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diff --git a/DC_Machines_and_Synchronous_Machines/ch4.ipynb b/DC_Machines_and_Synchronous_Machines/ch4.ipynb new file mode 100755 index 00000000..7e4b687b --- /dev/null +++ b/DC_Machines_and_Synchronous_Machines/ch4.ipynb @@ -0,0 +1,1114 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:e5bf1101b5ca7d663f8c7db6ba5353cd5daf17690d3f4785e774f0306b01e83e" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 4 : Synchronous Machines : Alternators" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.1 page no : 16" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Variables\n", + "Pole = 4.\n", + "Slots = 24.\n", + "Phase = 3. \t\t\t#number of phases\n", + "\n", + "# Calculations\n", + "n = Slots/Pole \t\t\t#slots per pole\n", + "m = Slots/Pole/Phase \t\t\t#slots per pole per phase\n", + "beeta = 180/n \t\t\t#Slot angle\n", + "\n", + "# results\n", + "print \"Slot angle : %.f degrees\"%beeta" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Slot angle : 30 degrees\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.2 page no : 26" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "Slots = 120.\n", + "Pole = 8.\n", + "Phase = 3. \t\t\t#number of phases\n", + "\n", + "# Calculations\n", + "n = Slots/Pole \t\t\t#Slots per Pole\n", + "m = Slots/Pole/Phase \t\t\t#Slots per Pole per Phase\n", + "beeta = 180/n \t\t\t#Slot angle in degree\n", + "K_d = math.sin(math.radians(m*beeta/2)) /(m*math.sin(math.radians(beeta/2))) \t\t\t#Distribution Factor\n", + "\n", + "# Results\n", + "print 'Distribution Factor:K_d = %.3f'%(K_d)\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Distribution Factor:K_d = 0.957\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.3 page no : 26" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "Slots = 36.\n", + "Pole = 4.\n", + "Phase = 3. \t\t\t#number of phases\n", + "n = Slots/Pole \t\t\t#Slots per pole\n", + "beeta = 180/n \t\t\t#Slot angle in degrees\n", + "\n", + "# Calculations\n", + "#coil is shorted by 1 slot i.e. by beeta degrees to full pitch dismath.tance\n", + "alpha = beeta \t\t\t#angle of short pitch\n", + "K_c = math.cos(math.radians(alpha/2)) \t\t\t#Coil span Factor\n", + "\n", + "# Results\n", + "print 'Coil Span Factor:K_c = %.4f'%(K_c)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Coil Span Factor:K_c = 0.9848\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.4 page no : 26" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "N_s = 250. \t\t\t#Synchronous speed in r.p.m\n", + "f = 50. \t\t\t#Frequency of generated e.m.f in hertz\n", + "Slots = 216.\n", + "phi = 30.*10**-3 \t\t\t#flux per pole in weber\n", + "\n", + "Pole = 120*f/N_s\n", + "n = Slots/Pole \t\t\t#Slots per Pole\n", + "m = n/3 \t\t\t#Slots per Pole per Phase\n", + "beeta = 180/n \t\t\t#Slot angle in degree\n", + "\n", + "# Calculations\n", + "K_d = math.sin(math.radians(m*beeta/2))/(m*math.sin(math.radians(beeta/2))) \t\t\t#distribution factor\n", + "K_c = 1 \t\t\t#Coil Span Factor for full pitch coils = 1\n", + "\n", + "Z = Slots*5 \t\t\t#Z is total no of conductors\n", + "Z_ph = Z/3 \t\t\t#Conductors Per Phase\n", + "T_ph = Z_ph/2 \t\t\t#Turns per phase\n", + "E_ph = 4.44*K_c*K_d*f*phi*T_ph \t\t\t#induced emf\n", + "E_line = E_ph*math.sqrt(3)\n", + "\n", + "# Results\n", + "print 'Induced e.m.f across the Terminals is %.2f V'%(E_line)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Induced e.m.f across the Terminals is 1992.90 V\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.5 page no : 27" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "Pole = 16.\n", + "N_s = 375. \t\t\t#synchronous speed in rpm\n", + "Slots = 144.\n", + "E_line = 2.657*10**3 \t\t\t#line value of emf across terminals\n", + "f = Pole*N_s/120 \t\t\t#frequency\n", + "\n", + "# Calculations\n", + "K_c = 1 \t\t\t#assuming full pitch winding Coil span Factor = 1\n", + "n = Slots/Pole \t\t\t#slots per pole\n", + "m = n/3 \t\t\t#slots per pole per phase\n", + "\n", + "beeta = 180/n\n", + "K_d = math.sin(math.radians(m*beeta/2)) /(m*math.sin(math.radians(beeta/2))) \t\t\t#Distribution Fcator\n", + "conductors_per_slot = 10\n", + "Z = Slots*conductors_per_slot \t\t\t#total conductors\n", + "\n", + "Z_ph = Z/3 \t\t\t#number of conductors per phase\n", + "T_ph = Z_ph/2 \t\t\t#no of turns per phase\n", + "E_ph = E_line/math.sqrt(3) \t\t\t#phase value of emf across terminals\n", + "\n", + "phi = E_ph/(4.44*K_c*K_d*f*T_ph) \t\t\t#E_ph = 4.44*K_c*K_d*f*phi*T_ph\n", + "\n", + "# Results\n", + "print 'Frequency of Induced e.m.f is %.0fHz \\nFlux per Pole is %.0f mWb'%(f,phi*1000)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Frequency of Induced e.m.f is 50Hz \n", + "Flux per Pole is 30 mWb\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.6 page no : 34" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "d = 0.25 \t\t\t#Diameter in metre\n", + "l = 0.3 \t\t\t#Length in metre\n", + "Pole = 4.\n", + "A1 = math.pi*d*l/Pole \t\t\t#Area of each fundamental pole\n", + "f = 50. \t\t\t#frequency in hertz\n", + "B_m1 = 0.15 \n", + "B_m3 = 0.03\n", + "B_m5 = 0.02 \t\t\t#Amplitude of 1st 3rd and 5th harmonics\n", + "phi_1 = (2/math.pi)*B_m1*A1 \t\t\t#average value of fundamental flux per pole in weber\n", + "\n", + "\n", + "# Calculations and Results\n", + "#PART A\n", + "E_c1 = 1.11*2*f*phi_1 \t\t\t#R.M.S value of fundamental frequency e.m.f generated in math.single conductor\n", + "Coil_span = (13./15)*180 \t\t\t#math.since winding coil span is 13/15 of pole pitch\n", + "alpha = 180-Coil_span\n", + "\n", + "#Pitch factor for 1st 3rd and 5th harmonic\n", + "K_c1 = math.cos(math.radians(alpha/2))\n", + "K_c3 = math.cos(math.radians(3*alpha/2))\n", + "K_c5 = math.cos(math.radians(5*alpha/2))\n", + "\n", + "#using E_cx = E_c1 * (B_mx/B_m1)\n", + "E_c3 = E_c1 * (B_m3/B_m1)\n", + "E_c5 = E_c1 * (B_m5/B_m1)\n", + "\n", + "E_t1 = K_c1 * (2*E_c1) \t\t\t#R.M.S Vaue of fundamental frequency EMF generated in 1 turn (in volts)\n", + "E_t3 = K_c3 * 2*E_c3\n", + "E_t5 = K_c5 * 2*E_c5\n", + "E_t = math.sqrt(E_t1**2 +E_t3**2 +E_t5**2)\n", + "V = 10*E_t \t\t\t#(number of turns per coil )* (Total e.m.f per turn)\n", + "print 'Voltage generated per coil is %.1f V'%(V)\n", + "\n", + "# PART B\n", + "#E_1ph = 4.44*K_c1*K_d1*phi_1*f*T_ph\n", + "T_ph = 200. \t\t\t#T_ph = (60 coils * 10 turns per coil)/3\n", + "\n", + "Total_Conductors = 1200. \t\t\t# 60 coils * 10 turns per coil * 2\n", + "Conductors_per_Slot = 20. \t\t\t#2 conductors per turn * 10 turns per slot\n", + "Slots = Total_Conductors/Conductors_per_Slot\n", + "\n", + "n = Slots/Pole\n", + "m = n/3\n", + "beeta = 180/n \t\t\t#Slot angle in degree\n", + "K_d1 = math.sin(math.radians(m*1*beeta/2)) /(m*math.sin(math.radians(1*beeta/2)))\n", + "K_d3 = math.sin(math.radians(m*3*beeta/2)) /(m*math.sin(math.radians(3*beeta/2)))\n", + "K_d5 = math.sin(math.radians(m*5*beeta/2)) /(m*math.sin(math.radians(5*beeta/2)))\n", + "\n", + "E_1ph = 4.44 * K_c1 * K_d1*phi_1 * f * T_ph\n", + "# using E_xph = E_1ph* (B_mx*K_cx*K_dx)/(B_m1*K_c1*K_d1)\n", + "E_3ph = E_1ph* (B_m3*K_c3*K_d3)/(B_m1*K_c1*K_d1)\n", + "E_5ph = E_1ph* (B_m5*K_c5*K_d5)/(B_m1*K_c1*K_d1)\n", + "E_ph = math.sqrt( E_1ph**2 + E_3ph**2 + E_5ph**2 ) \t\t\t#voltage generated per phase\n", + "print 'Voltage generated per phase is %.f V'%(E_ph)\n", + "\n", + "#PART c\n", + "E_line = math.sqrt(3) * math.sqrt( E_1ph**2 + E_5ph**2 ) \t\t\t#terminal voltage\n", + "print 'Terminal Voltage is %.1f V '%(E_line)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Voltage generated per coil is 12.4 V\n", + "Voltage generated per phase is 235 V\n", + "Terminal Voltage is 404.8 V \n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.7 page no : 38" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "Ns = 250. \t\t\t#Synchronous speed in rpm\n", + "f = 50.\n", + "Slots = 288.\n", + "E_line = 6600.\n", + "Pole = 120*f/Ns \n", + "n = Slots/Pole \t\t\t#slots per pole\n", + "m = n/3 \t\t\t#slots per pole per phase\n", + "beeta = 180/n \t\t\t#slot angle\n", + "conductors_per_slot = 32 \t\t\t#16 conductors per coil-side *2 coil-sides per slot\n", + "\n", + "# Calculations\n", + "K_d = math.sin(math.radians(m*beeta/2)) /(m*math.sin(math.radians(beeta/2))) \t\t\t#distribution factor\n", + "alpha = 2*beeta\t\t\t# angle of short pitch\n", + "K_c = math.cos(math.radians(alpha/2)) \t\t\t#coil span factor\n", + "Z = Slots*conductors_per_slot \t\t\t#total conductors\n", + "Z_ph = Z/3 \t\t\t#Conductors per phase\n", + "T_ph = Z_ph/2 \t\t\t#turns per phase\n", + "\n", + "E_ph = E_line/math.sqrt(3)\n", + "phi = E_ph/(4.44*K_c*K_d*f*T_ph) \t\t\t#Because E_ph = 4.44 *K_c *K_d *phi *f *T_ph\n", + "\n", + "# Results\n", + "print 'Flux per pole is %.0f mWb '%(phi*1000)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Flux per pole is 12 mWb \n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.8 page no : 40" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "Ns = 1500. \t\t\t#synchronous speed in rpm\n", + "Pole = 4.\n", + "Slots = 24.\n", + "conductor_per_slot = 8.\n", + "phi = 0.05 \t\t\t#flux per pole in weber\n", + "f = Pole*Ns/120 \t\t\t#frequenccy\n", + "n = Slots/Pole \t\t\t#slots per pole\n", + "m = n \t\t\t# as number of phases is 1\n", + "beeta = 180/n \t\t\t#slot angle\n", + "\n", + "# Calculations\n", + "K_d = math.sin(math.radians(m*beeta/2)) /(m*math.sin(math.radians(beeta/2))) \t\t\t#distribution factor\n", + "\n", + "#Full pitch = n = 6 slots\n", + "#(1/6)th of full pitch = 1slot\n", + "#angle of short pitch = 1 slot angle\n", + "alpha = beeta\n", + "K_c = math.cos(math.radians(alpha/2)) \t\t\t#coil span factor\n", + "\n", + "Z = conductor_per_slot*Slots \t\t\t#total conductors\n", + "Z_ph = Z \t\t\t# as number of phases is 1\n", + "T_ph = Z_ph/2 \t\t\t#turns per phase\n", + "E_ph = 4.44*K_c*K_d* phi *f *T_ph \t\t\t#induced emf\n", + "\n", + "# Results\n", + "print 'Induced e.m.f is %.1f V '%(E_ph)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Induced e.m.f is 662.8 V \n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.9 page no : 41" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "Pole = 48.\n", + "n = 9. \t\t\t#slots per pole\n", + "phi = 51.75*10**-3 \t\t\t#flux per pole in weber\n", + "Ns = 125.\n", + "f = Ns*Pole/120 \t\t\t#frequency\n", + "K_c = 1. \t\t\t#due to full pitch winding\n", + "m = n/3 \t\t\t#slots per pole per phase\n", + "beeta = 180/n \t\t\t#slot angle\n", + "\n", + "# Calculations\n", + "K_d = math.sin(math.radians(m*beeta/2)) /(m*math.sin(math.radians(beeta/2))) \t\t\t#distribution factor\n", + "conductor_per_slot = 4*2 \t\t\t#Each slot has 2 coil sides and each coil side has 4 conductors\n", + "Slots = n*Pole\n", + "Z = conductor_per_slot*Slots \t\t\t#total number of conductors\n", + "Z_ph = Z/3 \t\t\t#conductors per phase\n", + "T_ph = Z_ph/2 \t\t\t#turns per phase\n", + "E_ph = 4.44 *K_c *K_d *phi *f *T_ph \t\t\t#induced emf\n", + "\n", + "E_line = (math.sqrt(3))*E_ph \t\t\t#due to star connection\n", + "\n", + "# Results\n", + "print 'Induced e.m.f is %.0f kV '%(E_line/1000)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Induced e.m.f is 11 kV \n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.10 page no : 42" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "Slots = 180.\n", + "Pole = 12.\n", + "Ns = 600. \t\t\t#Synchronous speen in rpm\n", + "f = Pole*Ns/120 \t\t\t#frequency\n", + "phi = 0.05 \t\t\t#flux per pole in weber\n", + "\n", + "# Calculations and Results\n", + "#Part(i)\n", + "#Average EMF in a conductor = 2*f*phi\n", + "rms_value_1 = 1.11*2*f*phi \t\t\t#rms value of emf in a conductor\n", + "print 'i)r.m.s value of e.m.f in a conductor is %.2f V '%(rms_value_1)\n", + "\n", + "#part(ii)\n", + "#Average EMF in a turn = 4*f*phi\n", + "rms_value_2 = 1.11*4*f*phi\t\t\t#r.m.s value of e.m.f in a turn\n", + "print 'ii)r.m.s value of e.m.f in a turn is %.2f V '%(rms_value_2)\n", + "\n", + "#part(iii)\n", + "conductors_per_coilside = 10/2 \n", + "rms_value_3 = rms_value_2*conductors_per_coilside \t\t\t#r.m.s value of e.m.f in a coil\n", + "print 'iii)r.m.s value of e.m.f in a coil is %.1f V '%(rms_value_3)\n", + "\n", + "#part(iv)\n", + "conductors_per_slot = 10\n", + "Z = conductors_per_slot * Slots \t\t\t#total number of conductors\n", + "Z_ph = Z/3 \t\t\t#conductors per phase\n", + "T_ph = Z_ph/2 \t\t\t#turns per phase\n", + "n = Slots/Pole \t\t\t#slots per pole\n", + "m = n/3 \t\t\t#slots per pole per phase \n", + "beeta = 180/n \t\t\t#slot angle\n", + "\n", + "K_d = math.sin(math.radians(m*beeta/2)) /(m*math.sin(math.radians(beeta/2)))\n", + "K_c = 1 \t\t\t#distribution & coil-span factor\n", + "E_ph = rms_value_2*T_ph*K_d*K_c \t\t\t#induced emf\n", + "print 'iv)per phase induced e.m.f is %.1f V '%(E_ph)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "i)r.m.s value of e.m.f in a conductor is 6.66 V \n", + "ii)r.m.s value of e.m.f in a turn is 13.32 V \n", + "iii)r.m.s value of e.m.f in a coil is 66.6 V \n", + "iv)per phase induced e.m.f is 3822.9 V \n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.11 page no : 44" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "Pole = 8.\n", + "f = 50. \t\t\t#frequency\n", + "phi = 60.*10**-3 \t\t\t#flux per pole in weber\n", + "Slots = 96. \n", + "n = Slots/Pole \t\t\t#slots per pole\n", + "beeta = 180/n \t\t\t#slot angle \n", + "m = n/3 \t\t\t#slots per pole per phase\n", + "\n", + "# Calculations and Results\n", + "coil_pitch = 10*beeta \t\t\t#10 slots\n", + "alpha = 180-coil_pitch\n", + "K_c = math.cos(math.radians(alpha/2)) \t\t\t#coi;-span factor\n", + "K_d = math.sin(math.radians(m*beeta/2)) /(m*math.sin(math.radians(beeta/2))) \t\t\t#distribution factor\n", + "\n", + "conductors_per_slot = 4 \n", + "Z = Slots*conductors_per_slot \t\t\t#total conductors\n", + "Total_turns = Z/2 \n", + "T_ph = Total_turns/3 \t\t\t#turns per phase\n", + "\n", + "#part (i)\n", + "E_ph = 4.44 *K_c *K_d *phi *f *T_ph\n", + "print '\\The phase voltage is %.2f V '%(E_ph)\n", + "\n", + "#part(ii)\n", + "E_line = E_ph*math.sqrt(3)\n", + "print 'The Line Voltage is %.2f V '%(E_line)\n", + "\n", + "#part(iii)\n", + "I_ph = 650\n", + "I_l = I_ph \t\t\t# Star Connection\n", + "kVA_rating = math.sqrt(3)*E_line*I_l\n", + "print 'kVA rating is %.1f kVA '%(kVA_rating/1000)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\\The phase voltage is 788.57 V \n", + "The Line Voltage is 1365.84 V \n", + "kVA rating is 1537.7 kVA \n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.12 page no : 45" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "Ns = 600. \t\t\t#synchronous speed in rpm\n", + "Pole = 10.\n", + "l = 30./100 \t\t\t#divided by 100 for centimetre-metre conversion\n", + "Pole_pitch = 35./100 \t\t\t#numerically equal to pi*d/Pole\n", + "Phase = 3.\n", + "conductors_per_slot = 8.\n", + "A1 = Pole_pitch*l \t\t\t#Area of each fundamental pole\n", + "m = 3. \t\t\t#Slot per Pole per Phase\n", + "n = Phase*m \t\t\t#slots per pole\n", + "beeta = 180/n \t\t\t#slot angle\n", + "\n", + "B_m1 = 1.\n", + "B_m3 = 0.3\n", + "B_m5 = 0.2 \t\t\t#amplitude of 1st 3rd and 5th harmonic\n", + "phi_1 = (2/math.pi)*A1*B_m1 \t\t\t#average value of fundamental flux per pole \n", + "f = Ns*Pole/120 \t\t\t#frequency\n", + "\n", + "# Calculations\n", + "Coil_span = (8./9)*180\n", + "alpha = 180-Coil_span\n", + "#pitch factor for 1st 3rd and 5th harmonic\n", + "K_c1 = math.cos(math.radians(alpha/2)) \n", + "K_c3 = math.cos(math.radians(3*alpha/2))\n", + "K_c5 = math.cos(math.radians(5*alpha/2))\n", + "\n", + "# using K_dx = math.sin(m*x*beeta*(math.pi/180)/2) /(m*math.sin(x*beeta*(math.pi/180)/2))\n", + "#distribution factor for 1st 3rd and 5th harmonic\n", + "K_d1 = math.sin(math.radians(m*1*beeta/2)) /(m*math.sin(math.radians(1*beeta/2)))\n", + "K_d3 = math.sin(math.radians(m*3*beeta/2)) /(m*math.sin(math.radians(3*beeta/2)))\n", + "K_d5 = math.sin(math.radians(m*5*beeta/2)) /(m*math.sin(math.radians(5*beeta/2)))\n", + "\n", + "Slots = n*Pole\n", + "Total_conductors = conductors_per_slot * Slots\n", + "Total_turns = Total_conductors/2\n", + "T_ph = Total_turns/3 \t\t\t#turns per phase\n", + "\n", + "#EMF of 1st 3rd and 5th harmonic\n", + "E_1ph = 4.44 * K_c1 * K_d1*phi_1 * f * T_ph\n", + "E_3ph = E_1ph* (B_m3*K_c3*K_d3)/(B_m1*K_c1*K_d1)\n", + "E_5ph = E_1ph* (B_m5*K_c5*K_d5)/(B_m1*K_c1*K_d1)\n", + "\n", + "# Results\n", + "# using E_xph = E_1ph* (B_mx*K_cx*K_dx)/(B_m1*K_c1*K_d1)\n", + "E_ph = math.sqrt( E_1ph**2 + E_3ph**2 + E_5ph**2 )\n", + "print 'Phase value of induced e.m.f is %.2f V '%(E_ph)\n", + "E_line = math.sqrt(3) * math.sqrt( E_1ph**2 + E_5ph**2 )\t\t\t#no 3rd harmonic appears in line value\n", + "print 'line value of induced e.m.f is %.2f V '%(E_line)\n", + "\n", + "print 'Answer mismatches due to approximation'\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Phase value of induced e.m.f is 1711.94 V \n", + "line value of induced e.m.f is 2916.65 V \n", + "Answer mismatches due to approximation\n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.13 page no : 47" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "Pole = 16.\n", + "phi = 0.03 \t\t\t#flux per pole\n", + "Ns = 375. \t\t\t#synchronous speed in rpm\n", + "\n", + "# Calculations and Results\n", + "f = Ns*Pole/120 \t\t\t#frequency\n", + "print 'frequency is %.0f Hz '%(f)\n", + "Slots = 144\n", + "n = Slots/Pole \t\t\t#slots per pole\n", + "m = n/3 \t\t\t#slots per pole per phase\n", + "beeta = 180/n \t\t\t#slot angle\n", + "K_c = 1 \t\t\t#assuming Full-Pitch coil\n", + "Conductors_per_slot = 10\n", + "K_d = math.sin(math.radians(m*beeta/2)) /(m*math.sin(math.radians(beeta/2))) \t\t\t#distribution factor\n", + "\n", + "Total_conductors = Slots*Conductors_per_slot\n", + "Total_turns = Total_conductors/2\n", + "T_ph = Total_turns/3 \t\t\t#turns per phase\n", + "E_ph = 4.44* K_c* K_d*phi* f* T_ph\n", + "E_line = E_ph*math.sqrt(3)\n", + "print 'line voltage is %.2f V '%(E_line)\n", + "\n", + "# note : rounding off error." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "frequency is 50 Hz \n", + "line voltage is 2657.20 V \n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.14 page no : 48" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "Ns = 250. \t\t\t#Speed in rpm\n", + "f = 50. \t\t\t#frequency\n", + "I_l = 100.\n", + "Slots = 216.\n", + "Conductors_per_slot = 5\n", + "Pole = 120.*f/Ns\n", + "phi = 30.*10**-3\t\t\t#flux per pole in weber\n", + "Z = Slots*Conductors_per_slot \t\t\t#Total Conductors\n", + "Z_ph = Z/3 \t\t\t#conductors per phase\n", + "T_ph = Z_ph/2 \t\t\t#turns per phase\n", + "n = Slots/Pole \t\t\t#slots per pole\n", + "m = n/3 \t\t\t#slots per pole per phase\n", + "beeta = 180./n \t\t\t#Slot angle\n", + "\n", + "# Calculations\n", + "K_d = math.sin(math.radians(m*beeta/2)) /(m*math.sin(math.radians(beeta/2))) \t\t\t#distribution factor\n", + "\n", + "e_av = 2*f*phi \t\t\t#Average Value of EMF in each conductor\n", + "E_c = 1.11*(2*f*phi) \t\t\t#RMS value of EMF in each conductor\n", + "E = 2*E_c*K_d \t\t\t#RMS value of EMF in each turn\n", + "E_ph = T_ph*E \t\t\t#RMS value of EMF in each phase\n", + "E_line = E_ph*math.sqrt(3) \t\t\t#As Star Connected Alternator\n", + "\n", + "# Results\n", + "print 'RMS value of EMF in each phase = %.3f V'%(E_ph)\n", + "print 'RMS value of EMF line value = %.3f V'%(E_line)\n", + "kVA_rating = math.sqrt(3)*E_line*I_l\n", + "print 'kVA rating is %.3f kVA '%(kVA_rating/1000)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "RMS value of EMF in each phase = 1150.602 V\n", + "RMS value of EMF line value = 1992.902 V\n", + "kVA rating is 345.181 kVA \n" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.15 page no : 50" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "Pole = 10.\n", + "Slots = 90.\n", + "E_l = 11000.\n", + "f = 50.\n", + "phi = 0.15 \t\t\t#flux per pole in weber\n", + "n = Slots/Pole \t\t\t#slots per pole\n", + "m = n/3 \t\t\t#slots per pole per phase\n", + "beeta = 180/n \t\t\t#slot angle\n", + " \n", + "# Calculations \n", + "K_d = math.sin(math.radians(m*beeta/2)) /(m*math.sin(math.radians(beeta/2))) \t\t\t#distribution factor\n", + "K_c = 1 \t\t\t#coil span factor\n", + "\n", + "E_ph = E_l/math.sqrt(3)\n", + "T_ph = ( E_ph/(4.44*K_c*K_d*phi*f) )\n", + "#T_ph should necessarily be an integer\n", + "Z_ph = (T_ph)*2 \n", + "\n", + "# Results\n", + "print 'Required number of armature conductors is %d'%(Z_ph)\n", + "\n", + "# note : rounding off error." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Required number of armature conductors is 397\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.16 page no : 50" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "Pole = 10.\n", + "Ns = 600. \t\t\t#speen in rpm\n", + "conductor_per_slot = 8.\n", + "n = 12. \t\t\t#slots per pole\n", + "Slots = Pole*n \n", + "m = n/3 \t\t\t#slots per pole per phase \n", + "beeta = 180/n \t\t\t#slot angle\n", + "alpha = 2*beeta \t\t\t#short by 2 slots\n", + "\n", + "#flux per pole corresponding to 1st 3rd and 5th harmonic\n", + "phi_1 = 100*10**-3\n", + "phi_3 = (33./100)*phi_1\n", + "phi_5 = (20./100)*phi_1\n", + "\n", + "#coil span factor corresponding to 1st 3rd and 5th harmonic\n", + "K_c1 = math.cos(math.radians( alpha/2))\n", + "K_c3 = math.cos(math.radians( 3*alpha/2))\n", + "K_c5 = math.cos(math.radians( 5*alpha/2))\n", + "\n", + "# using K_dx = math.sin(m*x*beeta /2) /(m*math.sin(x*beeta /2))\n", + "#distribution factor corresponding to 1st 3rd and 5th harmonic\n", + "K_d1 = math.sin(math.radians(m*1*beeta/2)) /(m*math.sin(math.radians(1*beeta /2)))\n", + "K_d3 = math.sin(math.radians(m*3*beeta/2)) /(m*math.sin(math.radians(3*beeta /2)))\n", + "K_d5 = math.sin(math.radians(m*5*beeta/2)) /(m*math.sin(math.radians(5*beeta /2)))\n", + "\n", + "Z = conductor_per_slot*n*Pole \t\t\t#Total Conductors\n", + "Zph = Z/3 \t\t\t#conductors per phase\n", + "T_ph = Zph/2 \t\t\t#turns per phase\n", + "\n", + "f = Ns*Pole/120\n", + "E_1ph = 4.44*K_c1*K_d1*phi_1*f*T_ph\n", + "E_3ph = 4.44*K_c3*K_d3*phi_3*f*T_ph\n", + "E_5ph = 4.44*K_c5*K_d5*phi_5*f*T_ph\n", + "\n", + "E_ph = math.sqrt( E_1ph**2 + E_3ph**2 + E_5ph**2 )\n", + "\n", + "# Results\n", + "print 'Phase value of induced e.m.f is %.0f V '%(E_ph)\n", + "E_line = math.sqrt(3)*math.sqrt( E_1ph**2 + E_5ph**2 ) \t\t\t#In a line value 3rd harmonic doesnt appear\n", + "print 'line value of induced e.m.f is %d V '%(E_line)\n", + "\n", + "# note : rounding off error." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Phase value of induced e.m.f is 3330 V \n", + "line value of induced e.m.f is 5691 V \n" + ] + } + ], + "prompt_number": 25 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.17 page no : 52" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "Pole = 6.\n", + "Ns = 1000. \t\t\t#speed in rpm\n", + "d = 28./100 \t\t\t#Divided by 100 to convert from centimeters to metres\n", + "l = 23./100 \t\t\t#Divided by 100 to convert from centimeters to metres\n", + "m = 4. \t \t\t#slots per pole per phase\n", + "B_m1 = 0.87 \t\t\t#amplitude of 1st harmonic component of flux density\n", + "B_m3 = 0.24 \t\t\t#amplitude of 3rd harmonic component of flux density\n", + "Conductors_per_slot = 8\n", + "f = Ns*Pole/120 \t\t\t#frequency\n", + "A1 = math.pi*d*l/Pole \t\t\t#area of each fundamental pole\n", + "phi_1 = (2/math.pi)*A1*B_m1 \t\t\t#flux per pole in weber\n", + "n = m*3 \t\t \t#slots per pole\n", + "beeta = 180/n \t\t\t#slot angle\n", + "alpha = beeta \t\t\t#because of 1 slot short\n", + "\n", + "# Calculations\n", + "K_c1 = math.cos(math.radians(alpha/2)) \t\t\t#coil span factor corresponding to 1st harmonic\n", + "K_c3 = math.cos(math.radians(3*alpha/2))\t\t\t#coil span factor corresponding to 3rd harmonic\n", + "# using K_dx = math.sin(m*x*beeta*(math.pi/180)/2) /(m*math.sin(x*beeta*(math.pi/180)/2))\n", + "K_d1 = math.sin(math.radians(m*1*beeta/2)) /(m*math.sin(math.radians(1*beeta/2))) \t\t\t#distribution factor corresponding to 1st harmonic\n", + "K_d3 = math.sin(math.radians(m*3*beeta/2)) /(m*math.sin(math.radians(3*beeta/2))) \t\t\t#distribution factor corresponding to 3rd harmonic\n", + "\n", + "Slots = n*Pole\n", + "Z = Slots*Conductors_per_slot \t\t\t#total number of conductors\n", + "Z_ph = Z/3 \t\t\t#conductors per phase\n", + "T_ph = Z_ph/2 \t\t\t#turns per phase\n", + "\n", + "E_1ph = 4.44*K_c1*K_d1*phi_1*f*T_ph\n", + "E_3ph = E_1ph* (B_m3*K_c3*K_d3)/(B_m1*K_c1*K_d1) \t\t\t#using E_xph = E_1ph* (B_mx*K_cx*K_dx)/(B_m1*K_c1*K_d1)\n", + "E_ph = math.sqrt( E_1ph**2 + E_3ph**2 )\n", + "print 'r.m.s value of resultant voltage is %.1f V'%(E_ph)\n", + "E_line = math.sqrt(3)*E_1ph \t\t\t#For line Value 3rd harmonic does not appear\n", + "print 'line voltage is %.3f V'%(E_line)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "r.m.s value of resultant voltage is 383.7 V\n", + "line voltage is 654.560 V\n" + ] + } + ], + "prompt_number": 26 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.18 page no : 53" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "V_L = 125.\n", + "V_ph = V_L\n", + "VA = 600.*10**3\n", + "I_L = VA/(math.sqrt(3)*V_L) \t\t\t# Because VA = math.sqrt(3)* V_L * I_L\n", + "I_ph = I_L/(math.sqrt(3))\n", + "\n", + "# Calculations and Results\n", + "#After Reconnection\n", + "V_ph = 125\n", + "V_L = V_ph*math.sqrt(3)\n", + "print 'New rating in volts is %.3f V'%(V_L)\n", + "#Winding Impedances remain the same\n", + "I_ph = 1600\n", + "I_L = I_ph\n", + "\n", + "print 'New rating in amperes is %.0f A'%(I_L)\n", + "kVA = math.sqrt(3)*V_L*I_L*(10**-3)\n", + "print 'New rating in kVA is %.0f kVA'%(kVA)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "New rating in volts is 216.506 V\n", + "New rating in amperes is 1600 A\n", + "New rating in kVA is 600 kVA\n" + ] + } + ], + "prompt_number": 27 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.19 page no : 55" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "Pole = 4.\n", + "f = 50. \t\t\t#frequency\n", + "phi = 0.12 \t\t\t#flux per pole in weber\n", + "m = 4. \t\t\t# slot per pole per phase\n", + "conductor_per_slot = 4.\n", + "coilspan = 150.\n", + "Ns = 120*f/Pole \t\t\t#synchronous speed in rpm\n", + "n = m*3 \t \t\t#Slots per pole\n", + "beeta = 180/n \t\t\t#slot angle\n", + "\n", + "# Calculations\n", + "K_d = math.sin(math.radians(m*beeta/2)) /(m*math.sin(math.radians(beeta/2))) \t\t\t# distribution factor\n", + "alpha = 180-coilspan \t\t\t#angle of short pitch\n", + "K_c = math.cos((math.pi/180)*alpha/2) \t\t\t#coil span factor\n", + "Z = m*(n*Pole) \t\t\t# Also equal to (conductors/slots)*slots\n", + "Z_ph = Z/3 \t\t\t#conductors per phase\n", + "T_ph = Z_ph/2 \t\t\t#turns per phase\n", + "E_ph = 4.44*K_c*K_d*phi*f*T_ph\n", + "E_line = math.sqrt(3)*E_ph\n", + "\n", + "# Results\n", + "print 'e.m.f generated is %.2f Vphase, %.2f Vline)'%(E_ph,E_line)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "e.m.f generated is 788.57 Vphase, 1365.84 Vline)\n" + ] + } + ], + "prompt_number": 28 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
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