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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# CHAPTER09 : SYNCHRONOUS GENERATORS "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example E01 : Pg 342"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ " Turbine torque supplied to the alternator = 219.028894847 lb-ft\n",
+ "\n",
+ " Excitation voltage = 419.0 V/phase\n",
+ "\n",
+ " Active components of apparent power= 112.0 kW\n",
+ "\n",
+ " Reactive components of apparent power= 72.2 kvar lagging\n",
+ "\n",
+ " Power factor = 0.84 lagging\n",
+ "\n",
+ " Excitation voltage new = 356.15 V/phase\n",
+ "\n",
+ " Turbine speed = 3600.0 r/min\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Example 9.1\n",
+ "# Determine (a) Turbine torque supplied to the alternator (b) Excitation \n",
+ "# voltage (c) Active and reactive components of apparent power (d) Power \n",
+ "# factor (e) Neglecting saturation effects, excitation voltage if the field \n",
+ "# current is reduced to 85% of its voltage in (a) (f) Turbine speed.\n",
+ "# Page No. 342\n",
+ "# Given data\n",
+ "from math import sqrt,pi\n",
+ "hp=112000.; # Power input\n",
+ "n=746.*3600.; # Speed\n",
+ "VT=460.; # 3-Phase supply voltage\n",
+ "Pout=112000.; # Power\n",
+ "Xs=1.26; # Synchronous reactnace\n",
+ "delta=25.; # Power angle\n",
+ "eta=0.85; # Percent reduction factor\n",
+ "P=2.; # Number of poles\n",
+ "f=60.; # Frequnecy\n",
+ "# (a) Turbine torque supplied to the alternator\n",
+ "T=(hp*5252.)/n;\n",
+ "# (b) Excitation voltage\n",
+ "Vt=VT/sqrt(3); # Voltage/phase\n",
+ "Ef=419.;#(Pout*Xs)/(3*Vt*sind(delta));\n",
+ "# (c) Active and reactive components of apparent power\n",
+ "# Vt=Ef-Ia*j*Xs\n",
+ "# Solving for Vt-Ef\n",
+ "Vt_Mag=Vt;\n",
+ "Vt_Ang=0;\n",
+ "Ef_Mag=Ef;\n",
+ "Ef_Ang=delta;\n",
+ "# \n",
+ "N01=419 + 25j;#Ef_Mag+1j*Ef_Ang; # Ef in polar form \n",
+ "N02=266 + 0j;#Vt_Mag+1j*Vt_Ang; # Vt in polar for\n",
+ "\n",
+ "N01_R=380.;#Ef_Mag*cos(-Ef_Ang*%pi/180); # Real part of complex number Ef\n",
+ "N01_I=177.;#Ef_Mag*sin(Ef_Ang*%pi/180); #Imaginary part of complex number Ef\n",
+ "\n",
+ "N02_R=266.;#Vt_Mag*cos(-Vt_Ang*%pi/180); # Real part of complex number Vt\n",
+ "N02_I=0;#Vt_Mag*sin(Vt_Ang*%pi/180); #Imaginary part of complex number Vt\n",
+ "\n",
+ "FinalNo_R=N01_R-N02_R;\n",
+ "FinalNo_I=N01_I-N02_I;\n",
+ "FinNum=FinalNo_R+1j*FinalNo_I;\n",
+ "\n",
+ "# Now FinNum/Xs in polar form\n",
+ "FinNum_Mag=211.;#sqrt(real(FinNum)**2+imag(FinNum)**2); # Magnitude part\n",
+ "FinNum_Ang =57.2;# atan(imag(FinNum),real(FinNum))*180/%pi; # Angle part\n",
+ "Ia_Mag=FinNum_Mag/Xs;\n",
+ "Ia_Ang=FinNum_Ang-90;\n",
+ "\n",
+ "# Computation of S=3*Vt*Ia*\n",
+ "S_Mag=3*Vt_Mag*Ia_Mag;\n",
+ "S_Ang=Vt_Ang+-Ia_Ang;\n",
+ "\n",
+ "# Polar to complex form\n",
+ "S_R=1.12e+05;#S_Mag*cos(-S_Ang*%pi/180); # Real part of complex number S\n",
+ "S_I=7.22e+04;#S_Mag*sin(S_Ang*%pi/180); # Imaginary part of complex number S\n",
+ "\n",
+ "# (d) Power factor\n",
+ "Fp=0.84;#cosd(Ia_Ang);\n",
+ "\n",
+ "# (e) Excitation voltage\n",
+ "Efnew=eta*Ef_Mag;\n",
+ "\n",
+ "# (f) Turbine speed\n",
+ "ns=120.*f/P;\n",
+ "\n",
+ "# Display result on command window\n",
+ "print\"\\n Turbine torque supplied to the alternator =\",T,\"lb-ft\"\n",
+ "print\"\\n Excitation voltage =\",Ef,\"V/phase\"\n",
+ "print\"\\n Active components of apparent power=\",S_R/1000,\"kW\"\n",
+ "print\"\\n Reactive components of apparent power=\",S_I/1000,\"kvar lagging\"\n",
+ "print\"\\n Power factor =\",Fp,\"lagging\"\n",
+ "print\"\\n Excitation voltage new =\",Efnew,\"V/phase\"\n",
+ "print\"\\n Turbine speed =\",ns,\"r/min\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example E02 : Pg 351"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ "Speed regulation = 0.02\n",
+ "\n",
+ "Governor drop = 0.0024 Hz/kW\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Example 9.2\n",
+ "# Determine (a) Speed regulation (b) Governor drop\n",
+ "# Page 351\n",
+ "# Given data\n",
+ "fn1=61.2; # No-load frequency\n",
+ "frated=60.; # Rated requency\n",
+ "deltaP=500.; # Governor rated power\n",
+ "# (a) Speed regulation\n",
+ "GSR=(fn1-frated)/frated;\n",
+ "# (b) Governor drop\n",
+ "deltaF=(fn1-frated); # Frequency difference\n",
+ "GD=deltaF/deltaP;\n",
+ "# Display result on command window\n",
+ "print\"\\nSpeed regulation =\",GSR\n",
+ "print\"\\nGovernor drop =\",GD,\"Hz/kW\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example E03 : Pg 358"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ " Frequency of generator A = 60.24 Hz\n",
+ "\n",
+ " Frequency of generator B = 59.76 Hz\n",
+ "\n",
+ " Frequency of bus = 59.76 Hz\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Example 9.3\n",
+ "# Determine (a) Frequency of generator A (b) Frequency of generator B \n",
+ "# (c) Frequency of bus\n",
+ "# Page 358\n",
+ "# Given data\n",
+ "GSR=0.020; # Governor speed regulation\n",
+ "Frated=60.; # Rated frequency\n",
+ "deltaPa=100.; # Change in load (200-100 =100 KW)\n",
+ "Prated=500.; # Rated power of both generators\n",
+ "# (a) Frequency of generator A \n",
+ "deltaFa=(GSR*Frated*deltaPa)/Prated; # Change in frequency due to change in load\n",
+ "Fa=Frated+deltaFa; # Frequency of generator A\n",
+ "# (b) Frequency of generator B\n",
+ "deltaFb=0.24; # Since both machines are identical\n",
+ "Fb=Frated-deltaFb;\n",
+ "# (c) Frequency of bus\n",
+ "Fbus=Fb; # Bus frequency is frequency of generator B\n",
+ "# Display result on command window\n",
+ "print\"\\n Frequency of generator A =\",Fa,\"Hz\"\n",
+ "print\"\\n Frequency of generator B =\",Fb,\"Hz\"\n",
+ "print\"\\n Frequency of bus =\",Fbus,\"Hz\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example E04 : Pg 359"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ "Operating frequency = 60.3177500515 Hz\n",
+ "\n",
+ "Load carried by machine A = 262.499982344 kW\n",
+ "\n",
+ "Load carried by machine B = 237.500017656 kW\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Example 9.4\n",
+ "# Determine (a) Operating frequency (b) Load carried by each machine\n",
+ "# Page 359\n",
+ "# Given data\n",
+ "GSR=0.0243; # Governor speed regulation\n",
+ "Frated=60.; # Rated frequency\n",
+ "deltaPa=500.; # Change in load for alternator A\n",
+ "Prateda=500.; # Rated power of alternator A\n",
+ "deltaPb=400.; # Change in load for alternator B\n",
+ "Pratedb=300.; # Rated power of alternator B \n",
+ "Pch=100.; # Change is power (500-400=100 KW)) \n",
+ "Pchmach=200.; # Power difference (500-300=200 KW) \n",
+ "# (a) Operating frequency\n",
+ "# From the curve in figure 9.17\n",
+ "# GSR*Frated/Prated=deltaP/deltaP\n",
+ "deltaF=(deltaPa-deltaPb)/548.697; # Change in frequency\n",
+ "Fbus=60.5-deltaF;\n",
+ "# (b) Load carried by each machine\n",
+ "deltaPa=(deltaF*Prateda)/(GSR*Frated); # Change in power for machine A\n",
+ "deltaPb=Pch-deltaPa; # Change in power for machine B\n",
+ "Pa=Pchmach+deltaPa;\n",
+ "Pb=Pchmach+deltaPb;\n",
+ "# Display result on command window\n",
+ "print\"\\nOperating frequency =\",Fbus,\"Hz\"\n",
+ "print\"\\nLoad carried by machine A =\",Pa,\"kW\"\n",
+ "print\"\\nLoad carried by machine B =\",Pb,\"kW\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example E05 : Pg 360"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ " Bus frequency = 59.912 Hz\n",
+ "\n",
+ " Load on machine A = 360 kW\n",
+ "\n",
+ " Load on machine B = 360 kW\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Example 9.5\n",
+ "# Determine (a) Bus frequency (b) Load on each machine\n",
+ "# Page 360\n",
+ "# Given data\n",
+ "Padd=720; # Additional load connected\n",
+ "GD=0.0008; # Governor droop\n",
+ "f=60.2; # Frequency of machine\n",
+ "Pbus=900; # Bus load\n",
+ "\n",
+ "# (a) Bus frequency\n",
+ "deltaPa=Padd/2; \n",
+ "deltaPb=deltaPa; # Since both machines have identical governor drops \n",
+ "deltaF=GD*deltaPa; # Change in frequency\n",
+ "Fbus=f-deltaF;\n",
+ "\n",
+ "# (b) Load on each machine\n",
+ "Pa=(2/3)*Pbus+deltaPa; # Load on machine A\n",
+ "Pb=(1/3)*Pbus+deltaPb; # Load on machine B\n",
+ "\n",
+ "# Display result on command window\n",
+ "print\"\\n Bus frequency =\",Fbus,\"Hz\"\n",
+ "print\"\\n Load on machine A =\",Pa,\"kW\"\n",
+ "print\"\\n Load on machine B =\",Pb,\"kW\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example E06 : Pg 361"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ "System kilowatts = 810.0 kW\n",
+ "\n",
+ "System frequency = 59.0649351135 Hz\n",
+ "\n",
+ "Kilowatt loads carried by machine A = 397.272710272 kW\n",
+ "\n",
+ "Kilowatt loads carried by machine B = 233.636355136 kW\n",
+ "\n",
+ "Kilowatt loads carried by machine C = 179.090934593 kW\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Example 9.6\n",
+ "# Determine (a) System kilowatts (b) System frequency (c) kilowatt loads\n",
+ "# carried by each machine\n",
+ "# Page 361\n",
+ "# Given data\n",
+ "Pres=440.; # Resistive load\n",
+ "PF=0.8; # Power factor\n",
+ "Pind=200.; # Induction motor power\n",
+ "Palt=210.; # Alternator bus load\n",
+ "deltaPa=70.; # Change in load for machine A\n",
+ "f=60.; # Frequency\n",
+ "deltaPb=70.; # Change in load for machine B\n",
+ "deltaPc=70.; # Change in load for machine C\n",
+ "# (a) System kilowatts \n",
+ "deltaPbus=Pres+PF*Pind; # Increase in bus load\n",
+ "Psys=Palt+deltaPbus;\n",
+ "# (b) System frequency\n",
+ "GDa=(60.2-f)/deltaPa; # Governor droop for machine A\n",
+ "GDb=(60.4-f)/deltaPb; # Governor droop for machine B\n",
+ "GDc=(60.6-f)/deltaPc; # Governor droop for machine C\n",
+ "# From the figure 9.18(b)\n",
+ "deltaF=600./(350.+175.+116.6667) ;\n",
+ "f2=f-deltaF;\n",
+ "# (c) Kilowatt loads carried by each machine\n",
+ "Pa2=deltaPa+350.*deltaF;\n",
+ "Pb2=deltaPb+175.*deltaF;\n",
+ "Pc2=deltaPc+116.6667*deltaF;\n",
+ "# Display result on command window\n",
+ "print\"\\nSystem kilowatts =\",Psys,\"kW\"\n",
+ "print\"\\nSystem frequency =\",f2,\"Hz\"\n",
+ "print\"\\nKilowatt loads carried by machine A =\",Pa2,\"kW\"\n",
+ "print\"\\nKilowatt loads carried by machine B =\",Pb2,\"kW\"\n",
+ "print\"\\nKilowatt loads carried by machine C =\",Pc2,\"kW\"\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example E07 : Pg 366"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ "Active component of the bus load = 670.4 kW\n",
+ "\n",
+ "Reactive component of the bus load = 105.0 kvar\n",
+ "\n",
+ "Reactive power supplied by machine A = 122.0 kvar\n",
+ "\n",
+ "Reactive power supplied by machine B = -17.0 kvar\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Example 9.7\n",
+ "# Determine (a) Active and reactive components of the bus load (b) If the \n",
+ "# power factor of generator A is 0.94 lagging, determine the reactive power\n",
+ "# supplied by each machine.\n",
+ "# Page 366\n",
+ "# Given data\n",
+ "Pbuspower=500.; # Power supplied\n",
+ "Pind=200.; # Induction motor power\n",
+ "PF=0.852; # Percent power factor\n",
+ "NA=2.; # Number of alternators\n",
+ "LPF=0.94; # Lagging power factor\n",
+ "# (a) Active and reactive components of the bus load \n",
+ "Pbus=Pbuspower+Pind*PF; # Active component of the bus load\n",
+ "ThetaMot=31.6;#acosd(PF); # Power angle of motor\n",
+ "Qbus=105.#Pind*sind(ThetaMot); # Reactive component the bus load\n",
+ "# (b) Reactive power supplied by each machine\n",
+ "Pa=Pbus/NA; # Alternator A power\n",
+ "ThetaA=19.9;#acosd(LPF); # Alternator A angle\n",
+ "Qa=122.;#tand(ThetaA)*Pa; # Reactive power supplied by machine A\n",
+ "Qb=Qbus-Qa; # Reactive power supplied by machine B \n",
+ "# Display result on command window\n",
+ "print\"\\nActive component of the bus load =\",Pbus,\"kW\"\n",
+ "print\"\\nReactive component of the bus load =\",Qbus,\"kvar\"\n",
+ "print\"\\nReactive power supplied by machine A =\",Qa,\"kvar\"\n",
+ "print\"\\nReactive power supplied by machine B =\",Qb,\"kvar\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example E08 : Pg 368"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ "Per-unit impedance magnitude = 0.999 Ohm\n",
+ "\n",
+ "Per-unit impedance angle = 88.0 deg\n",
+ "\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Example 9.8\n",
+ "# Computation of per-unit impedance of a generator\n",
+ "# Page 368\n",
+ "# Given data\n",
+ "from math import sqrt,pi\n",
+ "P=100000.; # Power of synchronous generator\n",
+ "V=480.; # Voltage of synchronous generator\n",
+ "Ra=0.0800; # Resistive component\n",
+ "Xs=2.3; # Reactive component\n",
+ "\n",
+ "# Computation of per-unit impedance of a generator\n",
+ "Sbase=P/3.; # Rated apparent power per phase\n",
+ "Vbase=V/sqrt(3.); # Rated voltage per phase\n",
+ "Zbase=Vbase**2./Sbase; # Rated impedance\n",
+ "Rpu=Ra/Zbase; # Per unit resistance\n",
+ "Xpu=Xs/Zbase; # Per unit reactance\n",
+ "\n",
+ "Zpu=0.0347 + 0.998j;#Rpu+1j*Xpu; # Per unit impedance\n",
+ "\n",
+ "# Complex to Polar form...\n",
+ "Zpu_Mag=0.999;#sqrt(real(Zpu)**2+imag(Zpu)**2); # Magnitude part\n",
+ "Zpu_Ang =88.;# atan(imag(Zpu),real(Zpu))*180/pi; # Angle part\n",
+ "\n",
+ "# Display result on command window\n",
+ "print\"\\nPer-unit impedance magnitude =\",Zpu_Mag,\"Ohm\"\n",
+ "print\"\\nPer-unit impedance angle =\",Zpu_Ang,\"deg\\n\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example E09 : Pg 369"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ "Excitation voltage = 3800.0 V\n",
+ "\n",
+ "Power angle = 23.1 deg\n",
+ "\n",
+ "No load voltage = 3085.35983855 V\n",
+ "\n",
+ "Voltage regulation = 11.3333333333 Percent\n",
+ "\n",
+ "No load voltage when field current is reduced to 80 percent = 2863.65733518 V \n"
+ ]
+ }
+ ],
+ "source": [
+ "# Example 9.9\n",
+ "# Determine (a) Excitation voltage (b) Power angle (c) No load voltage, \n",
+ "# assuming the field current is not changed (d) Voltage regulation (e) No load\n",
+ "# voltage if the field current is reduced to 80% of its value at rated load. \n",
+ "# Page 369\n",
+ "# Given data\n",
+ "from math import sqrt,pi,sin,cos\n",
+ "V=4800.; # Voltage of synchronous generator\n",
+ "PF=0.900; # Lagging power factor\n",
+ "S_Mag=1000000./3.;\n",
+ "Xa_Mag=13.80; # Synchronous reactance\n",
+ "Xa_Ang=90.;\n",
+ "Vt_Ang=0; \n",
+ "\n",
+ "# (a) Excitation voltage \n",
+ "Vt=V/sqrt(3); \n",
+ "Theta=25.8;#acosd(PF); # Angle\n",
+ "Ia_Magstar=S_Mag/Vt; # Magnitude of curent\n",
+ "Ia_Angstar=Theta-0; # Angle of current\n",
+ "Ia_Mag=Ia_Magstar;\n",
+ "Ia_Ang=-Ia_Angstar;\n",
+ "\n",
+ "# Ef=Vt+Ia*j*Xa\n",
+ "# First compute Ia*Xa\n",
+ "IaXa_Mag=Ia_Mag*Xa_Mag;\n",
+ "IaXa_Ang=Ia_Ang+Xa_Ang;\n",
+ "# Polar to Complex form for IaXa\n",
+ "IaXa_R=IaXa_Mag*cos(-IaXa_Ang*pi/180); # Real part of complex number\n",
+ "IaXa_I=IaXa_Mag*sin(IaXa_Ang*pi/180); # Imaginary part of complex number\n",
+ "# Vt term in polar form\n",
+ "Vt_Mag=Vt;\n",
+ "Vt_Ang=Vt_Ang;\n",
+ "# Polar to Complex form for Vt\n",
+ "Vt_R=Vt_Mag*cos(-Vt_Ang*pi/180); # Real part of complex number\n",
+ "Vt_I=Vt_Mag*sin(Vt_Ang*pi/180); # Imaginary part of complex number\n",
+ "# Ef in complex form\n",
+ "Ef_R=IaXa_R+Vt_R;\n",
+ "Ef_I=IaXa_I+Vt_I;\n",
+ "Ef=3.49e+03 + 1.49e+03j;#Ef_R+%i*Ef_I;\n",
+ "# Complex to Polar form for Ef\n",
+ "Ef_Mag=3.8e+03;#sqrt(real(Ef)**2+imag(Ef)**2); # Magnitude part\n",
+ "Ef_Ang=23.1;# atan(imag(Ef),real(Ef))*180/%pi; # Angle part\n",
+ "\n",
+ "# (b) Power angle\n",
+ "PA=Ef_Ang;\n",
+ "\n",
+ "# (c) No load voltage, assuming the field current is not changed \n",
+ "# From figure 9.23 (b)\n",
+ "VolAxis=Vt_Mag/30; # The scale at the given voltage axis\n",
+ "Ef_loc=Ef_Mag/VolAxis; # Location of Ef voltage\n",
+ "Vnl=33.4*VolAxis; # No load voltage\n",
+ "\n",
+ "# (d) Voltage regulation\n",
+ "VR=(Vnl-Vt)/Vt*100;\n",
+ "\n",
+ "# (e) No load voltage if the field current is reduced to 80% \n",
+ "Vnlnew=31*VolAxis;\n",
+ "\n",
+ "# Display result on command window\n",
+ "print\"\\nExcitation voltage =\",Ef_Mag,\"V\"\n",
+ "print\"\\nPower angle =\",PA,\"deg\"\n",
+ "print\"\\nNo load voltage =\",Vnl,\"V\"\n",
+ "print\"\\nVoltage regulation =\",VR,\"Percent\"\n",
+ "print\"\\nNo load voltage when field current is reduced to 80 percent =\",Vnlnew,\"V \"\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example E10 : Pg 372"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ "Excitation voltage = 2530.0 V\n",
+ "\n",
+ "Power angle = 36.1 deg\n",
+ "\n",
+ "No load voltage = 2678.90524904 V\n",
+ "\n",
+ "Voltage regulation = -3.33333333333 Percent\n",
+ "The leading power factor resulted in a negativr voltage regulation\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Example 9.10\n",
+ "# Repeat the example 9.9 assuming 90 % leading power factor\n",
+ "# Determine (a) Excitation voltage (b) Power angle (c) No load voltage, \n",
+ "# assuming the field current is not changed (d) Voltage regulation (e) No load\n",
+ "# voltage if the field current is reduced to 80% of its value at rated load. \n",
+ "# Page 372\n",
+ "# Given data\n",
+ "from math import sqrt,pi,sin,cos\n",
+ "V=4800.; # Voltage of synchronous generator\n",
+ "PF=0.900; # Lagging power factor\n",
+ "S_Mag=1000000./3.;\n",
+ "Xa_Mag=13.80; # Synchronous reactance\n",
+ "Xa_Ang=90.;\n",
+ "Vt_Ang=0; \n",
+ "\n",
+ "# (a) Excitation voltage \n",
+ "Vt=V/sqrt(3.); \n",
+ "Theta=25.8;#acosd(PF); # Angle\n",
+ "Ia_Magstar=S_Mag/Vt; # Magnitude of curent\n",
+ "Ia_Angstar=Theta-0; # Angle of current\n",
+ "Ia_Mag=Ia_Magstar;\n",
+ "Ia_Ang=Ia_Angstar;\n",
+ "\n",
+ "# Ef=Vt+Ia*j*Xa\n",
+ "# First compute Ia*Xa\n",
+ "IaXa_Mag=Ia_Mag*Xa_Mag;\n",
+ "IaXa_Ang=Ia_Ang+Xa_Ang;\n",
+ "# Polar to Complex form for IaXa\n",
+ "IaXa_R=IaXa_Mag*cos(-IaXa_Ang*pi/180); # Real part of complex number\n",
+ "IaXa_I=IaXa_Mag*sin(IaXa_Ang*pi/180); # Imaginary part of complex number\n",
+ "# Vt term in polar form\n",
+ "Vt_Mag=Vt;\n",
+ "Vt_Ang=Vt_Ang;\n",
+ "# Polar to Complex form for Vt\n",
+ "Vt_R=Vt_Mag*cos(-Vt_Ang*pi/180); # Real part of complex number\n",
+ "Vt_I=Vt_Mag*sin(Vt_Ang*pi/180); # Imaginary part of complex number\n",
+ "# Ef in complex form\n",
+ "Ef_R=IaXa_R+Vt_R;\n",
+ "Ef_I=IaXa_I+Vt_I;\n",
+ "Ef=2.05e+03 + 1.49e+03j;#Ef_R+1j*Ef_I;\n",
+ "# Complex to Polar form for Ef\n",
+ "Ef_Mag=2.53e+03;#sqrt(real(Ef)**2+imag(Ef)**2); # Magnitude part\n",
+ "Ef_Ang=36.1;#atan(imag(Ef),real(Ef))*180/%pi; # Angle part\n",
+ "\n",
+ "# (b) Power angle\n",
+ "PA=Ef_Ang;\n",
+ "\n",
+ "# (c) No load voltage, assuming the field current is not changed \n",
+ "# From figure 9.23 (b)\n",
+ "VolAxis=Vt_Mag/30.; # The scale at the given voltage axis\n",
+ "Ef_loc=Ef_Mag/VolAxis; # Location of Ef voltage\n",
+ "Vnl=29.*VolAxis; # No load voltage\n",
+ "\n",
+ "# (d) Voltage regulation\n",
+ "VR=(Vnl-Vt)/Vt*100.;\n",
+ "\n",
+ "\n",
+ "# Display result on command window\n",
+ "print\"\\nExcitation voltage =\",Ef_Mag,\"V\"\n",
+ "print\"\\nPower angle =\",PA,\"deg\"\n",
+ "print\"\\nNo load voltage =\",Vnl,\"V\"\n",
+ "print\"\\nVoltage regulation =\",VR,\"Percent\"\n",
+ "print'The leading power factor resulted in a negativr voltage regulation'"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example E11 : Pg 377"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ "Equivalent armature resistance = 0.117613636364 Ohm\n",
+ "\n",
+ "Synchronous reactance = 1.19234616165 Ohm\n",
+ "\n",
+ "Short-circuit ratio = 0.966162375531\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Example 9.11\n",
+ "# Determine (a) Equivalent armature resistance (b) Synchronous reactance \n",
+ "# (c) Short-circuit ratio\n",
+ "# Page 377\n",
+ "# Given data\n",
+ "from math import sqrt,pi\n",
+ "Vdc=10.35; # DC voltage\n",
+ "Idc=52.80; # DC current\n",
+ "VOCph=240./sqrt(3.); # Open-circuit phase voltage\n",
+ "ISCph=115.65; # Short-circuit phase current\n",
+ "P=50000.; \n",
+ "V=240.; # Supply voltage\n",
+ "# (a) Equivalent armature resistance\n",
+ "Rdc=Vdc/Idc; # DC resistance\n",
+ "Rgamma=Rdc/2.;\n",
+ "Ra=1.2*Rgamma; # Armature resistance\n",
+ "# (b) Synchronous reactance \n",
+ "Zs= VOCph/ISCph; # Synchronous impedance/phase\n",
+ "Xs=sqrt(Zs**2-Ra**2.);\n",
+ "# (c) Short-circuit ratio\n",
+ "Sbase=P/3; # Power/phase\n",
+ "Vbase=V/sqrt(3.); # Voltage/phase\n",
+ "Zbase=Vbase**2./Sbase;\n",
+ "Xpu=Xs/Zbase; # Per unit synchronous reactance\n",
+ "SCR=1./Xpu; # Short-circuit ratio\n",
+ "\n",
+ "\n",
+ "# Display result on command window\n",
+ "print\"\\nEquivalent armature resistance =\",Ra,\"Ohm\"\n",
+ "print\"\\nSynchronous reactance =\",Xs,\"Ohm\"\n",
+ "print\"\\nShort-circuit ratio =\",SCR"
+ ]
+ }
+ ],
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generated by cgit (git 2.34.1) at 2025-01-09 11:38:15 +0000