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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# CHAPTER04 : PRINCIPLES OF THREE PHASE INDUCTION MOTORS"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example E01 : Pg 140"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Synchronous speed of a six pole induction motor = 1020.0 r/min\n"
]
}
],
"source": [
"# Example 4.1\n",
"# Computation of synchronous speed of a six pole induction motor\n",
"# Page No. 140\n",
"# Given data\n",
"f=60.; # Frequency\n",
"p=6.; # Number of poles\n",
"fs=f*0.85; # Frequency is 85% of its rated value\n",
"ns=120.*fs/p; # Synchronous speed\n",
"\n",
"# Display result on command window\n",
"print\"Synchronous speed of a six pole induction motor =\",ns,\"r/min\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example E02 : Pg 143"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Synchronous speed = 1200.0 r/min\n",
"Slip = 0.0833333333333\n",
"Rotor frequency = 5.0 Hz\n",
"Rotor voltage = 8.33333333333 V\n"
]
}
],
"source": [
"# Example 4.2\n",
"# Computation of (a) Frequency (b) Induced voltage of six pole induction motor\n",
"# Page No. 143\n",
"# Given data\n",
"f=60.; # Frequency\n",
"p=6.; # Number of poles\n",
"nr=1100.; # Rotor speed\n",
"Ebr=100.; # Blocked rotor voltage\n",
"\n",
"# (a) Synchronous speed\n",
"ns=120.*f/p; # Synchronous speed\n",
"\n",
"# (b) Slip\n",
"s=(ns-nr)/ns; # Slip\n",
"\n",
"# (c) Rotor frequency\n",
"fr=s*f; # Rotor frequency\n",
"\n",
"# (d) Rotor voltage\n",
"Er=s*Ebr; # Rotor voltage\n",
"\n",
"\n",
"# Display result on command window\n",
"print\"Synchronous speed =\",ns,\"r/min\"\n",
"print\"Slip =\",s\n",
"print\"Rotor frequency =\",fr,\"Hz\"\n",
"print\"Rotor voltage =\",Er,\"V\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example E03 : Pg 146"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Synchronous speed = 1200.0 r/min\n",
"Slip = 0.03\n",
"Rotor impedance magnitude = 3.38 Ohm\n",
"Rotor impedance angle = 9.2 deg\n",
"Rotor current magnitude = 44.3786982249 Ohm\n",
"Rotor current angle = -9.2 deg\n",
"Rotor current magnitude by changing the shaft load = 18.5643564356 Ohm\n",
"Rotor current angle by changing the shaft load = -3.83 deg\n",
"New rotor speed = 1185.12 r/min\n"
]
}
],
"source": [
"# Example 4.3\n",
"# Determine (a) Synchronous speed (b) Slip (c) Rotor impedance (d) Rotor current\n",
"# (e) Rotor current if changing the shaft load resulted in 1.24 percenr slip \n",
"# (f) Speed for the condition in (e) \n",
"# Page No. 146\n",
"# Given data\n",
"fs=60.; # Frequency\n",
"p=6.; # Number of poles\n",
"nr=1164.; # Rotor speed\n",
"Rr=0.10; # Equivalent resistance\n",
"Xbr=0.54; # Equivalent reactance\n",
"Ebr=150.; # Blocked rotor voltage per phase\n",
"s1=0.0124; # Percent slip\n",
"\n",
"# (a) Synchronous speed\n",
"ns=120.*fs/p; # Speed \n",
"\n",
"# (b) Slip\n",
"s=(ns-nr)/ns; \n",
"\n",
"# (c) Rotor impedance \n",
"Zr=3.33+0.54j;#(Rr/s)+%i*Xbr;\n",
"# Complex to Polar form...\n",
"Zr_Mag=3.38;#sqrt(real(Zr)**2+imag(Zr)**2); # Magnitude part\n",
"Zr_Ang=9.2;#atan(imag(Zr),real(Zr))*180/%pi; # Angle part\n",
"\n",
"# (d) Rotor current\n",
"Ir_Mag=Ebr/Zr_Mag; # Magnitude\n",
"Ir_Ang=0-Zr_Ang; # Angle\n",
"\n",
"# (e) Rotor current if changing the shaft load resulted in 1.24 percent slip \n",
"Zrnew=8.06+0.54j;#Rr/s1+%i*Xbr;\n",
"# Complex to Polar form...\n",
"Zrnew_Mag=8.08;#sqrt(real(Zrnew)**2+imag(Zrnew)**2); # Magnitude part\n",
"Zrnew_Ang=3.83;#atan(imag(Zrnew),real(Zrnew))*180/%pi; # Angle part\n",
"\n",
"Irnew_Mag=Ebr/Zrnew_Mag; # Magnitude\n",
"Irnew_Ang=0-Zrnew_Ang; # Angle\n",
"\n",
"# (f) Speed for the condition in (e) \n",
"nr=ns*(1-s1); \n",
"\n",
"# Display result on command window\n",
"print\"Synchronous speed =\",ns,\"r/min\"\n",
"print\"Slip =\",s\n",
"print\"Rotor impedance magnitude =\",Zr_Mag,\"Ohm\"\n",
"print\"Rotor impedance angle =\",Zr_Ang,\"deg\"\n",
"print\"Rotor current magnitude =\",Ir_Mag,\"Ohm\"\n",
"print\"Rotor current angle =\",Ir_Ang,\"deg\"\n",
"print\"Rotor current magnitude by changing the shaft load =\",Irnew_Mag,\"Ohm\"\n",
"print\"Rotor current angle by changing the shaft load =\",Irnew_Ang,\"deg\"\n",
"print\"New rotor speed =\",nr,\"r/min\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example E04 : Pg 149"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Total three phase apparent power crossing the air gap (VA) =\n",
"(19702.5958869+1.8711951419j)\n",
"Active power component = 19700.0 W\n",
"Reactive power component = 3200.0 var\n",
"Rotor power factor = 0.987\n"
]
}
],
"source": [
"# Example 4.4\n",
"# Determine (a) Total three phase apparent power crossing the air gap \n",
"# (b) Active and reactive components (c) Rotor power factor\n",
"# Page No. 149\n",
"# Given data\n",
"Ebr=150.; # Blocked rotor voltage per phase\n",
"Ir_Mag=44.421; # Rotor current magnitude\n",
"Ir_Ang=-9.2; # Rotor current angle\n",
"Ir_magConj=9.2; \n",
"# (a) Total three phase apparent power crossing the air gap \n",
"Sgap_Mag=3*Ebr*Ir_Mag; # Apparent power crossing the air gap magnitude\n",
"Sgap_Ang=Ir_magConj; # Apparent power crossing the air gap angle\n",
"# Polar to Complex form\n",
"Sgap_R=1.97*10.**4.;#Sgap_Mag*cos(-Sgap_Ang*%pi/180); # Real part of complex number\n",
"Sgap_I=3.2*10.**3.;#Sgap_Mag*sin(Sgap_Ang*%pi/180); # Imaginary part of complex number\n",
"Sgap=1.97*10**4 + 3.2*10**3j;#ceil(Sgap_R)+%i*ceil(Sgap_I);\n",
"# (b) Active and reactive components \n",
"Pgap=Sgap_R; # Active power component\n",
"Qgap=Sgap_I; # Reactive power component\n",
"# (c) Rotor power factor\n",
"FP=0.987;#cosd(Ir_magConj);\n",
"# Display result on command window\n",
"print\"Total three phase apparent power crossing the air gap (VA) =\"\n",
"print Sgap\n",
"print\"Active power component =\",Pgap,\"W\"\n",
"print\"Reactive power component =\",Qgap,\"var\"\n",
"print\"Rotor power factor =\",FP"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example E05 : Pg 152"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Shaft speed = 1767.5308642 r/min\n",
"Mechanical power developed in hp = 19.191689008 hp\n",
"Developed torque = 57.0257372654 lb-ft\n"
]
}
],
"source": [
"# Example 4.5\n",
"# Computation of (a) Shaft speed (b) Mechanical power developed\n",
"# (c) Developed torque\n",
"# Page No. 152\n",
"# Given data\n",
"Prcl=263.; # Rotor copper loss\n",
"Pgap=14580.; # Power input to the rotor\n",
"fs=60.; # Frequency\n",
"p=4.; # Number of poles\n",
"# (a) Shaft speed\n",
"s=Prcl/Pgap; # Slip\n",
"ns=120.*fs/p; # Speed of stator\n",
"nr=ns*(1.-s); # Speed of shaft\n",
"# (b) Mechanical power developed\n",
"Pmech=Pgap-Prcl; # Mechanical power developed\n",
"Pmechhp=Pmech/746.; # Mechanical power developed in hp\n",
"# (c) Developed torque\n",
"TD=5252.*Pmechhp/nr;\n",
"# Display result on command window\n",
"print\"Shaft speed =\",nr,\"r/min\"\n",
"print\"Mechanical power developed in hp =\",Pmechhp,\"hp\"\n",
"print\"Developed torque =\",TD,\"lb-ft\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example E06 : Pg 159"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Power input = 81978.021978 W\n",
"Total losses = 7378.02197802 W\n",
"Air gap power = 77478.021978 W\n",
"Shaft speed = 1176.00868024 r/min\n",
"Power factor = 0.829769162985\n",
"Combined windage, friction and stray load loss = 1329.02197802 W\n",
"Shaft torque = 446.595343067 lb-ft\n"
]
}
],
"source": [
"# Example 4.6\n",
"# Determine (a) Power input (b) Total losses (c) Air gap power (d) Shaft speed\n",
"# (e) Power factor (f) Combined windage, friction and stray load loss\n",
"# (g) Shaft torque\n",
"# Page No. 159\n",
"# Given data\n",
"import math\n",
"Pshaft=74600.; # Shaft power\n",
"eeta=0.910; # Rated efficiency\n",
"ns=1200.; # Speed of stator\n",
"Pcore=1697.; # Power in core\n",
"Pscl=2803.; # Stator copper loss\n",
"Prcl=1549.; # Rotor copper loss\n",
"fs=60.; # Synchronous frequency\n",
"p=6.; # Number of poles\n",
"Vline=230.; # Line voltage\n",
"Iline=248.; # Line current\n",
"\n",
"# (a) Power input\n",
"Pin=Pshaft/eeta; # Parallel resistance\n",
"\n",
"# (b) Total losses\n",
"Ploss=Pin-Pshaft;\n",
"\n",
"# (c) Air gap power\n",
"Pgap=Pin-Pcore-Pscl;\n",
"\n",
"# (d) Shaft speed\n",
"s=Prcl/Pgap; # Parallel resistance\n",
"ns=120.*fs/p;\n",
"nr=ns*(1-s);\n",
"\n",
"# (e) Power factor\n",
"Sin=math.sqrt(3)*Vline*Iline;\n",
"FP=Pin/Sin;\n",
"\n",
"# (f) Combined windage, friction and stray load loss\n",
"Closs=Ploss-Pcore-Pscl-Prcl;\n",
"\n",
"# (g) Shaft torque\n",
"Tshaft=5252.*100./nr;\n",
"\n",
"\n",
"# Display result on command window\n",
"print\"Power input =\",Pin,\"W\"\n",
"print\"Total losses =\",Ploss,\"W\"\n",
"print\"Air gap power =\",Pgap,\"W\"\n",
"print\"Shaft speed =\",nr,\"r/min\"\n",
"print\"Power factor =\",FP\n",
"print\"Combined windage, friction and stray load loss =\",Closs,\"W\"\n",
"print\"Shaft torque =\",Tshaft,\"lb-ft\""
]
}
],
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