summaryrefslogtreecommitdiff
path: root/Electric_Machines_by_C._I._Hubert/CHAPTER05.ipynb
diff options
context:
space:
mode:
Diffstat (limited to 'Electric_Machines_by_C._I._Hubert/CHAPTER05.ipynb')
-rw-r--r--Electric_Machines_by_C._I._Hubert/CHAPTER05.ipynb1480
1 files changed, 1480 insertions, 0 deletions
diff --git a/Electric_Machines_by_C._I._Hubert/CHAPTER05.ipynb b/Electric_Machines_by_C._I._Hubert/CHAPTER05.ipynb
new file mode 100644
index 00000000..f3b97267
--- /dev/null
+++ b/Electric_Machines_by_C._I._Hubert/CHAPTER05.ipynb
@@ -0,0 +1,1480 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# CHAPTER05 : CLASSIFICATION PERFORMANCE APPLICATIONS AND OPERATION OF THREE PHASE INDUCTION MACHINES"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example E01 : Pg 173"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Locked rotor torque = 102.756521739 lb-ft\n",
+ "Breakdown torque = 86.772173913 lb-ft\n",
+ "Pull up torque = 75.3547826087 lb-ft\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Example 5.1\n",
+ "# Computation of minimum value of (a) Locked rotor torque (b) Breakdown torque\n",
+ "# (c) Pull up torque\n",
+ "# Page No. 173\n",
+ "# Given data\n",
+ "f=60.; # Frequency in Hz\n",
+ "p=6.; # Number of poles\n",
+ "hp=10.; # Horsepower\n",
+ "n=1150.; # Rated speed of machine\n",
+ "ns=120.*f/p;\n",
+ "# (a) Locked rotor torque\n",
+ "Trated=hp*5252./n; # Rated torque \n",
+ "Tlockedrotor=2.25*Trated;\n",
+ "# (b) Breakdown torque\n",
+ "Tbreakdown=1.90*Trated;\n",
+ "# (c) Pull up torque\n",
+ "Tpullup=1.65*Trated;\n",
+ "# Display result on command window\n",
+ "print\"Locked rotor torque =\",Tlockedrotor,\"lb-ft\"\n",
+ "print\"Breakdown torque =\",Tbreakdown,\"lb-ft\"\n",
+ "print\"Pull up torque =\",Tpullup,\"lb-ft\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example E02 : Pg 180"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ "Slip = 0.0125\n",
+ "\n",
+ "Line current magnitude = 15.0898365811 A\n",
+ "\n",
+ "Line current angle = -30.2 deg\n",
+ "\n",
+ "Apparent power = 10390.9402326 W\n",
+ "\n",
+ "Active power = 6047.67163108 var\n",
+ "\n",
+ "Reactive power = 12022.7272727 VA\n",
+ "\n",
+ "Power factor of the motor = 0.864\n",
+ "\n",
+ "Equivalent rotor curret magnitude = 12.6578934123 A\n",
+ "\n",
+ "Equivalent rotor curret angle = -6.85 deg\n",
+ "\n",
+ "Stator copper loss = 136.621900826 W\n",
+ "\n",
+ "Rotor copper loss = 120.166699229 W\n",
+ "\n",
+ "Core loss = 606.519617558 W\n",
+ "\n",
+ "Air-gap power = 9613.33593829 W\n",
+ "\n",
+ "Mechanical power developed = 9493.16923906 W\n",
+ "\n",
+ "Developed torque = 56.3982375046 lb-ft\n",
+ "\n",
+ "Shaft horsepower = 12.5491045777 hp\n",
+ "\n",
+ "Shaft torque = 55.6184786853 lb-ft\n",
+ "\n",
+ "Effiency = 0.90094176325\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Example 5.2\n",
+ "# Determine (a) Slip (b) Line current (c) Apparent power, active power, \n",
+ "# reactive power and power factor of the motor (d) Equivalent rotor curret\n",
+ "# (e) Stator copper loss (f) Rotor copper loss (g) Core loss (h) Air-gap\n",
+ "# power (i) Mechanical power developed (j) Developed torque (k) Shaft \n",
+ "# horsepower (l) Shaft torque (m) Effiency \n",
+ "# Page No. 180\n",
+ "# Given data\n",
+ "from math import sqrt,pi,sin,cos \n",
+ "f=60.; # Frequency\n",
+ "P=6.; # Number of poles\n",
+ "nr=1185.;\n",
+ "R1=0.200; # Motor resistance\n",
+ "R2=0.250;\n",
+ "X1=1.20; # Motor reactance\n",
+ "X2=1.29;\n",
+ "Rfe=317.; # Field resistance\n",
+ "XM=42.; # Motor reactance\n",
+ "V=460.; # Voltage rating\n",
+ "PFPS=166.; # Stray loss\n",
+ "\n",
+ "# (a) Slip \n",
+ "ns=(120.*f)/P;\n",
+ "s=(ns-nr)/ns; # Speed difference\n",
+ "\n",
+ "# (b) Line current\n",
+ "Z2=20 + 1.29j;#(R2/s)+%i*X2;\n",
+ "# Complex to Polar form...\n",
+ "Z2_Mag=20.;#sqrt(real(Z2)**2+imag(Z2)**2); # Magnitude part\n",
+ "Z2_Ang =3.69;#atan(imag(Z2),real(Z2))*180/%pi; # Angle part\n",
+ "\n",
+ "Z0_Num_Mag=Rfe*XM; # Z0 numerator\n",
+ "Z0_Num_Ang=0+90; \n",
+ " \n",
+ "Z0_Den_R=Rfe; # Z0 denominator\n",
+ "Z0_Den_I=XM;\n",
+ "Z0_Den=317 + 42j;#Z0_Den_R+%i*Z0_Den_I;\n",
+ "# Complex to Polar form...\n",
+ "Z0_Den_Mag=320.;#sqrt(real(Z0_Den)**2+imag(Z0_Den)**2); # Magnitude part\n",
+ "Z0_Den_Ang =7.55;#atan(imag(Z0_Den),real(Z0_Den))*180/%pi; # Angle part\n",
+ "\n",
+ "Z0_Mag=Z0_Num_Mag/Z0_Den_Mag; # Magnitude of Z0\n",
+ "Z0_Ang=Z0_Num_Ang-Z0_Den_Ang; # Angle of Z0\n",
+ "\n",
+ "# Polar to Complex form\n",
+ "Z0_R=Z0_Mag*cos(-Z0_Ang*pi/180); # Real part of complex number\n",
+ "Z0_I=Z0_Mag*sin(Z0_Ang*pi/180); # Imaginary part of complex number\n",
+ "\n",
+ "# ZP computation\n",
+ "ZP_Num_Mag=Z2_Mag*Z0_Mag; # ZP numerator magnitude\n",
+ "ZP_Num_Ang=Z2_Ang+Z0_Ang; # ZP numerator angle\n",
+ "\n",
+ "ZP_Den_R=25.5;#real(Z2)+Z0_R; # Real part of ZP denominator\n",
+ "ZP_Den_I=42.6;#imag(Z2)+Z0_I; \n",
+ "ZP_Den=25.5 + 42.6j;#lZP_Den_R+%i*ZP_Den_I; # ZP in complex form\n",
+ "\n",
+ "# Complex to Polar form...\n",
+ "ZP_Den_Mag=49.6;#sqrt(real(ZP_Den)**2+imag(ZP_Den)**2); # Magnitude part\n",
+ "ZP_Den_Ang =59.1;#atan(imag(ZP_Den),real(ZP_Den))*180/%pi; # Angle part\n",
+ "\n",
+ "ZP_Mag=ZP_Num_Mag/ZP_Den_Mag; # Final vlaue of ZP in polar form\n",
+ "ZP_Ang=ZP_Num_Ang-ZP_Den_Ang;\n",
+ "# Polar to Complex form\n",
+ "ZP_R=ZP_Mag*cos(-ZP_Ang*pi/180); # Real part of complex number\n",
+ "ZP_I=ZP_Mag*sin(ZP_Ang*pi/180); # Imaginary part of complex number\n",
+ "\n",
+ "# Zin computation\n",
+ "ZP=15 + 7.65j;#ZP_R+%i*ZP_I; # Parallel impedance\n",
+ "Z1=0.2 + 1.2j;#R1+%i*X1;\n",
+ "Zin=Z1+ZP; # Input impedance\n",
+ "# Complex to Polar form...\n",
+ "Zin_Mag=17.6;#sqrt(real(Zin)**2+imag(Zin)**2); # Magnitude part\n",
+ "Zin_Ang =30.2;#atan(imag(Zin),real(Zin))*180/%pi; # Angle part\n",
+ "\n",
+ "# I1 computation\n",
+ "I1_Mag=(V/sqrt(3.))/Zin_Mag; # I1 magnitude\n",
+ "I1_Ang=0-Zin_Ang; # I1 angle\n",
+ "\n",
+ "# (c) Apparent power, active power, reactive power and power factor of the motor\n",
+ "S_Mag=3.*(V/sqrt(3.))*I1_Mag; # S magnitude\n",
+ "S_Ang=0-(-Zin_Ang); # S angle\n",
+ "\n",
+ "# Polar to Complex form\n",
+ "S_R=S_Mag*cos(-S_Ang*pi/180); # Real part of complex number\n",
+ "S_I=S_Mag*sin(S_Ang*pi/180); # Imaginary part of complex number\n",
+ "\n",
+ "FP=0.864;#cosd(S_Ang); # Power factor\n",
+ "\n",
+ "# (d) Equivalent rotor curret\n",
+ "E2_Mag=I1_Mag*ZP_Mag; # E2 magnitude\n",
+ "E2_Ang=I1_Ang+ZP_Ang; # E2 angle\n",
+ "\n",
+ "I2_Mag=E2_Mag/Z2_Mag; # I2 magnitude\n",
+ "I2_Ang=E2_Ang-Z2_Ang; # I2 angle\n",
+ "\n",
+ "# (e) Stator copper loss \n",
+ "Pscl=3.*I1_Mag**2.*R1;\n",
+ "\n",
+ "# (f) Rotor copper loss\n",
+ "Prel=3.*I2_Mag**2.*R2;\n",
+ "\n",
+ "# (g) Core loss \n",
+ "Pcore=3.*(E2_Mag**2./Rfe);\n",
+ "\n",
+ "# (h) Air-gap power\n",
+ "Pgap=Prel/s;\n",
+ "\n",
+ "# (i) Mechanical power developed\n",
+ "Pmech=Prel*(1.-s)/s;\n",
+ "\n",
+ "# (j) Developed torque \n",
+ "TD=(21.12*I2_Mag**2*R2)/(s*ns);\n",
+ "\n",
+ "# (k) Shaft horsepower\n",
+ "LOSS=Pscl+Prel+Pcore+PFPS;\n",
+ "Pshaft=(S_R-LOSS)/746.;\n",
+ "\n",
+ "# (l) Shaft torque\n",
+ "T=5252.*Pshaft/nr;\n",
+ "\n",
+ "# (m) Effiency \n",
+ "eta=Pshaft/S_R*746.;\n",
+ "\n",
+ "# Display result on command window\n",
+ "print\"\\nSlip =\",s\n",
+ "print\"\\nLine current magnitude =\",I1_Mag,\"A\"\n",
+ "print\"\\nLine current angle =\",I1_Ang,\"deg\"\n",
+ "print\"\\nApparent power =\",S_R,\"W\"\n",
+ "print\"\\nActive power =\",S_I,\"var\"\n",
+ "print\"\\nReactive power =\",S_Mag,\"VA\"\n",
+ "print\"\\nPower factor of the motor =\",FP\n",
+ "print\"\\nEquivalent rotor curret magnitude =\",I2_Mag,\"A\"\n",
+ "print\"\\nEquivalent rotor curret angle =\",I2_Ang,\"deg\"\n",
+ "print\"\\nStator copper loss =\",Pscl,\"W\"\n",
+ "print\"\\nRotor copper loss =\",Prel,\"W\"\n",
+ "print\"\\nCore loss =\",Pcore,\"W\"\n",
+ "print\"\\nAir-gap power =\",Pgap,\"W\"\n",
+ "print\"\\nMechanical power developed =\",Pmech,\"W\"\n",
+ "print\"\\nDeveloped torque =\",TD,\"lb-ft\"\n",
+ "print\"\\nShaft horsepower =\",Pshaft,\"hp\"\n",
+ "print\"\\nShaft torque =\",T,\"lb-ft\"\n",
+ "print\"\\nEffiency =\",eta"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example E03 : Pg 184"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ "Speed at which maximum torque is developed = 1531.8 r/min\n",
+ "\n",
+ "Maximum torque that the machine can develop = 366.489979327 lb-ft\n",
+ "\n",
+ "Rated shaft torque = 119.977155911 lb-ft\n",
+ "\n",
+ "Maximum torque is developed at slip of 0.1490 and \n",
+ "hence machine is placed in design A category\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Example 5.3\n",
+ "# Computation of (a) Speed at which maximum torque is developed (b) Maximum \n",
+ "# torque that the machine can develop (c) Rated shaft torque (d) Which NEMA \n",
+ "# design fits this motor?\n",
+ "# Page No. 184\n",
+ "# Given data\n",
+ "from math import sqrt\n",
+ "f=60.; # Frequency in Hz\n",
+ "p=4.; # Number of poles\n",
+ "hp=40.; # Horsepower\n",
+ "n=1751.; # Rated speed of machine\n",
+ "v=460./sqrt(3.); # Voltage\n",
+ "s=0.1490; # Slip\n",
+ "R2=0.153; # Rotor resistance \n",
+ "R1=0.102;\n",
+ "X1=0.409; # Rotor reactance\n",
+ "X2=0.613;\n",
+ "\n",
+ "# (a) Speed at which maximum torque is developed \n",
+ "STDmax=R2/(sqrt(R1**2.+(X1+X2)**2.));\n",
+ "ns=120.*f/p; #stator spped\n",
+ "nr=ns*(1.-s);\n",
+ "\n",
+ "# (b) Maximum torque that the machine can develop\n",
+ "TDmax=(21.12*v**2.)/(2.*ns*(sqrt(R1**2.+(X1+X2)**2.)+R1));\n",
+ "\n",
+ "# (c) Rated shaft torque\n",
+ "TDshaft=hp*5252./n;\n",
+ "\n",
+ "# Display result on command window\n",
+ "print\"\\nSpeed at which maximum torque is developed =\",nr,\"r/min\"\n",
+ "print\"\\nMaximum torque that the machine can develop =\",TDmax,\"lb-ft\"\n",
+ "print\"\\nRated shaft torque =\",TDshaft,\"lb-ft\"\n",
+ "print\"\\nMaximum torque is developed at slip of 0.1490 and \\nhence machine is placed in design A category\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example E04 : Pg 185"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ " Amount of torque that must be removed from the motor shaft = 28.3488636364 lb-ft\n",
+ "\n",
+ " Expected minimum starting torque for the lower voltage = 169.197954545 lb-ft\n",
+ "\n",
+ " Percent change in developed torque = -19.0 Percent\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Example 5.4\n",
+ "# Computation of (a) Amount of torque that must be removed from the motor \n",
+ "# shaft to maintain 1760r/min (b) Expected minimum startimg torque for the \n",
+ "# lower voltage (c) Percent change in developed torque caused by 10% drop in \n",
+ "# system voltage.\n",
+ "# Page No. 185\n",
+ "# Given data\n",
+ "hp=50.; # Horsepower\n",
+ "n=1760.; # Rated speed of machine\n",
+ "v1=460.;\n",
+ "# (a) Amount of torque that must be removed from the motor shaft to maintain \n",
+ "# 1760r/min\n",
+ "v2=v1*0.90;\n",
+ "Trated=hp*5252./n; #Rated torque \n",
+ "TD2=Trated*(v2/v1)**2.;\n",
+ "Treduction=Trated-TD2;\n",
+ "# (b) Expected minimum startimg torque for the lower voltage\n",
+ "Tlr=1.40*Trated;\n",
+ "Tlr2=Tlr*(v2/v1)**2;\n",
+ "# (c) Percent change in developed torque caused by 10% drop in system voltage\n",
+ "Tchange=(TD2-Trated)/Trated;\n",
+ "Tchanger=(Tlr2-Tlr)/Tlr;\n",
+ "# Display result on command window\n",
+ "print\"\\n Amount of torque that must be removed from the motor shaft =\",Treduction,\"lb-ft\"\n",
+ "print\"\\n Expected minimum starting torque for the lower voltage =\",Tlr2,\"lb-ft\"\n",
+ "print\"\\n Percent change in developed torque =\",Tchanger*100,\"Percent\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example E05 : Pg 187"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ "Shaft speed = 588.875 r/min\n",
+ "\n",
+ "Rotor current referred to the stator = 111.916287976 A\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Example 5.5\n",
+ "# Computation of minimum value of (a) Shaft speed (b) Rotor current referred \n",
+ "# to the stator\n",
+ "# Page No. 187\n",
+ "# Given data\n",
+ "from math import sqrt\n",
+ "f=60.; # Frequency in Hz\n",
+ "p=12.; # Number of poles\n",
+ "nr=591.1; # Rated speed of machine\n",
+ "v=575.; # Voltage rating of the machine\n",
+ "R2=0.055;\n",
+ "\n",
+ "# (a) Shaft speed\n",
+ "ns=120.*f/p; # Speed (r/min)\n",
+ "s1=(ns-nr)/ns; # Slip 1\n",
+ "s2=1.25*s1; # Slip 2\n",
+ "nr1=ns*(1.-s2);\n",
+ "\n",
+ "# (b) Rotor current referred to the stator\n",
+ "V=v/sqrt(3.);\n",
+ "I2=V*s2/R2;\n",
+ "\n",
+ "# Display result on command window\n",
+ "print\"\\nShaft speed =\",nr1,\"r/min\"\n",
+ "print\"\\nRotor current referred to the stator =\",I2,\"A\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example E06 : Pg 190"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ "New operating speed in case of voltage and frequency drop = 1100.72839506 r/min\n",
+ "\n",
+ "New shaft horsepower = 18.7358024691 hp\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Example 5.6\n",
+ "# Determine (a) New operating speed if a system disturbance causes a 10% drop\n",
+ "# in voltage and 6% drop in frequency (b) New shaft horsepower.\n",
+ "# Page No. 190\n",
+ "# Given data\n",
+ "etaV=0.90; # Efficiency related to voltage\n",
+ "V=230.; # Voltage\n",
+ "etaF=0.94; # Efficiency related to voltage\n",
+ "f=60.; # Frequency\n",
+ "N=6.; # Number of poles\n",
+ "nr1=1175.; # Speed of motor\n",
+ "P=20.; # Horsepower of motor\n",
+ "\n",
+ "# (a) New operating speed if a system disturbance causes a 10% drop in \n",
+ "# voltage and 6% drop in frequency\n",
+ "V2=etaV*V; # New voltage after 10% drop\n",
+ "f2=etaF*f; # New frequency after 6% drop\n",
+ "ns1=120.*f/N;\n",
+ "ns2=120.*0.94*f/N;\n",
+ "s1=(ns1-nr1)/ns1; # Speed difference\n",
+ "\n",
+ "s2=s1*((V/V2)**2.)*(f2/f); \n",
+ "nr2=ns2*(1.-s2); # New speed\n",
+ "\n",
+ "# (b) New shaft horsepower\n",
+ "P2=P*(nr2/nr1); # With a constant torque load T2=T1\n",
+ "\n",
+ "# Display result on command window\n",
+ "print\"\\nNew operating speed in case of voltage and frequency drop =\",nr2,\"r/min\"\n",
+ "print\"\\nNew shaft horsepower =\",P2,\"hp\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example E07 : Pg 192"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ " Expected locked-rotor line current = 173.32173913 A\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Example 5.7\n",
+ "# Determine expected locked-rotor line current\n",
+ "# Page No. 192\n",
+ "# Given data\n",
+ "Ir1=151.; # Rated current\n",
+ "V1=230.; # Rated voltage\n",
+ "V2=220.; # Motor starting voltage\n",
+ "F1=60.; # Rated frequency\n",
+ "F2=50.; # Motor starting frequency\n",
+ "# Expected locked-rotor line current\n",
+ "Ir2=Ir1*((V2/F2)/(V1/F1));\n",
+ "# Display result on command window\n",
+ "print\"\\n Expected locked-rotor line current =\",Ir2,\"A\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example E08 : Pg 193"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ "Expected minimum locked-rotor torque = 270.102857143 lb-ft\n",
+ "\n",
+ "Expected minimum locked-rotor torque after drop = 265.465984372 lb-ft\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Example 5.8\n",
+ "# Determine (a) Expected minimum locked-rotor torque (b) Repeat (a) when \n",
+ "# voltage and frequency dropped to 230V and 58Hz \n",
+ "# Page No. 193\n",
+ "# Given data\n",
+ "HPrated=75.; # Rated horsepower\n",
+ "nrated=1750.; # Rated speed\n",
+ "V1=240.; # Rated voltage\n",
+ "V2=230.; # Voltage after drop\n",
+ "F1=60.; # Rated frequency\n",
+ "F2=58.; # Frequency after drop\n",
+ "\n",
+ "# (a) Expected minimum locked-rotor torque\n",
+ "Trated=5252.*HPrated/nrated; # Rated torque\n",
+ "Tlr=Trated*1.2; # Minimum locked-rotor torque is 120% rated \n",
+ "\n",
+ "# (b) Expected minimum locked-rotor torque when voltage and frequency dropped \n",
+ "# to 230V and 58Hz \n",
+ "Tlr2=Tlr*((V2/F2)**2.)*((F1/V1)**2.);\n",
+ "\n",
+ "# Display result on command window\n",
+ "print\"\\nExpected minimum locked-rotor torque =\",Tlr,\"lb-ft\"\n",
+ "print\"\\nExpected minimum locked-rotor torque after drop =\",Tlr2,\"lb-ft\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example E09 : Pg 194"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ "Shaft speed = 1470.15519161 r/min\n",
+ "\n",
+ "Slip = 0.019896538928\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Example 5.9\n",
+ "# Determine (a) Shaft r/min (b) Slip \n",
+ "# Page No. 194\n",
+ "# Given data\n",
+ "from math import sqrt\n",
+ "F1=60.; # Rated frequency\n",
+ "N=4.; # Number of poles\n",
+ "F2=50.; # New frequency\n",
+ "ns=1770.; # Rated speed\n",
+ "\n",
+ "# (a) Shaft r/min\n",
+ "ns60=120.*F1/N; # Speed at rated ferquency \n",
+ "ns50=120.*F2/N; # Speed at 50 Hz frequency\n",
+ "s60=(ns60-ns)/ns60; # Slip at 60 Hz frequency\n",
+ "\n",
+ "# Using eq. (5.16) and by solving..s50=29.251/nr50\n",
+ "# Using eq. (4.3) and solving for nr50 we get the quadratic equation..\n",
+ "# Using various values of quadratic equations, we have\n",
+ "a=1.;\n",
+ "b=-1500.;\n",
+ "c=43876.5;\n",
+ "r1=(-b+sqrt(b**2-4*a*c))/(2.*a); # Root 1\n",
+ "\n",
+ "r2=(-b-sqrt(b**2-4*a*c))/(2.*a); # Root 2\n",
+ "# Answer 'r2' is not valid\n",
+ "\n",
+ "# (b) Slip \n",
+ "s50=(ns50-r1)/ns50;\n",
+ "\n",
+ "# Display result on command window\n",
+ "print\"\\nShaft speed =\",r1,\"r/min\"\n",
+ "print\"\\nSlip =\",s50"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example E10 : Pg 198"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ " Low range of rotor speed = 311.142857143 r/min\n",
+ "\n",
+ " High range of rotor speed = 504.0 r/min\n",
+ "\n",
+ " Required rheostat resistance = 0.114905179241 Ohm/phase\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Example 5.10\n",
+ "# Determine (a) Range of rotor speed (b) Required rheostat resistance\n",
+ "# Page No. 198\n",
+ "# Given data\n",
+ "from math import sqrt\n",
+ "F=60.; # Frequency of motor\n",
+ "P=14.; # Number of poles\n",
+ "SL=0.395; # Low speed point\n",
+ "SH=0.02; # High speed point\n",
+ "Stdmax=0.74; # Value at which TD is maximum (from curve B)\n",
+ "R1=0.403; # Motor resistance\n",
+ "R2=0.317;\n",
+ "X1=1.32; # Motor reactance\n",
+ "X2=1.32;\n",
+ "a=3.8; # Ratio of stator turns/phase to rotor turns/phase\n",
+ "\n",
+ "# (a) Range of rotor speed\n",
+ "ns=120.*F/P; # Speed\n",
+ "nrl=ns*(1.-SL); # Rotor low speed\n",
+ "nrh=ns*(1.-SH); # Rotor high speed\n",
+ "\n",
+ "# (b) Required rheostat resistance\n",
+ "Rrhe=Stdmax*(sqrt(R1**2.+(X1+X2)**2.))-R2;\n",
+ "Rehereq=Rrhe/a**2.;\n",
+ "\n",
+ "# Display result on command window\n",
+ "print\"\\n Low range of rotor speed =\",nrl,\"r/min\"\n",
+ "print\"\\n High range of rotor speed =\",nrh,\"r/min\"\n",
+ "print\"\\n Required rheostat resistance =\",Rehereq,\"Ohm/phase\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example E11 : Pg 201"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ " Rotor frequency = 0.795 Hz\n",
+ "\n",
+ " Slip at which TDmax occurs = 0.079830908464\n",
+ "\n",
+ " Rotor speed at 1/2 rated torque = 1488.075 r/min\n",
+ "\n",
+ " Required rheostat resistance = 0.0627232651992 Ohm/phase\n",
+ "\n",
+ " Rated torque = 1423.16160282 lb-ft\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Example 5.11\n",
+ "# Determine (a) Rotor frequency (b) Slip at which TDmax occurs (c) Rotor speed\n",
+ "# at 1/2 rated torque load (d) Required rheostat resistance (e) Rated torque\n",
+ "# Page No. 201\n",
+ "# Given data\n",
+ "from math import sqrt\n",
+ "S=0.0159; # Slip\n",
+ "Fbr=50.; # Rated frequency\n",
+ "R1=0.00536; # Motor resistance\n",
+ "R2=0.00613;\n",
+ "X1=0.0383; # Motor reactance\n",
+ "X2=0.0383;\n",
+ "Rrhe=0; # Initial rheostat resistance\n",
+ "P=4.; # Number of poles\n",
+ "NR=1000.; # Rated speed\n",
+ "s1=0.0159; # Slip of rheostat\n",
+ "a=2.; # Stator to rotor turns ratio\n",
+ "hp=400.; # Motor horsepower\n",
+ "\n",
+ "# (a) Rotor frequency\n",
+ "fr=S*Fbr;\n",
+ "\n",
+ "# (b) Slip at which TDmax occurs\n",
+ "Stdmax=(R2+Rrhe)/(sqrt(R1**2.+(X1+X2)**2.));\n",
+ "\n",
+ "# (c) Rotor speed at 1/2 rated torque load \n",
+ "s=S*(0.5)*(R2/R2); # Rotor speed at 1/2 rated torque\n",
+ "ns=120.*Fbr/P; \n",
+ "nr=ns*(1.-s); # Rotor speed\n",
+ "\n",
+ "# (d) Required rheostat resistance\n",
+ "s2=(ns-NR)/ns;\n",
+ "Rrhe2=((s2/s1)*(1./0.5)*(R2+Rrhe))-R2; # rheostat resistance\n",
+ "Rrheostat=Rrhe2/a**2.;\n",
+ "\n",
+ "# (e) Rated torque\n",
+ "nr1=ns*(1.-s1); # Rated speed\n",
+ "T=hp*5252./nr1;\n",
+ "\n",
+ "\n",
+ "\n",
+ "# Display result on command window\n",
+ "print\"\\n Rotor frequency =\",fr,\"Hz\"\n",
+ "print\"\\n Slip at which TDmax occurs =\",Stdmax\n",
+ "print\"\\n Rotor speed at 1/2 rated torque =\",nr,\"r/min\"\n",
+ "print\"\\n Required rheostat resistance =\",Rrheostat,\"Ohm/phase\"\n",
+ "print\"\\n Rated torque =\",T,\"lb-ft\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example E12 : Pg 202"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ "Percent change in rotor circuit resistance = 77.7777777778 Percent increase\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Example 5.12\n",
+ "# Determine the percent increase or decrease in rotor circuit resistance\n",
+ "# Page No. 202\n",
+ "# Given data\n",
+ "Stdmax1=0.45; # Maximum torque condition 1\n",
+ "Stdmax2=0.80; # Maximum torque condition 2\n",
+ "# Percent increase or decrease in rotor circuit resistance\n",
+ "PerCh=1/(Stdmax1/Stdmax2);\n",
+ "PerCh=PerCh-1;\n",
+ "# Display result on command window\n",
+ "print\"\\nPercent change in rotor circuit resistance =\",PerCh*100,\"Percent increase\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example E13 : Pg 208"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ " Lower limit of expected range of in-rush current = 1054.29179591 A\n",
+ "\n",
+ " Upper limit of expected range of in-rush current = 1186.0782704 A\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Example 5.13\n",
+ "# Determine the expected in-rush current\n",
+ "# Page No. 208\n",
+ "# Given data\n",
+ "from math import sqrt\n",
+ "kva1=5.6; # KVA/hp lower limit from table 5.9\n",
+ "hp=150.; # Motor horsepower\n",
+ "Vline=460.; # Line voltage\n",
+ "kva2=6.3; # KVA/hp upper limit from table 5.9\n",
+ "# Expected in-rush current\n",
+ "# Lower limit of expected range of in-rush current is\n",
+ "Ilrss=(kva1*hp*1000)/(sqrt(3)*Vline); \n",
+ "# Upper limit of expected range of in-rush current is\n",
+ "Iulss=(kva2*hp*1000)/(sqrt(3)*Vline); \n",
+ "# Display result on command window\n",
+ "print\"\\n Lower limit of expected range of in-rush current =\",Ilrss,\"A\"\n",
+ "print\"\\n Upper limit of expected range of in-rush current =\",Iulss,\"A\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example E14 : Pg 211"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ "Percent voltage unbalance = 2.58\n",
+ "\n",
+ "Expected approximate temperature rise = 124.64408 deg C\n",
+ "\n",
+ " Expected insulation life = 7.2476842001 years\n",
+ "\n",
+ " Required derating of motor = 27.6 hp\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Example 5.14\n",
+ "# Determine (a) Percent voltage unbalance (b) Expected approximate temp. rise\n",
+ "# if operating at rated load in a 40 deg ambient (c) Expected insulation life \n",
+ "# (d) Required derating of motor to prevent shortening isulation life.\n",
+ "# Page No. 211\n",
+ "# Given data\n",
+ "from math import sqrt\n",
+ "VL1=460.; # Line voltage 1\n",
+ "VL2=455.; # Line voltage 2\n",
+ "VL3=440.; # Line voltage 3 \n",
+ "Trated=110.; # Rated temp. (from table 5.8)\n",
+ "hp=30.; # Motor horsepower\n",
+ "\n",
+ "# (a) Percent voltage unbalance \n",
+ "Vavg=(VL1+VL2+VL3)/3.; # Average line voltage\n",
+ "\n",
+ "#VD1=abs(VL1-Vavg); # Voltage deviation from the average \n",
+ "#VD2=abs(VL2-Vavg); \n",
+ "#VD3=abs(VL3-Vavg); \n",
+ "#VD=[VD1 VD2 VD3]; \n",
+ "#VDMax=max(VD); # Choose maximum value of voltage deviation\n",
+ "PerUBV=2.58;#(VDMax/Vavg)*100;\n",
+ "\n",
+ "# (b) Expected approximate temp. rise if operating at rated load in a 40 deg\n",
+ "PerDeltaT=2.*PerUBV**2.; # Percent change in temp.\n",
+ "Tubv=Trated*(1.+(PerDeltaT/100.));\n",
+ "\n",
+ "# (c) Expected insulation life \n",
+ "DeltaT=Tubv-Trated; # Percent increase in motor temp.\n",
+ "RL=1./(2.**(DeltaT/10.)); # Relative life on insulation\n",
+ "EL=RL*20;\n",
+ "\n",
+ "# (d) Required derating of motor to prevent shortening isulation life\n",
+ "ReqDer=hp*0.92;\n",
+ "\n",
+ "# Display result on command window\n",
+ "print\"\\nPercent voltage unbalance =\",PerUBV\n",
+ "print\"\\nExpected approximate temperature rise =\",Tubv,\"deg C\"\n",
+ "print\"\\n Expected insulation life =\",EL,\"years\"\n",
+ "print\"\\n Required derating of motor =\",ReqDer,\"hp\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example E15 : Pg 213"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ " Motor resistance 1 = 0.119131367292 Ohm\n",
+ "\n",
+ " Motor reactance 1 = 0.567292225201 Ohm\n",
+ "\n",
+ " Motor resistance 2 = 0.11345844504 Ohm\n",
+ "\n",
+ " Motor reactance 2 = 0.100978016086 Ohm\n",
+ "\n",
+ " Field resistance = 113.45844504 Ohm\n",
+ "\n",
+ " Reactance of motor = 20.8763538874 Ohm\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Example 5.15\n",
+ "# Determine the machine parameters in ohms\n",
+ "# Page No. 213\n",
+ "# Given data\n",
+ "from math import sqrt \n",
+ "V=460.; # Motor voltage\n",
+ "hp=50.; # Motor horsepower\n",
+ "r1=0.021; # Resistance\n",
+ "r2=0.020;\n",
+ "x1=0.100; # Reactance\n",
+ "x2=0.0178;\n",
+ "rfe=20.; \n",
+ "Xm=3.68; # Motor reactance\n",
+ "\n",
+ "# Machine parameters in ohms\n",
+ "Vbase=V/sqrt(3.); # Base voltage\n",
+ "Pbase=hp*746./3.; # Base power\n",
+ "Zbase=Vbase**2./Pbase; # Base impedance\n",
+ "\n",
+ "R1=r1*Zbase;\n",
+ "X1=x1*Zbase;\n",
+ "R2=r2*Zbase;\n",
+ "X2=x2*Zbase;\n",
+ "Rfe=rfe*Zbase;\n",
+ "XM=Xm*Zbase;\n",
+ "\n",
+ "# Display result on command window\n",
+ "print\"\\n Motor resistance 1 =\",R1,\"Ohm\"\n",
+ "print\"\\n Motor reactance 1 =\",X1,\"Ohm\"\n",
+ "print\"\\n Motor resistance 2 =\",R2,\"Ohm\"\n",
+ "print\"\\n Motor reactance 2 =\",X2,\"Ohm\"\n",
+ "print\"\\n Field resistance =\",Rfe,\"Ohm\"\n",
+ "print\"\\n Reactance of motor =\",XM,\"Ohm\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example E16 : Pg 218"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ " Motor resistance 1 = 0.101694915254 Ohm/phase\n",
+ "\n",
+ " Motor reactance 1 = 0.407379662436 Ohm/phase\n",
+ "\n",
+ " Motor resistance 2 = 0.153299139443 Ohm/phase\n",
+ "\n",
+ " Motor reactance 2 = 0.611069493654 Ohm/phase\n",
+ "\n",
+ " Reactance of motor = 7.58314688225 Ohm/phase\n",
+ "\n",
+ " Combined friction, windage and core loss = 1446.05864407 W/phase\n",
+ "\n",
+ " No-load current as a percent of rated current = 56.5743944637 Percent\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Example 5.16\n",
+ "# Determine (a) R1, R2, X1, X2, XM and the combined core, friction and windage \n",
+ "# loss (b) Express the no-load current as a percent of rated current\n",
+ "# Page No. 218\n",
+ "# Given data\n",
+ "from math import sqrt\n",
+ "P3ph=2573.4; # 3-ph power of induction motor\n",
+ "Vline=36.2; # Line voltage\n",
+ "Iline=58; # Line current\n",
+ "P3phnl=4664.4; # No load power\n",
+ "Vlinenl=460.; # No load line volatge\n",
+ "Ilinenl=32.7; # No load line current\n",
+ "Vdc=12.; # DC voltage\n",
+ "Idc=59.; # DC current\n",
+ "F1=60.; # Rated frequency\n",
+ "F2=15.; # Test frequency\n",
+ "Irated=57.8; # Rated current\n",
+ " \n",
+ "# (a) R1, R2, X1, X2, XM and the combined core, friction and windage loss\n",
+ "Pbr15=P3ph/3.; # Power/phase\n",
+ "Vbr15=Vline/sqrt(3.); # Voltage/phase\n",
+ "Ibr15=Iline;\n",
+ "PNL=P3phnl/3.; # No load power/phase\n",
+ "VNL=Vlinenl/sqrt(3.); # No load voltage/phase\n",
+ "INL=Ilinenl; # No load current/phase\n",
+ "\n",
+ "# Determination of R1\n",
+ "Rdc=Vdc/Idc;\n",
+ "R1=Rdc/2.;\n",
+ "\n",
+ "# Determination of R2\n",
+ "Zbr15=Vbr15/Ibr15; # Impedance\n",
+ "Rbr15=Pbr15/Ibr15**2.;\n",
+ "R2=Rbr15-R1;\n",
+ "\n",
+ "# Determination of X1 and X2\n",
+ "Xbr15=sqrt(Zbr15**2.-Rbr15**2.);\n",
+ "Xbr60=Xbr15*(F1/F2);\n",
+ "X1=0.4*Xbr60; # From Table 5.10\n",
+ "X2=0.6*Xbr60;\n",
+ "\n",
+ "# Determination of XM\n",
+ "SNL=VNL*INL;\n",
+ "QNL=sqrt(SNL**2.-PNL**2.);\n",
+ "XNL=QNL/INL**2.;\n",
+ "XM=XNL-X1;\n",
+ "\n",
+ "# Determination of combined friction, windage and core loss\n",
+ "Ploss=PNL-(INL**2.*R1);\n",
+ "\n",
+ "# (b) No-load current as a percent of rated current\n",
+ "PerINL=INL*100./Irated;\n",
+ "\n",
+ "# Display result on command window\n",
+ "print\"\\n Motor resistance 1 =\",R1,\"Ohm/phase\"\n",
+ "print\"\\n Motor reactance 1 =\",X1,\"Ohm/phase\"\n",
+ "print\"\\n Motor resistance 2 = \",R2,\"Ohm/phase\"\n",
+ "print\"\\n Motor reactance 2 =\",X2,\"Ohm/phase\"\n",
+ "print\"\\n Reactance of motor =\",XM,\"Ohm/phase\"\n",
+ "print\"\\n Combined friction, windage and core loss =\",Ploss,\"W/phase\"\n",
+ "print\"\\n No-load current as a percent of rated current =\",PerINL,\"Percent\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example E17 : Pg 223"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Active power of the motor = -9232.86054488 W\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Example 5.17\n",
+ "# Determine the active power that the motor, driven as an induction generator\n",
+ "# delivers to the system.\n",
+ "# Page No. 223\n",
+ "# Given data\n",
+ "from math import sqrt,pi,sin,cos\n",
+ "ns=1200.; # Speed\n",
+ "nr=1215.;\n",
+ "R1=0.200; # Motor resistance\n",
+ "R2=0.250;\n",
+ "X1=1.20; # Motor reactance\n",
+ "X2=1.29;\n",
+ "Rfe=317.; # Field resistance\n",
+ "XM=42.; # Motor reactance\n",
+ "V=460.; # Voltage rating\n",
+ "\n",
+ "# Active power of the motor computation\n",
+ "s=(ns-nr)/ns; # Speed difference\n",
+ "Z2=-20 + 1.29j;#(R2/s)+%i*X2;\n",
+ "\n",
+ "# Complex to Polar form...\n",
+ "Z2_Mag=20.;#sqrt(real(Z2)**2+imag(Z2)**2); # Magnitude part\n",
+ "Z2_Ang =176.;#atan(imag(Z2),real(Z2))*180/%pi; # Angle part\n",
+ "\n",
+ "Z0_Num_Mag=Rfe*XM; # Z0 numerator\n",
+ "Z0_Num_Ang=0+90; \n",
+ " \n",
+ "Z0_Den_R=Rfe; # Z0 denominator\n",
+ "Z0_Den_I=XM;\n",
+ "Z0_Den=317 + 42j;#Z0_Den_R+%i*Z0_Den_I;\n",
+ "# Complex to Polar form...\n",
+ "Z0_Den_Mag=320.;#sqrt(real(Z0_Den)**2+imag(Z0_Den)**2); # Magnitude part\n",
+ "Z0_Den_Ang =7.55;#atan(imag(Z0_Den),real(Z0_Den))*180/%pi; # Angle part\n",
+ "\n",
+ "Z0_Mag=Z0_Num_Mag/Z0_Den_Mag; # Magnitude of Z0\n",
+ "Z0_Ang=Z0_Num_Ang-Z0_Den_Ang; # Angle of Z0\n",
+ "\n",
+ "# Polar to Complex form\n",
+ "Z0_R=Z0_Mag*cos(-Z0_Ang*pi/180); # Real part of complex number\n",
+ "Z0_I=Z0_Mag*sin(Z0_Ang*pi/180); # Imaginary part of complex number\n",
+ "\n",
+ "# ZP computation\n",
+ "ZP_Num_Mag=Z2_Mag*Z0_Mag; # ZP numerator magnitude\n",
+ "ZP_Num_Ang=Z2_Ang+Z0_Ang; # ZP numerator angle\n",
+ "\n",
+ "ZP_Den_R=-14.5;#real(Z2)+Z0_R; # Real part of ZP denominator\n",
+ "ZP_Den_I=42.6;#imag(Z2)+Z0_I; \n",
+ "ZP_Den=-14.5 + 42.6j;#ZP_Den_R+%i*ZP_Den_I; # ZP in complex form\n",
+ "\n",
+ "# Complex to Polar form...\n",
+ "ZP_Den_Mag=45.;#sqrt(real(ZP_Den)**2+imag(ZP_Den)**2); # Magnitude part\n",
+ "ZP_Den_Ang =109.;# atan(imag(ZP_Den),real(ZP_Den))*180/%pi; # Angle part\n",
+ "\n",
+ "ZP_Mag=ZP_Num_Mag/ZP_Den_Mag; # Final vlaue of ZP in polar form\n",
+ "ZP_Ang=ZP_Num_Ang-ZP_Den_Ang;\n",
+ "# Polar to Complex form\n",
+ "ZP_R=ZP_Mag*cos(-ZP_Ang*pi/180); # Real part of complex number\n",
+ "ZP_I=ZP_Mag*sin(ZP_Ang*pi/180); # Imaginary part of complex number\n",
+ "\n",
+ "# Zin computation\n",
+ "ZP=-16.1 + 9.3j;#ZP_R+%i*ZP_I; # Parallel impedance\n",
+ "Z1=0.2 + 1.2j;#R1+%i*X1;\n",
+ "Zin=Z1+ZP; # Input impedance\n",
+ "# Complex to Polar form...\n",
+ "Zin_Mag=19.;#sqrt(real(Zin)**2+imag(Zin)**2); # Magnitude part\n",
+ "Zin_Ang =146.;#atan(imag(Zin),real(Zin))*180/%pi; # Angle part\n",
+ "\n",
+ "# I1 computation\n",
+ "I1_Mag=(V/sqrt(3))/Zin_Mag; # I1 magnitude\n",
+ "I1_Ang=0-Zin_Ang; # I1 angle\n",
+ "\n",
+ "# S computation\n",
+ "S_Mag=3*(V/sqrt(3))*I1_Mag; # S magnitude\n",
+ "S_Ang=0-(-Zin_Ang); # S angle\n",
+ "\n",
+ "# Polar to Complex form\n",
+ "S_R=S_Mag*cos(-S_Ang*pi/180); # Real part of complex number\n",
+ "S_I=S_Mag*sin(S_Ang*pi/180); # Imaginary part of complex number\n",
+ "\n",
+ "# Display result on command window\n",
+ "print\"Active power of the motor =\",S_R,\"W\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example E18 : Pg 231"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ "Locked rotor torque = 719.215600351 lb-ft\n",
+ "\n",
+ "Expected average in-rush current = 1051.15402271 A\n",
+ "\n",
+ "Locked rotor torque when motor is started at reduced voltage = 303.868591148 lb-ft\n",
+ "\n",
+ "In-rush line current = 443.95 A\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Example 5.18\n",
+ "# Computation of (a) Locked rotor torque and the expected average in rush \n",
+ "# current (b) Repeat part (a) assuming motor is started at reduced voltage \n",
+ "# with 65% tap (c) In rush line current line current when starting at reduced \n",
+ "# voltage\n",
+ "# Page No. 231\n",
+ "# Given data\n",
+ "from math import sqrt\n",
+ "P=125.; # Rated Voltage\n",
+ "n=1141.; # Speed of machine\n",
+ "hp=125.; # Horsepower rating of device \n",
+ "Vline=460.; # Line voltage\n",
+ "ns=1200.; # Stator speed\n",
+ "s=0.125; # Slip\n",
+ "ILS=683.; # Current at low side\n",
+ "# (a) Locked rotor torque and the expected average in rush current\n",
+ "Trated=P*5252./(n); # Rated torque\n",
+ "Tlr=1.25*Trated; # Locked rotor torque\n",
+ "kVA=(6.3+7.1)/2.;\n",
+ "Ilr=(kVA*1000.*hp)/(Vline*sqrt(3.)); # In-rush current\n",
+ "# (b) Locked rotor torque and the expected average in rush current when motor \n",
+ "# is started at reduced voltage\n",
+ "V2=0.65*Vline; # Voltage impressed across the stator\n",
+ "I=Ilr*0.65; # Average in-rush current\n",
+ "T2=Tlr*(V2/Vline)**2.; # Locked rotor toreque\n",
+ "nr=ns*(1.-s);\n",
+ "# (c) In rush line current line current when starting at reduced voltage\n",
+ "a=1./0.65; # Bank ratio of autotransformer\n",
+ "IHS=ILS/a;\n",
+ "# Display result on command window\n",
+ "print\"\\nLocked rotor torque =\",Tlr,\"lb-ft\"\n",
+ "print\"\\nExpected average in-rush current =\",Ilr,\"A\"\n",
+ "print\"\\nLocked rotor torque when motor is started at reduced voltage =\",T2,\"lb-ft\"\n",
+ "print\"\\nIn-rush line current =\",IHS,\"A\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example E19 : Pg 233"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ " Locked rotor current per phase = 485.523078295 A\n",
+ "\n",
+ " Minimum locked rotor torque = 84.032 lb-ft\n",
+ "\n",
+ " Locked rotor current per phase when motor is delta connected = 1456.56923488 A\n",
+ "\n",
+ " Code letter = 19.3418647166\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Example 5.19\n",
+ "# Computation of (a) Locked rotor current per phase and minimum locked rotor \n",
+ "# torque when starting (b) Locked rotor current per phase when motor is delta \n",
+ "# connected (c) Code letter \n",
+ "# Page No.233\n",
+ "# Given data\n",
+ "from math import sqrt\n",
+ "V=460.; # Rated Voltage\n",
+ "Z=0.547; # Locked rotor impedance\n",
+ "n=1750.; # Speed of machine\n",
+ "hp=60.; # Horsepower rating of device\n",
+ "f=60.; # Frequency of motor \n",
+ "# (a) Locked rotor current per phase and minimum locked rotor torque \n",
+ "Vphase=V/sqrt(3.); # Voltage/phase\n",
+ "Ilr1=Vphase/Z; # Locked rotor current/phase\n",
+ "Trated=hp*5252./(n); # Rated torque\n",
+ "Tlr=1.4*Trated; # Locked rotor torque\n",
+ "T2=Tlr*(Vphase/V)**2.;\n",
+ "# (b) Locked rotor current per phase when motor is delta connected \n",
+ "Ilr=V/Z; # Locked rotor current/phase\n",
+ "Il=Ilr*sqrt(3.); # Line current\n",
+ "# (c) Code letter\n",
+ "Slr=sqrt(3.)*V*Il/1000.; # Code letter at rated voltage\n",
+ "kVA=Slr/f;\n",
+ "# Display result on command window\n",
+ "print\"\\n Locked rotor current per phase =\",Ilr1,\"A\"\n",
+ "print\"\\n Minimum locked rotor torque =\",T2,\"lb-ft\"\n",
+ "print\"\\n Locked rotor current per phase when motor is delta connected =\",Il,\"A\"\n",
+ "print\"\\n Code letter =\",kVA"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example E20 : Pg 235"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 20,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ "Resistance of the resistors required = 0.409208864143 Ohm\n",
+ "\n",
+ "Stator voltage per phase at locked rotor = 63.882 V\n",
+ "\n",
+ "Expected minimum locked rotor torque = 1.5 Trated\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Example 5.20\n",
+ "# Computation of (a) Resistance of the resistors required to limit the locked \n",
+ "# rotor current to 3 times rated current (b) Stator voltage per phase at \n",
+ "# locked rotor (c) Expected minimum locked rotor torque when starting as a \n",
+ "# percent of rated torque\n",
+ "# Page No. 235\n",
+ "# Given data\n",
+ "from math import sqrt\n",
+ "Ilr=3.*78.; # Locked rotor current\n",
+ "Vbranch=132.79; # Branch voltage\n",
+ "Rlr=0.2549; #Locked rotor resistance\n",
+ "Xlr=0.0978; #Locked rotor impedance\n",
+ "f=60.; #Frequency of motor \n",
+ "Zlr=0.273;\n",
+ "\n",
+ "# (a) Resistance of the resistors required to limit the locked rotor current \n",
+ "# to 3 times rated current\n",
+ "Rex=sqrt((Vbranch**2./Ilr**2.)-(Rlr**2.))-Xlr;\n",
+ "\n",
+ "# (b) Stator voltage per phase at locked rotor \n",
+ "IZlr=Ilr*Zlr;\n",
+ "VT1_N=IZlr;\n",
+ "\n",
+ "# (c) Expected minimum locked rotor torque when starting as a percent of \n",
+ "# rated torque\n",
+ "# From table 5.1 --> Minimum locked rotor torque = 150% rated torque\n",
+ "\n",
+ "# Display result on command window\n",
+ "\n",
+ "print\"\\nResistance of the resistors required =\",Rex,\"Ohm\"\n",
+ "print\"\\nStator voltage per phase at locked rotor =\",VT1_N,\"V\"\n",
+ "print'\\nExpected minimum locked rotor torque = 1.5 Trated'"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example E21 : Pg 236"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 21,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ "The inductance of each series connected inductor = 4.44444609821 mH\n",
+ "\n",
+ "The voltage rating of each series connected inductor = 80.4248018577 V\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Example 5.21\n",
+ "# Computation of Inductance and voltage rating of each series connected \n",
+ "# inductor required to limit the starting current to approximately 2*Irated. \n",
+ "# Page No. 236\n",
+ "# Given data\n",
+ "from math import sqrt,pi\n",
+ "KVA=6.7; # Average locked rotor KVA/hp\n",
+ "hp=7.5; # Motor horsepower\n",
+ "Vline=208.; # Line voltage\n",
+ "I=48.; # Total current\n",
+ "Rlr=0.294; # Locked rotor resistance\n",
+ "Xlr=0.809; # Locked rotor impedance\n",
+ "f=60.; # Frequency of motor\n",
+ "\n",
+ "# Corresponding approximate load current\n",
+ "Ilr=KVA*1000.*hp/(sqrt(3.)*Vline); \n",
+ "Vphase=Vline/sqrt(3.); # Voltage/phase\n",
+ "\n",
+ "# Applying ohm's law to one phase\n",
+ "Zlr=Vphase/Ilr; # Impedance\n",
+ "Xex=sqrt((Vphase**2./I**2.)-(Rlr**2.))-Xlr;\n",
+ "L=Xex/(2.*pi*f);\n",
+ "L=L*10.**03;\n",
+ "VXl=I*Xex;\n",
+ "\n",
+ "# Display result on command window\n",
+ "print\"\\nThe inductance of each series connected inductor =\",L,\"mH\"\n",
+ "print\"\\nThe voltage rating of each series connected inductor =\",VXl,\"V\""
+ ]
+ }
+ ],
+ "metadata": {
+ "anaconda-cloud": {},
+ "kernelspec": {
+ "display_name": "Python [Root]",
+ "language": "python",
+ "name": "Python [Root]"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.12"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
generated by cgit (git 2.34.1) at 2024-12-23 02:01:44 +0000