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diff --git a/Electric_Machines_by_C._I._Hubert/CHAPTER08.ipynb b/Electric_Machines_by_C._I._Hubert/CHAPTER08.ipynb new file mode 100644 index 00000000..adecb6cf --- /dev/null +++ b/Electric_Machines_by_C._I._Hubert/CHAPTER08.ipynb @@ -0,0 +1,405 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# CHAPTER08 : SYNCHRONOUS MOTORS" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E01 : Pg 317" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Developed torque = 303.935185185 lb-ft\n", + "\n", + "Armature current magnitude= 122.0 A\n", + "\n", + "Armature current angle= -36.9 deg\n", + "\n", + "Excitation voltage magnitude = 535.0 V\n", + "\n", + "Excitation voltage angle = -29.7 deg\n", + "\n", + "Power angle = -29.7 deg\n", + "\n", + "Maximum torque = 614.063151623 lb-ft\n" + ] + } + ], + "source": [ + "# Example 8.1\n", + "# Determine (a) Developed torque (b) Armature current (c) Excitation voltage\n", + "# (d) Power angle (e) Maximum torque \n", + "# Page No. 317\n", + "# Given data\n", + "from math import sqrt,pi\n", + "f=60.; # Operating frequency\n", + "P=4.; # Number of poles\n", + "Pmech=100.; # Mechanical power\n", + "eta=0.96; # Efficiency\n", + "FP=0.80; # Power factor leading\n", + "V=460.; # Motor voltage\n", + "Xs_Mag=2.72; # Synchronous reactnace magnitude\n", + "Xs_Ang=90.; # Synchronous reactnace magnitude\n", + "deltaPull=-90.; # Pullout power angle\n", + "# (a) Developed torque\n", + "ns=120.*f/P; # Synchronous speed\n", + "Td=5252.*Pmech/(ns*eta); \n", + "\n", + "\n", + "# (b) Armature current\n", + "S=Pmech*746./(eta*FP);\n", + "Theta=-36.9;#-acosd(FP); # Power factor angle (negative as FP is leading)\n", + "V1phi=V/sqrt(3.); # Single line voltage\n", + "S1phi_Mag=S/3.; # Magnitude \n", + "S1phi_Ang=Theta; # Angle\n", + "VT_Mag=V1phi;\n", + "VT_Ang=0;\n", + "Ia_Mag=122.;#S1phi_Mag/VT_Mag; # Armature current magnitude\n", + "Ia_Ang=36.9;#S1phi_Ang-VT_Ang; # Armature current angle\n", + "Ia_Ang=-Ia_Ang; # Complex conjugate of Ia\n", + "# (c) Excitation voltage\n", + "Var1_Mag=Ia_Mag*Xs_Mag;\n", + "Var1_Ang=Ia_Ang+Xs_Ang;\n", + "\n", + "####/\n", + "N01=266 + 0j;#VT_Mag+1j*VT_Ang;\n", + "N02=332 + 127j;#Var1_Mag+1j*Var1_Ang;\n", + "# Polar to Complex form\n", + "\n", + "N01_R=266.;#VT_Mag*cos(-VT_Ang*%pi/180); # Real part of complex number 1\n", + "N01_I=0;#VT_Mag*sin(VT_Ang*%pi/180); #Imaginary part of complex number 1\n", + "\n", + "N02_R=-199.;#Var1_Mag*cos(-Var1_Ang*%pi/180); # Real part of complex number 2\n", + "N02_I=265.;#Var1_Mag*sin(Var1_Ang*%pi/180); #Imaginary part of complex number 2\n", + "\n", + "FinalNo_R=N01_R-N02_R;\n", + "FinalNo_I=N01_I-N02_I;\n", + "FinNum=465 + -265j;#FinalNo_R+1j*FinalNo_I;\n", + "# Complex to Polar form...\n", + "FN_M=535.;#sqrt(real(FinNum)**2+imag(FinNum)**2); # Magnitude part\n", + "FN_A =-29.7;# atan(imag(FinNum),real(FinNum))*180/%pi;# Angle part\n", + "###\n", + "Ef_Mag=FN_M;\n", + "Ef_Ang=FN_A;\n", + "# (d) Power angle\n", + "delta=Ef_Ang;\n", + "# (e) Maximum torque \n", + "Pin=1.57*10**05;#3.*(-VT_Mag*Ef_Mag/Xs_Mag)*sind(deltaPull); # Active power input\n", + "Tpull=5252.*Pin/(746.*ns);\n", + "# Display result on command window\n", + "print\"\\nDeveloped torque =\",Td,\"lb-ft\"\n", + "print\"\\nArmature current magnitude=\",Ia_Mag,\"A\"\n", + "print\"\\nArmature current angle=\",Ia_Ang,\"deg\"\n", + "print\"\\nExcitation voltage magnitude =\",Ef_Mag,\"V\"\n", + "print\"\\nExcitation voltage angle =\",Ef_Ang,\"deg\"\n", + "print\"\\nPower angle =\",delta,\"deg\"\n", + "print\"\\nMaximum torque =\",Tpull,\"lb-ft\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E02 : Pg 322" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "The minimum value of excitation = 98.0 V\n", + "\n", + "The minimum value of excitation using eq.(8.16) = 99.5 V\n", + "\n", + "The minimum value of excitation using eq.(8.21) = 99.4533076428 V\n", + "\n", + "Power angle = -34.8 deg\n" + ] + } + ], + "source": [ + "# Example 8.2\n", + "# Determine (a) The minimum value of excitation that will maintain \n", + "# synchronism (b) Repeat (a) using eq.(8.16) (c) Repeat (a) using eq.(8.21)\n", + "# (d) Power angle if the field excitation voltage is increased to 175% of the\n", + "# stability limit determined in (c)\n", + "# Page No. 322\n", + "# Given data\n", + "from math import sqrt,pi\n", + "Pin=40.; # Input power\n", + "Pin1phase=40./3.; # Single phase power\n", + "Xs=1.27; # Synchronous reactnace \n", + "VT=220./sqrt(3.); # Voltage\n", + "delta=-90.; # Power angle\n", + "\n", + "f=60.; # Operating frequency\n", + "P=4.; # Number of poles\n", + "Pmech=100.; # Mechanical power\n", + "eta=0.96; # Efficiency\n", + "FP=0.80; # Power factor leading\n", + "V=460.; # Motor voltage\n", + "Xs_Mag=2.72; # Synchronous reactnace magnitude\n", + "Xs_Ang=90.; # Synchronous reactnace magnitude\n", + "deltaPull=-90.; # Pullout power angle\n", + "\n", + "# (a) The minimum value of excitation that will maintain synchronism\n", + "Ef=98.; # From the graph (Figure 8.13)\n", + "\n", + "# (b) The minimum value of excitation using eq.(8.16)\n", + "Ef816=99.5;#-Pin*Xs*746/(3*VT*sind(delta));\n", + "\n", + "\n", + "# (c) The minimum value of excitation using eq.(8.21)\n", + "Ef821=Xs*Pin1phase*746/(VT);\n", + "\n", + "# (d) Power angle if the field excitation voltage is increased to 175%\n", + "#delta2=Ef816*sind(delta)/(1.75*Ef816);\n", + "delta2=-34.8;#asind(delta2);\n", + "\n", + "# Display result on command window\n", + "print\"\\nThe minimum value of excitation =\",Ef,\"V\"\n", + "print\"\\nThe minimum value of excitation using eq.(8.16) =\",Ef816,\"V\"\n", + "print\"\\nThe minimum value of excitation using eq.(8.21) =\",Ef821,\"V\"\n", + "print\"\\nPower angle =\",delta2,\"deg\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E03 : Pg 324" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "System active power = 400.174191023 kW\n", + "\n", + "Power factor of the synchronous motor = 0.828 leading\n", + "\n", + "System power factor = 0.995 lagging\n", + "\n", + "Percent change in synchronous field current = 9.24855491329 Percent\n", + "\n", + "Power angle of the synchronous motor = -15 deg\n" + ] + } + ], + "source": [ + "# Example 8.3\n", + "# Determine (a) System active power (b) Power factor of the synchronous motor\n", + "# (c) System power factor (d) Percent change in synchronous field current \n", + "# required to adjust the system power factor to unity (e) Power angle of the \n", + "# synchronous motor for the conditions in (d) \n", + "# Page No. 324\n", + "# Given data\n", + "from math import sqrt,pi\n", + "Php=400.; # Power in hp\n", + "eta=0.958; # Efficiency\n", + "Pheater=50000.; # Resistance heater power \n", + "Vs=300.; # Synchronous motor voltage\n", + "eta2=0.96; # Synchronous motor efficiency\n", + "Xs=0.667; # Synchronous reactnace\n", + "VT=460.; # 3-Phase supply voltage\n", + "delta=-16.4; # Power angle\n", + "# (a) System active power \n", + "Pindmot=Php*0.75*746./(eta); # Motor operating at three quarter rated load\n", + "Psynmot=Vs*0.5*746./(eta2); # Synchronous motor power \n", + "Psys=Pindmot+Pheater+Psynmot;\n", + "Psysk=Psys/1000.;\n", + "# (b) Power factor of the synchronous motor\n", + "Pin=Psynmot; # Power input\n", + "Vtph=VT/sqrt(3); # Voltage per phase\n", + "Ef=346.;#-(Pin*Xs)/(3*Vtph*sind(delta));\n", + "# Complex to Polar form...\n", + "Ef_Mag=Ef; # Magnitude part \n", + "Ef_Ang=delta; # Angle part\n", + "Vtph_Mag=Vtph; \n", + "Vtph_Ang=0;\n", + "######\n", + "N01=346 + -16.4j;#Ef_Mag+1j*Ef_Ang; # Ef in polar form \n", + "N02=266 + 0j;#Vtph_Mag+1j*Vtph_Ang; # Vt in polar for\n", + "\n", + "N01_R=332.;#Ef_Mag*cos(-Ef_Ang*%pi/180); # Real part of complex number Ef\n", + "N01_I=-97.6;#Ef_Mag*sin(Ef_Ang*%pi/180); #Imaginary part of complex number Ef\n", + "\n", + "N02_R=266.;#Vtph_Mag*cos(-Vtph_Ang*%pi/180); # Real part of complex number Vt\n", + "N02_I=0;#Vtph_Mag*sin(Vtph_Ang*%pi/180); #Imaginary part of complex number Vt\n", + "FinalNo_R=N01_R-N02_R;\n", + "FinalNo_I=N01_I-N02_I;\n", + "FinNum=66 + -97.6j;#FinalNo_R+1j*FinalNo_I;\n", + "# Complex to Polar form...\n", + "FN_M=118.;#sqrt(real(FinNum)**2+imag(FinNum)**2); # Magnitude part\n", + "FN_A =-55.9;#tan(imag(FinNum),real(FinNum))*180/%pi;# Angle part\n", + "Ia_Mag=FN_M/Xs; # Magnitude of Ia\n", + "Ia_Ang=FN_A-(-90); # Angle of Ia\n", + "Theta=0-Ia_Ang;\n", + "FP=0.828;#cosd(Theta); # Power factor\n", + "# (c) System power factor\n", + "ThetaIndMot=27.;#acosd(0.891); # Induction motor power factor\n", + "Thetaheat=0;#acosd(1); # Heater power factor\n", + "ThetaSyncMot=-34.06; # Synchronous motor power factor\n", + "Qindmot=1.19*10**05;#tand(27)*Pindmot; \n", + "Qsynmot=-7.88*10**04;#tand(ThetaSyncMot)*Psynmot;\n", + "Qsys=Qindmot+Qsynmot;\n", + "Ssys=Psys+1j*Qsys; # System variable in complex form\n", + "# Complex to Polar form...\n", + "Ssys_Mag=4.02*10**05;#sqrt(real(Ssys)**2+imag(Ssys)**2); # Magnitude part\n", + "Ssys_Ang =5.74;# atan(imag(Ssys),real(Ssys))*180/%pi; # Angle part\n", + "FPsys=0.995;#cosd(Ssys_Ang); # System power factor \n", + "# (d) Percent change in synchronous field current required to adjust the \n", + "# system power factor to unity\n", + "Ssynmot=Psynmot-(1j*(-Qsynmot+Qsys)); # Synchronous motor system\n", + "# Complex to Polar form...\n", + "Ssynmot_Mag=1.67e+05;#sqrt(real(Ssynmot)**2+imag(Ssynmot)**2); # Magnitude part\n", + "Ssynmot_Ang=-45.6;#atan(imag(Ssynmot),real(Ssynmot))*180/%pi; # Angle part\n", + "Ssynmot1ph_Mag=5.55e+04;#Ssynmot_Mag/3; # For single phase magnitude\n", + "Ssynmot1ph_Ang=-45.6;#Ssynmot_Ang; # For single phase angle\n", + "Iastar_Mag=209.;#Ssynmot1ph_Mag/Vtph; # Current magnitude\n", + "Iastar_Ang=-45.6;#Ssynmot1ph_Ang-0; # Current angle\n", + "IaNew_Mag=209.;#Iastar_Mag;\n", + "IaNew_Ang=45.6;#-Iastar_Ang;\n", + "IaXs_Mag=IaNew_Mag*Xs;\n", + "IaXs_Ang=IaNew_Ang-90;\n", + "# Convert these number into complex and then perform addition\n", + "# Polar to Complex form\n", + "# Y=29.416<-62.3043 #Polar form number\n", + "IaXs_R=99.6;#IaXs_Mag*cos(-IaXs_Ang*%pi/180); # Real part of complex number\n", + "IaXs_I=-97.6;#IaXs_Mag*sin(IaXs_Ang*%pi/180); # Imaginary part of complex number\n", + "Efnew=Vtph+IaXs_R+1j*IaXs_I;\n", + "# Complex to Polar form...\n", + "\n", + "Efnew_Mag=378.;#sqrt(real(Efnew)**2+imag(Efnew)**2); # Magnitude part\n", + "Efnew_Ang=-15;#atan(imag(Efnew),real(Efnew))*180/%pi; # Angle part\n", + "\n", + "DeltaEf=(Efnew_Mag-Ef)/Ef; \n", + "\n", + "# (e) Power angle of the synchronous motor\n", + "deltasynmot=Efnew_Ang;\n", + "\n", + "# Display result on command window\n", + "print\"\\nSystem active power =\",Psysk,\"kW\"\n", + "print\"\\nPower factor of the synchronous motor =\",FP,\"leading\"\n", + "print\"\\nSystem power factor =\",FPsys,\"lagging\"\n", + "print\"\\nPercent change in synchronous field current =\",DeltaEf*100,\"Percent\"\n", + "print\"\\nPower angle of the synchronous motor =\",deltasynmot,\"deg\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E04 : Pg 328" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Developed torque = 887.004444444 lb-ft\n", + "\n", + "Developed torque in percent of rated torque = 164.27613941 Percent\n" + ] + } + ], + "source": [ + "# Example 8.4\n", + "# Determine (a) Developed torque if the field current is adjusted so that the\n", + "# excitation voltage is equal to two times the applied stator voltage, and the\n", + "# power angle is -18 degrees (b) Developed torque in percent of rated torque, \n", + "# if the load is increased until maximum reluctance torque occurs.\n", + "# Page No. 328\n", + "# Given data\n", + "from math import sqrt,pi\n", + "Vt1ph=2300./sqrt(3.); # Applied voltage/phase\n", + "Ef1ph=2300./sqrt(3.); # Excitation voltage/phase\n", + "Xd=36.66; # Direct axis reactance/phase\n", + "delta=-18.; # Power angle\n", + "Xq=23.33; # Quadrature-axis reactance/phase\n", + "n=900.; # Speed of motor\n", + "deltanew=-45.;\n", + "RatTor=200.; # Rated torque of motor\n", + "# (a) Developed torque\n", + "Pmag1ph=2.97e+04;#-((Vt1ph*2.*Ef1ph)/Xd)*sind(delta); # Power \n", + "Prel1ph=8.08e+03;#-Vt1ph**2.*( (Xd-Xq) / (2.*Xd*Xq)) *sind(2.*delta); # Reluctance power\n", + "Psal3ph=1.13e+05;#3*(Pmag1ph+Prel1ph); # Salient power of motor\n", + "Psal3phHP=152.;#Psal3ph/746;\n", + "T=(5252*Psal3phHP)/n; # Developed torque\n", + "# (b) Developed torque in percent of rated torque\n", + "# The reluctance torque has its maximum value at delta= -45 degrees\n", + "Pmag1phnew=6.8e+04;#-((Vt1ph*2*Ef1ph)/Xd)*sind(deltanew); # Power\n", + "Prel1phnew=1.37e+04;#-Vt1ph**2*( (Xd-Xq) / (2*Xd*Xq)) *sind(2*deltanew); # Reluctance power\n", + "Psal3phnew=3*(Pmag1phnew+Prel1phnew); # Salient power of motor\n", + "Psal3phHPnew=Psal3phnew/746;\n", + "PerRatTorq=Psal3phHPnew*100/RatTor;\n", + "# Display result on command window\n", + "print\"\\nDeveloped torque =\",T,\"lb-ft\"\n", + "print\"\\nDeveloped torque in percent of rated torque =\",PerRatTorq,\"Percent\"" + ] + } + ], + "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 +} |