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author | priyanka | 2015-06-24 15:03:17 +0530 |
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committer | priyanka | 2015-06-24 15:03:17 +0530 |
commit | b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b (patch) | |
tree | ab291cffc65280e58ac82470ba63fbcca7805165 /1092/CH9 | |
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Diffstat (limited to '1092/CH9')
-rwxr-xr-x | 1092/CH9/EX9.1/Example9_1.sce | 34 | ||||
-rwxr-xr-x | 1092/CH9/EX9.10/Example9_10.sce | 64 | ||||
-rwxr-xr-x | 1092/CH9/EX9.11/Example9_11.sce | 81 | ||||
-rwxr-xr-x | 1092/CH9/EX9.12/Example9_12.sce | 47 | ||||
-rwxr-xr-x | 1092/CH9/EX9.13/Example9_13.sce | 35 | ||||
-rwxr-xr-x | 1092/CH9/EX9.14/Example9_14.sce | 29 | ||||
-rwxr-xr-x | 1092/CH9/EX9.15/Example9_15.sce | 143 | ||||
-rwxr-xr-x | 1092/CH9/EX9.16/Example9_16.sce | 52 | ||||
-rwxr-xr-x | 1092/CH9/EX9.17/Example9_17.sce | 77 | ||||
-rwxr-xr-x | 1092/CH9/EX9.18/Example9_18.sce | 70 | ||||
-rwxr-xr-x | 1092/CH9/EX9.19/Example9_19.sce | 53 | ||||
-rwxr-xr-x | 1092/CH9/EX9.2/Example9_2.sce | 35 | ||||
-rwxr-xr-x | 1092/CH9/EX9.3/Example9_3.sce | 37 | ||||
-rwxr-xr-x | 1092/CH9/EX9.4/Example9_4.sce | 30 | ||||
-rwxr-xr-x | 1092/CH9/EX9.5/Example9_5.sce | 41 | ||||
-rwxr-xr-x | 1092/CH9/EX9.6/Example9_6.sce | 67 | ||||
-rwxr-xr-x | 1092/CH9/EX9.7/Example9_7.sce | 54 | ||||
-rwxr-xr-x | 1092/CH9/EX9.8/Example9_8.sce | 90 | ||||
-rwxr-xr-x | 1092/CH9/EX9.9/Example9_9.sce | 77 |
19 files changed, 1116 insertions, 0 deletions
diff --git a/1092/CH9/EX9.1/Example9_1.sce b/1092/CH9/EX9.1/Example9_1.sce new file mode 100755 index 000000000..87435c925 --- /dev/null +++ b/1092/CH9/EX9.1/Example9_1.sce @@ -0,0 +1,34 @@ +// Electric Machinery and Transformers
+// Irving L kosow
+// Prentice Hall of India
+// 2nd editiom
+
+// Chapter 9: POLYPHASE INDUCTION (ASYNCHRONOUS) DYNAMOS
+// Example 9-1
+
+clear; clc; close; // Clear the work space and console.
+
+// Given data
+phase = 3 ; // Number of phases
+n = 3 ; // Slots per pole per phase
+f = 60 ; // Line frequency in Hz
+
+// Calculations
+// case a
+P = 2 * n ; // Number of poles produced
+Total_slots = n * P * phase ; // Total number of slots on the stator
+
+// case b
+S_b = (120*f)/P ; // Speed in rpm of the rotating magnetic field
+
+// case c
+f_c = 50 ; // Changed line frequency in Hz
+S_c = (120*f_c)/P ; // Speed in rpm of the rotating magnetic field
+
+// Display the results
+disp("Example 9-1 Solution : ");
+printf(" \n a: P = %d poles \n Total slots = %d slots \n", P ,Total_slots );
+
+printf(" \n b: S = %d rpm @ f = %d Hz \n ", S_b , f );
+
+printf(" \n c: S = %d rpm @ f = %d Hz ", S_c ,f_c );
diff --git a/1092/CH9/EX9.10/Example9_10.sce b/1092/CH9/EX9.10/Example9_10.sce new file mode 100755 index 000000000..6a5e01bd5 --- /dev/null +++ b/1092/CH9/EX9.10/Example9_10.sce @@ -0,0 +1,64 @@ +// Electric Machinery and Transformers
+// Irving L kosow
+// Prentice Hall of India
+// 2nd editiom
+
+// Chapter 9: POLYPHASE INDUCTION (ASYNCHRONOUS) DYNAMOS
+// Example 9-10
+
+clear; clc; close; // Clear the work space and console.
+
+// Given data
+P = 4 ; // Number of poles in WRIM
+f = 60 ; // Frequency in Hz
+V = 220 ; // Line voltage in volt
+V_p = 220 ; // Phase voltage in volt (delta connection)
+hp_WRIM = 1 ; // Power rating of WRIM in hp
+S_r = 1740 ; // Full-load rated speed in rpm
+R_r = 0.3 ; // rotor resistance per phase in ohm/phase
+R_x = 0.7 ; // Added resistance in ohm/phase
+X_lr =1 ; // Locked rotor reactance in ohm
+
+// Calculations
+S = (120*f)/P ; // Speed in rpm of the rotating magnetic field
+// case a
+E_lr = V_p / 4 ; // Locked-rotor voltage per phase
+
+// case b
+s = ( S - S_r)/S ; // slip
+I_r = E_lr / sqrt( (R_r/s)^2 + (X_lr)^2 ); // Rotor current per phase at rated speed
+
+// case c
+P_in = ((I_r)^2 * R_r)/s ; // Rated rotor power input per phase
+
+// case d
+P_RL = (I_r)^2 * R_r ; // Rated copper loss per phase
+
+// case e
+P_d_W = P_in - P_RL ; // Rotor power developed per phase in W
+P_d_hp = P_d_W/746 ; // Rotor power developed per phase in hp
+
+// case f
+hp = P_d_hp ; // Rotor power developed per phase in hp
+T_d1 = (hp*5252)/S_r ; // Rotor torque developed in lb-ft per phase by method 1
+T_d2 = 7.04*(P_in/S) ; // Rotor torque developed in lb-ft per phase by method 2
+
+T_dm = 3*T_d1 ; // Total rotor torque in lb-ft
+
+// Display the results
+disp("Example 9-10 Solution : ");
+printf(" \n a: Locked-rotor voltage per phase : \n E_lr = %d V \n ",E_lr);
+
+printf(" \n b: slip : \n s = %.2f \n",s);
+printf(" \n Rotor current per phase at rated speed:\n I_r = %.3f A/phase \n ",I_r);
+
+printf(" \n c: Rated rotor power input per phase :\n P_in = %d W/phase \n ",P_in);
+
+printf(" \n d: Rated copper loss per phase : \n P_RL = %.2f W \n ",P_RL);
+
+printf(" \n e: Rotor power developed per phase in W :\n P_d = %.1f W/phase ",P_d_W);
+printf(" \n\n Rotor power developed per phase in hp :\n P_d = %.2f hp/phase \n ",P_d_hp);
+
+printf(" \n f: Rotor torque developed in lb-ft per phase :\n T_d = %.1f lb-ft (method 1)",T_d1);
+printf(" \n\n T_d = %.1f lb-ft (method 2)",T_d2);
+printf(" \n\n Total rotor torque : \n T_dm = %.1f lb-ft )\n ",T_dm);
diff --git a/1092/CH9/EX9.11/Example9_11.sce b/1092/CH9/EX9.11/Example9_11.sce new file mode 100755 index 000000000..0cf623d34 --- /dev/null +++ b/1092/CH9/EX9.11/Example9_11.sce @@ -0,0 +1,81 @@ +// Electric Machinery and Transformers
+// Irving L kosow
+// Prentice Hall of India
+// 2nd editiom
+
+// Chapter 9: POLYPHASE INDUCTION (ASYNCHRONOUS) DYNAMOS
+// Example 9-11
+
+clear; clc; close; // Clear the work space and console.
+
+// Given data
+// 3-phase WRIM
+V_L = 208 ; // Voltage rating of the WRIM in volt
+P = 6 ; // Number of poles in WRIM
+f = 60 ; // Frequency in Hz
+P_o = 7.5 ; // Power rating of WRIM in hp
+S_r = 1125 ; // Full-load rotor speed in rpm
+R_r = 0.08 ; // Rotor resistance in ohm/phase
+X_lr = 0.4 ; // Locked rotor resistance in ohm/phase
+
+// Calculations
+S = (120*f)/P ; // Speed in rpm of the rotating magnetic field
+// case a
+E_lr = (V_L / sqrt(3))/2 ; // Locked rotor voltage per phase
+
+// case b
+s = (S - S_r)/S ; // Full-load rated slip
+I_r = E_lr / sqrt( (R_r/s)^2 + (X_lr)^2 ); // Rotor current in A per phase at rated speed
+
+// case c
+P_in = ( (I_r)^2 * R_r )/s ; // Rated rotor power input per phase in (W/phase)
+
+// case d
+P_RL = ( (I_r)^2 * R_r ); // Rated rotor copper loss per phase (in W/phase)
+
+// case e
+// Subscript W in P_d indicates calculating P_d in W
+P_d_W = P_in - P_RL ; // Rotor power developed per phase (in W/phase)
+// Subscript hp in P_d indicates calculating P_d in hp
+P_d_hp = P_d_W/746 ; // Rotor power developed per phase (in hp/phase)
+
+// case f
+// subscript 1 in T_d indicates method 1 for calculating T_d
+hp = P_d_hp ;
+T_d1 = (hp*5252)/S_r ; // Rotor torque developed per phase in lb-ft
+
+// subscript 2 in T_d indicates method 2 for calculating T_d
+T_d2 = 7.04*(P_in/S); // Rotor torque developed per phase in lb-ft
+
+// case g
+T_dm = 3*T_d1 ; // Total rotor torque in lb-ft
+
+// case h
+T_o = 7.04*(P_o*746)/S_r ; // Total output rotor torque in lb-ft
+
+// Display the results
+disp("Example 9-11 Solution : ");
+
+printf(" \n Note: Slight variations in the answers I_r,P_in,P_RL,P_d,T_d ");
+printf(" \n are because of non-approximation of E_lr and (R_r/s)^2 + (X_lr)^2");
+printf(" \n while calulating in scilab.\n");
+
+printf(" \n a: Locked rotor voltage per phase :\n E_lr = %d V\n",E_lr);
+
+printf(" \n b: slip :\n s = %.4f ",s);
+printf(" \n\n Rotor current per phase at rated speed :\n I_r = %.2f A/phase\n",I_r);
+
+printf(" \n c: Rated rotor power input per phase :\n P_in = %.f W/phase\n",P_in);
+
+printf(" \n d: Rated rotor copper loss per phase :\n P_RL = %.1f W/phase\n",P_RL);
+
+printf(" \n e: Rotor power developed per phase ");
+printf(" \n P_d = %.f W/phase \n P_d = %.2f hp/phase\n",P_d_W,P_d_hp);
+
+printf(" \n f: Rotor torque developed per phase : ");
+printf(" \n (method 1)\n T_d = %.1f lb-ft/phase",T_d1);
+printf(" \n\n (method 2)\n T_d = %.1f lb-ft/phase\n",T_d2);
+
+printf(" \n g: Total rotor torque : \n T_dm = %d lb-ft\n",T_dm);
+
+printf(" \n h: Total output rotor torque : \n T_o = %d lb-ft",T_o);
diff --git a/1092/CH9/EX9.12/Example9_12.sce b/1092/CH9/EX9.12/Example9_12.sce new file mode 100755 index 000000000..34e176054 --- /dev/null +++ b/1092/CH9/EX9.12/Example9_12.sce @@ -0,0 +1,47 @@ +// Electric Machinery and Transformers +// Irving L kosow +// Prentice Hall of India +// 2nd editiom + +// Chapter 9: POLYPHASE INDUCTION (ASYNCHRONOUS) DYNAMOS +// Example 9-12 + +clear; clc; close; // Clear the work space and console. + +// Given data as per Ex.9-10 +P = 4 ; // Number of poles in WRIM +f = 60 ; // Frequency in Hz +V = 220 ; // Line voltage in volt +V_p = 220 ; // Phase voltage in volt (delta connection) +hp_WRIM = 1 ; // Power rating of WRIM in hp +S_r = 1740 ; // Full-load rated speed in rpm +R_r = 0.3 ; // rotor resistance per phase in ohm/phase +R_x = 0.7 ; // Added resistance in ohm/phase +X_lr = 1 ; // Locked rotor reactance in ohm + +// Calculations from Ex.9-10 +E_lr = V_p / 4 ; // Locked-rotor voltage per phase +S = (120*f)/P ; // Speed in rpm of the rotating magnetic field + +// Calculations (Ex.9-12) +P_in = (E_lr)^2 / (2*X_lr); // rotor power input(RPI) in W/phase +P_in_total = P_in * 3 ; // Total 3-phase rotor power input(RPI) in W + +T_max = 7.04*(P_in_total/S); // Maximum torque developed in lb-ft + +s_b = R_r / X_lr ; // Slip + +s = s_b; +S_r = S*(1 - s); // Rotor speed in rpm for T_max + +// Display the results +disp("Example 9-12 Solution : "); + +printf(" \n Rotor power input (RPI) per phase is : "); +printf(" \n P_in = %.1f W/phase \n",P_in); + +printf(" \n The total 3-phase rotor power input (RPI) is : "); +printf(" \n P_in = %.1f W\n",P_in_total); + +printf(" \n Substituting in Eq.(9-19),\n T_max = %.2f lb-ft\n",T_max); +printf(" \n Then, s_b = %.1f \n and S_r = %d rpm",s_b,S_r); diff --git a/1092/CH9/EX9.13/Example9_13.sce b/1092/CH9/EX9.13/Example9_13.sce new file mode 100755 index 000000000..063a6bf6b --- /dev/null +++ b/1092/CH9/EX9.13/Example9_13.sce @@ -0,0 +1,35 @@ +// Electric Machinery and Transformers +// Irving L kosow +// Prentice Hall of India +// 2nd editiom + +// Chapter 9: POLYPHASE INDUCTION (ASYNCHRONOUS) DYNAMOS +// Example 9-13 + +clear; clc; close; // Clear the work space and console. + +// Given data as per Ex.9-10 +P = 4 ; // Number of poles in WRIM +f = 60 ; // Frequency in Hz +V = 220 ; // Line voltage in volt +V_p = 220 ; // Phase voltage in volt (delta connection) +hp_WRIM = 1 ; // Power rating of WRIM in hp +S_r = 1740 ; // Full-load rated speed in rpm +R_r = 0.3 ; // rotor resistance per phase in ohm/phase +R_x = 0.7 ; // Added resistance in ohm/phase +X_lr = 1 ; // Locked rotor reactance in ohm + +// Calculations +E_lr = V_p / 4 ; // Locked-rotor voltage per phase +S = (120*f)/P ; // Speed in rpm of the rotating magnetic field + +// Total 3-phase rotor power input(RPI) in W +P_in = 3 * ( (E_lr)^2 ) / ( (R_r)^2 + (X_lr)^2 ) * R_r ; + +T_s = 7.04 * (P_in/S); // Starting torque developed in lb-ft + +// Display the results +disp("Example 9-13 Solution : "); + +printf(" \n P_in = %.f W \n",P_in); +printf(" \n From Eq.(9-19),starting torque is : \n T_s = %.2f lb-ft",T_s); diff --git a/1092/CH9/EX9.14/Example9_14.sce b/1092/CH9/EX9.14/Example9_14.sce new file mode 100755 index 000000000..e1715c743 --- /dev/null +++ b/1092/CH9/EX9.14/Example9_14.sce @@ -0,0 +1,29 @@ +// Electric Machinery and Transformers +// Irving L kosow +// Prentice Hall of India +// 2nd editiom + +// Chapter 9: POLYPHASE INDUCTION (ASYNCHRONOUS) DYNAMOS +// Example 9-14 + +clear; clc; close; // Clear the work space and console. + +// Given data +T_max = 17.75 ; // Maximum torque developed in lb-ft +s_max = 0.3 ; // Slip for which T_max occurs +s_a = 0.0333 ; // slip (case a) +s_b = 1.0 ; // slip (case b) + +// Calculations +// Subscript a in T indicates case a +T_a = T_max * ( 2 / ((s_max/s_a) + (s_a/s_max)) ); // Full-load torque in lb-ft + +// Subscript b in T indicates case b +T_b = T_max * ( 2 / ((s_max/s_b) + (s_b/s_max)) ); // Starting torque in lb-ft + +// Display the results +disp("Example 9-14 Solution : "); + +printf(" \n a: Full-load torque at slip = %.4f \n T = %.1f lb-ft\n",s_a,T_a); + +printf(" \n b: Starting torque at slip = %.1f \n T = %.2f lb-ft\n",s_b,T_b); diff --git a/1092/CH9/EX9.15/Example9_15.sce b/1092/CH9/EX9.15/Example9_15.sce new file mode 100755 index 000000000..22d24921c --- /dev/null +++ b/1092/CH9/EX9.15/Example9_15.sce @@ -0,0 +1,143 @@ +// Electric Machinery and Transformers +// Irving L kosow +// Prentice Hall of India +// 2nd editiom + +// Chapter 9: POLYPHASE INDUCTION (ASYNCHRONOUS) DYNAMOS +// Example 9-15 + +clear; clc; close; // Clear the work space and console. + +// Given data +// 3-phase Y-connected SCIM +P = 4 ; // Number of poles in SCIM +S_r = 1746 ; // Rated rotor speed in rpm +V = 220 ; // Voltage rating of SCIM in volt +f = 60 ; // Frequency in Hz +P_hp = 10 ; // power rating of SCIM in hp +R_a = 0.4 ; // Armature resistance in ohm +R_r = 0.14 ; // Rotor resistance in ohm +jXm = 16 ; // Reactance in ohm +jXs = 0.35 ; // Synchronous reactance in ohm +jXlr = 0.35 ; // Locked rotor reactance in ohm +P_r_total = 360 ; // Total rotational losses in W + +// Calculations +V_p = V / sqrt(3); // Voltage per phase in volt + +S = (120*f)/P ; // Speed in rpm of the rotating magnetic field +// preliminary calculations +s = ( S - S_r)/S ; // slip + +disp("Example 9-15 :"); + +printf(" \n From Fig.9-13,using the format method of mesh analysis,we may"); +printf(" \n write the array by inspection :\n"); +printf(" \n __________________________________________________________"); +printf(" \n I_1(A) \t\t I_2(A) \t\t V(volt)"); +printf(" \n __________________________________________________________"); +printf(" \n (0.4 + j16.35) \t -(0 + j16) \t\t (127 + j0)"); +printf(" \n -(0 + j16) \t\t (4.67 + j16.35) \t 0"); +printf(" \n __________________________________________________________"); + +A = [ (0.4 + %i*16.35) -%i*16 ; (-%i*16) (4.67 + %i*16.35) ]; // Matrix containing above mesh eqns array +delta = det(A); // Determinant of A + +// case a : Stator armature current I_p in A +I_p = det( [ (127+%i*0) (-%i*16) ; 0 (4.67 + %i*16.35) ] ) / delta ; +I_p_m = abs(I_p);//I_p_m=magnitude of I_p in A +I_p_a = atan(imag(I_p) /real(I_p))*180/%pi;//I_p_a=phase angle of I_p in degrees +I_1 = I_p ; // Stator armature current in A + +// case b : Rotor current I_r per phase in A +I_r = det( [ (0.4 + %i*16.35) (127+%i*0) ; (-%i*16) 0 ] ) / delta ; +I_r_m = abs(I_r);//I_r_m=magnitude of I_r in A +I_r_a = atan(imag(I_r) /real(I_r))*180/%pi;//I_r_a=phase angle of I_r in degrees + +// case c +theta_1 = I_p_a ; // Motor PF angle in degrees +cos_theta1 = cosd(theta_1); // Motor PF + +// case d +I_p = I_p_m ; // Stator armature current in A +SPI = V_p * I_p * cos_theta1 ; // Stator Power Input in W + +// case e +SCL = (I_p)^2 * R_a ; // Stator Copper Loss in W + +// case f +// Subscripts 1 and 2 for RPI indicates two methods of calculating RPI +RPI_1 = SPI - SCL ; // Rotor Power Input in W +RPI_2 = (I_r_m)^2 * (R_r/s); // Rotor Power Input in W +RPI =RPI_1 ; + +// case g +// Subscripts 1 , 2 and 3 for RPD indicates three methods of calculating RPD +RPD_1 = RPI * ( 1 - s ); // Rotor Power Developed in W +RCL = s*(RPI); // Rotor copper losses in W +RPD_2 = RPI - RCL ; // Rotor Power Developed in W +RPD_3 = (I_r_m)^2 * R_r * ((1-s)/s); // Rotor Power Developed in W +RPD = RPD_1 ; + +// case h +P_r = P_r_total / 3 ; // Rotational Losses per phase in W +P_o = RPD - P_r ; // Rotor power per phase in W +P_to = 3*P_o ; // Total rotor power in W + +// case i +T = 7.04 * (P_to/S_r); // Total 3-phase torque in lb-ft + +// case j +P_t = P_to ; +hp = P_t / 746 ; // Output horsepower + +// case k +P_in = SPI ; // Input power to stator in W +eta = P_o / P_in * 100 ; // Motor efficiency at rated load + +// Display the results +disp("Solution : "); +printf(" \n Preliminary calculations\n"); +printf(" \n Slip : s = %.2f \n R_r/s = %.2f ohm \n",s,R_r/s); + +printf(" \n Determinant Δ = ");disp(delta); + +printf(" \n a: Stator armature current :\n I_p in A = ");disp(I_1); +printf(" \n I_p = I_1 = %.2f <%.2f A \n ",I_p_m , I_p_a ); + +printf(" \n b: Rotor current per phase :\n I_r in A = ");disp(I_r); +printf(" \n I_r = I_2 = %.3f <%.2f A \n ",I_r_m , I_r_a ); + +printf(" \n c: Motor PF :\n cosӨ1 = %.4f \n",cos_theta1); + +printf(" \n d: Stator Power Input :\n SPI = %d W \n",SPI); + +printf(" \n e: Stator Copper Loss :\n SCL = %.f W \n",SCL); + +printf(" \n f: Rotor Power Input :\n RPI = %d W(method 1) ", RPI_1); +printf(" \n RPI = %.f W (method 2)\n",RPI_2); +printf(" \n Note: RPI calculated by 2nd method slightly varies from that of"); +printf(" \n textbook value because of non-approximation of I_r while"); +printf(" \n calculating in scilab.\n") + +printf(" \n g: Rotor Power Developed :\n RPD = %.f W \n",RPD_1); +printf(" \n Rotor copper loss :\n RCL = %d W\n",RCL); +printf(" \n RPD = %.f W \n RPD = %d W \n ",RPD_2,RPD_3); + +printf(" \n h: Rotor power per phase :\n P_o/φ = %f W/φ ",P_o); +printf(" \n\n Total rotor power:\n P_to = %f W \n",P_to); +printf(" \n Above P_o/φ and P_to values are not approximated while calculating in "); +printf(" \n SCILAB.So,they vary slightly from textbook values.\n"); + +printf(" \n i: Total 3-phase output torque :\n T = %.f lb-ft\n",T); + +printf(" \n j: Output horsepower : \n hp = %.1f hp \n",hp); + +printf(" \n k: Motor efficiency at rated load :\n η = %.1f percent \n",eta) + +printf(" \n Power flow diagram (per phase)\n"); +printf(" \n SPI----------> RPI---------> RPD----------> P_o"); +printf(" \n (%d W) | (%d W) | (%d W) | (%d W)",SPI,RPI_1,RPD_3,P_o); +printf(" \n | | |"); +printf(" \n SCL RCL P_r"); +printf(" \n (%.f W) (%d W) (%d W)",SCL,RCL,P_r); diff --git a/1092/CH9/EX9.16/Example9_16.sce b/1092/CH9/EX9.16/Example9_16.sce new file mode 100755 index 000000000..ddd6436ec --- /dev/null +++ b/1092/CH9/EX9.16/Example9_16.sce @@ -0,0 +1,52 @@ +// Electric Machinery and Transformers +// Irving L kosow +// Prentice Hall of India +// 2nd editiom + +// Chapter 9: POLYPHASE INDUCTION (ASYNCHRONOUS) DYNAMOS +// Example 9-16 + +clear; clc; close; // Clear the work space and console. + +// Given data +// three-phase SCIM +V = 208 ; // Rated voltage in volt +P_o = 15 ; // Rated power in hp +I = 42 ; // Rated current in A +I_st = 252 ; // Starting current in A +T_st = 120 ; // Full-voltage starting torque in lb-ft +tap = 60*(1/100) ; // Tapping in % employed by compensator + +// Calculations +// case a +I_sm = tap * I_st ; // Motor starting current in A at reduced voltage + +// case b +I_L = tap * I_sm ; // Motor line current in A(neglecting tarnsformer exciting +// current and losses) + +// case c +T_s = (tap)^2 * T_st ; // Motor starting torque at reduced voltage in lb-ft + +// case d +percent_I_L = I_L / I_st * 100 ; // Percent line current at starting + +// case e +percent_T_st = T_s / T_st * 100 ; // Percent motor starting torque + +// Display the results +disp("Example 9-16 Solution : "); + +printf(" \n a: Motor starting current at reduced voltage : "); +printf(" \n I_sm = %.1f A to the motor.\n",I_sm); + +printf(" \n b: Motor line current neglecting tarnsformer exciting current and losses :"); +printf(" \n I_L = %.2f A drawn from the mains.\n",I_L); + +printf(" \n c: Motor starting torque at reduced voltage :\n T_s = %.1f lb-ft\n",T_s); + +printf(" \n d: Percent line current at starting : "); +printf(" \n = %.f percent of line current at full voltage.\n",percent_I_L); + +printf(" \n e: Percent motor starting torque : "); +printf(" \n = %d percent of starting torque at full voltage.\n",percent_T_st); diff --git a/1092/CH9/EX9.17/Example9_17.sce b/1092/CH9/EX9.17/Example9_17.sce new file mode 100755 index 000000000..d0fb0539f --- /dev/null +++ b/1092/CH9/EX9.17/Example9_17.sce @@ -0,0 +1,77 @@ +// Electric Machinery and Transformers +// Irving L kosow +// Prentice Hall of India +// 2nd editiom + +// Chapter 9: POLYPHASE INDUCTION (ASYNCHRONOUS) DYNAMOS +// Example 9-17 + +clear; clc; close; // Clear the work space and console. + +// Given data +// three-phase SCIM +V_o = 220 ; // Rated voltage in volt +P = 4 ; // Number of poles in SCIM +P_o = 10 ; // Rated power in hp +f = 60 ; // Frequency in Hz(assume,not given) +T_o = 30 ; // Rated torque in lb-ft +S_r = 1710 ; // Rated rotor speed in rpm +V_n1 = 242 ; // Impressed stator voltage in volt(case a) +V_n2 = 198 ; // Impressed stator voltage in volt(case b) + +// Calculations +S = (120*f)/P ; // Speed in rpm of the rotating magnetic field +// case a : Impressed stator voltage = 242 V +s_o = (S - S_r)/S ; // Rated slip + +T_n1 = T_o * (V_n1/V_o)^2 ; // New torque in lb-ft + +s_n1 = s_o * (T_o/T_n1); // New slip + +S_rn1 = S*(1 - s_n1); + +// case b : Impressed stator voltage = 198 V +T_n2 = T_o * (V_n2/V_o)^2 ; // New torque in lb-ft + +s_n2 = s_o * (T_o/T_n2); // New slip + +S_rn2 = S*(1 - s_n2); + +// case c +// Subscript a in percent_slip and percent_speed indicates part a +percent_slip_a = (s_o - s_n1)/s_o * 100 ; // Percent change in slip in part(a) + +percent_speed_a = (S_rn1 - S_r)/S_r * 100; // Percent change in speed in part(a) + +// case d +// Subscript b in percent_slip and percent_speed indicates part b +percent_slip_b = (s_n2 - s_o)/s_o * 100 ; // Percent change in slip in part(b) + +percent_speed_b = (S_r - S_rn2)/S_r * 100; // Percent change in speed in part(b) + +// Display the results +disp("Example 9-17 Solution : "); + +printf(" \n a: Rated slip :\n s = %.2f\n",s_o); +printf(" \n For impressed stator voltage = %d V \n ",V_n1); +printf(" \n New torque :\n T_n = %.1f lb-ft \n ",T_n1); +printf(" \n New slip :\n s_n = %f \n ",s_n1); +printf(" \n New rotor speed :\n S_r = %f rpm \n",S_rn1); + +printf(" \n b: For impressed stator voltage = %d V \n ",V_n2); +printf(" \n New torque :\n T_n = %.1f lb-ft \n ",T_n2); +printf(" \n New slip :\n s_n = %f \n ",s_n2); +printf(" \n New rotor speed :\n S_r = %f rpm \n",S_rn2); + +printf(" \n c: Percent change in slip in part(a)"); +printf(" \n = %.1f percent decrease.\n",percent_slip_a); +printf(" \n Percent change in speed in part(a)"); +printf(" \n = %.2f percent increase \n",percent_speed_a); + +printf(" \n d: Percent change in slip in part(b)"); +printf(" \n = %.2f percent increase.\n",percent_slip_b); +printf(" \n Percent change in speed in part(b)"); +printf(" \n = %.2f percent decrease\n",percent_speed_b); + +printf(" \n SLIGHT VARIATIONS IN PERCENT CHANGE IN SLIP AND SPEED ARE DUE TO"); +printf(" \n NON-APPROXIMATION OF NEW SLIPS AND NEW SPEEDS CALCULATED IN SCILAB.") diff --git a/1092/CH9/EX9.18/Example9_18.sce b/1092/CH9/EX9.18/Example9_18.sce new file mode 100755 index 000000000..8a77f567b --- /dev/null +++ b/1092/CH9/EX9.18/Example9_18.sce @@ -0,0 +1,70 @@ +// Electric Machinery and Transformers +// Irving L kosow +// Prentice Hall of India +// 2nd editiom + +// Chapter 9: POLYPHASE INDUCTION (ASYNCHRONOUS) DYNAMOS +// Example 9-18 + +clear; clc; close; // Clear the work space and console. + +// Given data +// three-phase WRIM +V_o = 220 ; // Rated voltage in volt +P_o = 10 ; // Rated power in hp +P = 4 ; // Number of poles in WRIM(assumption) +f = 60 ; // Frequency in Hz(assume,not given) +R_ro = 0.3 ; // Rotor resistance in ohm +T_o = 30 ; // Rated torque in lb-ft +S_r = 1750 ; // Rated rotor speed in rpm +R_r_ext = 1.7 ; // External rotor resistance in ohm/phase inserted in the rotor ckt +R_rn = R_ro + R_r_ext ; // Total rotor resistance in ohm + +V_n1 = 240 ; // Impressed stator voltage in volt(case a) +V_n2 = 208 ; // Impressed stator voltage in volt(case b) +V_n3 = 110 ; // Impressed stator voltage in volt(case c) + +// Calculations +S = (120*f)/P ; // Speed in rpm of the rotating magnetic field + +// case a : Impressed stator voltage = 240 V +s_o = (S - S_r)/S ; // Rated slip + +T_n1 = T_o * (V_n1/V_o)^2 ; // New torque in lb-ft + +s_n1 = s_o * (T_o/T_n1) * (R_rn/R_ro); // New slip + +S_rn1 = S*(1 - s_n1); + +// case b : Impressed stator voltage = 208 V +T_n2 = T_o * (V_n2/V_o)^2 ; // New torque in lb-ft + +s_n2 = s_o * (T_o/T_n2) * (R_rn/R_ro); // New slip + +S_rn2 = S*(1 - s_n2); + +// case c : Impressed stator voltage = 110 V +T_n3 = T_o * (V_n3/V_o)^2 ; // New torque in lb-ft + +s_n3 = s_o * (T_o/T_n3) * (R_rn/R_ro); // New slip + +S_rn3 = S*(1 - s_n3); + +// Display the results +disp("Example 9-18 Solution : "); + +printf(" \n a: Rated slip :\n s = %f\n",s_o); +printf(" \n For impressed stator voltage = %d V \n ",V_n1); +printf(" \n New torque :\n T_n = %.1f lb-ft \n ",T_n1); +printf(" \n New slip :\n s_n = %f \n ",s_n1); +printf(" \n New rotor speed :\n S_r = %f rpm \n",S_rn1); + +printf(" \n b: For impressed stator voltage = %d V \n ",V_n2); +printf(" \n New torque :\n T_n = %.2f lb-ft \n ",T_n2); +printf(" \n New slip :\n s_n = %f \n ",s_n2); +printf(" \n New rotor speed :\n S_r = %f rpm \n",S_rn2); + +printf(" \n c: For impressed stator voltage = %d V \n ",V_n3); +printf(" \n New torque :\n T_n = %.1f lb-ft \n ",T_n3); +printf(" \n New slip :\n s_n = %f \n ",s_n3); +printf(" \n New rotor speed :\n S_r = %f rpm \n",S_rn3); diff --git a/1092/CH9/EX9.19/Example9_19.sce b/1092/CH9/EX9.19/Example9_19.sce new file mode 100755 index 000000000..b6d9bda71 --- /dev/null +++ b/1092/CH9/EX9.19/Example9_19.sce @@ -0,0 +1,53 @@ +// Electric Machinery and Transformers +// Irving L kosow +// Prentice Hall of India +// 2nd editiom + +// Chapter 9: POLYPHASE INDUCTION (ASYNCHRONOUS) DYNAMOS +// Example 9-19 + +clear; clc; close; // Clear the work space and console. + +// Given data +P = 8 ; // Number of poles in WRIM +f = 60 ; // Operating frequency of the WRIM in Hz +/// WRIM is driven by variable-speed prime mover as a frequency changer +S_con_a1 = 1800 ; // Speed of the convertor in rpm +S_con_a2 = 450 ; // Speed of the convertor in rpm + +f_con_b1 = 25 ; // Frequency of an induction converter in Hz +f_con_b2 = 400 ; // Frequency of an induction converter in Hz +f_con_b3 = 120 ; // Frequency of an induction converter in Hz + +// Calculations +S = (120*f)/P ; // Speed in rpm of the rotating magnetic field + +// case a +// Subscript a1 in f_con indicates case a 1st frequecy in Hz +f_con_a1 = f*(1 + S_con_a1/S); // Frequency of an induction converter in Hz + +// Subscript a2 in f_con indicates case a 2nd frequency in Hz +f_con_a2 = f*(1 - S_con_a2/S); // Frequency of an induction converter in Hz + +// case b +// Subscript b1 in S-con indicates case b 1st speed of converter in rpm +S_con_b1 = ( -1 + f_con_b1/f) * S ; // Speed of the convertor in rpm + +// Subscript b2 in S-con indicates case b 2nd speed of converter in rpm +S_con_b2 = ( -1 + f_con_b2/f) * S ; // Speed of the convertor in rpm + +// Subscript b3 in S-con indicates case b 3rd speed of converter in rpm +S_con_b3 = ( -1 + f_con_b3/f) * S ; // Speed of the convertor in rpm + + +// Display the results +disp("Example 9-19 Solution : "); + +printf(" \n Using Eq.(9-26),\n"); + +printf(" \n a: f_con = %d Hz for %d rpm in opposite direction\n",f_con_a1,S_con_a1); +printf(" \n f_con = %d Hz for %d rpm in same direction\n",f_con_a2,S_con_a2); + +printf(" \n b: 1. S_con = %.f rpm, or %.f rpm in same direction.\n",S_con_b1,abs(S_con_b1)); +printf(" \n 2. S_con = %d rpm in opposite direction.\n",S_con_b2); +printf(" \n 3. S_con = %d rpm in opposite direction to rotating stator flux.\n",S_con_b3); diff --git a/1092/CH9/EX9.2/Example9_2.sce b/1092/CH9/EX9.2/Example9_2.sce new file mode 100755 index 000000000..28f36e6da --- /dev/null +++ b/1092/CH9/EX9.2/Example9_2.sce @@ -0,0 +1,35 @@ +// Electric Machinery and Transformers
+// Irving L kosow
+// Prentice Hall of India
+// 2nd editiom
+
+// Chapter 9: POLYPHASE INDUCTION (ASYNCHRONOUS) DYNAMOS
+// Example 9-2
+
+clear; clc; close; // Clear the work space and console.
+
+// Given data
+
+s_a = 5*(1/100); // Slip (case a)
+s_b = 7*(1/100); // Slip (case b)
+
+// Given data and calculated values from Ex.9-1
+f_a = 60 ; // Line frequency in Hz (case a)
+f_b = 50 ; // Line frequency in Hz (case b)
+S_a = 1200 ; // Speed in rpm of the rotating magnetic field (case a)
+S_b = 1000 ; // Speed in rpm of the rotating magnetic field (case b)
+
+// Calculations
+
+// case a
+S_r_a = S_a * ( 1 - s_a ); // Rotor speed in rpm when slip is 5% (case a)
+
+// case b
+S_r_b = S_b * ( 1 - s_b ); // Rotor speed in rpm when slip is 7% (case b)
+
+// Display the results
+disp("Example 9-2 Solution : ");
+
+printf(" \n a: S_r = %.f rpm @ s = %.2f \n ", S_r_a ,s_a );
+
+printf(" \n b: S_r = %.f rpm @ s = %.2f ", S_r_b ,s_b );
diff --git a/1092/CH9/EX9.3/Example9_3.sce b/1092/CH9/EX9.3/Example9_3.sce new file mode 100755 index 000000000..5a5029e16 --- /dev/null +++ b/1092/CH9/EX9.3/Example9_3.sce @@ -0,0 +1,37 @@ +// Electric Machinery and Transformers
+// Irving L kosow
+// Prentice Hall of India
+// 2nd editiom
+
+// Chapter 9: POLYPHASE INDUCTION (ASYNCHRONOUS) DYNAMOS
+// Example 9-3
+
+clear; clc; close; // Clear the work space and console.
+
+// Given data
+P = 4 ; // Number of poles in Induction motor
+f = 60 ; // Frequency in Hz
+s_f = 5*(1/100) ; // Full-load rotor slip
+
+// Calculations
+
+// case a
+// slip, s = (S -S_r)/S ;
+// where S = Speed in rpm of the rotating magnetic field and
+// S_r = Speed in rpm of the rotor
+s = 1 ; // Slip = 1, at the instant of starting, since S_r is zero
+f_r_a = s * f ; // Rotor frequency in Hz at the instant of starting
+
+// case b
+f_r_b = s_f * f ;// Full-load rotor frequency in Hz
+
+// Display the results
+disp("Example 9-3 Solution : ");
+
+printf(" \n a: At the instant of starting, slip s = (S -S_r)/S ; ");
+printf(" \n where S_r is the rotor speed. Since the rotor speed at the ");
+printf(" \n instant of starting is zero, s = (S - 0)/S = 1 , or unity slip.");
+printf(" \n\n The rotor frequency is \n f_r = %d Hz \n\n ", f_r_a);
+
+printf(" \n b: At full-load,the slip is 5 percent(as given), and therefore");
+printf(" \n s = %.2f \n f_r = %d Hz " , s_f , f_r_b);
diff --git a/1092/CH9/EX9.4/Example9_4.sce b/1092/CH9/EX9.4/Example9_4.sce new file mode 100755 index 000000000..d6b0a3377 --- /dev/null +++ b/1092/CH9/EX9.4/Example9_4.sce @@ -0,0 +1,30 @@ +// Electric Machinery and Transformers
+// Irving L kosow
+// Prentice Hall of India
+// 2nd editiom
+
+// Chapter 9: POLYPHASE INDUCTION (ASYNCHRONOUS) DYNAMOS
+// Example 9-4
+
+clear; clc; close; // Clear the work space and console.
+
+// Given data
+P = 4 ; // Number of poles in the IM
+hp = 50 ; // rating of the IM in hp
+V_o = 208 ; // Voltage rating of the IM in volt
+T_orig = 225 ; // Starting torque in lb-ft
+I_orig = 700 ; // Instantaneous startign current in A at rated voltage
+V_s = 120 ; // Reduced 3-phase voltage supplied in volt
+
+// Calculations
+// case a
+T_s = T_orig * (V_s/V_o)^2 ; // Starting torque in lb-ft after application of V_s
+
+// case b
+I_s = I_orig * (V_s/V_o) ; // Starting current in A after application of V_s
+
+// Display the results
+disp("Example 9-4 Solution : ");
+printf(" \n a: Starting torque :\n T_s = %.f lb-ft \n",T_s );
+
+printf(" \n b: Starting current :\n I_s = %d A \n",I_s );
diff --git a/1092/CH9/EX9.5/Example9_5.sce b/1092/CH9/EX9.5/Example9_5.sce new file mode 100755 index 000000000..bb0e0a36d --- /dev/null +++ b/1092/CH9/EX9.5/Example9_5.sce @@ -0,0 +1,41 @@ +// Electric Machinery and Transformers
+// Irving L kosow
+// Prentice Hall of India
+// 2nd editiom
+
+// Chapter 9: POLYPHASE INDUCTION (ASYNCHRONOUS) DYNAMOS
+// Example 9-5
+
+clear; clc; close; // Clear the work space and console.
+
+// Given data
+P = 8 ; // Number of poles in the SCIM
+f = 60 ; // Frequency in Hz
+R_r = 0.3 ; // Rotor resistance per phase in ohm
+S_r = 650 ; // Speed in rpm at which motor stalls
+
+// Calculations
+// case a
+S = (120*f)/P ; // Speed in rpm of the rotating magnetic field
+s_b = (S - S_r)/S ; // Breakdown Slip
+
+// case b
+X_lr = R_r / s_b ; // Locked rotor reactance in ohm
+
+// case c
+f_r = s_b * f ; // Rotor frequency in Hz, at the maximum torque point
+
+// case d
+s = 5*(1/100);// Rated slip
+S_r = S * (1 - s); // Full-load in rpm speed at rated slip
+
+// Display the results
+disp("Example 9-5 Solution : ");
+printf(" \n a: S = %d rpm \n s_b = %.3f \n", S , s_b );
+
+printf(" \n b: X_b = %.2f ohm \n ", X_lr );
+
+printf(" \n c: f_r = %.1f Hz \n ", f_r );
+
+printf(" \n d: S = %d rpm \n ", S_r );
+
diff --git a/1092/CH9/EX9.6/Example9_6.sce b/1092/CH9/EX9.6/Example9_6.sce new file mode 100755 index 000000000..90d9834c2 --- /dev/null +++ b/1092/CH9/EX9.6/Example9_6.sce @@ -0,0 +1,67 @@ +// Electric Machinery and Transformers
+// Irving L kosow
+// Prentice Hall of India
+// 2nd editiom
+
+// Chapter 9: POLYPHASE INDUCTION (ASYNCHRONOUS) DYNAMOS
+// Example 9-6
+
+clear; clc; close; // Clear the work space and console.
+
+// Given data
+P = 8 ; // Number of poles in the SCIM
+f = 60 ; // Frequency in Hz
+R_r = 0.3 ; // rotor resistance per phase in ohm/phase
+R_x = 0.7 ; // Added resistance in ohm/phase
+R_r_total = R_r + R_x ; // Total resistance per phase in ohm
+S_r = 875 ; // Full-load Speed in rpm
+
+
+// Calculated values from Ex.9-6
+S = 900 ; // Speed in rpm of the rotating magnetic field
+X_lr = 1.08 ; // Locked rotor reactance in ohm
+
+// Calculations
+// case a
+s = (S - S_r)/S ; // Full-load slip,short circuited
+s_r = R_r_total / R_r * s; // New full-load slip with added resistance
+
+S_r_new = S*(1-s_r); // New full-load speed in rpm
+
+// case b
+// Neglecting constant Kn_t ,since we are taking torque ratios
+T_o = ( R_r / ((R_r)^2 + (X_lr)^2) ); // Original torque
+T_f = ( R_r + R_x) / ( (R_r + R_x)^2 + (X_lr)^2 ); // Original torque
+
+torque_ratio = T_f / T_o ; // Ratio of final torque to original torque
+T_final = 2*torque_ratio ;
+
+// Display the results
+disp("Example 9-6 Solution : ");
+printf(" \n a: The full-load slip,short circuited,is ");
+printf(" \n s = %.4f \n",s );
+printf(" \n Since slip is proportional to rotor resistance and since the ");
+printf(" \n increased rotor resistance is R_r = %.1f + %.1f = %d ,",R_x,R_r,R_r_total);
+printf(" \n the new full-load slip with added resistance is : ");
+printf(" \n s_r = %.4f \n",s_r);
+printf(" \n The new full-load speed is : " );
+printf(" \n S(1-s) = %.f rpm \n",S_r_new );
+
+printf(" \n b: The original starting torque T_o was twice the full-load torque");
+printf(" \n with a rotor resistance of %.1f ohm and a rotor reactance of %.2f ohm",R_r,X_lr);
+printf(" \n (Ex.9-5).The new starting torque conditions may be summarized by the ");
+printf(" \n following table and compared from Eq.(9-14),where T_o ");
+printf(" \n is the original torque and T_f is the new torque.");
+
+printf(" \n _________________________________________");
+printf(" \n Condition \t R_r \t X_lr \t T_starting ");
+printf(" \n \t ohm \t ohm \t ");
+printf(" \n _________________________________________");
+printf(" \n Original : \t %.1f \t %.2f \t 2*T_n ",R_r,X_lr);
+printf(" \n New : \t %.1f \t %.2f \t ? ",R_r_total,X_lr);
+printf(" \n _________________________________________\n");
+
+printf(" \n T_o = %.2f * K_n_t",T_o);
+printf(" \n T_f = %.3f * K_n_t",T_f);
+printf(" \n T_f/T_o = %.2f and T_f = %.2f * T_o\n ",torque_ratio,torque_ratio);
+printf(" \n Therefore,\n T_f = %.3f * T_n",T_final);
diff --git a/1092/CH9/EX9.7/Example9_7.sce b/1092/CH9/EX9.7/Example9_7.sce new file mode 100755 index 000000000..af4cfa69f --- /dev/null +++ b/1092/CH9/EX9.7/Example9_7.sce @@ -0,0 +1,54 @@ +// Electric Machinery and Transformers
+// Irving L kosow
+// Prentice Hall of India
+// 2nd editiom
+
+// Chapter 9: POLYPHASE INDUCTION (ASYNCHRONOUS) DYNAMOS
+// Example 9-7
+
+clear; clc; close; // Clear the work space and console.
+
+// Given data
+P = 8 ; // Number of poles in the SCIM
+f = 60 ; // Frequency in Hz
+R_r = 0.3 ; // Rotor resistance per phase in ohm
+R_x = 0.7 ; // Added resistance in ohm/phase
+R_r_total = R_r + R_x ; // Total resistance per phase in ohm
+X_lr = 1.08 ; // Locked rotor reactance in ohm
+S_r = 650 ; // Speed in rpm at which motor stalls
+E_lr = 112 ; // Induced voltage per phase
+
+// Calculations
+// case a
+Z_lr = R_r + %i*X_lr ; // Locked rotor impedance per phase
+Z_lr_m = abs(Z_lr);//Z_lr_m = magnitude of Z_lr in ohm
+Z_lr_a = atan(imag(Z_lr) /real(Z_lr))*180/%pi;//Z_lr_a=phase angle of Z_lr in degrees
+
+I_r = E_lr / Z_lr_m ; // Rotor current per phase
+cos_theta_r = cosd(Z_lr_a); // rotor power factor with the rotor short-circuited
+cos_theta = R_r / Z_lr_m ; // rotor power factor with the rotor short-circuited
+
+// case b
+// 1 at the end of Z_lr1 is just used for showing its different form Z_lr
+// and for ease in calculations
+Z_lr1 = R_r_total + %i*X_lr ; // Locked rotor impedance per phase
+Z_lr1_m = abs(Z_lr1);//Z_lr1_m = magnitude of Z_lr1 in ohm
+Z_lr1_a = atan(imag(Z_lr1) /real(Z_lr1))*180/%pi;//Z_lr1_a=phase angle of Z_lr1 in degrees
+
+I_r1 = E_lr / Z_lr1_m ; // Rotor current per phase
+cos_theta_r1 = cosd(Z_lr1_a); // rotor power factor with the rotor short-circuited
+cos_theta1 = R_r_total / Z_lr1_m ; // rotor power factor with the rotor short-circuited
+
+// Display the results
+disp("Example 9-7 Solution : ");
+printf(" \n a: The locked-rotor impedance per phase is : ");
+printf(" \n Z_lr in ohm = "),disp(Z_lr);
+printf(" \n Z_lr = %.2f <%.1f ohm \n",Z_lr_m,Z_lr_a);
+printf(" \n I_r = %.f A \n",I_r);
+printf(" \n cosθ_r = cos(%.1f) = %.3f or \n cosθ = R_r/Z_lr = %.3f",Z_lr_a,cos_theta_r,cos_theta);
+
+printf(" \n\n\n b: The locked-rotor impedance with added rotor resistance per phase is : ");
+printf(" \n Z_lr in ohm = "),disp(Z_lr1);
+printf(" \n Z_lr = %.2f <%.1f ohm \n",Z_lr1_m,Z_lr1_a);
+printf(" \n I_r = %.1f A \n",I_r1);
+printf(" \n cosθ_r = cos(%.1f) = %.3f or \n cosθ = R_r/Z_lr = %.3f",Z_lr1_a,cos_theta_r1,cos_theta1);
diff --git a/1092/CH9/EX9.8/Example9_8.sce b/1092/CH9/EX9.8/Example9_8.sce new file mode 100755 index 000000000..d84dc04d8 --- /dev/null +++ b/1092/CH9/EX9.8/Example9_8.sce @@ -0,0 +1,90 @@ +// Electric Machinery and Transformers
+// Irving L kosow
+// Prentice Hall of India
+// 2nd editiom
+
+// Chapter 9: POLYPHASE INDUCTION (ASYNCHRONOUS) DYNAMOS
+// Example 9-8
+
+clear; clc; close; // Clear the work space and console.
+
+// Given data (Exs.9-5 through 9-7)
+P = 8 ; // Number of poles in the SCIM
+f = 60 ; // Frequency in Hz
+R_r = 0.3 ; // Rotor resistance per phase in ohm
+X_lr = 1.08 ; // Locked rotor reactance in ohm
+S_r = 650 ; // Speed in rpm at which motor stalls
+E_lr = 112 ; // Induced voltage per phase
+
+disp("Example 9-8 : ");
+printf(" \n The new and the original conditions may be summarized in the following table\n");
+printf(" \n _________________________________________________________");
+printf(" \n Condition \t R_r \t\t X_lr \t\t T_starting ");
+printf(" \n \t ohm \t\t ohm \t ");
+printf(" \n _________________________________________________________");
+printf(" \n Original : \t %.1f \t\t %.2f \t\t T_o = 2*T_n ",R_r,X_lr);
+printf(" \n New :\t(%.1f+R_x) \t %.2f \t\t T_n = 2*T_n ",R_r,X_lr);
+printf(" \n _________________________________________________________\n");
+
+// Calculating
+// case a
+// Neglecting constant Kn_t ,since we are equating torque T_o and T_n
+T_o = ( R_r / ((R_r)^2 + (X_lr)^2) ); // Original torque
+
+// T_o = K_n_t*( 0.3 / ((0.3)^2 + (1.08)^2) );
+// T_n = K_n_t*( 0.3 + R_x) / ( (0.3 + R_x)^2 + (1.08)^2 );
+// T_n = T_o
+// Simplyifing yields
+// 0.3 + R_x = 0.24[(0.3+R_x)^2 + (1.08)^2]
+// Expanding and combining the terms yields
+// 0.24*(R_x)^2 - 0.856*R_x = 0
+// This is a quadratic equation having two roots,which may be factored as
+// R_x*(0.24*R_x - 0.856) = 0,yielding
+// R_x = 0 and R_x = 0.856/0,24 = 3.57
+R_x = poly(0,'R_x'); // Defining a polynomial with variable 'R_x' with root at 0
+a = 0.24 ; // coefficient of x^2
+b = -0.856 ; // coefficient of x
+c = 0 ; // constant
+
+// Roots of p
+R_x1 = ( -b + sqrt (b^2 -4*a*c ) ) /(2* a);
+R_x2=( -b - sqrt (b^2 -4*a*c ) ) /(2* a);
+// Consider R_x>0 value,
+R_x = R_x1;
+
+R_T = R_r + R_x ; // Total rotor resistance in ohm
+
+// case b
+Z_T = R_T + %i*X_lr ; // Total impedance in ohm
+Z_T_m = abs(Z_T);//Z_T_m = magnitude of Z_T in ohm
+Z_T_a = atan(imag(Z_T) /real(Z_T))*180/%pi;//Z_T_a=phase angle of Z_T in degrees
+
+cos_theta = R_T / Z_T_m ; // Rotor PF that will produce the same starting torque
+
+// case c
+Z_r = Z_T_m ; // Impedance in ohm
+I_r = E_lr / Z_r ; // Starting current in A
+
+// Display the results
+disp("Solution : ");
+
+printf(" \n a: T_o = %.2f * K_n_t ",T_o );
+printf(" \n T_n = %.2f * K_n_t \n",T_o );
+printf(" \n Simplyifing yields");
+printf(" \n 0.3 + R_x = 0.24[(0.3+R_x)^2 + (1.08)^2]");
+printf(" \n Expanding and combining the terms yields");
+printf(" \n 0.24*(R_x)^2 - 0.856*R_x = 0");
+printf(" \n This is a quadratic equation having two roots,which may be factored as");
+printf(" \n R_x*(0.24*R_x - 0.856) = 0,yielding");
+printf(" \n R_x = 0 ohm and R_x = 0.856/0.24 = 3.57 ohm\n\n This proves that ");
+printf(" \n Original torque is produced with an external resistance of either ");
+printf(" \n zero or 12 times the origianl rotor resistance.Therefore,\n");
+printf(" \n R_T = R_r + R_x = %.2f ohm \n",R_T);
+
+printf(" \n b: Z_T in ohm = ");disp(Z_T);
+printf(" \n Z_T = %.2f <%.1f ohm ",Z_T_m,Z_T_a);
+printf(" \n cosӨ = R_T / Z_T = %.3f or \n cosӨ = cosd(%.1f) = %.3f\n",cos_theta,Z_T_a,cosd(Z_T_a));
+
+printf(" \n c: I_r = E_lr / Z_r = %.f A \n\n This proves that,",I_r);
+printf(" \n Rotor current at starting is now only 28 percent of the original");
+printf(" \n starting current in part(a) of Ex.9-7");
diff --git a/1092/CH9/EX9.9/Example9_9.sce b/1092/CH9/EX9.9/Example9_9.sce new file mode 100755 index 000000000..647a6926d --- /dev/null +++ b/1092/CH9/EX9.9/Example9_9.sce @@ -0,0 +1,77 @@ +// Electric Machinery and Transformers
+// Irving L kosow
+// Prentice Hall of India
+// 2nd editiom
+
+// Chapter 9: POLYPHASE INDUCTION (ASYNCHRONOUS) DYNAMOS
+// Example 9-9
+
+clear; clc; close; // Clear the work space and console.
+
+// Given data
+P = 8 ; // Number of poles in the SCIM
+f = 60 ; // Frequency in Hz
+S_r = 875 ; // Full-load Speed in rpm with rotor short-circuited
+R_r = 0.3 ; // rotor resistance per phase in ohm/phase
+R_x = 0.7 ; // Added resistance in ohm/phase
+R_x_a = 1.7 ; // Added resistance in ohm/phase (case a)
+R_x_b = 2.7 ; // Added resistance in ohm/phase (case b)
+R_x_c = 3.7 ; // Added resistance in ohm/phase (case c)
+R_x_d = 4.7 ; // Added resistance in ohm/phase (case d)
+
+// Calculations
+S = (120*f)/P ; // Speed in rpm of the rotating magnetic field
+s_o = (S - S_r)/S ; // Slip at rotor speed 875 rpm
+
+// case a
+s_r_a = s_o * (R_r + R_x_a)/R_r; // Rated slip
+S_r_a = S * (1 - s_r_a); // Full-load speed in rpm for added resistance R_x_a
+
+// case b
+s_r_b = s_o * (R_r + R_x_b)/R_r; // Rated slip
+S_r_b = S * (1 - s_r_b); // Full-load speed in rpm for added resistance R_x_b
+
+// case c
+s_r_c = s_o * (R_r + R_x_c)/R_r; // Rated slip
+S_r_c = S * (1 - s_r_c); // Full-load speed in rpm for added resistance R_x_c
+
+// case d
+s_r_d = s_o * (R_r + R_x_d)/R_r; // Rated slip
+S_r_d = S * (1 - s_r_d); // Full-load speed in rpm for added resistance R_x_d
+
+// Display the results
+disp("Example 9-9 Solution : ");
+
+printf(" \n Slip s_r = s_o*(R_r+R_x)/R_r \n Rotor speed S_r = S_o*(1-s)\n");
+
+printf(" \n Calculated value of s_o = %f , instead of 0.0278(textbook)",s_o)
+printf(" \n so slight variations in the answers below.\n");
+
+printf(" \n a: When R_x = %.1f ohm ",R_x_a);
+printf(" \n s_r = %.3f \n S_r = %.1f rpm \n",s_r_a,S_r_a );
+
+printf(" \n b: When R_x = %.1f ohm ",R_x_b);
+printf(" \n s_r = %.3f \n S_r = %.1f rpm \n",s_r_b,S_r_b );
+
+printf(" \n c: When R_x = %.1f ohm ",R_x_c);
+printf(" \n s_r = %.3f \n S_r = %.1f rpm \n",s_r_c,S_r_c );
+
+printf(" \n d: When R_x = %.1f ohm ",R_x_d);
+printf(" \n s_r = %.3f \n S_r = %.1f rpm \n",s_r_d,S_r_d );
+
+printf(" \n This example,verifies that slip is proportional to rotor resistance");
+printf(" \n as summarized below.");
+
+printf(" \n ___________________________________________________________________");
+printf(" \n R_T(ohm) = R_r+R_x \t\t Slip \t\t Full-load Speed(rpm)");
+printf(" \n ___________________________________________________________________");
+printf(" \n Given \t\t\t Given \t\t Given \t\ ");
+printf(" \n 0.3 \t\t\t 0.0278 \t 875 ");
+printf(" \n 0.3+0.1 = 1.0 \t\t 0.0926 \t 817");
+printf(" \n ___________________________________________________________________");
+printf(" \n Given \t\t\t Calculated \t Calculated \t\ ");
+printf(" \n a. %.1f + %.1f = %.1f \t\t %.3f \t\t %.1f ",R_r,R_x_a,R_r+R_x_a,s_r_a,S_r_a);
+printf(" \n b. %.1f + %.1f = %.1f \t\t %.3f \t\t %.1f ",R_r,R_x_b,R_r+R_x_b,s_r_b,S_r_b);
+printf(" \n c. %.1f + %.1f = %.1f \t\t %.3f \t\t %.1f ",R_r,R_x_c,R_r+R_x_c,s_r_c,S_r_c);
+printf(" \n d. %.1f + %.1f = %.1f \t\t %.3f \t\t %.1f ",R_r,R_x_d,R_r+R_x_d,s_r_d,S_r_d);
+printf(" \n ___________________________________________________________________");
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