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diff --git a/Fundamentals_of_Electrical_Machines/CH_7.ipynb b/Fundamentals_of_Electrical_Machines/CH_7.ipynb new file mode 100755 index 00000000..167a7464 --- /dev/null +++ b/Fundamentals_of_Electrical_Machines/CH_7.ipynb @@ -0,0 +1,400 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "CHAPTER 7: THREE-PHASE INDUCTION MOTOR"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.1, Page number 246-247"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "V = 230.0 #Supply voltage(V)\n",
+ "P = 4.0 #Number of poles\n",
+ "f = 50.0 #Frequency(Hz)\n",
+ "N_l = 1445.0 #Full load speed(rpm)\n",
+ "\n",
+ "#Calculation\n",
+ "#For case(i)\n",
+ "N_s = 120*f/P #Synchronous speed(rpm)\n",
+ "#For case(ii)\n",
+ "s = (N_s-N_l)/N_s #Slip\n",
+ "#For case(iii)\n",
+ "f_r = s*f #Rotor frequency(Hz)\n",
+ "\n",
+ "#Result\n",
+ "print('(i) Synchronous speed , N_s = %.f rpm' %N_s)\n",
+ "print('(ii) Slip , s = %.4f ' %s)\n",
+ "print('(iii) Rotor frequency , f_r = %.1f Hz' %f_r)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(i) Synchronous speed , N_s = 1500 rpm\n",
+ "(ii) Slip , s = 0.0367 \n",
+ "(iii) Rotor frequency , f_r = 1.8 Hz\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.2, Page number 247-248"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "E_BR = 120.0 #Voltage under blocked condition(V)\n",
+ "P = 4.0 #Number of poles\n",
+ "f = 50.0 #Frequency(Hz)\n",
+ "N_l = 1450.0 #Speed(rpm)\n",
+ "\n",
+ "#Calculation\n",
+ "N_s = 120*f/P #Synchronous speed(rpm)\n",
+ "s = (N_s-N_l)/N_s #Slip\n",
+ "f_r = s*f #Rotor frequency(Hz)\n",
+ "E_r = s*E_BR #Rotor voltage(V)\n",
+ "\n",
+ "#Result\n",
+ "print('Synchronous speed , N_s = %.f rpm' %N_s)\n",
+ "print('Rotor frequency , f_r = %.2f Hz' %f_r)\n",
+ "print('Rotor voltage , E_r = %.2f V' %E_r)\n",
+ "print('\\nNOTE : Changes in answer is due to precision i.e more number of decimal places')"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Synchronous speed , N_s = 1500 rpm\n",
+ "Rotor frequency , f_r = 1.67 Hz\n",
+ "Rotor voltage , E_r = 4.00 V\n",
+ "\n",
+ "NOTE : Changes in answer is due to precision i.e more number of decimal places\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.3, Page number 250"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "V_0 = 230.0 #Supply voltage(V)\n",
+ "P = 4.0 #Number of poles\n",
+ "T_0 = 230.0 #Original torque(N-m)\n",
+ "V_s = 150.0 #Stator voltage(V)\n",
+ "I_0 = 560.0 #Starting current(A)\n",
+ "\n",
+ "#Calculation\n",
+ "T_st = (V_s/V_0)**2*T_0 #Starting torque(N-m)\n",
+ "I_st = I_0*(V_s/V_0) #Starting current(A)\n",
+ "\n",
+ "#Result\n",
+ "print('Starting torque , T_st = %.1f N-m' %T_st)\n",
+ "print('Starting current , I_st = %.1f A' %I_st)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Starting torque , T_st = 97.8 N-m\n",
+ "Starting current , I_st = 365.2 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.4, Page number 254"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "f = 50.0 #Frequency(Hz)\n",
+ "P = 8.0 #Number of poles\n",
+ "a = 0.03 #Full load slip\n",
+ "R_2 = 0.01 #Rotor resistance per phase(ohm)\n",
+ "X_2 = 0.1 #Standstill reactance per phase(ohm)\n",
+ "\n",
+ "#Calculation\n",
+ "#For case(i)\n",
+ "N_s = 120*f/P #Synchronous speed(rpm)\n",
+ "s = R_2/X_2 #Slip at maximum torque\n",
+ "N_l = (1-s)*N_s #Rotor speed at maximum torque(rpm)\n",
+ "#For case(ii)\n",
+ "T = (s**2+a**2)/(2*a*s) #Ratio of maximum torque to full load torque\n",
+ "\n",
+ "#Result\n",
+ "print('(i) Speed at which maximum torque occurs , N_l = %.f rpm' %N_l)\n",
+ "print('(ii) Ratio of the maximum torque to full load torque , T_max/T_f = %.2f ' %T)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(i) Speed at which maximum torque occurs , N_l = 675 rpm\n",
+ "(ii) Ratio of the maximum torque to full load torque , T_max/T_f = 1.82 \n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.5, Page number 260"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "V = 440.0 #Supply voltage(V)\n",
+ "P = 4.0 #Number of poles\n",
+ "P_ag = 1500.0 #Rotor input(W)\n",
+ "P_rcu = 250.0 #Copper loss(W)\n",
+ "f = 50.0 #Frequency(Hz)\n",
+ "\n",
+ "#Calculation\n",
+ "#For case(i)\n",
+ "s = P_rcu/P_ag #Slip\n",
+ "#For case(ii)\n",
+ "N_s = 120*f/P #Synchronous speed(rpm)\n",
+ "#For case(iii)\n",
+ "N_l = (1-s)*N_s #Shaft speed(rpm)\n",
+ "#For case(iv)\n",
+ "P_mech = (1-s)*P_ag #Mechanical power developed(W)\n",
+ "\n",
+ "#Result\n",
+ "print('(i) Slip , s = %.2f' %s)\n",
+ "print('(ii) Synchronous speed , N_s = %.f rpm' %N_s)\n",
+ "print('(iii) Shaft speed , N_l = %.f rpm' %N_l)\n",
+ "print('(iv) Mechanical power developed , P_mech = %.f W' %P_mech)\n",
+ "print('\\nNOTE : Changes in answer is due to precision i.e more number of decimal places')"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(i) Slip , s = 0.17\n",
+ "(ii) Synchronous speed , N_s = 1500 rpm\n",
+ "(iii) Shaft speed , N_l = 1250 rpm\n",
+ "(iv) Mechanical power developed , P_mech = 1250 W\n",
+ "\n",
+ "NOTE : Changes in answer is due to precision i.e more number of decimal places\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.6, Page number 264"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Variable declaration\n",
+ "V_1 = 150.0 #Supply voltage(V)\n",
+ "P = 4.0 #Number of poles\n",
+ "f = 50.0 #Frequency(Hz)\n",
+ "Z_1 = complex(0.12,0.16) #Per phase standstill stator impedance(ohm)\n",
+ "Z_2 = complex(0.22,0.28) #Per phase standstill rotor impedance(ohm)\n",
+ "\n",
+ "#Calculation\n",
+ "Z_eq = Z_1+Z_2 #Equivalent impedance(ohm)\n",
+ "R_eq = Z_eq.real\n",
+ "P_mech = 3*V_1**2/(2*(R_eq+abs(Z_eq)))*10**-3 #Maximum mechanical power developed(kW)\n",
+ "R_2 = Z_2.real\n",
+ "s_mp = R_2/(abs(Z_eq)+R_2) #Slip\n",
+ "W_s = 2*math.pi*2*f/P #Synchronous speed(rad/s)\n",
+ "W = (1-s_mp)*W_s #Speed of rotor(rad/s)\n",
+ "T_mxm = P_mech*1000/W #Maximum torque(N-m) \n",
+ "\n",
+ "#Result\n",
+ "print('Maximum mechanical power , P_mech = %.2f kW' %P_mech)\n",
+ "print('Maximum torque , T_mxm = %.2f N-m' %T_mxm)\n",
+ "print('Slip , s_mp = %.2f ' %s_mp)\n",
+ "print('\\nNOTE : Changes in answer is due to precision i.e more number of decimal places')"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Maximum mechanical power , P_mech = 37.66 kW\n",
+ "Maximum torque , T_mxm = 334.65 N-m\n",
+ "Slip , s_mp = 0.28 \n",
+ "\n",
+ "NOTE : Changes in answer is due to precision i.e more number of decimal places\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.7, Page number 265-266"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "V = 440.0 #Supply voltage(V)\n",
+ "P = 6.0 #Number of poles\n",
+ "f = 50.0 #Frequency(Hz)\n",
+ "P_a = 45000.0 #Input power(W)\n",
+ "N_l = 900.0 #Speed(rpm)\n",
+ "P_tloss = 2000.0 #Total stator losses(W)\n",
+ "P_fw = 1000.0 #Friction and windage losses(W)\n",
+ "\n",
+ "#Calculation\n",
+ "N_s = 120*f/P #Synchronous speed(rpm)\n",
+ "s = (N_s-N_l)/N_s #Slip\n",
+ "P_ag = (P_a-P_tloss) #Air gap power(W)\n",
+ "P_rcu = s*P_ag #Rotor copper loss(W)\n",
+ "P_mech = P_ag-P_rcu #Mechanical power(W)\n",
+ "P_0 = P_mech-(P_tloss+P_fw) #Output power(W)\n",
+ "n = (P_0/P_ag)*100 #Efficiency(percent)\n",
+ "\n",
+ "#Result\n",
+ "print('(i) Slip , s = %.1f ' %s)\n",
+ "print('(ii) Rotor copper loss , P_rcu = %.f W' %P_rcu)\n",
+ "print('(iii) Shaft or Output power , P_0 = %.f W' %P_0)\n",
+ "print('(iv) Efficiency , \u03b7 = %.f percent' %n)\n",
+ "print('\\nNOTE : ERROR : Friction & windage losses are 1 kW not 1.5 kW as given in textbook question')"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(i) Slip , s = 0.1 \n",
+ "(ii) Rotor copper loss , P_rcu = 4300 W\n",
+ "(iii) Shaft or Output power , P_0 = 35700 W\n",
+ "(iv) Efficiency , \u03b7 = 83 percent\n",
+ "\n",
+ "NOTE : ERROR : Friction & windage losses are 1 kW not 1.5 kW as given in textbook question\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.8, Page number 268-269"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "v_s = 120.0 #Train speed(km/h)\n",
+ "f = 50.0 #Stator frequency(Hz)\n",
+ "\n",
+ "#Calculation\n",
+ "v_s1 = v_s*1000/(60*60) #Train speed(m/s)\n",
+ "w = v_s1/(2*f) #Length of the pole-pitch(m)\n",
+ "\n",
+ "#Result\n",
+ "print('Length of the pole-pitch of linear induction motor , w = %.2f m' %w)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Length of the pole-pitch of linear induction motor , w = 0.33 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
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