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diff --git a/Electric_Machines_by_C._I._Hubert/CHAPTER04.ipynb b/Electric_Machines_by_C._I._Hubert/CHAPTER04.ipynb new file mode 100644 index 00000000..02abb244 --- /dev/null +++ b/Electric_Machines_by_C._I._Hubert/CHAPTER04.ipynb @@ -0,0 +1,396 @@ +{ + "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\"" + ] + } + ], + "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 +} |