{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# CHAPTER06 : SINGLE PHASE INDUCTION MOTORS" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example E01 : Pg 257" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", " Main winding current magnitude = 29.8 A\n", "\n", " Main winding current angle = -60.3 deg\n", "\n", " Auxillary winding current magnitude = 9.66 A\n", "\n", " Auxillary winding current angle = -42.6 deg\n", "\n", " Phase displacement angle = 17.7 deg\n", "\n", " Locked rotor torque in terms of the machine constant = 87.4 .Ksp\n", "\n", " External resistance required = 5.25 Ohm\n", "\n", " Locked rotor torque = 22.5 .Ksp\n", "\n", " Percent increase in locked rotor torque = -74.2562929062 Percent increase\n" ] } ], "source": [ "# Example 6.1\n", "# Determine (a) Locked rotor current in each winding (b) Phase displacement\n", "# angle between the two currents (c) Locked rotor torque in terms of the\n", "# machine constant (d) External resistance required in series with the auxillary\n", "# winding in order to obtain a 30 degree phase displacement between the currents\n", "# in the two windings (e) Locked rotor torque for the conditions in (d) \n", "# (f) Percent increase in locked rotor torque due to the addition of external\n", "# resistance \n", "# Page No. 257\n", "# Given data\n", "Zmw=2.00+1j*3.50 # Main winding impedance\n", "Zaw=9.15+1j*8.40 # Auxillary winding impedance\n", "VT=120.; # Transformer voltage\n", "Xaw=8.40; # Auxillary winding reactance\n", "Raw=9.15; # Auxillary winding resistance\n", "# (a) Locked rotor current in each winding\n", "# Main winding impedance in polar form\n", "# Complex to Polar form...\n", "Zmw_Mag=4.03;#sqrt(real(Zmw)**2+imag(Zmw)**2); # Magnitude part\n", "Zmw_Ang=60.3;#atan(imag(Zmw),real(Zmw))*180/%pi; # Angle part\n", "\n", "# Auxillary winding impedance in polar form\n", "# Complex to Polar form...\n", "Zaw_Mag=12.4;#sqrt(real(Zaw)**2+imag(Zaw)**2); # Magnitude part\n", "Zaw_Ang=42.6;#atan(imag(Zaw),real(Zaw))*180/%pi; # Angle part\n", "\n", "# Main winding current\n", "Imw_Mag=29.8;#VT/Zmw_Mag; # Main winding current magnitude\n", "Imw_Ang=-60.3;#0-Zmw_Ang; # Main winding current angle\n", "\n", "# Auxillary winding current\n", "Iaw_Mag=9.66;#VT/Zaw_Mag; # Auxillary winding current magnitude\n", "Iaw_Ang=-42.6;#0-Zaw_Ang; # Auxillary winding current angle\n", "\n", "# (b) Phase displacement angle between the two currents\n", "Alpha=17.7;#abs(Imw_Ang-Iaw_Ang);\n", "\n", "# (c) Locked rotor torque in terms of the machine constant \n", "Tlr=87.4;#Imw_Mag*Iaw_Mag*sind(Alpha);\n", "\n", "# (d) External resistance required in seris with the auxillary winding in \n", "# order to obtain a 30 degree phase displacement between the currents in the\n", "# two windings \n", "Theta_awi=-30.3;#Imw_Ang+30; # Required phase angle\n", "Theta_awz=30.3;#-Theta_awi;\n", "Rx=5.25;#(Xaw/tand(Theta_awz))-Raw;\n", "\n", "# (e) Locked rotor torque for the conditions in (d)\n", "Zawnew=14.4 + 8.4j;#Raw+Rx+1j*Xaw; # Auxillary winding impedance\n", "# Complex to Polar form...\n", "Zmwnew_Mag=16.7;#sqrt(real(Zawnew)**2+imag(Zawnew)**2); # Magnitude part\n", "Zmwnew_Ang=30.3;#atan(imag(Zawnew),real(Zawnew))*180/%pi; # Angle part\n", "\n", "Iawnew_Mag=7.2;#VT/Zmwnew_Mag; # Auxillary winding current magnitude\n", "Iawnew_Ang=-30.3;#0-Zmwnew_Ang; # Auxillary winding current magnitude\n", "Tlenew=22.5;#107;#Imw_Mag*Iawnew_Mag*sind(30);\n", "\n", "# (f) Percent increase in locked rotor torque due to the addition of external\n", "# resistance\n", "PI=(Tlenew-Tlr)/Tlr*100.;\n", "\n", "\n", "# Display result on command window\n", "print\"\\n Main winding current magnitude =\",Imw_Mag,\"A\"\n", "print\"\\n Main winding current angle =\",Imw_Ang,\"deg\"\n", "print\"\\n Auxillary winding current magnitude =\",Iaw_Mag,\"A\"\n", "print\"\\n Auxillary winding current angle =\",Iaw_Ang,\"deg\"\n", "print\"\\n Phase displacement angle =\",Alpha,\"deg\"\n", "print\"\\n Locked rotor torque in terms of the machine constant =\",Tlr,\".Ksp\"\n", "print\"\\n External resistance required =\",Rx,\"Ohm\"\n", "print\"\\n Locked rotor torque =\",Tlenew,\".Ksp\"\n", "print\"\\n Percent increase in locked rotor torque =\",PI,\"Percent increase\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example E02 : Pg 265" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", " Required capacitance = 1281.76980266 microF\n", "\n", " Percent increase in locked rotor torque = 216.526610644 Percent\n" ] } ], "source": [ "# Example 6.2\n", "# Determine (a) Capacitance required in series with the auxillary winding \n", "# in order to obtain a 90 degree phase displacement between the current in \n", "# the main winding and the current in the auxillary winding at locked rotor \n", "# (b) Locked rotor torque in terms of the machine constant \n", "# Page No. 265\n", "# Given data\n", "from math import sqrt,pi\n", "Zmw=2.00+1j*3.50 # Main winding impedance\n", "Zaw=9.15+1j*8.40 # Auxillary winding impedance\n", "VT=120.; # Transformer voltage\n", "Xaw=8.40; # Auxillary winding reactance\n", "Raw=9.15; # Auxillary winding resistance\n", "f=60.; # Frequency\n", "Tlr=107.1; # Original torque\n", "\n", "# (a) Capacitance required in series with the auxillary winding \n", "# Main winding impedance in polar form\n", "# Complex to Polar form...\n", "Zmw_Mag=4.03;#sqrt(real(Zmw)**2.+imag(Zmw)**2.); # Magnitude part\n", "Zmw_Ang=60.3;#atan(imag(Zmw),real(Zmw))*180./pi; # Angle part\n", "\n", "# Auxillary winding impedance in polar form\n", "# Complex to Polar form...\n", "Zaw_Mag=12.4;#sqrt(real(Zaw)**2.+imag(Zaw)**2.); # Magnitude part\n", "Zaw_Ang=42.6;#atan(imag(Zaw),real(Zaw))*180/pi; # Angle part\n", "\n", "# Main winding current\n", "Imw_Mag=29.8;#VT/Zmw_Mag; # Main winding current magnitude\n", "Imw_Ang=-60.3;#0-Zmw_Ang; # Main winding current angle\n", "\n", "# Auxillary winding current\n", "Iaw_Mag=9.66;#VT/Zaw_Mag; # Auxillary winding current magnitude\n", "Iaw_Ang=-42.6;#0-Zaw_Ang; # Auxillary winding current angle\n", "\n", "Theta_awi=90-60.26; # Required phase angle\n", "Theta_awz=-Theta_awi;\n", "\n", "Xc=13.6;#Xaw-Raw*tand(Theta_awz); # Capacitive reactance\n", "\n", "C=1./2.*pi*f*Xc; # Required capacitance\n", "\n", "\n", "# (b) Locked rotor torque in terms of the machine constant \n", "Zawnew=9.15 + -5.23j;#Raw+1j*Xaw-1j*Xc; # Auxillary winding impedance\n", "# Complex to Polar form...\n", "Zawnew_Mag=10.5;#sqrt(real(Zawnew)**2+imag(Zawnew)**2); # Magnitude part\n", "Zawnew_Ang=-29.7;#atan(imag(Zawnew),real(Zawnew))*180/%pi; # Angle part\n", "\n", "Iawnew_Mag=11.4;#VT/Zawnew_Mag; # Auxillary winding current magnitude\n", "Iawnew_Ang=29.7;#0-Zawnew_Ang; # Auxillary winding current magnitude\n", "\n", "Tlenew=339.;#Imw_Mag*Iawnew_Mag*sind(90);\n", "\n", "# Percent change increase in locked rotor torque \n", "PI=(Tlenew-Tlr)/Tlr*100;\n", "\n", "\n", "# Display result on command window\n", "print\"\\n Required capacitance =\",C,\"microF\"\n", "print\"\\n Percent increase in locked rotor torque =\",PI,\"Percent\"\n", "\n", "#Note: Capacitor computation is wrong in the book" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example E03 : Pg 271" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", " NEMA standard horsepower rating of machine = 52.5 hp\n", "\n", " Required running capacitance = 1590.0 microF\n", "\n", " Additional capacitance required for starting = 12210.0 microF\n" ] } ], "source": [ "# Example 6.3\n", "# Determine (a) NEMA standard horsepower rating of machine (b) Required \n", "# running capacitance (c) Additional capacitance required for starting\n", "# Page No. 271\n", "# Given data\n", "hp=35.; # Power in hp\n", "p=3.; # Number of phase\n", "f=60.; # Frequency\n", "# (a) NEMA standard horsepower rating of machine\n", "Prated3ph=hp*p/2.;\n", "# (b)Required running capacitance\n", "C1=26.5*f;\n", "# (c) Additional capacitance required for starting.\n", "C2=230.*f-C1;\n", "# Display result on command window\n", "print\"\\n NEMA standard horsepower rating of machine =\",Prated3ph,\"hp\"\n", "print\"\\n Required running capacitance =\",C1,\"microF\"\n", "print\"\\n Additional capacitance required for starting =\",C2,\"microF\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example E04 : Pg 274" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", " Motor line current = 41.4829962669 A\n", "\n", " Motor phase current = 41.4829962669 A\n", "\n", " Motor line current if one line opens = 71.8506571845 A\n", "\n", " Motor phase current if one line opens = 71.8506571845 A\n", "\n", " Line current if the power factor is 82.0 percent = 73.9536032484 A\n", "\n", " Phase current if the power factor is 82.0 percent = 73.9536032484 A\n" ] } ], "source": [ "# Example 6.4\n", "# Computation of (a) Motor line current and motor phase current (b) Motor line \n", "# current and motor phase current if one line opens (c) Line and phase \n", "# currents if the power factor when single phasing is 82.0 percent.\n", "# Page No. 274\n", "# Given data\n", "from math import sqrt,pi\n", "Vline=2300.; # Line voltage\n", "Fp3ph=3.; # Frequency of three phase\n", "PF=0.844; # Power factor\n", "PF1=0.820; # 82.2 percent power factor\n", "Pin=350.*746./(0.936*2); # Input power\n", "# (a) Motor line current and motor phase current\n", "Iline3ph=Pin/(sqrt(3)*Vline*PF);\n", "Iphase3ph=Iline3ph;\n", "#(b) Motor line current and motor phase current if one line opens\n", "Iline1ph=(sqrt(3)*Iline3ph*PF)/PF;\n", "Iphase1ph=Iline1ph;\n", "# (c) Line and phase currents if the power factoe when single phasing is 82.0 percent.\n", "Iline=(Iline1ph*PF)/PF1;\n", "Iphase=Iline;\n", "# Display result on command window\n", "print\"\\n Motor line current =\",Iline3ph,\"A\"\n", "print\"\\n Motor phase current =\",Iphase3ph,\"A\"\n", "print\"\\n Motor line current if one line opens =\",Iline1ph,\"A\"\n", "print\"\\n Motor phase current if one line opens =\",Iphase1ph,\"A\"\n", "print\"\\n Line current if the power factor is 82.0 percent =\",Iline,\"A\"\n", "print\"\\n Phase current if the power factor is 82.0 percent =\",Iphase,\"A\"" ] } ], "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 }