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diff --git a/Fundamentals_of_Electrical_Machines/CH_11.ipynb b/Fundamentals_of_Electrical_Machines/CH_11.ipynb new file mode 100755 index 00000000..3c86183e --- /dev/null +++ b/Fundamentals_of_Electrical_Machines/CH_11.ipynb @@ -0,0 +1,354 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "CHAPTER 11: SINGLE-PHASE MOTORS"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.1, Page number 354-355"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "V = 220.0 #Supply voltage(V)\n",
+ "P = 4.0 #Number of poles\n",
+ "f = 50.0 #Frequency(Hz)\n",
+ "N_l = 1450.0 #Speed(rpm)\n",
+ "R_2 = 10.0 #Rotor resistance at standstill(ohm)\n",
+ "\n",
+ "#Calculation\n",
+ "N_s = 120*f/P #Synchronous speed(rpm)\n",
+ "#For case(i)\n",
+ "s_f = (N_s-N_l)/N_s #Slip due to forward field\n",
+ "#For case(ii)\n",
+ "s_b = 2-s_f #Slip due to backward field\n",
+ "#For case(iii)\n",
+ "R_f = R_2/s_f #Effective rotor resistance due to forward slip(ohm)\n",
+ "R_b = R_2/(2-s_f) #Effective rotor resistance due to backward slip(ohm)\n",
+ "\n",
+ "#Result\n",
+ "print('(i) Slip due to forward field , s_f = %.2f ' %s_f)\n",
+ "print('(ii) Slip due to backward field , s_b = %.2f ' %s_b)\n",
+ "print('(iii) Effective rotor resistance due to forward slip , R_f = %.2f ohm' %R_f)\n",
+ "print(' Effective rotor resistance due to backward slip , R_b = %.2f ohm' %R_b)\n",
+ "print('\\nNOTE : Changes in answer from that of textbook is due to precision')"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(i) Slip due to forward field , s_f = 0.03 \n",
+ "(ii) Slip due to backward field , s_b = 1.97 \n",
+ "(iii) Effective rotor resistance due to forward slip , R_f = 300.00 ohm\n",
+ " Effective rotor resistance due to backward slip , R_b = 5.08 ohm\n",
+ "\n",
+ "NOTE : Changes in answer from that of textbook is due to precision\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.2, Page number 357-358"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import cmath\n",
+ "\n",
+ "#Variable declaration\n",
+ "V_t = 220.0 #Supply voltage(V)\n",
+ "R_1 = 6.0 #Resistance(ohm)\n",
+ "R_2 = 6.0 #Resistance(ohm)\n",
+ "X_1 = 10.0 #Inductive reactance(ohm)\n",
+ "X_2 = 10.0 #Inductive reactance(ohm)\n",
+ "N = 1500.0 #Speed(rpm)\n",
+ "s = 0.03 #Slip\n",
+ "X_m = 150.0 #Inductive reactance(ohm)\n",
+ "\n",
+ "#Calculation\n",
+ "Z_f = 0.5*complex(0,X_m)*complex(R_2/s,X_2)/complex(R_2/s,X_2+X_m) #Impedance due to forward field(ohm)\n",
+ "Z_b = 0.5*complex(0,X_m)*complex(R_2/(2-s),X_2)/complex(R_2/(2-s),X_2+X_m) #Impedance due to backward field(ohm)\n",
+ "Z_t = complex(R_1+Z_f+Z_b,X_1) #Total impedance(ohm)\n",
+ "#For case(i)\n",
+ "I_1 = V_t/Z_t #Input current(A)\n",
+ "#For case(ii)\n",
+ "P_i = V_t*abs(I_1) #Input power(W)\n",
+ "#For case(iii)\n",
+ "R_f = Z_f.real\n",
+ "R_b = Z_b.real\n",
+ "P_d = abs(I_1)**2*(R_f-R_b)*(1-s) #Power developed(W)\n",
+ "#For case(iv)\n",
+ "T_d = 9.55*P_d/N #Torque(N-m)\n",
+ "\n",
+ "#Result\n",
+ "print('(i) Input current , I_1 = %.2f\u2220%.1f\u00b0 A' %(abs(I_1),cmath.phase(I_1)*180/math.pi))\n",
+ "print('(ii) Input power , P_i = %.2f W' %P_i)\n",
+ "print('(iii) Power developed , P_d = %.1f W' %P_d)\n",
+ "print('(iv) Torque developed , T_d = %.2f N-m' %T_d)\n",
+ "print('\\nNOTE : Case(ii) is not solved in textbook but solved here')\n",
+ "print(' ERROR : Calculation mistake in Z_b in textbook solution')"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(i) Input current , I_1 = 2.94\u2220-56.2\u00b0 A\n",
+ "(ii) Input power , P_i = 646.10 W\n",
+ "(iii) Power developed , P_d = 275.8 W\n",
+ "(iv) Torque developed , T_d = 1.76 N-m\n",
+ "\n",
+ "NOTE : Case(ii) is not solved in textbook but solved here\n",
+ " ERROR : Calculation mistake in Z_b in textbook solution\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.3, Page number 363-364"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import cmath\n",
+ "\n",
+ "#Variable declaration\n",
+ "V_t = 220.0 #Supply voltage(V)\n",
+ "f = 50.0 #Frequency(Hz)\n",
+ "Z_m = complex(3,5) #Main winding impedance of motor(ohm)\n",
+ "Z_s = complex(5,3) #Starting impedance of motor(ohm)\n",
+ "\n",
+ "#Calculation\n",
+ "#For case(i)\n",
+ "alpha_s = cmath.phase(Z_s) #Starting winding impedance angle(radians)\n",
+ "I_s = V_t/Z_s #Starting current(A)\n",
+ "#For case(ii)\n",
+ "alpha_m = cmath.phase(Z_m) #Main winding impedance angle(radians)\n",
+ "I_m = V_t/Z_m #Main winding current(A)\n",
+ "#For case(iii)\n",
+ "a = alpha_m-alpha_s #Angle of line current(radians)\n",
+ "I = (abs(I_s)**2+abs(I_m)**2+2*abs(I_s)*abs(I_m)*math.cos(a))**0.5 #Line current(A)\n",
+ "\n",
+ "#Result\n",
+ "print('(i) Starting current , I_s = %.1f\u2220%.2f\u00b0 A' %(abs(I_s),cmath.phase(I_s)*180/math.pi))\n",
+ "print('(ii) Main winding current , I_m = %.1f\u2220%.f\u00b0 A' %(abs(I_m),cmath.phase(I_m)*180/math.pi))\n",
+ "print('(iii) Line current , I = %.1f A' %I)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(i) Starting current , I_s = 37.7\u2220-30.96\u00b0 A\n",
+ "(ii) Main winding current , I_m = 37.7\u2220-59\u00b0 A\n",
+ "(iii) Line current , I = 73.2 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.4, Page number 364"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import cmath\n",
+ "\n",
+ "#Variable declaration\n",
+ "V_t = 220.0 #Supply voltage(V)\n",
+ "f = 50.0 #Frequency(Hz)\n",
+ "Z_m = complex(4,3.5) #Main winding impedance of motor(ohm)\n",
+ "Z_s = complex(5,3) #Starting impedance of motor(ohm)\n",
+ "\n",
+ "#Calculation\n",
+ "alpha_m = cmath.phase(Z_m) #Main winding impedance angle(radians)\n",
+ "alpha_s = (alpha_m)-(90*math.pi/180) #Angle of starting winding current(radians)\n",
+ "X_c = Z_s.imag-Z_s.real*math.tan(alpha_s) #Reactance connected in series with starting winding(ohm)\n",
+ "C = 1/(2*math.pi*f*X_c)*10**6 #Starting capacitance for getting maximum torque(\u00b5F)\n",
+ "\n",
+ "#Result\n",
+ "print('Starting capacitance for getting maximum torque , C = %.f \u00b5F' %C)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Starting capacitance for getting maximum torque , C = 365 \u00b5F\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.5, Page number 370-371"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "f = 50.0 #Supply frequency(Hz)\n",
+ "V_nl = 100.0 #No-load voltage(V)\n",
+ "I_nl = 2.5 #No-load current(A)\n",
+ "P_nl = 60.0 #No-load power(W)\n",
+ "V_br = 60.0 #Block rotor voltage(V)\n",
+ "I_br = 3.0 #Block rotor current(A)\n",
+ "P_br = 130.0 #Block rotor power(W)\n",
+ "R_1 = 2.0 #Main winding resistance(ohm)\n",
+ "\n",
+ "#Calculation\n",
+ "Z_br = V_br/I_br #Impedance due to blocked rotor test(ohm)\n",
+ "R_br = P_br/I_br**2 #Resistance due to blocked rotor test(ohm)\n",
+ "X_br = (Z_br**2-R_br**2)**0.5 #Reactance under blocked rotor condition(ohm)\n",
+ "X_1 = 0.5*X_br #Leakage reactance(ohm)\n",
+ "X_2 = X_1 #Leakage reactance(ohm)\n",
+ "R_2 = R_br-R_1 #Rotor circuit resistance(ohm)\n",
+ "Z_nl = V_nl/I_nl #Impedance due to no-load(ohm)\n",
+ "R_nl = P_nl/I_nl**2 #Resistance due to no-load(ohm)\n",
+ "X_nl = (Z_nl**2-R_nl**2)**0.5 #Reactance due to no-load(ohm)\n",
+ "X_m = 2*(X_nl-X_1-0.5*X_2) #Magnetizing reactance(ohm)\n",
+ "P_rot = P_nl-I_nl**2*(R_1+(R_2/4)) #Rotational loss(W)\n",
+ "\n",
+ "#Result\n",
+ "print('Equivalent circuit parameters of the motor')\n",
+ "print('Under Blocked rotor test :')\n",
+ "print('Input impedance , Z_br = %.f ohm' %Z_br)\n",
+ "print('Total resistance , R_br = %.1f ohm' %R_br)\n",
+ "print('Total reactance , X_br = %.1f ohm' %X_br)\n",
+ "print('Rotor circuit resistance , R_2 = %.1f ohm' %R_2)\n",
+ "print('Leakage reactances , X_1 = X_2 = %.1f ohm' %X_1)\n",
+ "print('\\nUnder No load test :')\n",
+ "print('Input impedance , Z_nl = %.f ohm' %Z_nl)\n",
+ "print('No-load resistance , R_nl = %.1f ohm' %R_nl)\n",
+ "print('No-load reactance , X_nl = %.1f ohm' %X_nl)\n",
+ "print('Magnetizing reactance , X_m = %.1f ohm' %X_m)\n",
+ "print('Rotational loss , P_rot = %.f W' %P_rot)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Equivalent circuit parameters of the motor\n",
+ "Under Blocked rotor test :\n",
+ "Input impedance , Z_br = 20 ohm\n",
+ "Total resistance , R_br = 14.4 ohm\n",
+ "Total reactance , X_br = 13.8 ohm\n",
+ "Rotor circuit resistance , R_2 = 12.4 ohm\n",
+ "Leakage reactances , X_1 = X_2 = 6.9 ohm\n",
+ "\n",
+ "Under No load test :\n",
+ "Input impedance , Z_nl = 40 ohm\n",
+ "No-load resistance , R_nl = 9.6 ohm\n",
+ "No-load reactance , X_nl = 38.8 ohm\n",
+ "Magnetizing reactance , X_m = 56.9 ohm\n",
+ "Rotational loss , P_rot = 28 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 11.6, Page number 372"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "r_t = 36.0 #Number of rotor teeth\n",
+ "N = 4.0 #Number of stator phases\n",
+ "\n",
+ "#Calculation\n",
+ "#For case(i)\n",
+ "T_p = 360/r_t #Tooth pitch(degree)\n",
+ "#For case(ii)\n",
+ "teta = 360/(N*r_t) #Step angle(degree)\n",
+ "\n",
+ "#Result\n",
+ "print('(i) Tooth pitch , T_p = %.f\u00b0 ' %T_p)\n",
+ "print('(ii) Step angle , \u03b8 = %.1f\u00b0 ' %teta)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(i) Tooth pitch , T_p = 10\u00b0 \n",
+ "(ii) Step angle , \u03b8 = 2.5\u00b0 \n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file |