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authorprashantsinalkar2017-10-10 12:27:19 +0530
committerprashantsinalkar2017-10-10 12:27:19 +0530
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diff --git a/3574/CH8/EX8.1/EX8_1.png b/3574/CH8/EX8.1/EX8_1.png
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+// Example 8.1
+// Determine (a) Developed torque (b) Armature current (c) Excitation voltage
+// (d) Power angle (e) Maximum torque
+// Page No. 317
+
+clc;
+clear;
+close;
+
+// Given data
+f=60; // Operating frequency
+P=4; // Number of poles
+Pmech=100; // Mechanical power
+eta=0.96; // Efficiency
+FP=0.80; // Power factor leading
+V=460; // Motor voltage
+Xs_Mag=2.72; // Synchronous reactnace magnitude
+Xs_Ang=90; // Synchronous reactnace magnitude
+deltaPull=-90; // Pullout power angle
+// (a) Developed torque
+ns=120*f/P; // Synchronous speed
+Td=5252*Pmech/(ns*eta);
+
+
+// (b) Armature current
+S=Pmech*746/(eta*FP);
+Theta=-acosd(FP); // Power factor angle (negative as FP is leading)
+V1phi=V/sqrt(3); // Single line voltage
+S1phi_Mag=S/3; // Magnitude
+S1phi_Ang=Theta; // Angle
+VT_Mag=V1phi;
+VT_Ang=0;
+Ia_Mag=S1phi_Mag/VT_Mag; // Armature current magnitude
+Ia_Ang=S1phi_Ang-VT_Ang; // Armature current angle
+Ia_Ang=-Ia_Ang; // Complex conjugate of Ia
+
+// (c) Excitation voltage
+Var1_Mag=Ia_Mag*Xs_Mag;
+Var1_Ang=Ia_Ang+Xs_Ang;
+
+/////////
+N01=VT_Mag+%i*VT_Ang;
+N02=Var1_Mag+%i*Var1_Ang;
+// Polar to Complex form
+
+N01_R=VT_Mag*cos(-VT_Ang*%pi/180); // Real part of complex number 1
+N01_I=VT_Mag*sin(VT_Ang*%pi/180); //Imaginary part of complex number 1
+
+N02_R=Var1_Mag*cos(-Var1_Ang*%pi/180); // Real part of complex number 2
+N02_I=Var1_Mag*sin(Var1_Ang*%pi/180); //Imaginary part of complex number 2
+
+FinalNo_R=N01_R-N02_R;
+FinalNo_I=N01_I-N02_I;
+FinNum=FinalNo_R+%i*FinalNo_I;
+// Complex to Polar form...
+
+FN_M=sqrt(real(FinNum)^2+imag(FinNum)^2); // Magnitude part
+FN_A = atan(imag(FinNum),real(FinNum))*180/%pi;// Angle part

+//////
+Ef_Mag=FN_M;
+Ef_Ang=FN_A;
+// (d) Power angle
+delta=Ef_Ang;
+
+// (e) Maximum torque
+Pin=3*(-VT_Mag*Ef_Mag/Xs_Mag)*sind(deltaPull); // Active power input
+Tpull=5252*Pin/(746*ns);
+
+
+
+// Display result on command window
+printf("\n Developed torque = %0.0f lb-ft ",Td);
+printf("\n Armature current magnitude= %0.2f A ",Ia_Mag);
+printf("\n Armature current angle= %0.2f deg ",Ia_Ang);
+printf("\n Excitation voltage magnitude = %0.0f V ",Ef_Mag);
+printf("\n Excitation voltage angle = %0.1f deg ",Ef_Ang);
+printf("\n Power angle = %0.1f deg ",delta);
+printf("\n Maximum torque = %0.0f lb-ft ",Tpull);
+
+
diff --git a/3574/CH8/EX8.2/EX8_2.png b/3574/CH8/EX8.2/EX8_2.png
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+// Example 8.2
+// Determine (a) The minimum value of excitation that will maintain
+// synchronism (b) Repeat (a) using eq.(8.16) (c) Repeat (a) using eq.(8.21)
+// (d) Power angle if the field excitation voltage is increased to 175% of the
+// stability limit determined in (c)
+// Page No. 322
+
+clc;
+clear;
+close;
+
+// Given data
+Pin=40; // Input power
+Pin1phase=40/3; // Single phase power
+Xs=1.27; // Synchronous reactnace
+VT=220/sqrt(3); // Voltage
+delta=-90; // Power angle
+
+f=60; // Operating frequency
+P=4; // Number of poles
+Pmech=100; // Mechanical power
+eta=0.96; // Efficiency
+FP=0.80; // Power factor leading
+V=460; // Motor voltage
+Xs_Mag=2.72; // Synchronous reactnace magnitude
+Xs_Ang=90; // Synchronous reactnace magnitude
+deltaPull=-90; // Pullout power angle
+
+// (a) The minimum value of excitation that will maintain synchronism
+Ef=98; // From the graph (Figure 8.13)
+
+// (b) The minimum value of excitation using eq.(8.16)
+Ef816=-Pin*Xs*746/(3*VT*sind(delta));
+
+
+// (c) The minimum value of excitation using eq.(8.21)
+Ef821=Xs*Pin1phase*746/(VT);
+
+// (d) Power angle if the field excitation voltage is increased to 175%
+delta2=Ef816*sind(delta)/(1.75*Ef816);
+delta2=asind(delta2);
+
+// Display result on command window
+printf("\n The minimum value of excitation = %0.0f V ",Ef);
+printf("\n The minimum value of excitation using eq.(8.16) = %0.0f V ",Ef816);
+printf("\n The minimum value of excitation using eq.(8.21) = %0.0f V ",Ef821);
+printf("\n Power angle = %0.0f deg ",delta2);
diff --git a/3574/CH8/EX8.3/EX8_3.png b/3574/CH8/EX8.3/EX8_3.png
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+// Example 8.3
+// Determine (a) System active power (b) Power factor of the synchronous motor
+// (c) System power factor (d) Percent change in synchronous field current
+// required to adjust the system power factor to unity (e) Power angle of the
+// synchronous motor for the conditions in (d)
+// Page No. 324
+
+clc;
+clear;
+close;
+
+// Given data
+
+Php=400; // Power in hp
+eta=0.958; // Efficiency
+Pheater=50000; // Resistance heater power
+Vs=300; // Synchronous motor voltage
+eta2=0.96; // Synchronous motor efficiency
+Xs=0.667; // Synchronous reactnace
+VT=460; // 3-Phase supply voltage
+delta=-16.4; // Power angle
+
+// (a) System active power
+Pindmot=Php*0.75*746/(eta); // Motor operating at three quarter rated load
+Psynmot=Vs*0.5*746/(eta2); // Synchronous motor power
+Psys=Pindmot+Pheater+Psynmot;
+Psysk=Psys/1000;
+
+// (b) Power factor of the synchronous motor
+Pin=Psynmot; // Power input
+Vtph=VT/sqrt(3); // Voltage per phase
+Ef=-(Pin*Xs)/(3*Vtph*sind(delta));
+// Complex to Polar form...
+
+Ef_Mag=Ef; // Magnitude part
+Ef_Ang=delta; // Angle part

+Vtph_Mag=Vtph;
+Vtph_Ang=0;
+////////////
+N01=Ef_Mag+%i*Ef_Ang; // Ef in polar form
+N02=Vtph_Mag+%i*Vtph_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=Vtph_Mag*cos(-Vtph_Ang*%pi/180); // Real part of complex number Vt
+N02_I=Vtph_Mag*sin(Vtph_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;
+// Complex to Polar form...
+
+FN_M=sqrt(real(FinNum)^2+imag(FinNum)^2); // Magnitude part
+FN_A = atan(imag(FinNum),real(FinNum))*180/%pi;// Angle part

+
+Ia_Mag=FN_M/Xs; // Magnitude of Ia
+Ia_Ang=FN_A-(-90); // Angle of Ia
+Theta=0-Ia_Ang;
+FP=cosd(Theta); // Power factor
+
+
+// (c) System power factor
+ThetaIndMot=acosd(0.891); // Induction motor power factor
+Thetaheat=acosd(1); // Heater power factor
+ThetaSyncMot=-34.06; // Synchronous motor power factor
+Qindmot=tand(27)*Pindmot;
+Qsynmot=tand(ThetaSyncMot)*Psynmot;
+Qsys=Qindmot+Qsynmot;
+Ssys=Psys+%i*Qsys; // System variable in complex form
+
+// Complex to Polar form...
+
+Ssys_Mag=sqrt(real(Ssys)^2+imag(Ssys)^2); // Magnitude part
+Ssys_Ang = atan(imag(Ssys),real(Ssys))*180/%pi; // Angle part

+
+FPsys=cosd(Ssys_Ang); // System power factor
+
+// (d) Percent change in synchronous field current required to adjust the
+// system power factor to unity
+
+Ssynmot=Psynmot-(%i*(-Qsynmot+Qsys)); // Synchronous motor system
+
+// Complex to Polar form...
+
+Ssynmot_Mag=sqrt(real(Ssynmot)^2+imag(Ssynmot)^2); // Magnitude part
+Ssynmot_Ang=atan(imag(Ssynmot),real(Ssynmot))*180/%pi; // Angle part

+
+Ssynmot1ph_Mag=Ssynmot_Mag/3; // For single phase magnitude
+Ssynmot1ph_Ang=Ssynmot_Ang; // For single phase angle
+
+Iastar_Mag=Ssynmot1ph_Mag/Vtph; // Current magnitude
+Iastar_Ang=Ssynmot1ph_Ang-0; // Current angle
+
+IaNew_Mag=Iastar_Mag;
+IaNew_Ang=-Iastar_Ang;
+
+IaXs_Mag=IaNew_Mag*Xs;
+IaXs_Ang=IaNew_Ang-90;
+
+// Convert these number into complex and then perform addition
+// Polar to Complex form
+
+// Y=29.416<-62.3043 //Polar form number
+IaXs_R=IaXs_Mag*cos(-IaXs_Ang*%pi/180); // Real part of complex number
+IaXs_I=IaXs_Mag*sin(IaXs_Ang*%pi/180); // Imaginary part of complex number
+Efnew=Vtph+IaXs_R+%i*IaXs_I;
+// Complex to Polar form...
+
+Efnew_Mag=sqrt(real(Efnew)^2+imag(Efnew)^2); // Magnitude part
+Efnew_Ang=atan(imag(Efnew),real(Efnew))*180/%pi; // Angle part

+
+DeltaEf=(Efnew_Mag-Ef)/Ef;
+
+// (e) Power angle of the synchronous motor
+deltasynmot=Efnew_Ang;
+
+// Display result on command window
+printf("\n System active power = %0.1f kW ",Psysk);
+printf("\n Power factor of the synchronous motor = %0.3f leading ",FP);
+printf("\n System power factor = %0.3f lagging ",FPsys);
+printf("\n Percent change in synchronous field current = %0.2f Percent ",DeltaEf*100);
+printf("\n Power angle of the synchronous motor = %0.2f deg ",deltasynmot);
diff --git a/3574/CH8/EX8.4/EX8_4.png b/3574/CH8/EX8.4/EX8_4.png
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+// Example 8.4
+// Determine (a) Developed torque if the field current is adjusted so that the
+// excitation voltage is equal to two times the applied stator voltage, and the
+// power angle is -18 degrees (b) Developed torque in percent of rated torque,
+// if the load is increased until maximum reluctance torque occurs.
+// Page No. 328
+
+clc;
+clear;
+close;
+
+// Given data
+Vt1ph=2300/sqrt(3); // Applied voltage/phase
+Ef1ph=2300/sqrt(3); // Excitation voltage/phase
+Xd=36.66; // Direct axis reactance/phase
+delta=-18; // Power angle
+Xq=23.33; // Quadrature-axis reactance/phase
+n=900; // Speed of motor
+deltanew=-45;
+RatTor=200; // Rated torque of motor
+// (a) Developed torque
+Pmag1ph=-((Vt1ph*2*Ef1ph)/Xd)*sind(delta); // Power
+Prel1ph=-Vt1ph^2*( (Xd-Xq) / (2*Xd*Xq)) *sind(2*delta); // Reluctance power
+Psal3ph=3*(Pmag1ph+Prel1ph); // Salient power of motor
+Psal3phHP=Psal3ph/746;
+T=(5252*Psal3phHP)/n; // Developed torque
+
+// (b) Developed torque in percent of rated torque
+// The reluctance torque has its maximum value at delta= -45 degrees
+Pmag1phnew=-((Vt1ph*2*Ef1ph)/Xd)*sind(deltanew); // Power
+Prel1phnew=-Vt1ph^2*( (Xd-Xq) / (2*Xd*Xq)) *sind(2*deltanew); // Reluctance power
+Psal3phnew=3*(Pmag1phnew+Prel1phnew); // Salient power of motor
+Psal3phHPnew=Psal3phnew/746;
+PerRatTorq=Psal3phHPnew*100/RatTor;
+
+// Display result on command window
+printf("\n Developed torque = %0.0f lb-ft ",T);
+printf("\n Developed torque in percent of rated torque = %0.0f Percent ",PerRatTorq);