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authorprashantsinalkar2017-10-10 12:27:19 +0530
committerprashantsinalkar2017-10-10 12:27:19 +0530
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treedbb9e3ddb5fc829e7c5c7e6be99b2c4ba356132c /3574/CH9
parentb1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b (diff)
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diff --git a/3574/CH9/EX9.1/EX9_1.png b/3574/CH9/EX9.1/EX9_1.png
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+// Example 9.1
+// Determine (a) Turbine torque supplied to the alternator (b) Excitation
+// voltage (c) Active and reactive components of apparent power (d) Power
+// factor (e) Neglecting saturation effects, excitation voltage if the field
+// current is reduced to 85% of its voltage in (a) (f) Turbine speed.
+// Page No. 342
+
+clc;
+clear;
+close;
+
+// Given data
+hp=112000; // Power input
+n=746*3600; // Speed
+VT=460; // 3-Phase supply voltage
+Pout=112000; // Power
+Xs=1.26; // Synchronous reactnace
+delta=25; // Power angle
+eta=0.85; // Percent reduction factor
+P=2; // Number of poles
+f=60; // Frequnecy
+
+// (a) Turbine torque supplied to the alternator
+T=(hp*5252)/n;
+
+// (b) Excitation voltage
+Vt=VT/sqrt(3); // Voltage/phase
+Ef=(Pout*Xs)/(3*Vt*sind(delta));
+
+// (c) Active and reactive components of apparent power
+// Vt=Ef-Ia*j*Xs
+// Solving for Vt-Ef
+Vt_Mag=Vt;
+Vt_Ang=0;
+Ef_Mag=Ef;
+Ef_Ang=delta;
+//
+N01=Ef_Mag+%i*Ef_Ang; // Ef in polar form
+N02=Vt_Mag+%i*Vt_Ang; // Vt in polar for
+
+N01_R=Ef_Mag*cos(-Ef_Ang*%pi/180); // Real part of complex number Ef
+N01_I=Ef_Mag*sin(Ef_Ang*%pi/180); //Imaginary part of complex number Ef
+
+N02_R=Vt_Mag*cos(-Vt_Ang*%pi/180); // Real part of complex number Vt
+N02_I=Vt_Mag*sin(Vt_Ang*%pi/180); //Imaginary part of complex number Vt
+
+FinalNo_R=N01_R-N02_R;
+FinalNo_I=N01_I-N02_I;
+FinNum=FinalNo_R+%i*FinalNo_I;
+
+// Now FinNum/Xs in polar form
+FinNum_Mag=sqrt(real(FinNum)^2+imag(FinNum)^2); // Magnitude part
+FinNum_Ang = atan(imag(FinNum),real(FinNum))*180/%pi; // Angle part

+Ia_Mag=FinNum_Mag/Xs;
+Ia_Ang=FinNum_Ang-90;
+
+// Computation of S=3*Vt*Ia*
+S_Mag=3*Vt_Mag*Ia_Mag;
+S_Ang=Vt_Ang+-Ia_Ang;
+
+// Polar to complex form
+S_R=S_Mag*cos(-S_Ang*%pi/180); // Real part of complex number S
+S_I=S_Mag*sin(S_Ang*%pi/180); // Imaginary part of complex number S
+
+// (d) Power factor
+Fp=cosd(Ia_Ang);
+
+// (e) Excitation voltage
+Efnew=eta*Ef_Mag;
+
+// (f) Turbine speed
+ns=120*f/P;
+
+// Display result on command window
+printf("\n Turbine torque supplied to the alternator = %0.1f lb-ft ",T);
+printf("\n Excitation voltage = %0.1f V/phase ",Ef);
+printf("\n Active components of apparent power= %0.0f kW ",S_R/1000);
+printf("\n Reactive components of apparent power= %0.1f kvar lagging ",S_I/1000);
+printf("\n Power factor = %0.2f lagging ",Fp);
+printf("\n Excitation voltage new = %0.1f V/phase ",Efnew);
+printf("\n Turbine speed = %0.0f r/min ",ns);
diff --git a/3574/CH9/EX9.10/EX9_10.png b/3574/CH9/EX9.10/EX9_10.png
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+// Example 9.10
+// Repeat the example 9.9 assuming 90 % leading power factor
+// Determine (a) Excitation voltage (b) Power angle (c) No load voltage,
+// assuming the field current is not changed (d) Voltage regulation (e) No load
+// voltage if the field current is reduced to 80% of its value at rated load.
+// Page 372
+
+clc;
+clear;
+close;
+
+// Given data
+V=4800; // Voltage of synchronous generator
+PF=0.900; // Lagging power factor
+S_Mag=1000000/3;
+Xa_Mag=13.80; // Synchronous reactance
+Xa_Ang=90;
+Vt_Ang=0;
+
+// (a) Excitation voltage
+Vt=V/sqrt(3);
+Theta=acosd(PF); // Angle
+Ia_Magstar=S_Mag/Vt; // Magnitude of curent
+Ia_Angstar=Theta-0; // Angle of current
+Ia_Mag=Ia_Magstar;
+Ia_Ang=Ia_Angstar;
+
+// Ef=Vt+Ia*j*Xa
+// First compute Ia*Xa
+IaXa_Mag=Ia_Mag*Xa_Mag;
+IaXa_Ang=Ia_Ang+Xa_Ang;
+// Polar to Complex form for IaXa
+IaXa_R=IaXa_Mag*cos(-IaXa_Ang*%pi/180); // Real part of complex number
+IaXa_I=IaXa_Mag*sin(IaXa_Ang*%pi/180); // Imaginary part of complex number
+// Vt term in polar form
+Vt_Mag=Vt;
+Vt_Ang=Vt_Ang;
+// Polar to Complex form for Vt
+Vt_R=Vt_Mag*cos(-Vt_Ang*%pi/180); // Real part of complex number
+Vt_I=Vt_Mag*sin(Vt_Ang*%pi/180); // Imaginary part of complex number
+// Ef in complex form
+Ef_R=IaXa_R+Vt_R;
+Ef_I=IaXa_I+Vt_I;
+Ef=Ef_R+%i*Ef_I;
+// Complex to Polar form for Ef
+Ef_Mag=sqrt(real(Ef)^2+imag(Ef)^2); // Magnitude part
+Ef_Ang= atan(imag(Ef),real(Ef))*180/%pi; // Angle part

+
+// (b) Power angle
+PA=Ef_Ang;
+
+// (c) No load voltage, assuming the field current is not changed
+// From figure 9.23 (b)
+VolAxis=Vt_Mag/30; // The scale at the given voltage axis
+Ef_loc=Ef_Mag/VolAxis; // Location of Ef voltage
+Vnl=29*VolAxis; // No load voltage
+
+// (d) Voltage regulation
+VR=(Vnl-Vt)/Vt*100;
+
+
+// Display result on command window
+printf("\n Excitation voltage = %0.0f V ",Ef_Mag);
+printf("\n Power angle = %0.1f deg ",PA);
+printf("\n No load voltage = %0.0f V ",Vnl);
+printf("\n Voltage regulation = %0.2f Percent ",VR);
+disp('The leading power factor resulted in a negativr voltage regulation')
+
diff --git a/3574/CH9/EX9.11/EX9_11.png b/3574/CH9/EX9.11/EX9_11.png
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+// Example 9.11
+// Determine (a) Equivalent armature resistance (b) Synchronous reactance
+// (c) Short-circuit ratio
+// Page 377
+
+clc;
+clear;
+close;
+
+// Given data
+Vdc=10.35; // DC voltage
+Idc=52.80; // DC current
+VOCph=240/sqrt(3); // Open-circuit phase voltage
+ISCph=115.65; // Short-circuit phase current
+P=50000;
+V=240; // Supply voltage
+
+// (a) Equivalent armature resistance
+Rdc=Vdc/Idc; // DC resistance
+Rgamma=Rdc/2;
+Ra=1.2*Rgamma; // Armature resistance
+
+// (b) Synchronous reactance
+Zs= VOCph/ISCph; // Synchronous impedance/phase
+Xs=sqrt(Zs^2-Ra^2);
+
+// (c) Short-circuit ratio
+Sbase=P/3; // Power/phase
+Vbase=V/sqrt(3); // Voltage/phase
+Zbase=Vbase^2/Sbase;
+Xpu=Xs/Zbase; // Per unit synchronous reactance
+SCR=1/Xpu; // Short-circuit ratio
+
+
+// Display result on command window
+printf("\n Equivalent armature resistance = %0.4f Ohm ",Ra);
+printf("\n Synchronous reactance = %0.4f Ohm ",Xs);
+printf("\n Short-circuit ratio = %0.3f ",SCR);
+
diff --git a/3574/CH9/EX9.2/EX9_2.png b/3574/CH9/EX9.2/EX9_2.png
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+// Example 9.2
+// Determine (a) Speed regulation (b) Governor drop
+// Page 351
+
+clc;
+clear;
+close;
+
+// Given data
+fn1=61.2; // No-load frequency
+frated=60; // Rated requency
+deltaP=500; // Governor rated power
+// (a) Speed regulation
+GSR=(fn1-frated)/frated;
+
+// (b) Governor drop
+deltaF=(fn1-frated); // Frequency difference
+GD=deltaF/deltaP;
+
+// Display result on command window
+printf("\n Speed regulation = %0.2f ",GSR);
+printf("\n Governor drop = %0.5f Hz/kW ",GD);
+
diff --git a/3574/CH9/EX9.3/EX9_3.png b/3574/CH9/EX9.3/EX9_3.png
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+// Example 9.3
+// Determine (a) Frequency of generator A (b) Frequency of generator B
+// (c) Frequency of bus
+// Page 358
+
+clc;
+clear;
+close;
+
+// Given data
+GSR=0.020; // Governor speed regulation
+Frated=60; // Rated frequency
+deltaPa=100; // Change in load (200-100 =100 KW)
+Prated=500; // Rated power of both generators
+
+
+// (a) Frequency of generator A
+deltaFa=(GSR*Frated*deltaPa)/Prated; // Change in frequency due to change in load
+Fa=Frated+deltaFa; // Frequency of generator A
+
+// (b) Frequency of generator B
+deltaFb=0.24; // Since both machines are identical
+Fb=Frated-deltaFb;
+
+// (c) Frequency of bus
+Fbus=Fb; // Bus frequency is frequency of generator B
+
+// Display result on command window
+printf("\n Frequency of generator A = %0.2f Hz ",Fa);
+printf("\n Frequency of generator B = %0.2f Hz ",Fb);
+printf("\n Frequency of bus = %0.2f Hz ",Fbus);
+
diff --git a/3574/CH9/EX9.4/EX9_4.png b/3574/CH9/EX9.4/EX9_4.png
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+// Example 9.4
+// Determine (a) Operating frequency (b) Load carried by each machine
+// Page 359
+
+clc;
+clear;
+close;
+
+// Given data
+GSR=0.0243; // Governor speed regulation
+Frated=60; // Rated frequency
+deltaPa=500; // Change in load for alternator A
+Prateda=500; // Rated power of alternator A
+deltaPb=400; // Change in load for alternator B
+Pratedb=300; // Rated power of alternator B
+Pch=100; // Change is power (500-400=100 KW))
+Pchmach=200; // Power difference (500-300=200 KW)
+
+// (a) Operating frequency
+// From the curve in figure 9.17
+// GSR*Frated/Prated=deltaP/deltaP
+
+deltaF=(deltaPa-deltaPb)/548.697; // Change in frequency
+Fbus=60.5-deltaF;
+
+
+// (b) Load carried by each machine
+deltaPa=(deltaF*Prateda)/(GSR*Frated); // Change in power for machine A
+deltaPb=Pch-deltaPa; // Change in power for machine B
+Pa=Pchmach+deltaPa;
+Pb=Pchmach+deltaPb;
+
+// Display result on command window
+printf("\n Operating frequency = %0.3f Hz ",Fbus);
+printf("\n Load carried by machine A = %0.2f kW",Pa);
+printf("\n Load carried by machine B = %0.2f kW",Pb);
+
diff --git a/3574/CH9/EX9.5/EX9_5.png b/3574/CH9/EX9.5/EX9_5.png
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+// Example 9.5
+// Determine (a) Bus frequency (b) Load on each machine
+// Page 360
+
+clc;
+clear;
+close;
+
+// Given data
+Padd=720; // Additional load connected
+GD=0.0008; // Governor droop
+f=60.2; // Frequency of machine
+Pbus=900; // Bus load
+
+// (a) Bus frequency
+deltaPa=Padd/2;
+deltaPb=deltaPa; // Since both machines have identical governor drops
+deltaF=GD*deltaPa; // Change in frequency
+Fbus=f-deltaF;
+
+// (b) Load on each machine
+Pa=(2/3)*Pbus+deltaPa; // Load on machine A
+Pb=(1/3)*Pbus+deltaPb; // Load on machine B
+
+// Display result on command window
+printf("\n Bus frequency = %0.2f Hz ",Fbus);
+printf("\n Load on machine A = %0.0f kW",Pa);
+printf("\n Load on machine B = %0.0f kW",Pb);
+
diff --git a/3574/CH9/EX9.6/EX9_6.png b/3574/CH9/EX9.6/EX9_6.png
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+// Example 9.6
+// Determine (a) System kilowatts (b) System frequency (c) kilowatt loads
+// carried by each machine
+// Page 361
+
+clc;
+clear;
+close;
+
+// Given data
+Pres=440; // Resistive load
+PF=0.8; // Power factor
+Pind=200; // Induction motor power
+Palt=210; // Alternator bus load
+deltaPa=70; // Change in load for machine A
+f=60; // Frequency
+deltaPb=70; // Change in load for machine B
+deltaPc=70; // Change in load for machine C
+
+// (a) System kilowatts
+deltaPbus=Pres+PF*Pind; // Increase in bus load
+Psys=Palt+deltaPbus;
+
+// (b) System frequency
+GDa=(60.2-f)/deltaPa; // Governor droop for machine A
+GDb=(60.4-f)/deltaPb; // Governor droop for machine B
+GDc=(60.6-f)/deltaPc; // Governor droop for machine C
+// From the figure 9.18(b)
+deltaF=600/(350+175+116.6667) ;
+f2=f-deltaF;
+
+// (c) Kilowatt loads carried by each machine
+Pa2=deltaPa+350*deltaF;
+Pb2=deltaPb+175*deltaF;
+Pc2=deltaPc+116.6667*deltaF;
+
+// Display result on command window
+printf("\n System kilowatts = %0.0f kW ",Psys);
+printf("\n System frequency = %0.2f Hz",f2);
+printf("\n Kilowatt loads carried by machine A = %0.1f kW",Pa2);
+printf("\n Kilowatt loads carried by machine B = %0.1f kW",Pb2);
+printf("\n Kilowatt loads carried by machine C = %0.1f kW",Pc2);
diff --git a/3574/CH9/EX9.7/EX9_7.png b/3574/CH9/EX9.7/EX9_7.png
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+// Example 9.7
+// Determine (a) Active and reactive components of the bus load (b) If the
+// power factor of generator A is 0.94 lagging, determine the reactive power
+// supplied by each machine.
+// Page 366
+
+clc;
+clear;
+close;
+
+// Given data
+Pbuspower=500; // Power supplied
+Pind=200; // Induction motor power
+PF=0.852; // Percent power factor
+NA=2; // Number of alternators
+LPF=0.94; // Lagging power factor
+
+// (a) Active and reactive components of the bus load
+Pbus=Pbuspower+Pind*PF; // Active component of the bus load
+ThetaMot=acosd(PF); // Power angle of motor
+Qbus=Pind*sind(ThetaMot); // Reactive component the bus load
+
+// (b) Reactive power supplied by each machine
+Pa=Pbus/NA; // Alternator A power
+ThetaA=acosd(LPF); // Alternator A angle
+Qa=tand(ThetaA)*Pa; // Reactive power supplied by machine A
+Qb=Qbus-Qa; // Reactive power supplied by machine B
+
+
+// Display result on command window
+printf("\n Active component of the bus load = %0.2f kW ",Pbus);
+printf("\n Reactive component of the bus load = %0.1f kvar",Qbus);
+printf("\n Reactive power supplied by machine A = %0.1f kvar",Qa);
+printf("\n Reactive power supplied by machine B = %0.1f kvar",Qb);
diff --git a/3574/CH9/EX9.8/EX9_8.png b/3574/CH9/EX9.8/EX9_8.png
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+// Example 9.8
+// Computation of per-unit impedance of a generator
+// Page 368
+
+clc;
+clear;
+close;
+
+// Given data
+P=100000; // Power of synchronous generator
+V=480; // Voltage of synchronous generator
+Ra=0.0800; // Resistive component
+Xs=2.3; // Reactive component
+
+// Computation of per-unit impedance of a generator
+Sbase=P/3; // Rated apparent power per phase
+Vbase=V/sqrt(3); // Rated voltage per phase
+Zbase=Vbase^2/Sbase; // Rated impedance
+Rpu=Ra/Zbase; // Per unit resistance
+Xpu=Xs/Zbase; // Per unit reactance
+
+Zpu=Rpu+%i*Xpu; // Per unit impedance
+
+// Complex to Polar form...
+Zpu_Mag=sqrt(real(Zpu)^2+imag(Zpu)^2); // Magnitude part
+Zpu_Ang = atan(imag(Zpu),real(Zpu))*180/%pi; // Angle part

+
+// Display result on command window
+printf("\n Per-unit impedance magnitude = %0.4f Ohm ",Zpu_Mag);
+printf("\n Per-unit impedance angle = %0.2f deg ",Zpu_Ang);
diff --git a/3574/CH9/EX9.9/EX9_9.png b/3574/CH9/EX9.9/EX9_9.png
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diff --git a/3574/CH9/EX9.9/EX9_9.sce b/3574/CH9/EX9.9/EX9_9.sce
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+// Example 9.9
+// Determine (a) Excitation voltage (b) Power angle (c) No load voltage,
+// assuming the field current is not changed (d) Voltage regulation (e) No load
+// voltage if the field current is reduced to 80% of its value at rated load.
+// Page 369
+
+clc;
+clear;
+close;
+
+// Given data
+V=4800; // Voltage of synchronous generator
+PF=0.900; // Lagging power factor
+S_Mag=1000000/3;
+Xa_Mag=13.80; // Synchronous reactance
+Xa_Ang=90;
+Vt_Ang=0;
+
+// (a) Excitation voltage
+Vt=V/sqrt(3);
+Theta=acosd(PF); // Angle
+Ia_Magstar=S_Mag/Vt; // Magnitude of curent
+Ia_Angstar=Theta-0; // Angle of current
+Ia_Mag=Ia_Magstar;
+Ia_Ang=-Ia_Angstar;
+
+// Ef=Vt+Ia*j*Xa
+// First compute Ia*Xa
+IaXa_Mag=Ia_Mag*Xa_Mag;
+IaXa_Ang=Ia_Ang+Xa_Ang;
+// Polar to Complex form for IaXa
+IaXa_R=IaXa_Mag*cos(-IaXa_Ang*%pi/180); // Real part of complex number
+IaXa_I=IaXa_Mag*sin(IaXa_Ang*%pi/180); // Imaginary part of complex number
+// Vt term in polar form
+Vt_Mag=Vt;
+Vt_Ang=Vt_Ang;
+// Polar to Complex form for Vt
+Vt_R=Vt_Mag*cos(-Vt_Ang*%pi/180); // Real part of complex number
+Vt_I=Vt_Mag*sin(Vt_Ang*%pi/180); // Imaginary part of complex number
+// Ef in complex form
+Ef_R=IaXa_R+Vt_R;
+Ef_I=IaXa_I+Vt_I;
+Ef=Ef_R+%i*Ef_I;
+// Complex to Polar form for Ef
+Ef_Mag=sqrt(real(Ef)^2+imag(Ef)^2); // Magnitude part
+Ef_Ang= atan(imag(Ef),real(Ef))*180/%pi; // Angle part

+
+// (b) Power angle
+PA=Ef_Ang;
+
+// (c) No load voltage, assuming the field current is not changed
+// From figure 9.23 (b)
+VolAxis=Vt_Mag/30; // The scale at the given voltage axis
+Ef_loc=Ef_Mag/VolAxis; // Location of Ef voltage
+Vnl=33.4*VolAxis; // No load voltage
+
+// (d) Voltage regulation
+VR=(Vnl-Vt)/Vt*100;
+
+// (e) No load voltage if the field current is reduced to 80%
+Vnlnew=31*VolAxis;
+
+// Display result on command window
+printf("\n Excitation voltage = %0.0f V ",Ef_Mag);
+printf("\n Power angle = %0.1f deg ",PA);
+printf("\n No load voltage = %0.0f V ",Vnl);
+printf("\n Voltage regulation = %0.0f Percent ",VR);
+printf("\n No load voltage when field current is reduced to 80 percent = %0.0f V ",Vnlnew);