system voltage
Tchange=(TD2-Trated)/Trated;
Tchanger=(Tlr2-Tlr)/Tlr;
# Display result on command window
print"\n Amount of torque that must be removed from the motor shaft =",Treduction,"lb-ft"
print"\n Expected minimum starting torque for the lower voltage =",Tlr2,"lb-ft"
print"\n Percent change in developed torque =",Tchanger*100,"Percent"
# Example 5.5
# Computation of minimum value of (a) Shaft speed (b) Rotor current referred
# to the stator
# Page No. 187
# Given data
from math import sqrt
f=60.; # Frequency in Hz
p=12.; # Number of poles
nr=591.1; # Rated speed of machine
v=575.; # Voltage rating of the machine
R2=0.055;
# (a) Shaft speed
ns=120.*f/p; # Speed (r/min)
s1=(ns-nr)/ns; # Slip 1
s2=1.25*s1; # Slip 2
nr1=ns*(1.-s2);
# (b) Rotor current referred to the stator
V=v/sqrt(3.);
I2=V*s2/R2;
# Display result on command window
print"\nShaft speed =",nr1,"r/min"
print"\nRotor current referred to the stator =",I2,"A"
# Example 5.6
# Determine (a) New operating speed if a system disturbance causes a 10% drop
# in voltage and 6% drop in frequency (b) New shaft horsepower.
# Page No. 190
# Given data
etaV=0.90; # Efficiency related to voltage
V=230.; # Voltage
etaF=0.94; # Efficiency related to voltage
f=60.; # Frequency
N=6.; # Number of poles
nr1=1175.; # Speed of motor
P=20.; # Horsepower of motor
# (a) New operating speed if a system disturbance causes a 10% drop in
# voltage and 6% drop in frequency
V2=etaV*V; # New voltage after 10% drop
f2=etaF*f; # New frequency after 6% drop
ns1=120.*f/N;
ns2=120.*0.94*f/N;
s1=(ns1-nr1)/ns1; # Speed difference
s2=s1*((V/V2)**2.)*(f2/f);
nr2=ns2*(1.-s2); # New speed
# (b) New shaft horsepower
P2=P*(nr2/nr1); # With a constant torque load T2=T1
# Display result on command window
print"\nNew operating speed in case of voltage and frequency drop =",nr2,"r/min"
print"\nNew shaft horsepower =",P2,"hp"
# Example 5.7
# Determine expected locked-rotor line current
# Page No. 192
# Given data
Ir1=151.; # Rated current
V1=230.; # Rated voltage
V2=220.; # Motor starting voltage
F1=60.; # Rated frequency
F2=50.; # Motor starting frequency
# Expected locked-rotor line current
Ir2=Ir1*((V2/F2)/(V1/F1));
# Display result on command window
print"\n Expected locked-rotor line current =",Ir2,"A"
# Example 5.8
# Determine (a) Expected minimum locked-rotor torque (b) Repeat (a) when
# voltage and frequency dropped to 230V and 58Hz
# Page No. 193
# Given data
HPrated=75.; # Rated horsepower
nrated=1750.; # Rated speed
V1=240.; # Rated voltage
V2=230.; # Voltage after drop
F1=60.; # Rated frequency
F2=58.; # Frequency after drop
# (a) Expected minimum locked-rotor torque
Trated=5252.*HPrated/nrated; # Rated torque
Tlr=Trated*1.2; # Minimum locked-rotor torque is 120% rated
# (b) Expected minimum locked-rotor torque when voltage and frequency dropped
# to 230V and 58Hz
Tlr2=Tlr*((V2/F2)**2.)*((F1/V1)**2.);
# Display result on command window
print"\nExpected minimum locked-rotor torque =",Tlr,"lb-ft"
print"\nExpected minimum locked-rotor torque after drop =",Tlr2,"lb-ft"
# Example 5.9
# Determine (a) Shaft r/min (b) Slip
# Page No. 194
# Given data
from math import sqrt
F1=60.; # Rated frequency
N=4.; # Number of poles
F2=50.; # New frequency
ns=1770.; # Rated speed
# (a) Shaft r/min
ns60=120.*F1/N; # Speed at rated ferquency
ns50=120.*F2/N; # Speed at 50 Hz frequency
s60=(ns60-ns)/ns60; # Slip at 60 Hz frequency
# Using eq. (5.16) and by solving..s50=29.251/nr50
# Using eq. (4.3) and solving for nr50 we get the quadratic equation..
# Using various values of quadratic equations, we have
a=1.;
b=-1500.;
c=43876.5;
r1=(-b+sqrt(b**2-4*a*c))/(2.*a); # Root 1
r2=(-b-sqrt(b**2-4*a*c))/(2.*a); # Root 2
# Answer 'r2' is not valid
# (b) Slip
s50=(ns50-r1)/ns50;
# Display result on command window
print"\nShaft speed =",r1,"r/min"
print"\nSlip =",s50
# Example 5.10
# Determine (a) Range of rotor speed (b) Required rheostat resistance
# Page No. 198
# Given data
from math import sqrt
F=60.; # Frequency of motor
P=14.; # Number of poles
SL=0.395; # Low speed point
SH=0.02; # High speed point
Stdmax=0.74; # Value at which TD is maximum (from curve B)
R1=0.403; # Motor resistance
R2=0.317;
X1=1.32; # Motor reactance
X2=1.32;
a=3.8; # Ratio of stator turns/phase to rotor turns/phase
# (a) Range of rotor speed
ns=120.*F/P; # Speed
nrl=ns*(1.-SL); # Rotor low speed
nrh=ns*(1.-SH); # Rotor high speed
# (b) Required rheostat resistance
Rrhe=Stdmax*(sqrt(R1**2.+(X1+X2)**2.))-R2;
Rehereq=Rrhe/a**2.;
# Display result on command window
print"\n Low range of rotor speed =",nrl,"r/min"
print"\n High range of rotor speed =",nrh,"r/min"
print"\n Required rheostat resistance =",Rehereq,"Ohm/phase"
# Example 5.11
# Determine (a) Rotor frequency (b) Slip at which TDmax occurs (c) Rotor speed
# at 1/2 rated torque load (d) Required rheostat resistance (e) Rated torque
# Page No. 201
# Given data
from math import sqrt
S=0.0159; # Slip
Fbr=50.; # Rated frequency
R1=0.00536; # Motor resistance
R2=0.00613;
X1=0.0383; # Motor reactance
X2=0.0383;
Rrhe=0; # Initial rheostat resistance
P=4.; # Number of poles
NR=1000.; # Rated speed
s1=0.0159; # Slip of rheostat
a=2.; # Stator to rotor turns ratio
hp=400.; # Motor horsepower
# (a) Rotor frequency
fr=S*Fbr;
# (b) Slip at which TDmax occurs
Stdmax=(R2+Rrhe)/(sqrt(R1**2.+(X1+X2)**2.));
# (c) Rotor speed at 1/2 rated torque load
s=S*(0.5)*(R2/R2); # Rotor speed at 1/2 rated torque
ns=120.*Fbr/P;
nr=ns*(1.-s); # Rotor speed
# (d) Required rheostat resistance
s2=(ns-NR)/ns;
Rrhe2=((s2/s1)*(1./0.5)*(R2+Rrhe))-R2; # rheostat resistance
Rrheostat=Rrhe2/a**2.;
# (e) Rated torque
nr1=ns*(1.-s1); # Rated speed
T=hp*5252./nr1;
# Display result on command window
print"\n Rotor frequency =",fr,"Hz"
print"\n Slip at which TDmax occurs =",Stdmax
print"\n Rotor speed at 1/2 rated torque =",nr,"r/min"
print"\n Required rheostat resistance =",Rrheostat,"Ohm/phase"
print"\n Rated torque =",T,"lb-ft"
# Example 5.12
# Determine the percent increase or decrease in rotor circuit resistance
# Page No. 202
# Given data
Stdmax1=0.45; # Maximum torque condition 1
Stdmax2=0.80; # Maximum torque condition 2
# Percent increase or decrease in rotor circuit resistance
PerCh=1/(Stdmax1/Stdmax2);
PerCh=PerCh-1;
# Display result on command window
print"\nPercent change in rotor circuit resistance =",PerCh*100,"Percent increase"
# Example 5.13
# Determine the expected in-rush current
# Page No. 208
# Given data
from math import sqrt
kva1=5.6; # KVA/hp lower limit from table 5.9
hp=150.; # Motor horsepower
Vline=460.; # Line voltage
kva2=6.3; # KVA/hp upper limit from table 5.9
# Expected in-rush current
# Lower limit of expected range of in-rush current is
Ilrss=(kva1*hp*1000)/(sqrt(3)*Vline);
# Upper limit of expected range of in-rush current is
Iulss=(kva2*hp*1000)/(sqrt(3)*Vline);
# Display result on command window
print"\n Lower limit of expected range of in-rush current =",Ilrss,"A"
print"\n Upper limit of expected range of in-rush current =",Iulss,"A"
# Example 5.14
# Determine (a) Percent voltage unbalance (b) Expected approximate temp. rise
# if operating at rated load in a 40 deg ambient (c) Expected insulation life
# (d) Required derating of motor to prevent shortening isulation life.
# Page No. 211
# Given data
from math import sqrt
VL1=460.; # Line voltage 1
VL2=455.; # Line voltage 2
VL3=440.; # Line voltage 3
Trated=110.; # Rated temp. (from table 5.8)
hp=30.; # Motor horsepower
# (a) Percent voltage unbalance
Vavg=(VL1+VL2+VL3)/3.; # Average line voltage
#VD1=abs(VL1-Vavg); # Voltage deviation from the average
#VD2=abs(VL2-Vavg);
#VD3=abs(VL3-Vavg);
#VD=[VD1 VD2 VD3];
#VDMax=max(VD); # Choose maximum value of voltage deviation
PerUBV=2.58;#(VDMax/Vavg)*100;
# (b) Expected approximate temp. rise if operating at rated load in a 40 deg
PerDeltaT=2.*PerUBV**2.; # Percent change in temp.
Tubv=Trated*(1.+(PerDeltaT/100.));
# (c) Expected insulation life
DeltaT=Tubv-Trated; # Percent increase in motor temp.
RL=1./(2.**(DeltaT/10.)); # Relative life on insulation
EL=RL*20;
# (d) Required derating of motor to prevent shortening isulation life
ReqDer=hp*0.92;
# Display result on command window
print"\nPercent voltage unbalance =",PerUBV
print"\nExpected approximate temperature rise =",Tubv,"deg C"
print"\n Expected insulation life =",EL,"years"
print"\n Required derating of motor =",ReqDer,"hp"
# Example 5.15
# Determine the machine parameters in ohms
# Page No. 213
# Given data
from math import sqrt
V=460.; # Motor voltage
hp=50.; # Motor horsepower
r1=0.021; # Resistance
r2=0.020;
x1=0.100; # Reactance
x2=0.0178;
rfe=20.;
Xm=3.68; # Motor reactance
# Machine parameters in ohms
Vbase=V/sqrt(3.); # Base voltage
Pbase=hp*746./3.; # Base power
Zbase=Vbase**2./Pbase; # Base impedance
R1=r1*Zbase;
X1=x1*Zbase;
R2=r2*Zbase;
X2=x2*Zbase;
Rfe=rfe*Zbase;
XM=Xm*Zbase;
# Display result on command window
print"\n Motor resistance 1 =",R1,"Ohm"
print"\n Motor reactance 1 =",X1,"Ohm"
print"\n Motor resistance 2 =",R2,"Ohm"
print"\n Motor reactance 2 =",X2,"Ohm"
print"\n Field resistance =",Rfe,"Ohm"
print"\n Reactance of motor =",XM,"Ohm"
# Example 5.16
# Determine (a) R1, R2, X1, X2, XM and the combined core, friction and windage
# loss (b) Express the no-load current as a percent of rated current
# Page No. 218
# Given data
from math import sqrt
P3ph=2573.4; # 3-ph power of induction motor
Vline=36.2; # Line voltage
Iline=58; # Line current
P3phnl=4664.4; # No load power
Vlinenl=460.; # No load line volatge
Ilinenl=32.7; # No load line current
Vdc=12.; # DC voltage
Idc=59.; # DC current
F1=60.; # Rated frequency
F2=15.; # Test frequency
Irated=57.8; # Rated current
# (a) R1, R2, X1, X2, XM and the combined core, friction and windage loss
Pbr15=P3ph/3.; # Power/phase
Vbr15=Vline/sqrt(3.); # Voltage/phase
Ibr15=Iline;
PNL=P3phnl/3.; # No load power/phase
VNL=Vlinenl/sqrt(3.); # No load voltage/phase
INL=Ilinenl; # No load current/phase
# Determination of R1
Rdc=Vdc/Idc;
R1=Rdc/2.;
# Determination of R2
Zbr15=Vbr15/Ibr15; # Impedance
Rbr15=Pbr15/Ibr15**2.;
R2=Rbr15-R1;
# Determination of X1 and X2
Xbr15=sqrt(Zbr15**2.-Rbr15**2.);
Xbr60=Xbr15*(F1/F2);
X1=0.4*Xbr60; # From Table 5.10
X2=0.6*Xbr60;
# Determination of XM
SNL=VNL*INL;
QNL=sqrt(SNL**2.-PNL**2.);
XNL=QNL/INL**2.;
XM=XNL-X1;
# Determination of combined friction, windage and core loss
Ploss=PNL-(INL**2.*R1);
# (b) No-load current as a percent of rated current
PerINL=INL*100./Irated;
# Display result on command window
print"\n Motor resistance 1 =",R1,"Ohm/phase"
print"\n Motor reactance 1 =",X1,"Ohm/phase"
print"\n Motor resistance 2 = ",R2,"Ohm/phase"
print"\n Motor reactance 2 =",X2,"Ohm/phase"
print"\n Reactance of motor =",XM,"Ohm/phase"
print"\n Combined friction, windage and core loss =",Ploss,"W/phase"
print"\n No-load current as a percent of rated current =",PerINL,"Percent"
# Example 5.17
# Determine the active power that the motor, driven as an induction generator
# delivers to the system.
# Page No. 223
# Given data
from math import sqrt,pi,sin,cos
ns=1200.; # Speed
nr=1215.;
R1=0.200; # Motor resistance
R2=0.250;
X1=1.20; # Motor reactance
X2=1.29;
Rfe=317.; # Field resistance
XM=42.; # Motor reactance
V=460.; # Voltage rating
# Active power of the motor computation
s=(ns-nr)/ns; # Speed difference
Z2=-20 + 1.29j;#(R2/s)+%i*X2;
# Complex to Polar form...
Z2_Mag=20.;#sqrt(real(Z2)**2+imag(Z2)**2); # Magnitude part
Z2_Ang =176.;#atan(imag(Z2),real(Z2))*180/%pi; # Angle part
Z0_Num_Mag=Rfe*XM; # Z0 numerator
Z0_Num_Ang=0+90;
Z0_Den_R=Rfe; # Z0 denominator
Z0_Den_I=XM;
Z0_Den=317 + 42j;#Z0_Den_R+%i*Z0_Den_I;
# Complex to Polar form...
Z0_Den_Mag=320.;#sqrt(real(Z0_Den)**2+imag(Z0_Den)**2); # Magnitude part
Z0_Den_Ang =7.55;#atan(imag(Z0_Den),real(Z0_Den))*180/%pi; # Angle part
Z0_Mag=Z0_Num_Mag/Z0_Den_Mag; # Magnitude of Z0
Z0_Ang=Z0_Num_Ang-Z0_Den_Ang; # Angle of Z0
# Polar to Complex form
Z0_R=Z0_Mag*cos(-Z0_Ang*pi/180); # Real part of complex number
Z0_I=Z0_Mag*sin(Z0_Ang*pi/180); # Imaginary part of complex number
# ZP computation
ZP_Num_Mag=Z2_Mag*Z0_Mag; # ZP numerator magnitude
ZP_Num_Ang=Z2_Ang+Z0_Ang; # ZP numerator angle
ZP_Den_R=-14.5;#real(Z2)+Z0_R; # Real part of ZP denominator
ZP_Den_I=42.6;#imag(Z2)+Z0_I;
ZP_Den=-14.5 + 42.6j;#ZP_Den_R+%i*ZP_Den_I; # ZP in complex form
# Complex to Polar form...
ZP_Den_Mag=45.;#sqrt(real(ZP_Den)**2+imag(ZP_Den)**2); # Magnitude part
ZP_Den_Ang =109.;# atan(imag(ZP_Den),real(ZP_Den))*180/%pi; # Angle part
ZP_Mag=ZP_Num_Mag/ZP_Den_Mag; # Final vlaue of ZP in polar form
ZP_Ang=ZP_Num_Ang-ZP_Den_Ang;
# Polar to Complex form
ZP_R=ZP_Mag*cos(-ZP_Ang*pi/180); # Real part of complex number
ZP_I=ZP_Mag*sin(ZP_Ang*pi/180); # Imaginary part of complex number
# Zin computation
ZP=-16.1 + 9.3j;#ZP_R+%i*ZP_I; # Parallel impedance
Z1=0.2 + 1.2j;#R1+%i*X1;
Zin=Z1+ZP; # Input impedance
# Complex to Polar form...
Zin_Mag=19.;#sqrt(real(Zin)**2+imag(Zin)**2); # Magnitude part
Zin_Ang =146.;#atan(imag(Zin),real(Zin))*180/%pi; # Angle part
# I1 computation
I1_Mag=(V/sqrt(3))/Zin_Mag; # I1 magnitude
I1_Ang=0-Zin_Ang; # I1 angle
# S computation
S_Mag=3*(V/sqrt(3))*I1_Mag; # S magnitude
S_Ang=0-(-Zin_Ang); # S angle
# Polar to Complex form
S_R=S_Mag*cos(-S_Ang*pi/180); # Real part of complex number
S_I=S_Mag*sin(S_Ang*pi/180); # Imaginary part of complex number
# Display result on command window
print"Active power of the motor =",S_R,"W"
# Example 5.18
# Computation of (a) Locked rotor torque and the expected average in rush
# current (b) Repeat part (a) assuming motor is started at reduced voltage
# with 65% tap (c) In rush line current line current when starting at reduced
# voltage
# Page No. 231
# Given data
from math import sqrt
P=125.; # Rated Voltage
n=1141.; # Speed of machine
hp=125.; # Horsepower rating of device
Vline=460.; # Line voltage
ns=1200.; # Stator speed
s=0.125; # Slip
ILS=683.; # Current at low side
# (a) Locked rotor torque and the expected average in rush current
Trated=P*5252./(n); # Rated torque
Tlr=1.25*Trated; # Locked rotor torque
kVA=(6.3+7.1)/2.;
Ilr=(kVA*1000.*hp)/(Vline*sqrt(3.)); # In-rush current
# (b) Locked rotor torque and the expected average in rush current when motor
# is started at reduced voltage
V2=0.65*Vline; # Voltage impressed across the stator
I=Ilr*0.65; # Average in-rush current
T2=Tlr*(V2/Vline)**2.; # Locked rotor toreque
nr=ns*(1.-s);
# (c) In rush line current line current when starting at reduced voltage
a=1./0.65; # Bank ratio of autotransformer
IHS=ILS/a;
# Display result on command window
print"\nLocked rotor torque =",Tlr,"lb-ft"
print"\nExpected average in-rush current =",Ilr,"A"
print"\nLocked rotor torque when motor is started at reduced voltage =",T2,"lb-ft"
print"\nIn-rush line current =",IHS,"A"
# Example 5.19
# Computation of (a) Locked rotor current per phase and minimum locked rotor
# torque when starting (b) Locked rotor current per phase when motor is delta
# connected (c) Code letter
# Page No.233
# Given data
from math import sqrt
V=460.; # Rated Voltage
Z=0.547; # Locked rotor impedance
n=1750.; # Speed of machine
hp=60.; # Horsepower rating of device
f=60.; # Frequency of motor
# (a) Locked rotor current per phase and minimum locked rotor torque
Vphase=V/sqrt(3.); # Voltage/phase
Ilr1=Vphase/Z; # Locked rotor current/phase
Trated=hp*5252./(n); # Rated torque
Tlr=1.4*Trated; # Locked rotor torque
T2=Tlr*(Vphase/V)**2.;
# (b) Locked rotor current per phase when motor is delta connected
Ilr=V/Z; # Locked rotor current/phase
Il=Ilr*sqrt(3.); # Line current
# (c) Code letter
Slr=sqrt(3.)*V*Il/1000.; # Code letter at rated voltage
kVA=Slr/f;
# Display result on command window
print"\n Locked rotor current per phase =",Ilr1,"A"
print"\n Minimum locked rotor torque =",T2,"lb-ft"
print"\n Locked rotor current per phase when motor is delta connected =",Il,"A"
print"\n Code letter =",kVA
# Example 5.20
# Computation of (a) Resistance of the resistors required to limit the locked
# rotor current to 3 times rated current (b) Stator voltage per phase at
# locked rotor (c) Expected minimum locked rotor torque when starting as a
# percent of rated torque
# Page No. 235
# Given data
from math import sqrt
Ilr=3.*78.; # Locked rotor current
Vbranch=132.79; # Branch voltage
Rlr=0.2549; #Locked rotor resistance
Xlr=0.0978; #Locked rotor impedance
f=60.; #Frequency of motor
Zlr=0.273;
# (a) Resistance of the resistors required to limit the locked rotor current
# to 3 times rated current
Rex=sqrt((Vbranch**2./Ilr**2.)-(Rlr**2.))-Xlr;
# (b) Stator voltage per phase at locked rotor
IZlr=Ilr*Zlr;
VT1_N=IZlr;
# (c) Expected minimum locked rotor torque when starting as a percent of
# rated torque
# From table 5.1 --> Minimum locked rotor torque = 150% rated torque
# Display result on command window
print"\nResistance of the resistors required =",Rex,"Ohm"
print"\nStator voltage per phase at locked rotor =",VT1_N,"V"
print'\nExpected minimum locked rotor torque = 1.5 Trated'
# Example 5.21
# Computation of Inductance and voltage rating of each series connected
# inductor required to limit the starting current to approximately 2*Irated.
# Page No. 236
# Given data
from math import sqrt,pi
KVA=6.7; # Average locked rotor KVA/hp
hp=7.5; # Motor horsepower
Vline=208.; # Line voltage
I=48.; # Total current
Rlr=0.294; # Locked rotor resistance
Xlr=0.809; # Locked rotor impedance
f=60.; # Frequency of motor
# Corresponding approximate load current
Ilr=KVA*1000.*hp/(sqrt(3.)*Vline);
Vphase=Vline/sqrt(3.); # Voltage/phase
# Applying ohm's law to one phase
Zlr=Vphase/Ilr; # Impedance
Xex=sqrt((Vphase**2./I**2.)-(Rlr**2.))-Xlr;
L=Xex/(2.*pi*f);
L=L*10.**03;
VXl=I*Xex;
# Display result on command window
print"\nThe inductance of each series connected inductor =",L,"mH"
print"\nThe voltage rating of each series connected inductor =",VXl,"V"