From b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b Mon Sep 17 00:00:00 2001 From: priyanka Date: Wed, 24 Jun 2015 15:03:17 +0530 Subject: initial commit / add all books --- 1938/CH6/EX6.10/6_10.sce | 33 +++++++++++++++++++++++++++++++++ 1938/CH6/EX6.11/6_11.sce | 38 ++++++++++++++++++++++++++++++++++++++ 1938/CH6/EX6.12/6_12.sce | 28 ++++++++++++++++++++++++++++ 1938/CH6/EX6.13/6_13.jpg | Bin 0 -> 41130 bytes 1938/CH6/EX6.13/6_13.sce | 30 ++++++++++++++++++++++++++++++ 1938/CH6/EX6.14/6_14.sce | 24 ++++++++++++++++++++++++ 1938/CH6/EX6.15/6_15.jpg | Bin 0 -> 163890 bytes 1938/CH6/EX6.15/6_15.sce | 35 +++++++++++++++++++++++++++++++++++ 1938/CH6/EX6.16/6_16.sce | 16 ++++++++++++++++ 1938/CH6/EX6.17/6_17.jpg | Bin 0 -> 50720 bytes 1938/CH6/EX6.17/6_17.sce | 20 ++++++++++++++++++++ 1938/CH6/EX6.18/6_18.jpg | Bin 0 -> 1647073 bytes 1938/CH6/EX6.18/6_18.sce | 23 +++++++++++++++++++++++ 1938/CH6/EX6.19/6_19.sce | 18 ++++++++++++++++++ 1938/CH6/EX6.2/6_2.sce | 16 ++++++++++++++++ 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create mode 100755 1938/CH6/EX6.40/6_40.sce create mode 100755 1938/CH6/EX6.41/6_41.sce create mode 100755 1938/CH6/EX6.42/6_42.sce create mode 100755 1938/CH6/EX6.43/6_43.sce create mode 100755 1938/CH6/EX6.5/6_5.sce create mode 100755 1938/CH6/EX6.6/6_6.sce create mode 100755 1938/CH6/EX6.7/6_7.jpg create mode 100755 1938/CH6/EX6.7/6_7.sce create mode 100755 1938/CH6/EX6.8/6_8.jpg create mode 100755 1938/CH6/EX6.8/6_8.sce create mode 100755 1938/CH6/EX6.9/6_9.jpg create mode 100755 1938/CH6/EX6.9/6_9.sce (limited to '1938/CH6') diff --git a/1938/CH6/EX6.10/6_10.sce b/1938/CH6/EX6.10/6_10.sce new file mode 100755 index 000000000..bea4e828a --- /dev/null +++ b/1938/CH6/EX6.10/6_10.sce @@ -0,0 +1,33 @@ +clc,clear +printf('Example 6.10\n\n') +//note that a new function p2z has been defined below for direct representation of complex numbers in polar form +function [FUN] = p2z(RRRR,Theeeta) + FUN = RRRR.*exp(%i*%pi*Theeeta/180.); +endfunction + +V_l=6000 +V_ph=V_l/sqrt(3) +VA=2000*10^3 +I_FL=VA/(V_l*sqrt(3)) +X_s=complex(0,6) //synchronous reactance +P=8 +f=50 + +delta_mech=%pi/180 //phase displacemant in degree mechanical +//phase displacemant in degree electrical +delta_elec=delta_mech*(P/2) //P/2 is pole pairs(and not poles) + +phi=acosd(0.8) +V=p2z(V_ph,phi) +E=V+I_FL*X_s +//E leads I by phasemag(E). V leads I by phasemag(V) + +delta=(%pi/180)* (phasemag(E)-phasemag(V) ) //power angle in radians +P_SY=abs(E)*abs(V)*cos(delta)*sin(delta_elec)/abs(X_s) //synchronising power +P_SY_total=3*P_SY //totla synchronising power +printf('Total synchronising power is %.3f kW',10^-3*P_SY_total) + +N_s=120*f/P //in rpm +n_s=(N_s)/60 //in rps +T_SY=P_SY_total/(2*%pi*n_s) +printf('\nSynchronising torque is %.0f N-m',T_SY) diff --git a/1938/CH6/EX6.11/6_11.sce b/1938/CH6/EX6.11/6_11.sce new file mode 100755 index 000000000..343e2271c --- /dev/null +++ b/1938/CH6/EX6.11/6_11.sce @@ -0,0 +1,38 @@ +clc,clear +printf('Example 6.11\n\n') + +//note that a new function p2z has been defined below for direct representation of complex numbers in polar form +function [FUN] = p2z(RRRR,Theeeta) + FUN = RRRR.*exp(%i*%pi*Theeeta/180.); +endfunction + +V_l=3300 +V_ph=V_l/sqrt(3) +VA=3*10^6 +I_FL=VA/(V_l*sqrt(3)) +IX_s=(25/100)*V_ph //product of I and X_s +X_s=complex(0,IX_s/I_FL) //synchronous reactance +N_s=1000 //in rpm +P=6 +f=50 + +delta_dash_mech=%pi/180 +delta_dash_elec=delta_dash_mech*(P/2) //P/2 is pole pairs(and not poles) + +I=I_FL +phi=acosd(0.8) +V=p2z(V_ph,phi) +E=V+I*X_s +//E leads I by phasemag(E). V leads I by phasemag(V) + +delta=(%pi/180)* (phasemag(E)-phasemag(V) ) //power angle in radians +P_SY=abs(E)*abs(V)*cos(delta)*sin(delta_dash_elec)/abs(X_s) //Synchronising power per phase +printf('Synchronising power is %.3f kW',10^-3*P_SY) +P_SY_total=3*P_SY //Total synchronising power + +N_s=120*f/P //in rpm +n_s=(N_s)/60 //in rps +T_SY=P_SY_total/(2*%pi*n_s) +printf('\nSynchronising torque is %.0f N-m',T_SY) + +printf('\n\nAnswer mismatches due to approximation') diff --git a/1938/CH6/EX6.12/6_12.sce b/1938/CH6/EX6.12/6_12.sce new file mode 100755 index 000000000..5c53e84d8 --- /dev/null +++ b/1938/CH6/EX6.12/6_12.sce @@ -0,0 +1,28 @@ +clc,clear +printf('Example 6.12\n\n') + +V_l=3300 +V_ph=V_l/sqrt(3) +VA=3*10^6 +I_FL=VA/(V_l*sqrt(3)) +IX_s=(20/100)*V_ph //product of I and X_s +X_s=complex(0,IX_s/I_FL) //synchronous reactance +N_s=1000 +P=6 +f=50 + +delta_dash_mech=%pi/180 //phase displacement in degree mechanical +//phase displacement in degree electrical +delta_dash_elec=delta_dash_mech*(P/2) //P/2 is pole pairs(and not poles) + +E=V_ph +Z_s=X_s //since R=0 +P_SY=abs(E)*abs(V_ph)*delta_dash_elec/abs(Z_s) //Synchronising power per phase +printf('Synchronising power is %.3f kW',10^-3*P_SY) +P_SY_total=3*P_SY //Total synchronising power +printf('\n3 phase synchronising power is %.3f kW',10^-3*P_SY_total) + +N_s=120*f/P //in rpm +n_s=(N_s)/60 //in rps +T_SY=P_SY_total/(2*%pi*n_s) +printf('\nSynchronising torque is %.0f N-m',T_SY) diff --git a/1938/CH6/EX6.13/6_13.jpg b/1938/CH6/EX6.13/6_13.jpg new file mode 100755 index 000000000..1713b0614 Binary files /dev/null and b/1938/CH6/EX6.13/6_13.jpg differ diff --git a/1938/CH6/EX6.13/6_13.sce b/1938/CH6/EX6.13/6_13.sce new file mode 100755 index 000000000..f2c185b83 --- /dev/null +++ b/1938/CH6/EX6.13/6_13.sce @@ -0,0 +1,30 @@ +clc,clear +printf('Example 6.13\n\n') + +V_L=11*10^3 +V_ph=V_L/sqrt(3) +VA=700*10^3 +I_FL=VA/(sqrt(3)*V_L) //full load current +IR_a=(1.5/100)*V_ph //product of I and R_a +R_a=IR_a/I_FL +IX_s=(14/100)*V_ph // product of I and X_s +X_s=IX_s/I_FL //synchronous reactance + +//at full load and 0.8 pf +I=I_FL +phi=acos(0.8) +V_ph=complex(V_ph*cos(phi),V_ph*sin(phi)) //just introduced the angle +E_ph=sqrt( (abs(V_ph)*cos(phi)+ IR_a)^2+ (abs(V_ph)*sin(phi)+ IX_s)^2 ) + +Poles=4,f=50 //poles and frequency +delta=asin( (abs(V_ph)*sin(phi)+IX_s)/E_ph) -phi +delta_dash_mech=(%pi/180) //displacement in degree mechanical +//displacement in degree electrical +delta_dash_elec=delta_dash_mech*(Poles/2) +P_SY=abs(E_ph)*abs(V_ph)*cos(delta)*sin(delta_dash_elec)/X_s //synchronising power per phase +P_SY_total=3*P_SY //total synchronising power + +ns=120*f/(60*Poles) //in r.p.s +T_SY=P_SY_total/(2*%pi*ns) //Synchronising torque +printf('Synchronising power is %.2fkW\n',P_SY_total/1000) +printf('Synchronising torque is %.2f N-m',T_SY) diff --git a/1938/CH6/EX6.14/6_14.sce b/1938/CH6/EX6.14/6_14.sce new file mode 100755 index 000000000..4e28afaf0 --- /dev/null +++ b/1938/CH6/EX6.14/6_14.sce @@ -0,0 +1,24 @@ +clc,clear +printf('Example 6.14\n\n') + +V_l=9*10^3 +V_ph=V_l/sqrt(3) +VA=5.5*10^6 +I_FL=VA/(V_l*sqrt(3)) +IX_s=(25/100)*V_ph //product of I and X_s +X_s=complex(0,IX_s/I_FL) //synchronous reactance +N_s=1500 //in rpm +n_s=N_s/60 //in rps +f=50,P=120*f/N_s //frequency and pole + +delta_dash_mech=%pi/180 //displacemnt in degree mechanical +//displacemnt in degree electrical +delta_dash_elec=delta_dash_mech*(P/2) //P/2 is pole pairs(and not poles) + +E=V_ph +P_SY=abs(E)*abs(V_ph)*delta_dash_elec/abs(X_s) //Synchronising power per phase +P_SY_total=3*P_SY //Total synchronising power + +T_SY=P_SY_total/(2*%pi*n_s) +printf('\nSynchronising torque is %.2f N-m',T_SY) +printf('\nAnswer mismatches due to approximation') diff --git a/1938/CH6/EX6.15/6_15.jpg b/1938/CH6/EX6.15/6_15.jpg new file mode 100755 index 000000000..7a78b1b80 Binary files /dev/null and b/1938/CH6/EX6.15/6_15.jpg differ diff --git a/1938/CH6/EX6.15/6_15.sce b/1938/CH6/EX6.15/6_15.sce new file mode 100755 index 000000000..26c99672a --- /dev/null +++ b/1938/CH6/EX6.15/6_15.sce @@ -0,0 +1,35 @@ +clc,clear +printf('Example 6.15\n\n') + +V_L=6*10^3 +V_ph=V_L/sqrt(3) +VA=2000*10^3 +I_FL=VA/(sqrt(3)*V_L) ,I=I_FL + +X_s=1.2,R_a=0.01 //both per unit +IR_a=(1/100)*V_ph //product of I and R_a +R_a=IR_a/I_FL +IX_s=(120/100)*V_ph //product of I and X_s +//IX_s=(12/100)*V_ph // this is the mistake made in the textbook +X_s=IX_s/I_FL + +//at full load and 0.8 pf +phi=acos(0.8) +//V_ph=complex(V_ph*cos(phi),V_ph*sin(phi)) //just introduced the angle +E_ph=sqrt( (abs(V_ph)*cos(phi)+ IR_a)^2+ (abs(V_ph)*sin(phi)+ IX_s)^2 ) +Poles=8,f=50 + +delta=asin( (abs(V_ph)*sin(phi)+IX_s)/E_ph) -phi +delta_dash_mech=(%pi/180) //displacemnt in degree mechanical +//displacemnt in degree electrical +delta_dash_elec=delta_dash_mech*(Poles/2) +P_SY=abs(E_ph)*abs(V_ph)*cos(delta)*sin(delta_dash_elec)/X_s //synchronising power per phase +P_SY_total=3*P_SY //total synchronising power + +ns=120*f/(60*Poles) //in r.p.s +T_SY=P_SY_total/(2*%pi*ns) //Synchronising torque + +printf('Synchronising power is %.2f kW\n',P_SY_total/1000) +printf('Synchronising torque is %.2f N-m',T_SY) + +printf('\n\nNote that answer obtained doesnt match with textbook due to the following reasons: \n(i)IX_s is considered wrong in textbook.\nIt should have been 4156.92(instead of 415.692) \nTo verify this use commented statement of IX_s (line 13)and notice that it matches with textbook ans then' ) diff --git a/1938/CH6/EX6.16/6_16.sce b/1938/CH6/EX6.16/6_16.sce new file mode 100755 index 000000000..784300d04 --- /dev/null +++ b/1938/CH6/EX6.16/6_16.sce @@ -0,0 +1,16 @@ +clc,clear +printf('Example 6.16\n\n') + +E=11*10^3/sqrt(3) +I_sc=1000,Pole=2,f=50 +delta_dash_mech=1*%pi/180 //displacemnt in degree mechanical +//displacemnt in degree electrical +delta_dash_elec=delta_dash_mech*(Pole/2) +P_SY=E*I_sc*delta_dash_mech //synchronising power per phase +P_SY_total=P_SY*3 //total synchronising power + +ns=120*f/(60*Pole) //in r.p.s +T_SY=P_SY_total/(2*%pi*ns) //Synchronising torque + +printf('Synchronising power is %.2f kW\n',P_SY_total/1000) +printf('Synchronising torque is %.2f N-m',T_SY) diff --git a/1938/CH6/EX6.17/6_17.jpg b/1938/CH6/EX6.17/6_17.jpg new file mode 100755 index 000000000..dcdadc934 Binary files /dev/null and b/1938/CH6/EX6.17/6_17.jpg differ diff --git a/1938/CH6/EX6.17/6_17.sce b/1938/CH6/EX6.17/6_17.sce new file mode 100755 index 000000000..c862100b3 --- /dev/null +++ b/1938/CH6/EX6.17/6_17.sce @@ -0,0 +1,20 @@ +clc,clear +printf('Example 6.17\n\n') +//Line PQ for Altermnator 1, and PR for alternaator 2.AB is at frequency x from P where total load is 30 MW +QT=25,PT=2,//PC=x +SR=25,PS=1.5 + +//using similarity of triangles PAC and PQT +AC_by_PC=(QT/PT)// because (AC/QT)=(PC/PT) +//using similarity of triangles PCB and PSR +CB_by_PC=(SR/PS) + +AC_by_x=AC_by_PC //which implies AC=12.5*x +CB_by_x=CB_by_PC //which implies CB=16.67*x + +AC_plus_CB=30 //total load at the frequency at P is 30 MW +x= AC_plus_CB/(AC_by_x + CB_by_x) +AC=12.5*x +CB=16.67*x +frequency=50-x +printf('Loads shared by alternator 1 and 2 are %.2f MW and %.2f MW respectively',AC,CB) diff --git a/1938/CH6/EX6.18/6_18.jpg b/1938/CH6/EX6.18/6_18.jpg new file mode 100755 index 000000000..8ff024583 Binary files /dev/null and b/1938/CH6/EX6.18/6_18.jpg differ diff --git a/1938/CH6/EX6.18/6_18.sce b/1938/CH6/EX6.18/6_18.sce new file mode 100755 index 000000000..ca1a30f4f --- /dev/null +++ b/1938/CH6/EX6.18/6_18.sce @@ -0,0 +1,23 @@ +clc,clear +printf('Example 6.18\n\n') +//note that a new function p2z has been defined below for direct representation of complex numbers in polar form +function [FUN] = p2z(RRRR,Theeeta) + FUN = RRRR.*exp(%i*%pi*Theeeta/180.); +endfunction + +load_total=1600*10^3 +pf=1/sqrt(2) //lag +V_L=6600 +I_L=p2z(load_total/(sqrt(3)*V_L*pf),-1*acosd(pf)) +I_1=p2z(90,-1*acosd(0.8)) +I_2=I_L-I_1 +phi=abs(phasemag(I_2)) +I_a=abs(I_2) +R_a=1.05,X_s=5 //resistance and synchronous reactance per phase +V_ph=V_L/sqrt(3) +E_ph=sqrt( (V_ph*cos(phi)+I_a*R_a )^2 + ( V_ph*sin(phi)+I_a*X_s )^2 ) +E_line=sqrt(3)*E_ph + +printf('Excitation of second alternator is %.2f V ',E_line) +printf('\n The corresponding field current from the graph is about 310 A\n\n') +printf('Note: The answer obtained will differ from textbook answer because of higher degree \nof accuracy while storing I_2 and the improper rounding off of I_2 in the textbook') diff --git a/1938/CH6/EX6.19/6_19.sce b/1938/CH6/EX6.19/6_19.sce new file mode 100755 index 000000000..b55154582 --- /dev/null +++ b/1938/CH6/EX6.19/6_19.sce @@ -0,0 +1,18 @@ +clc,clear +printf('Example 6.19\n\n') + +V_L=10*10^3 +V_ph=V_L/sqrt(3) +VA=5*10^6 +I_FL=VA/(sqrt(3)*V_L) //full-load current +IX_s=(20/100)*V_ph //product of I and X_s +X_s=IX_s/I_FL //synchronous reactance +P=4 +delta_dash_mech=1*(%pi/180) //displacement in degree mechanical +//displacement in degree electrical +delta_dash_elec=delta_dash_mech*(P/2) +E=V_ph //at no load +P_SY= delta_dash_elec*E^2/X_s //synchronising power per phase +P_SY_total=P_SY*3 //Total synchronising power + +printf('Synchronising power per phase is %.2fkW\nTotal synchronising power is %.2fkW ',P_SY/1000,P_SY_total/1000) diff --git a/1938/CH6/EX6.2/6_2.sce b/1938/CH6/EX6.2/6_2.sce new file mode 100755 index 000000000..4fd405e4d --- /dev/null +++ b/1938/CH6/EX6.2/6_2.sce @@ -0,0 +1,16 @@ +clc,clear +printf('Example 6.2\n\n') + +X_d=0.7 , X_q=0.4 //direct and quadrature axis synchronous reactance p.u. +R_a=0 +phi=acos(0.8) //Lag + +V_t=1 //assumed rated terminal Voltage +I_a=1 //Full-load armature current + +psi=atan( (V_t*sin(phi)+I_a*X_q)/(V_t*cos(phi)+I_a*R_a) ) +delta=psi-phi +I_d=I_a*sin(psi) +I_q=I_a*cos(psi) +E_f=V_t*cos(delta)+I_d*X_d+I_q*R_a +printf('Total e.m.f induced on open circuit is %.4f p.u.',E_f) diff --git a/1938/CH6/EX6.20/6_20.jpg b/1938/CH6/EX6.20/6_20.jpg new file mode 100755 index 000000000..6df2542e6 Binary files /dev/null and b/1938/CH6/EX6.20/6_20.jpg differ diff --git a/1938/CH6/EX6.20/6_20.sce b/1938/CH6/EX6.20/6_20.sce new file mode 100755 index 000000000..ebf997886 --- /dev/null +++ b/1938/CH6/EX6.20/6_20.sce @@ -0,0 +1,23 @@ +clc,clear +printf('Example 6.20\n\n') + +Power_total=1.414 //per unit +V_L=1 //per unit +phi_t=acos(0.707) +I_L_T=Power_total/(sqrt(3)*V_L*cos(phi_t)) //Total current +//Current supplied by each alternator +I_1=I_L_T/2 +I_2=I_1 +V_ph=V_L/sqrt(3) + +phi=acos(0.707) +R_a=0,X_s=0.6 //resistacne and synchronous reactance +E_ph=sqrt( (V_ph*cos(phi)+ I_1*R_a)^2 + (V_ph*sin(phi)+I_1*X_s)^2 ) +delta= atan((I_1*X_s+V_ph*sin(phi)) / (V_ph*cos(phi))) - phi //power angle + +printf('EMF is %.4f p.u. and power angle is %.2f degrees ',E_ph,delta*(180/%pi)) +printf('\n\nFollowing assumptions were made :\n') +printf('1.Terminal or bus bar voltage at ppoint of connection is constant\n') +printf('2.The alternators are identical and are initially equally excited\n') +printf('3.The power supplied by prime movers is adjusted so that each machine carries half the load represented by external impedance Z=R+ j 2pifL , where R and L are constant\n') +printf('4.The stator resistance is negligible') diff --git a/1938/CH6/EX6.21/6_21.sce b/1938/CH6/EX6.21/6_21.sce new file mode 100755 index 000000000..a394d2a07 --- /dev/null +++ b/1938/CH6/EX6.21/6_21.sce @@ -0,0 +1,18 @@ +clc,clear +printf('Example 6.21\n\n') + +V_l=480 +X_d=0.1,X_q=0.075,R_a=0 //armature resistance and synchronous reactance of direct,quadrature axis +I_l=1200 +I_ph=I_l/sqrt(3) +V_ph=V_l +V_t=V_l,I_a=I_ph +phi=acos(0.8) +psi=atan( (V_t*sin(phi)+I_a*X_q)/(V_t*cos(phi)+I_a*R_a) ) +delta=psi-phi + +I_d=I_a*sin(psi) +I_q=I_a*cos(psi) +E_f=V_t*cos(delta)+I_d*X_d+I_q*R_a + +printf('Excitation e.m.f is %.2f V ',E_f) diff --git a/1938/CH6/EX6.22/6_22.sce b/1938/CH6/EX6.22/6_22.sce new file mode 100755 index 000000000..518782824 --- /dev/null +++ b/1938/CH6/EX6.22/6_22.sce @@ -0,0 +1,22 @@ +clc,clear +printf('Example 6.22\n\n') + +VA=3.5*10^6 +P=32 //Poles +Power=2.5*10^6 //In watts +V_l=6.6*10^3 +phi=acos(0.8) +I_l=Power/(V_l*cos(phi)*sqrt(3)) +X_d=9.6,X_q=6,R_a=0 //armature resistance and synchronous reactance of direct,quadrature axis + +V_t=V_l/sqrt(3) +psi=atan( (V_t*sin(phi)+I_l*X_q)/(V_t*cos(phi)+I_l*R_a) ) +delta=psi-phi +I_s=I_l +I_d=I_s*sin(psi) +I_q=I_s*cos(psi) +E_f=V_t*cos(delta)+I_d*X_d+I_q*R_a + +regulation=100*(E_f-V_t)/V_t +printf('percentage regulation is %.2f percent',regulation) +printf('\nExcitation emf= %.0f V',E_f) diff --git a/1938/CH6/EX6.23/6_23.sce b/1938/CH6/EX6.23/6_23.sce new file mode 100755 index 000000000..c164e4907 --- /dev/null +++ b/1938/CH6/EX6.23/6_23.sce @@ -0,0 +1,20 @@ +clc,clear +printf('Example 6.23\n\n') + +X_d=7.6,X_q=4.5,R_a=0.15 //armature resistance and synchronous reactance of direct,quadrature axisV_l=13.8*10^3 +V_l=13.8*10^3 +V_t=V_l/sqrt(3) +phi=acos(0.8) +VA=25*10^6 +I_a=VA/(sqrt(3)*V_l) +psi=atan( (V_t*cos(phi)+I_a*X_q)/(V_t*sin(phi)+I_a*R_a) ) + +delta=psi-phi +I_s=I_a +I_d=I_s*sin(psi) +I_q=I_s*cos(psi) + +E_f=V_t*cos(delta)+I_d*X_d+I_q*R_a +regulation=100*(E_f-V_t)/V_t + +printf('percentage regulation is %.2f percent',regulation) diff --git a/1938/CH6/EX6.24/6_24.sce b/1938/CH6/EX6.24/6_24.sce new file mode 100755 index 000000000..ff0df37b0 --- /dev/null +++ b/1938/CH6/EX6.24/6_24.sce @@ -0,0 +1,17 @@ +clc,clear +printf('Example 6.24\n\n') + +X_d=1,X_q=0.6,R_a=0 //armature resistance and synchronous reactance of direct,quadrature axis +phi=acos(0.8) //lag +V_t=1 +I_a=1 //full load +psi=atan( (V_t*sin(phi)+I_a*X_q)/(V_t*cos(phi)+I_a*R_a) ) + +delta=psi-phi +I_s=I_a +I_d=I_a*sin(psi) +I_q=I_a*cos(psi) + +E_f=V_t*cos(delta)+I_d*X_d+I_q*R_a +regulation=100*(E_f-V_t)/V_t +printf('percentage regulation is %.2f percent',regulation) diff --git a/1938/CH6/EX6.25/6_25.sce b/1938/CH6/EX6.25/6_25.sce new file mode 100755 index 000000000..c9f779bf3 --- /dev/null +++ b/1938/CH6/EX6.25/6_25.sce @@ -0,0 +1,15 @@ +clc,clear +printf('Example 6.25\n\n') + +I_a=10 +phi=20 //lag and degrees +V_t=400 +X_d=10,X_q=6.5,R_a=0 //armature resistance and synchronous reactance of direct,quadrature axis + +psi=atand( (V_t*sind(phi)+I_a*X_q)/(V_t*cosd(phi)+I_a*R_a) ) +delta=psi-phi +I_d=I_a*sind(psi) +I_q=I_a*cosd(psi) + +printf('Load angle is %.2f degrees \n',delta) +printf('I_d and I_q are %.4f A and %.4f A respectively ',I_d,I_q ) diff --git a/1938/CH6/EX6.26/6_26.sce b/1938/CH6/EX6.26/6_26.sce new file mode 100755 index 000000000..622f3e19e --- /dev/null +++ b/1938/CH6/EX6.26/6_26.sce @@ -0,0 +1,30 @@ +clc,clear +printf('Example 6.26\n\n') + +X_d=0.8,X_q=0.5,R_a=0.02 //armature resistance and synchronous reactance of direct,quadrature axis + +//case(i) lag +phi=acos(0.8) +V_t=1 +I_a=1//full-load +psi=atan( (V_t*sin(phi)+I_a*X_q)/(V_t*cos(phi)+I_a*R_a) ) +delta=psi-phi + +I_d=I_a*sin(psi) +I_q=I_a*cos(psi) + +E_f=V_t*cos(delta)+I_d*X_d+I_q*R_a +regulation=100*(E_f-V_t)/V_t +printf('percentage regulation at 0.8 pf lag is %.2f percent',regulation) + +//case(ii) lead +phi2=-1*acos(0.8) //minus sign because of leading pf +psi2=atan( (V_t*sin(phi2)+I_a*X_q)/(V_t*cos(phi2)+I_a*R_a) ) +delta2=psi2-phi2 + +I_d2=I_a*sin(psi2) +I_q2=I_a*cos(psi2) + +E_f2=V_t*cos(delta2)+I_d2*X_d+I_q2*R_a +regulation2=100*(E_f2-V_t)/V_t +printf('\npercentage regulation at 0.8 pf lead is %.2f percent',regulation2) diff --git a/1938/CH6/EX6.27/6_27.sce b/1938/CH6/EX6.27/6_27.sce new file mode 100755 index 000000000..c3d873593 --- /dev/null +++ b/1938/CH6/EX6.27/6_27.sce @@ -0,0 +1,23 @@ +clc,clear +printf('Example 6.27\n\n') + +kW=[800,500,1000,600] +cosphi=[1,0.9,0.8,0.9] +tanphi=tan(acos(cosphi)) +kVAR=kW.*tanphi + +kW_total=kW(1)+kW(2)+kW(3)+kW(4) +kVAR_total=kVAR(1)+kVAR(2)+kVAR(3)+-1*kVAR(4) //4th case is leading + +phi_c=atan(kVAR_total/kW_total) //total power factor angle +phi_1=acos(0.95)//pf of machine 1 +kW_1=1000 //active component of machine 1 +kVAR_1=kW_1*tan(phi_1) //reactive component of machine 1 +kW_2=kW_total - kW_1 //active component of machine 1 +kVAR_2=kVAR_total-kVAR_1 //reactive component of machine 2 + +phi_2=atan(kVAR_2/kW_2) +pf_2=cos(phi_2) //power factor of machine 2 + +printf('Output of second alternator= %.0f kW',kW_2) +printf('\npower factor of machine 2 = %.2f and lagging',pf_2) diff --git a/1938/CH6/EX6.28/6_28.sce b/1938/CH6/EX6.28/6_28.sce new file mode 100755 index 000000000..3046729ec --- /dev/null +++ b/1938/CH6/EX6.28/6_28.sce @@ -0,0 +1,21 @@ +clc,clear +printf('Example 6.28\n\n') + +kW=[250,300,150] +cosphi=[0.9,0.75,0.8] //all lagging +tanphi=tan(acos(cosphi)) +kVAR=kW.*tanphi + +kW_total=kW(1)+kW(2)+kW(3) +kVAR_total=kVAR(1)+kVAR(2)+kVAR(3) + +phi_1=acos(0.8)//pf of machine 1 +kW_1=100 //active component of machine 1 +kVAR_1=kW_1*tan(phi_1) //reactive component of machine 1 +kW_2=kW_total - kW_1 //active component of machine 1 +kVAR_2=kVAR_total-kVAR_1 //reactive component of machine 2 +phi_2=atan(kVAR_2/kW_2) +pf_2=cos(phi_2) //power factor of machine 2 + +printf('Output of second alternator= %.0f kW',kW_2) +printf('\npower factor of machine 2 = %.4f and lagging',pf_2) diff --git a/1938/CH6/EX6.29/6_29.sce b/1938/CH6/EX6.29/6_29.sce new file mode 100755 index 000000000..3a8d4283b --- /dev/null +++ b/1938/CH6/EX6.29/6_29.sce @@ -0,0 +1,24 @@ +clc,clear +printf('Example 6.29\n\n') + +V_L=6.6*10^3 +V_ph=V_L/sqrt(3) +V_t=V_ph +X_d=9.6,X_q=6,R_a=0 //armature resistance and synchronous reactance of direct,quadrature axis +VA=3.5*10^6 +I_L=VA/(sqrt(3)*V_L) + +P=2.5*10^6,phi=acos(0.8) +I_a=P/(sqrt(3)*V_L*cos(phi)) +psi=atan( (V_t*sin(phi)+ I_a*X_q)/(V_t*cos(phi)+ I_a*R_a) ) + +delta=psi-phi +I_d=I_a*sin(psi) +I_q=I_a*cos(phi) + +E_f=V_t*cos(delta)+I_d*X_d+I_q*R_a +regulation=100*(E_f-V_t)/V_t +P_max=(V_ph^2/2)*((X_d-X_q)/(X_d*X_q))*(sin(2*delta)) + +printf('percentage voltage regulation is %.2f percent',regulation) +printf('\nPower under open circuit is %.1f kW per phase',P_max/1000) diff --git a/1938/CH6/EX6.3/6_3.sce b/1938/CH6/EX6.3/6_3.sce new file mode 100755 index 000000000..ab19695f2 --- /dev/null +++ b/1938/CH6/EX6.3/6_3.sce @@ -0,0 +1,28 @@ +clc,clear +printf('Example 6.3\n\n') + +//note that a new function p2z has been defined below for direct representation of complex numbers in polar form +function [FUN] = p2z(RRRR,Theeeta) + FUN = RRRR.*exp(%i*%pi*Theeeta/180.); +endfunction + +Z1=complex(0,3) //impedance of alternator 1 +Z2=complex(0,4) //impedance of alternator 2 +Z=6 //load +E1=p2z(220,0) //induced emf vector on no load +E2=p2z(220,10)//induced emf vector on no load + +I1=((E1-E2)*Z+E1*Z2)/(Z*(Z1+Z2)+Z1*Z2) +I2=((E2-E1)*Z+E2*Z1)/(Z*(Z1+Z2)+Z1*Z2) + +phi1=phasemag(I1) //Phasemag returns the angle of complex number in degrees +phi2=phasemag(I2) //Phasemag returns the angle of complex number in degrees + +I=I1+I2 +V=I*Z //Terminal voltage +printf('(i) Terminal voltage is %.1f volts at %.2f degrees\n',abs(V),phasemag(V)) +printf('(ii) Currents are %.2f A at %.2f degrees and %.2f A at %.2f degrees\n Total current is %.2f A at %.2f degrees ',abs(I1),phasemag(I1),abs(I2),phasemag(I2),abs(I),phasemag(I)) + +P1=abs(V)*abs(I1)*cosd(phi1) +P2=abs(V)*abs(I2)*cosd(phi2) +printf('\n(iii)Power delivered is %.2f watts and %.2f watts',P1,P2) diff --git a/1938/CH6/EX6.30/6_30.sce b/1938/CH6/EX6.30/6_30.sce new file mode 100755 index 000000000..0e93ef101 --- /dev/null +++ b/1938/CH6/EX6.30/6_30.sce @@ -0,0 +1,29 @@ +clc,clear +printf('Example 6.30\n\n') + +V_L=3.3*10^3 +V_ph=V_L/sqrt(3) +VA=3*10^6 +I_FL=VA/(sqrt(3)*V_L) +IX_s=(25/100)*V_ph //product of I and X_s +X_s=complex(0,IX_s/I_FL) +N_s=1000 //in r.p.m + +Poles=6,f=50 +delta_dash_mech=(%pi/180) //displacement in degree mechanical +//displacement in degree electrical +delta_dash_elec=delta_dash_mech*(Poles/2) + +I=I_FL,phi=acos(0.8) +V=complex(V_ph*cos(phi),V_ph*sin(phi)) +E= V+ I*X_s + +delta=(%pi/180)*phasemag(E)-phi //E leads I by (%pi/180)*phasemag(E) and V leads I by phi radians +P_SY=abs(E)*abs(V_ph)*cos(delta)*sin(delta_dash_elec)/abs(X_s) //synchronising power per phase +P_SY_total=3*P_SY //total synchronising power + +ns=120*f/(60*Poles) //in r.p.m +T_SY=P_SY_total/(2*%pi*ns) //Synchronising torque +printf('Synchronising power per phase is %.3f kW\n',P_SY/1000) +printf('Synchronising torque is %.0f N-m',T_SY) +printf('\n\nAnswer mismatches due to improper approximation') diff --git a/1938/CH6/EX6.31/6_31.sce b/1938/CH6/EX6.31/6_31.sce new file mode 100755 index 000000000..a8e0513ba --- /dev/null +++ b/1938/CH6/EX6.31/6_31.sce @@ -0,0 +1,25 @@ +clc,clear +printf('Example 6.31\n\n') + +V_L=3.3*10^3 +V_ph=V_L/sqrt(3) +VA=3*10^6 +I_FL=VA/(sqrt(3)*V_L) +IX_s=(20/100)*V_ph //product of I and X_s +X_s=complex(0,IX_s/I_FL) +N_s=1000 //in r.p.m +Poles=6,f=50 + +delta_dash_mech=(%pi/180) //displacement in degree mechanical +//displacement in degree electrical +delta_dash_elec=delta_dash_mech*(Poles/2) + +//E=V as the alternator is on no-load and X_s=Z_s +P_SY=abs(V_ph)^2*(delta_dash_elec)/abs(X_s) //synchronising power per phase +P_SY_total=3*P_SY //total synchronising power + +ns=120*f/(60*Poles) //in r.p.s +T_SY=P_SY_total/(2*%pi*ns) //Synchronising torque +printf('Synchronising power per phase is %.3f kW\n',P_SY/1000) +printf('Total Synchronising power is %.3f kW',P_SY_total/1000) +printf('\nSynchronising torque is %.0f N-m',T_SY) diff --git a/1938/CH6/EX6.32/6_32.jpg b/1938/CH6/EX6.32/6_32.jpg new file mode 100755 index 000000000..6c38a11a7 Binary files /dev/null and b/1938/CH6/EX6.32/6_32.jpg differ diff --git a/1938/CH6/EX6.32/6_32.sce b/1938/CH6/EX6.32/6_32.sce new file mode 100755 index 000000000..fdbca2b8d --- /dev/null +++ b/1938/CH6/EX6.32/6_32.sce @@ -0,0 +1,32 @@ +clc,clear +printf('Example 6.32\n\n') + +V_L=11*10^3 +V_ph=V_L/sqrt(3) +VA=700*10^3 +I_FL=VA/(sqrt(3)*V_L) +IX_s=(14/100)*V_ph //product of I and X_s +X_s=IX_s/I_FL +//X_s=complex(0,IX_s/I_FL) +IR_a=(1.5/100)*V_ph //product of I and R_a +R_a=IR_a/I_FL + +I=I_FL,phi=acos(0.8) +V=complex(V_ph*cos(phi),V_ph*sin(phi)) +E_ph=sqrt( (V_ph*cos(phi)+IR_a)^2 +(V_ph*sin(phi)+IX_s)^2 ) + +delta=asin((V_ph*sin(phi)+IX_s)/E_ph) -phi + +Poles=4,f=50 +delta_dash_mech=(%pi/180) //phase displacemnt in degree mechanical +delta_dash_elec=delta_dash_mech*(Poles/2)//phase displacemnt in degree electrical + +P_SY=abs(V_ph)*abs(E_ph)*cos(delta)*sin(delta_dash_elec)/abs(X_s) //synchronising power per phase +P_SY_total=3*P_SY //total synchronising power + +ns=120*f/(60*Poles) //in r.p.s +T_SY=P_SY_total/(2*%pi*ns) //Synchronising torque +printf('Synchronising power per phase is %.3f kW\n',P_SY/1000) +printf('Synchronising power is %.3f kW ; ',P_SY/1000) +printf('Total Synchronising power is %.3f kW',P_SY_total/1000) +printf('\nSynchronising torque is %.2f N-m',T_SY) diff --git a/1938/CH6/EX6.33/6_33.sce b/1938/CH6/EX6.33/6_33.sce new file mode 100755 index 000000000..b6e6c0403 --- /dev/null +++ b/1938/CH6/EX6.33/6_33.sce @@ -0,0 +1,27 @@ +clc,clear +printf('Example 6.33\n\n') +//note that a new function p2z has been defined below for direct representation of complex numbers in polar form +function [FUN] = p2z(RRRR,Theeeta) + FUN = RRRR.*exp(%i*%pi*Theeeta/180.); +endfunction + +Z1=complex(0,2) +Z2=complex(0,3) +Z=6 +E1=p2z(230,0) +E2=p2z(230,10) + +I1=((E1-E2)*Z+E1*Z2)/(Z*(Z1+Z2)+Z1*Z2) +I2=((E2-E1)*Z+E2*Z1)/(Z*(Z1+Z2)+Z1*Z2) + +phi1=phasemag(I1) //Phasemag returns the angle of complex number in degrees +phi2=phasemag(I2) //Phasemag returns the angle of complex number in degrees + +I=I1+I2 +V=I*Z //Terminal voltage +printf('(i) Terminal voltage is %.2f volts at %.1f degrees\n',abs(V),phasemag(V)) +printf('(ii) Currents are %.2f A at %.0f degrees and %.2f A at %.2f degrees\n Total current is %.2f A at %.1f degrees ',abs(I1),phasemag(I1),abs(I2),phasemag(I2),abs(I),phasemag(I)) + +P1=abs(V)*abs(I1)*cosd(phi1) +P2=abs(V)*abs(I2)*cosd(phi2) +printf('\n(iii)Power delivered %.2f watts and %.2f watts',P1,P2) diff --git a/1938/CH6/EX6.34/6_34.sce b/1938/CH6/EX6.34/6_34.sce new file mode 100755 index 000000000..3e31f18ee --- /dev/null +++ b/1938/CH6/EX6.34/6_34.sce @@ -0,0 +1,16 @@ +clc,clear +printf('Example 6.34\n\n') + +X_d=0.8,X_q=0.5 //both per unit +R_a=0 //assumed +phi=acos(0.8) +V_t=1//pu +I_a=1 //full-load + +psi=atan( (V_t*sin(phi)+I_a*X_q)/(V_t*cos(phi)+I_a*R_a) ) +delta=psi-phi +I_d=I_a*sin(psi) +I_q=I_a*cos(psi) +E_f=V_t*cos(delta)+I_d*X_d+I_q*R_a + +printf('Open circuit voltage is %.3f p.u.',E_f) diff --git a/1938/CH6/EX6.35/6_35.sce b/1938/CH6/EX6.35/6_35.sce new file mode 100755 index 000000000..d112e4257 --- /dev/null +++ b/1938/CH6/EX6.35/6_35.sce @@ -0,0 +1,25 @@ +clc,clear +printf('Example 6.35\n\n') + +V_L=6600,I_L=110,phi_1=acos(0.9) //lagging +kW=[400,1000,400,300]*10^3 +cosphi=[1,0.71,0.8,0.9] +tanphi=tan(acos(cosphi)) +kVAR=kW.*tanphi + +kW_total=kW(1)+kW(2)+kW(3)+kW(4) +kVAR_total=kVAR(1)+kVAR(2)+kVAR(3)+kVAR(4) + +phi_c=atan(kVAR_total/kW_total) //total power factor angle +load_1=sqrt(3)*V_L*I_L*cos(phi_1) + +kW_1=load_1 //active component of machine 1 +kVAR_1=kW_1*tan(phi_1) //reactive component of machine 1 +kW_2=kW_total - kW_1 //active component of machine 1 +kVAR_2=kVAR_total-kVAR_1 //reactive component of machine 2 + +phi_2=atan(kVAR_2/kW_2) +pf_2=cos(phi_2) //power factor of machine 2 + +printf('Output of second alternator= %.2f kW',kW_2/1000) +printf('\nPower factor of machine 2 = %.4f and lagging',pf_2) diff --git a/1938/CH6/EX6.36/6_36.jpg b/1938/CH6/EX6.36/6_36.jpg new file mode 100755 index 000000000..324ec1efb Binary files /dev/null and b/1938/CH6/EX6.36/6_36.jpg differ diff --git a/1938/CH6/EX6.36/6_36.sce b/1938/CH6/EX6.36/6_36.sce new file mode 100755 index 000000000..619b67c74 --- /dev/null +++ b/1938/CH6/EX6.36/6_36.sce @@ -0,0 +1,26 @@ +clc,clear +printf('Example 6.36\n\n') + +V_L=11000 +V_ph=V_L/sqrt(3) +VA=2*10^6,phi=acos(0.8) +I_FL=VA/(sqrt(3)*V_L) +phi_1=acos(0.8) +IX_s=(20/100)*V_ph //product of I and X_s +X_s=IX_s/I_FL +I_1=I_FL +BC=I_1*cos(phi_1)*X_s +AB=I_1*sin(phi_1)*X_s , OA=V_ph +OC=sqrt( (OA+AB)^2+(BC)^2 ) ,E_1=OC +E_2=1.25*E_1,OE=E_2 +DE=BC +AD=sqrt(OE^2-DE^2) -OA //because OE=sqrt( (OA+AD)^2 + (DE)^2 ) + +I_2sinphi2=AD/X_s +I_2cosphi2=I_1*cos(phi) +I_2=sqrt( (I_2cosphi2)^2 + (I_2sinphi2)^2 ) +phi2=atan( I_2sinphi2/ I_2cosphi2 ) +new_pf=cos(phi2) + +printf('Machine current is %.2f A \n',I_2) +printf('Power factor is %.4f lagging',new_pf) diff --git a/1938/CH6/EX6.37/6_37.sce b/1938/CH6/EX6.37/6_37.sce new file mode 100755 index 000000000..2d5adba0b --- /dev/null +++ b/1938/CH6/EX6.37/6_37.sce @@ -0,0 +1,34 @@ +clc,clear +printf('Example 6.37\n\n') +//note that a new function p2z has been defined below for direct representation of complex numbers in polar form +function [FUN] = p2z(RRRR,Theeeta) + FUN = RRRR.*exp(%i*%pi*Theeeta/180.); +endfunction + +P_out=3000*10^3 +V_L=6.6*10^3,V_ph=V_L/sqrt(3) +phi=acos(0.8) +I_L=p2z(P_out/(sqrt(3)*V_L*cos(phi)),-1*(180/%pi)*phi) + +P_out1=P_out/2 +I_L1=150 //given +phi_L1=acos( P_out1/(sqrt(3)*V_L*I_L1) ) +I_L1=p2z(I_L1,-1*(180/%pi)*phi_L1) + +I_L2=I_L-I_L1 +pf_2=cosd(phasemag(I_L2)) +Z_1=complex(0.5,10) +I_1=I_L1 +E_1=V_ph + I_1*Z_1 +delta_1=(%pi/180)*phasemag(E_1) //load angle of alternator 1 +E_1L=sqrt(3)*E_1 + +Z_2=complex(0.4,12) +I_2=I_L2 +E_2=V_ph + I_2*Z_2 +delta_2=(%pi/180)*phasemag(E_2) //load angle of alternator 2 + +printf('Part(i)\nCurrents are %.0f A at %.1f degrees and %.1f A at %.1f degrees\nTotal current is %.0f at %.2f\n',abs(I_L1),phasemag(I_L1),abs(I_L2),phasemag(I_L2),abs(I_L),phasemag(I_L)) +printf('Part(ii)\nPower factor is %.4f and lagging\n',cos(phi_L1)) +printf('Part(iii)\nemf are %.2f V at %.2f degrees and %.4f V at %.0f degrees\n',abs(E_1),phasemag(E_1),abs(E_2),phasemag(E_2)) +printf('Part(iv)\nPower angles are %.2f degrees and %.0f degrees \n',(180/%pi)*delta_1,(180/%pi)*delta_2) diff --git a/1938/CH6/EX6.38/6_38.jpg b/1938/CH6/EX6.38/6_38.jpg new file mode 100755 index 000000000..07e7a0bbb Binary files /dev/null and b/1938/CH6/EX6.38/6_38.jpg differ diff --git a/1938/CH6/EX6.38/6_38.sce b/1938/CH6/EX6.38/6_38.sce new file mode 100755 index 000000000..7fa95646a --- /dev/null +++ b/1938/CH6/EX6.38/6_38.sce @@ -0,0 +1,22 @@ +clc,clear +printf('Example 6.38\n\n') + +Z1=complex(0.2,2) +Z2=Z1 +ZL=complex(3,4) +Z=ZL +E1=complex(2000,0) +E2=complex(2200,100) + +I1=((E1-E2)*Z+E1*Z2)/(Z*(Z1+Z2)+Z1*Z2) +I2=((E2-E1)*Z+E2*Z1)/(Z*(Z1+Z2)+Z1*Z2) + +IL=I1+I2 +V=IL*Z //Terminal voltage + +phi1=phasemag(V)-phasemag(I1) //Phasemag returns the angle of complex number in degrees +phi2=phasemag(V)-phasemag(I2) //Phasemag returns the angle of complex number in degrees + +Pout1=sqrt(3)*sqrt(3)*abs(V)*abs(I1)*cosd(phi1) +Pout2=sqrt(3)*sqrt(3)*abs(V)*abs(I2)*cosd(phi2) +printf('\nPower delivered is %.2f kW and %.2f kW at power-factors %.4f lag and %.4f lag respectively',Pout1/1000,Pout2/1000,cosd(phi1),cosd(phi2)) diff --git a/1938/CH6/EX6.39/6_39.sce b/1938/CH6/EX6.39/6_39.sce new file mode 100755 index 000000000..c2f86e764 --- /dev/null +++ b/1938/CH6/EX6.39/6_39.sce @@ -0,0 +1,25 @@ +clc,clear +printf('Example 6.39\n\n') + +f=50 +P=12 +V_L=6600 +V_ph=V_L/sqrt(3) +VA=2000*10^3 +I_FL=VA/(sqrt(3)*V_L) + +IX_s=(25/100)*V_ph //product of I and X_s +X_s=complex(0,IX_s/I_FL) +N_s=12*f/P //in rpm +delta_dash_mech=(%pi/180) //phase displacemnt in degree mechanical +delta_dash_elec=delta_dash_mech*(P/2) //phase displacemnt in degree electrical + +phi=acos(0.8) //lag +I=complex(I_FL*cos(-1*phi),I_FL*sin(-1*phi)) +V=V_ph +E=V + I*X_s +delta=phasemag(E)*(%pi/180) +P_SY=abs(E)*abs(V)*cos(delta)*sin(delta_dash_elec)/abs(X_s) +P_SY_total=3*P_SY +printf('\nSynchronising power is %.2f kW',P_SY/1000) +printf('\nTotal synchronising power is %.2f kW',P_SY_total/1000) diff --git a/1938/CH6/EX6.4/6_4.sce b/1938/CH6/EX6.4/6_4.sce new file mode 100755 index 000000000..6ec656633 --- /dev/null +++ b/1938/CH6/EX6.4/6_4.sce @@ -0,0 +1,21 @@ +clc,clear +printf('Example 6.4\n\n') + +V_l=10000 +V_ph=V_l/sqrt(3) +VA=10*10^6 +I_FL=VA/(V_l*sqrt(3)) //Current at full laod +IX_s=(20/100)*V_ph //product of I and X_s + +X_s=IX_s/I_FL +N_s=1500 +f=50 +P=120*f/N_s //poles + +delta_dash_mech=%pi/180 //phase displacement in degree mechanical +delta_dash_elec=delta_dash_mech*(P/2) //P/2 is pole pairs(and not poles) +E=V_ph //since alternator is on no-load +P_SY=delta_dash_elec*E^2/X_s //Synchronous Power +P_SY_3ph=P_SY*3 //For 3 phases + +printf('Synchronising Power of armature is %.3f kW.\nSynchronising Power for 3 phase is %.3f kW',P_SY*10^-3,P_SY_3ph*10^-3) diff --git a/1938/CH6/EX6.40/6_40.jpg b/1938/CH6/EX6.40/6_40.jpg new file mode 100755 index 000000000..10cfbf523 Binary files /dev/null and b/1938/CH6/EX6.40/6_40.jpg differ diff --git a/1938/CH6/EX6.40/6_40.sce b/1938/CH6/EX6.40/6_40.sce new file mode 100755 index 000000000..89324be78 --- /dev/null +++ b/1938/CH6/EX6.40/6_40.sce @@ -0,0 +1,24 @@ +clc,clear +printf('Example 6.40\n\n') + +V_L=22000 +V_ph=V_L/sqrt(3) +power=230*10^6 +phi=acos(1) +I_FL=power/(sqrt(3)*V_L*cos(phi)) +I_1=I_FL +X_s=1.2 + +E_1=sqrt( V_ph^2 + (I_1*X_s)^2 ) +E_2=1.3*E_1 +AC= sqrt( E_2^2-(I_1*X_s)^2 ) -V_ph // because E^2=(V_ph+AC)^2+(I_1*X_s)^2 +I2X_S=AC + +I_2cosphi2=I_1 //because phi_2=acos(I_1/I_2) //from ACD +I_2sinphi2=AC/X_s +I_2=sqrt( (I_2cosphi2)^2 + (I_2sinphi2)^2 ) +phi2=atan( I_2sinphi2/ I_2cosphi2 ) +new_pf=cos(phi2) + +printf('Machine current is %.2f A \n',I_2) +printf('Power factor is %.4f and lagging',new_pf) diff --git a/1938/CH6/EX6.41/6_41.sce b/1938/CH6/EX6.41/6_41.sce new file mode 100755 index 000000000..3bf957da2 --- /dev/null +++ b/1938/CH6/EX6.41/6_41.sce @@ -0,0 +1,33 @@ +clc,clear +printf('Example 6.41\n\n') +//note that a new function p2z has been defined below for direct representation of complex numbers in polar form +function [FUN] = p2z(RRRR,Theeeta) + FUN = RRRR.*exp(%i*%pi*Theeeta/180.); +endfunction + +P_out=1500*10^3 +V_L=3.3*10^3 +phi=acos(0.8) +I_L=p2z(P_out/(sqrt(3)*V_L*cos(phi)),-1*acosd(0.8)) + +I_L1_magnitude=150 //given +P_out1=(3*10^6)/2 //because load is EQUALLY shared between 2 alternators +pf_L1=P_out1/(sqrt(3)*2*V_L*I_L1_magnitude) //operating pf of alternator 1 +phi1=acosd(pf_L1) +I_L1=p2z(I_L1_magnitude,-1*phi1) +I_L2=I_L-I_L1 //because I_L=I_L1 + I_L2 +pf_L2=cosd(phasemag(I_L2)) + +V_ph=6.6*10^3/sqrt(3) +Z_1=complex(0.5,10) +I_1=I_L1 +E_1= V_ph + I_1*Z_1 +delta_1=phasemag(E_1) //load angle of alternator 1 +I_2=I_L2 + +Z_2=complex(0.4,12) +E_2= V_ph + I_2*Z_2 +delta_2=phasemag(E_2) //load angle of alternator 1 + +printf('for machine 1\ncurrent is %.0f A at %.2f degrees\nPower factor of %.4f lag\ninduced emf of %.2f V\nload angle of %.2f degrees',abs(I_L1),phasemag(I_L1),pf_L1,abs(E_1),delta_1) +printf('\n\nfor machine 2\ncurrent is %.1f A at %.1f degrees\nPower factor of %.4f lag\ninduced emf of %.2f V\nload angle of %.0f degrees',abs(I_L2),phasemag(I_L2),pf_L2,abs(E_2),delta_2) diff --git a/1938/CH6/EX6.42/6_42.sce b/1938/CH6/EX6.42/6_42.sce new file mode 100755 index 000000000..a6a33dd39 --- /dev/null +++ b/1938/CH6/EX6.42/6_42.sce @@ -0,0 +1,19 @@ +clc,clear +printf('Example 6.42\n\n') + +V_l=230 +VA=5*10^3 +X_d=12,X_q=7,R_a=0 //armature resistance and synchronous reactance of direct,quadrature axis +phi=acos(1) + +I_l=VA/(V_l*sqrt(3)) +V_ph=V_l/sqrt(3) +V_t=V_ph,I_a=I_l + +psi=atan( (V_t*sin(phi)+I_a*X_q)/(V_t*cos(phi)+I_a*R_a) ) +delta=psi-phi +I_d=I_a*sin(psi) +I_q=I_a*cos(psi) +E_f=V_t*cos(delta)+I_d*X_d+I_q*R_a + +printf('Excitation voltage is %.3f V ',E_f) diff --git a/1938/CH6/EX6.43/6_43.sce b/1938/CH6/EX6.43/6_43.sce new file mode 100755 index 000000000..095fdd865 --- /dev/null +++ b/1938/CH6/EX6.43/6_43.sce @@ -0,0 +1,25 @@ +clc,clear +printf('Example 6.43\n\n') + +V_l=6.6*10^3 +V_t=V_l/sqrt(3) +X_d=23.2,X_q=14.5,R_a=0 //armature resistance and synchronous reactance of direct,quadrature axis +VA=1800*10^3 +phi=acos(0.8) //lag + +I_a=VA/(V_l*sqrt(3)) + +psi=atan( (V_t*sin(phi)-I_a*X_q)/(V_t*cos(phi)-I_a*R_a) ) //minus sign in numerator and denomenator for motors +delta=psi+phi +I_d=I_a*sin(psi) +I_q=I_a*cos(psi) +E_f=V_t*cos(delta)-I_d*X_d-I_q*R_a +printf('Excitation emf = %.4f V\n',E_f) +//P_m= ( V_t*E_f*sin(delta)/X_d ) + ((1/X_q)-(1/X_d))*0.5*sin(2*delta)*V_t^2 +//P_m=0.4996*cos(delta)+0.1877*sin(2*delta) +//for maximum power output, differenciate and equate to zero + +delta_max=63.4 //degree + +P_m_max=((1/X_q)-(1/X_d))*0.5*sind(2*delta_max)*V_t^2 //Maximuum load supplied with E_f=0 +printf('Maximum load the motor can supply is %.4f MW per phase ',P_m_max*10^-6 ) diff --git a/1938/CH6/EX6.5/6_5.sce b/1938/CH6/EX6.5/6_5.sce new file mode 100755 index 000000000..b6e457b7e --- /dev/null +++ b/1938/CH6/EX6.5/6_5.sce @@ -0,0 +1,46 @@ +clc,clear +printf('Example 6.5\n\n') +//note that a new function p2z has been defined below for direct representation of complex numbers in polar form +function [FUN] = p2z(RRRR,Theeeta) + FUN = RRRR.*exp(%i*%pi*Theeeta/180.); +endfunction + +V_L=6.6*10^3 +V_ph=V_L/sqrt(3) +VA=3*10^6 +I_FL=VA/(V_L*sqrt(3)) //full load current +P=8,f=50 //poles and frequency + +X_s=complex(0,2.9)//X_s=2.9 +delta_dash_mech=%pi/180 +delta_dash_elec=delta_dash_mech*(P/2) //P/2 is pole pairs(and not poles) + +//part(i) +E=V_ph +P_SY=delta_dash_elec*E^2/abs(X_s) //Synchronous Power per phase +P_SY_3ph=P_SY*3 //For 3 phases +printf('(i) Synchronising power at no load is %.3f kW',P_SY*10^-3) +printf('\n Total synchronising power at no load is %.2f kW\n',P_SY_3ph*10^-3) + +N_s=120*f/P //in rpm +n_s=(N_s)/60 //in rps +T_SY=P_SY_3ph/(2*%pi*n_s) +printf('\nSynchronous torque per mechanical degree of phase displacement is %.2f * 10^3 N-m',T_SY*10^-3) + +//part(ii) +phi=acosd(0.85) +I=p2z(I_FL,0) +V=p2z(V_ph,phi) + +E=V+I*X_s +//E leads I by phasemag(E). V leads I by phasemag(V) + +delta=(%pi/180)* (phasemag(E)-phasemag(V) ) //power angle in radians +P_SY2=abs(E)*abs(V)*cos(delta)*sin(delta_dash_elec)/abs(X_s) + +P_SY_total_2=3*P_SY2 +//n_s=T_SY/(P_SY/(2*%pi) ) //because T_SY=P_SY/(2*%pi*n_s) +printf('\n\n(ii)Total synchronising power is %.0f kW',P_SY_total_2*10^-3) + +T_SY2=P_SY_total_2/(2*%pi*n_s) +printf('\nSynchronising torque is %.2f * 10^3 N-m',T_SY2/1000) diff --git a/1938/CH6/EX6.6/6_6.sce b/1938/CH6/EX6.6/6_6.sce new file mode 100755 index 000000000..627bebe6d --- /dev/null +++ b/1938/CH6/EX6.6/6_6.sce @@ -0,0 +1,29 @@ +clc,clear +printf('Example 6.6\n\n') +//note that a new function p2z has been defined below for direct representation of complex numbers in polar form +function [FUN] = p2z(RRRR,Theeeta) + FUN = RRRR.*exp(%i*%pi*Theeeta/180.); +endfunction + +V_l=10*10^3 +V_ph=V_l/sqrt(3) +R_a=0.4 +Z=complex(R_a,6) +I_a=p2z(300,-acosd(0.8)) +E=V_ph+I_a*Z + +phi=acos(0.8) +alternator_op_ph=V_ph*abs(I_a)*cos(phi) //Power delivered to infinite bus per phase + +//Power deliered to the altrernator = Power delivewred to bus bar + I^2*R losses in armature +alternator_power= alternator_op_ph+ abs(I_a)^2*R_a + +//this power developed remains constant.change pf to 1 and calculate corresponding armature current +//alternator_power=V_ph*I_a1*cos(phi1)+I_a1^2*0.4 +//solve the quadratic equation 0.4 I_a1^2+5773.50 I_a1- 1421640 =0 +I_a1=(-1*V_ph+sqrt(V_ph^2-4*R_a*-1*alternator_power))/(2*R_a) + +//also as follows +E1=V_ph+I_a1*Z +decrease=100*(abs(E)-abs(E1))/abs(E) +printf('Percentage decrease in induced e.m.f is %.1f percent',decrease) diff --git a/1938/CH6/EX6.7/6_7.jpg b/1938/CH6/EX6.7/6_7.jpg new file mode 100755 index 000000000..d77d5707b Binary files /dev/null and b/1938/CH6/EX6.7/6_7.jpg differ diff --git a/1938/CH6/EX6.7/6_7.sce b/1938/CH6/EX6.7/6_7.sce new file mode 100755 index 000000000..be43842c6 --- /dev/null +++ b/1938/CH6/EX6.7/6_7.sce @@ -0,0 +1,28 @@ +clc,clear +printf('Example 6.7\n\n') + +//Line PQ for Altermnator 1, and PR for alternaator 2.AB is at frequency x from P where total load is 3000 kW +QC=2000,PS=2.5,//PC=x +TR=2000,PT=2 + +//using similarity of triangles PAC and PQS +AC_by_PC=(QC/PS)// because (AC/QC)=(PC/PS) +//using similarity of triangles PCB and PTR +CB_by_PC=(TR/PT) // because (CB/TR)=(PC/PT) + +AC_by_x=AC_by_PC //which implies AC=12.5*x +CB_by_x=CB_by_PC //which implies CB=16.67*x + +AC_plus_CB=3000 //total load at the frequency at P is 30 kW +x= AC_plus_CB/(AC_by_x + CB_by_x) +AC=AC_by_x * x +CB=CB_by_x * x +frequency=50-x +printf('Loads shared by alternator 1 and 2 are %.2f kW and %.2f kW respectively',AC,CB) + +//construction for max load: RT is extended to cut PQ at X. +QS=2000,RT=2000 //see figure +XT=QS*(PT/PS) +RX=RT+XT //maximum load + +printf('\nMaximum load is %.0f kW',RX) diff --git a/1938/CH6/EX6.8/6_8.jpg b/1938/CH6/EX6.8/6_8.jpg new file mode 100755 index 000000000..43e333f6c Binary files /dev/null and b/1938/CH6/EX6.8/6_8.jpg differ diff --git a/1938/CH6/EX6.8/6_8.sce b/1938/CH6/EX6.8/6_8.sce new file mode 100755 index 000000000..ef4b798c3 --- /dev/null +++ b/1938/CH6/EX6.8/6_8.sce @@ -0,0 +1,22 @@ +clc,clear +printf('Example 6.8\n\n') + +P_out=1500*10^3 +V_L=11000 +phi=acos(0.8) +I_L=P_out/(sqrt(3)*V_L*cos(phi)) + +I_L_actv=I_L*cos(phi) //wattful or active component of current +I_L_reactive=I_L*sin(phi) //wattless or reactive component of current + +I_each=I_L/2 //in identical conditions +I_arm1=45 //given +I_1_reactive=sqrt(I_arm1^2-39.364^2 ) //from the power triangle +I_2_reactive=59.046-21.80 +I_a_2=sqrt( 39.364^2 + I_2_reactive^2 ) //required armature current of 2nd alternator +printf('Required armature current of second alternator is %.4f A\n',I_a_2) +//power factors of 2 machines +cos_phi1=39.364/45 +cos_phi2=39.364/54.1921 + +printf('Power factors are %.4f lagging and %.4f lagging',cos_phi1,cos_phi2) diff --git a/1938/CH6/EX6.9/6_9.jpg b/1938/CH6/EX6.9/6_9.jpg new file mode 100755 index 000000000..298e464cf Binary files /dev/null and b/1938/CH6/EX6.9/6_9.jpg differ diff --git a/1938/CH6/EX6.9/6_9.sce b/1938/CH6/EX6.9/6_9.sce new file mode 100755 index 000000000..b197cdd00 --- /dev/null +++ b/1938/CH6/EX6.9/6_9.sce @@ -0,0 +1,21 @@ +clc,clear +printf('Example 6.9\n\n') + +//Line AB for Altermnator 1, and AC for alternator 2.AF is at frequency x measured from A where total load is 3000 kW +BO=2000,AO=5//AF=x +DC=2000,AD=3,//AF=x + +//using similarity of triangles AEF and ABO +EF_by_AF=(BO/AO)// because (EF/BO)=(AF/AO) +//using similarity of triangles AFG and ADC +FG_by_AF=(DC/AD) //because (FG/DC)=(AF/AD) + +EF_by_x=EF_by_AF //which implies EF=400*x +FG_by_x=FG_by_AF //which implies FG=666.67*x + +EF_plus_FG=3000 //total load at the frequency at P is 3000 kW +x= EF_plus_FG/(EF_by_x + FG_by_x) +EF=(BO/AO)*x +FG=(DC/AD)*x + +printf('Loads shared by machine 1 and 2 are %.0f kW and %.0f kW respectively',EF,FG) -- cgit