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diff --git a/DC_Machines_and_Synchronous_Machines/ch7.ipynb b/DC_Machines_and_Synchronous_Machines/ch7.ipynb new file mode 100755 index 00000000..a22a6459 --- /dev/null +++ b/DC_Machines_and_Synchronous_Machines/ch7.ipynb @@ -0,0 +1,1711 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:95ca4467d5385b9a67e6a4c31c682e32bf0713e6d2ff74a5a89a56c51df83062" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 7 : Synchronous Motors" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.1 Page no : 27" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "import numpy as np\n", + "\n", + "# Variables\n", + "V_l = 400.\n", + "R_a = 0.2\n", + "X_s = 2. \t\t\t#armature resistance and synchronous reactance\n", + "I_L = 25.\n", + "I_aph = I_L\n", + "V_ph = V_l/math.sqrt(3)\n", + "Z_s = complex(R_a,X_s) \t\t\t#synchronous impedance\n", + "angle = math.atan(Z_s.imag/Z_s.real)\n", + "angle = math.degrees(angle)\n", + "E_Rph=I_aph*abs(Z_s)\n", + "theta = (math.pi/180.)*angle \n", + "\n", + "# Calculations and Results\n", + "#case 1\n", + "phi = math.acos(0.8) \t\t\t#lagging\n", + "E_bph = math.sqrt( (E_Rph)**2 + (V_ph)**2 -2*E_Rph*V_ph*math.cos(theta-phi) )\n", + "print 'i)Back EMF induced with 0.8 lagging pf is %.3f V'%(E_bph)\n", + "\n", + "#case 2\n", + "phi = math.acos(0.9) \t\t\t#leading\n", + "E_bph = math.sqrt( (E_Rph)**2 + (V_ph)**2 -2*E_Rph*V_ph*math.cos(theta+phi) )\n", + "print 'ii)Back EMF induced with 0.8 lagging pf is %.3f V'%(E_bph)\n", + "\n", + "#case 3\n", + "phi = math.acos(1)\n", + "E_bph = math.sqrt( (E_Rph)**2 + (V_ph)**2 -2*E_Rph*V_ph*math.cos(theta) )\n", + "print 'iii)Back EMF induced with 0.8 lagging pf is %.3f V'%(E_bph)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "i)Back EMF induced with 0.8 lagging pf is 200.386 V\n", + "ii)Back EMF induced with 0.8 lagging pf is 252.678 V\n", + "iii)Back EMF induced with 0.8 lagging pf is 231.406 V\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.2 Page no : 28" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "from numpy import *\n", + "\n", + "# Variables\n", + "V_l = 500.\n", + "R_a = 0.4\n", + "X_s = 4. \t\t\t#armature resistance and synchronous reactance\n", + "Z_s = complex(R_a,X_s)\t\t\t#synchronous impedance\n", + "angle = math.degrees(math.atan(Z_s.imag/Z_s.real))\n", + "theta = (math.pi/180)*angle\t\t\t#phasemag returns angle in degrees,not radians\n", + "V_ph = V_l/math.sqrt(3)\n", + "I_l = 50.\n", + "I_aph = I_l\n", + "E_Rph = I_aph*abs(Z_s)\n", + "\n", + "# Calculations and Results\t\t\n", + "#case 1\n", + "E_bline = 600\n", + "E_bph = E_bline/math.sqrt(3)\n", + "phi = math.acos( (-E_bph**2 + E_Rph**2 + V_ph**2 )/(2*E_Rph*V_ph) ) -theta \t\t\t#leading\n", + "#because E_bph = math.sqrt( (E_Rph)**2 + (V_ph)**2 -2*E_Rph*V_ph*math.cos(theta+phi) )\n", + "print 'i)power factor is %.4f leading'%(cos(phi))\n", + "\n", + "#case 2\n", + "E_bline = 380\n", + "E_bph = E_bline/math.sqrt(3)\n", + "phi = theta-math.acos( (-E_bph**2 + E_Rph**2 + V_ph**2 )/(2*E_Rph*V_ph) ) \t\t\t#leading\n", + "#because E_bph = math.sqrt( (E_Rph)**2 + (V_ph)**2 -2*E_Rph*V_ph*math.cos(theta-phi)\n", + "print 'ii)power factor is %.4f lagging'%(cos(phi))\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "i)power factor is 0.9977 leading\n", + "ii)power factor is 0.8197 lagging\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.3 Page no : 29" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "V_L = 6600.\n", + "P_out = 500.*10**3\n", + "eta = 83./100 \t\t\t#efficiency\n", + "R_a = 0.3\n", + "X_s = 3.2 \t\t\t#armature resistance and synchronous reactance\n", + "Z_s = complex(R_a,X_s) \t\t\t#synchronous impedance\n", + "angle = math.degrees(math.atan(Z_s.imag/Z_s.real))\n", + "theta = (math.pi/180)* angle \t\t\t#phasemag returns the angle in degrees not radians\n", + "phi = math.acos(0.8) \t\t\t#leading\n", + "V_ph = V_L/math.sqrt(3)\n", + "P_in = P_out/eta\n", + "\n", + "# Calculations and Results\n", + "I_L = P_in/ (math.sqrt(3) * V_L * math.cos(phi) )\n", + "\n", + "# because P_in = math.sqrt(3) * V_L * I_L * math.cos(phi)\n", + "I_aph = I_L\n", + "E_Rph = I_aph*abs(Z_s)\n", + "E_bph = math.sqrt( (E_Rph)**2 + (V_ph)**2 -2*E_Rph*V_ph*math.cos(theta+phi) )\n", + "print 'i) Generated EmF on full loaad is %.2f V'%(E_bph)\n", + "\n", + "delta = math.degrees(math.asin( (E_Rph/E_bph))*math.sin(theta+phi) )\n", + "#This is obtained after applying sune rule to triangle OAB from thre phasor diagram\n", + "print 'ii) load angle is %.2f degrees'%(delta)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "i) Generated EmF on full loaad is 3925.33 V\n", + "ii) load angle is 2.64 degrees\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.4 Page no : 32" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "from numpy import roots\n", + "\n", + "# Variables\n", + "V_L = 500.\n", + "V_ph = V_L/math.sqrt(3)\n", + "phi = math.acos(0.9) \t\t\t\t#lagging\n", + "output_power = 17.*10**3\n", + "R_a = 0.8 \t\t\t\t\t\t\t#armaature reactance\n", + "mechanical_losses = 1300. \t\t\t#mechanical losses is W\n", + "P_m = output_power+mechanical_losses \t\t\t#gross mechanical power developed\n", + "\n", + "# P_m = input_power - stator losses\n", + "# input_power = 3* V_ph * I_aph * math.cos(phi)\n", + "# Stator losses = 3*I_aph**2*R_a\n", + "# solving above equations we get 2.4 I_a**2 - 779/.4225*I_a + 18300 = 0\n", + "I_a_eqn = [2.4, -779.4225, 18300]\n", + "I_a_roots = roots(I_a_eqn)\n", + "I_a = I_a_roots[1] \t\t\t#neglecting higher value\n", + "I_aph = I_a\n", + "print 'Current drawn by the motor is %.3f A'%(I_a)\n", + "\n", + "input_power = 3* V_ph * I_aph * math.cos(phi)\n", + "eta = 100*output_power/input_power\n", + "print 'Full load efficiency is %.2f percent'%(eta)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Current drawn by the motor is 25.478 A\n", + "Full load efficiency is 85.61 percent\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.5 Page no : 44" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "#subscript 1 is for industrial load and 2 for synchronous motor\n", + "P_1 = 800. \t\t\t# Active power in KW\n", + "phi_1 = math.acos(0.6) \t\t\t#lagging\n", + "Q_1 = P_1*math.tan(phi_1) \t\t\t#reactive power by load 1\n", + "\n", + "# Calculations and Results\n", + "output_power = 200.\n", + "eta = 91./100 \t\t\t#efficiency of synchronous motor\n", + "input_power = output_power/eta\n", + "P_2 = input_power\t\t\t# active power drawn by synchronous motor\n", + "P_T = P_1 + P_2 \t\t\t#combined total load of industry and synchronous motor\n", + "phi_T = math.acos(0.92 )\t\t\t#lagging\n", + "Q_T = P_T* math.tan(phi_T) \t\t\t#from power triangle\n", + "Q_2 = Q_T - Q_1 \t\t\t#it turns out to be negative indicating its leading nature\n", + "S_2 = math.sqrt( P_2**2 + Q_2**2 )\n", + "print 'Desired kVA rating of Synchronous motor is %.3f kVA'%(S_2)\n", + "\n", + "phi_2 = math.atan (Q_2/P_2)\n", + "print 'Power factor of synchronous motor is %.4f LEADING'%(math.cos(phi_2))\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Desired kVA rating of Synchronous motor is 669.353 kVA\n", + "Power factor of synchronous motor is 0.3283 LEADING\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.6 Page no : 47" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "V_L = 400.\n", + "output_power = 37.3*1000 \t\t\t#Watts on full load\n", + "Z_s = complex(0.2,1.6) \t\t\t#synchronous impedance\n", + "angle = math.degrees(math.atan(Z_s.imag/Z_s.real))\n", + "theta = (math.pi/180)*angle \t\t\t#phase mag returns the angle in degrees and not raidians\n", + "phi = math.acos(0.9) \t\t\t#leading\n", + "V_ph = V_L/math.sqrt(3)\n", + "eta = 88. \t\t\t#efficiency in percentage\n", + "\n", + "# Calculations\n", + "input_power = 100*output_power/eta\n", + "I_L = input_power/(math.sqrt(3)*V_L*math.cos(phi))\n", + "I_aph = I_L\n", + "E_Rph = I_aph*abs(Z_s)\n", + "\n", + "E_bph = math.sqrt( (E_Rph)**2 + (V_ph)**2 -2*E_Rph*V_ph*math.cos(theta+phi) )\n", + "E_line = math.sqrt(3)*E_bph\n", + "\n", + "# Results\n", + "print 'Induced EMF is %.2f V and its line value is %.2f V'%(E_bph,E_line)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Induced EMF is 285.65 V and its line value is 494.75 V\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.7 Page no : 48" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "V_L = 400.\n", + "input_power = 20.*1000 \n", + "R_a = 0.\n", + "X_s = 4. \t\t\t#armature reactance and synchronous reactance\n", + "Z_s = complex(R_a,X_s) \t\t\t#synchronous impedance\n", + "angle = math.degrees(math.atan(Z_s.imag))\n", + "\n", + "theta = (math.pi/180)*angle \t\t\t#phase mag returns the angle in degrees and not raidians\n", + "V_ph = V_L/math.sqrt(3)\n", + "E_bline = 550. \t\t\t#star connection\n", + "E_bph = E_bline/math.sqrt(3)\n", + "\n", + "# Calculations\n", + "I_a_cos_phi = input_power/(math.sqrt(3)*V_L) \t\t\t#product of I_a and math.cos(phi)\n", + "I_a_sin_phi = ( math.sqrt(E_bph**2- (abs(Z_s)*I_a_cos_phi)**2 ) -V_ph )/abs(Z_s)\t\t\t#from triangle DAB\n", + "phi = math.atan(I_a_sin_phi/I_a_cos_phi)\n", + "I_a = I_a_cos_phi/math.cos(phi) \n", + "\n", + "# Results\n", + "print 'Motor power fctor is %.3f Leading'%(cos(phi))\n", + "print 'Current drawn by the motor is %.2f A'%(I_a)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Motor power fctor is 0.872 Leading\n", + "Current drawn by the motor is 33.11 A\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.8 Page no : 50" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "V_L = 3300.\n", + "V_ph = V_L/math.sqrt(3)\n", + "R_a = 2.\n", + "X_s = 18. \t\t\t#armature reactance and synchronous reactance\n", + "Z_s = complex(R_a,X_s)\t\t\t#synchronous impedance\n", + "angle = math.degrees(math.atan(Z_s.imag/Z_s.real))\n", + "\n", + "theta = (math.pi/180)*angle \t\t\t#phasemag returns angle in degrees not radians\n", + "E_bline = 3800.\n", + "E_bph = E_bline/math.sqrt(3)\n", + "\n", + "#part(i)\n", + "P_m_max = (E_bph*V_ph/abs(Z_s))- (E_bph**2/abs(Z_s))*math.cos(theta)\n", + "print 'i)Max total mechanical power developed that motor can develop is %.2f W per phase'%(P_m_max)\n", + "\n", + "#part(ii)\n", + "#from phasor diagram applying math.comath.sine rule to triangle OAB\n", + "E_Rph = math.sqrt( E_bph**2 + V_ph**2 -2*E_bph*V_ph*math.cos(theta) ) \n", + "I_aph = E_Rph/abs(Z_s)\n", + "print 'ii)Current at max power developed is %.1f A'%(I_aph)\n", + "\n", + "copper_loss = 3* I_aph**2 * R_a\n", + "P_in_max_total = 3 * P_m_max \t\t\t#input power at max power developed\n", + "total_P_in = P_in_max_total + copper_loss \t\t\t#total input power \n", + "pf = total_P_in/(math.sqrt(3)*I_aph*V_L)\n", + "print 'Power factor at max power developed is %.3f leading'%(pf)\n", + "\n", + "\n", + "# 'Answer in part1 mismatched because of improper approximation in book'\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "i)Max total mechanical power developed that motor can develop is 201452.30 W per phase\n", + "ii)Current at max power developed is 151.4 A\n", + "Power factor at max power developed is 0.857 leading\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.9 Page no : 51" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "V_L = 500.\n", + "R_a = 0.03\n", + "X_s = 0.3 \t\t\t#armature reactance and synchronous reactance\n", + "Z_s = complex(R_a,X_s)\t\t\t#synchronous impedance\n", + "angle = math.degrees(math.atan(Z_s.imag/Z_s.real))\n", + "\n", + "theta = (math.pi/180)*angle \t\t\t#phasemag returns angle in degrees not radians\n", + "phi = math.acos(0.8)\n", + "eta = 93/100.\n", + "output_power = 100.*746\n", + "input_power = output_power/eta\n", + "I_L = input_power/(math.sqrt(3)*V_L*math.cos(phi))\n", + "I_aph = I_L\n", + "E_Rph = I_aph*abs(Z_s)\n", + "\n", + "#from the phasor diagram\n", + "E_bph = math.sqrt( E_Rph**2 + (V_L/math.sqrt(3))**2 - 2*E_Rph*(V_L/math.sqrt(3))*math.cos(phi+theta) ) \n", + "\n", + "cu_losses = 3*(I_aph)**2*R_a \t\t\t#total copper losses\n", + "P_m = input_power - cu_losses \t\t\t#total mechanical power developed\n", + "\n", + "print 'EMF developed per phase is %.4f V \\nTotal mechanical power developed is %.1f watts'%(E_bph,P_m)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "EMF developed per phase is 308.1880 V \n", + "Total mechanical power developed is 79008.6 watts\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.10 Page no : 53" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "V_L = 415.\n", + "V_ph = V_L \t\t\t#due to delta connection\n", + "E_bline = 520.\n", + "R_a = 0.5\n", + "X_s = 4. \t\t\t#armature reactance and synchronous reactance\n", + "Z_s = complex(R_a,X_s) \t\t\t#synchronous impedance\n", + "angle = math.degrees(math.atan(Z_s.imag/Z_s.real))\n", + "\n", + "theta = (math.pi/180.)*angle \t\t\t#phasemag returns angle in degrees not radians\n", + "\n", + "delta = theta \t\t\t#for maximum power\n", + "P_m_max = (E_bline*V_ph/abs(Z_s))- (E_bline**2/abs(Z_s))*math.cos(theta)\n", + "P_m_max_total = 3* P_m_max\n", + "fi_loss = 1000. \t\t\t#frictional and iron losses\n", + "P_out_total = P_m_max_total-fi_loss \n", + "\n", + "HP_output = P_out_total/746 \t\t\t#converting watts to horse power\n", + "print 'HP output for maximum power output is %.2f HP'%(HP_output)\n", + "\n", + "#from the phasor diagram\n", + "E_Rph = math.sqrt( E_bline**2 + V_ph**2 -2*E_bline*V_ph*math.cos(delta) ) \n", + "I_aph = E_Rph/abs(Z_s)\n", + "I_L = I_aph*math.sqrt(3)\n", + "print 'Line current is %f A'%(I_L)\n", + "cu_loss_total = 3*(I_aph)**2*R_a \t\t\t#total copper losses\n", + "input_power = P_m_max_total+ cu_loss_total\n", + "pf = input_power/(math.sqrt(3)*I_L*V_L) \t\t\t#leading\n", + "print 'Power factor for maximum power output is %.2f leading '%(pf)\n", + "\n", + "eta = 100*P_out_total /input_power\n", + "print 'Efficiency for maximum power output is %.2f percent'%(eta)\n", + "\n", + "# 'Answer might mismatch because of improper approximation done in book'\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "HP output for maximum power output is 180.48 HP\n", + "Line current is 268.015479 A\n", + "Power factor for maximum power output is 0.89 leading \n", + "Efficiency for maximum power output is 78.48 percent\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.11 Page no : 54" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "P = 8.\n", + "f = 50. \t\t\t#Pole and frequency\n", + "N_s = 120.*f/P \t\t\t#synchronous speed\n", + "V_L = 6.6*10**3 \n", + "V_ph = V_L/math.sqrt(3)\n", + "Z_s = complex(0.66,6.6) \t\t\t#synchronous impedance\n", + "angle = math.degrees(math.atan(Z_s.imag/Z_s.real))\n", + "\n", + "theta = (math.pi/180)*angle \t\t\t#phasemag returns angle in degree not radians\n", + "E_bph = 4500.\n", + "input_power = 2500.*10**3\n", + "I_a_cosphi = input_power/(math.sqrt(3)*V_L) \t\t\t#Its product of I_a and math.cos(phi);I_a = I_l for star conneted load\n", + "\n", + "# Calculations\n", + "#applying math.comath.sine rule to triangle ABC from phasor diagram and solve \n", + "#math.tan(phi)**2 + 5.2252 math.tan(phi)-2.2432 = 0\n", + "p = [1, 5.2252, -2.2432]\n", + "tan_phi = roots(p)\n", + "phi = math.atan(tan_phi[1])\n", + "pf = math.cos(phi)\n", + "I_a = I_a_cosphi/ math.cos(phi)\n", + "\n", + "#apply math.sine rule to triangle ABC\n", + "delta = math.asin(I_a*abs(Z_s)*math.sin(theta+phi)/E_bph)\n", + "P_m = 3*E_bph*I_a*math.cos(delta+phi)\n", + "T_g = P_m/(2*math.pi*N_s/60)\n", + "\n", + "# Results\n", + "print 'i)Torque developed is %f N-m'%(T_g)\n", + "print 'ii)Input current is %.4f A'%(I_a)\n", + "print 'iii)Power factor is %.4f leading'%(pf)\n", + "print 'iv)Power angle is %.2f degrees '%((180/math.pi)*delta)\n", + "\n", + "# note : rounding off error." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "i)Torque developed is 30437.047497 N-m\n", + "ii)Input current is 235.4472 A\n", + "iii)Power factor is 0.9288 leading\n", + "iv)Power angle is 19.48 degrees \n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.12 Page no : 57" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "from numpy import roots\n", + "\n", + "# Variables\n", + "input_power = 15.*10**3\n", + "V_L = 400.\n", + "V_ph = V_L/math.sqrt(3)\n", + "E_b = 480.\n", + "E_bph = E_b/math.sqrt(3)\n", + "Z_s = complex(1,5) \t\t\t#synchronous impedance\n", + "angle = math.degrees(math.atan(Z_s.imag/Z_s.real))\n", + "\n", + "theta = (math.pi/180)*angle \t\t\t#phasemag returns angle in degree not radians\n", + "\n", + "# Calculations\n", + "I_a_cosphi = input_power/(math.sqrt(3)*V_L) \t\t\t#product of I_a & math.cos(phi)\n", + "#Applying math.comath.sine rule to triangle OAB and solving\n", + "#math.tan(phi)**2+ 4.101*math.tan(phi)-1.7499 = 0\n", + "p = [1,4.101,-1.7449]\n", + "tan_phi = roots(p)\n", + "phi = math.atan(tan_phi[1]) \t\t\t#ignoring negative vaule\n", + "I_a = I_a_cosphi/ math.cos(phi)\n", + "\n", + "#applying math.sine rule to Triangle OAB\n", + "delta = math.asin( I_a*abs(Z_s)* math.sin(theta+phi)/E_bph )\n", + "\n", + "# Results\n", + "print 'Load angle is %.1f degrees'%(delta*180/math.pi)\n", + "print 'Armature current is %.4f A'%(I_a)\n", + "print 'Power factor is %.3f leading'%(cos(phi))\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Load angle is 24.9 degrees\n", + "Armature current is 23.2283 A\n", + "Power factor is 0.932 leading\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.13 Page no : 59" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "from numpy import roots\n", + "\n", + "# Variables\n", + "V_L = 400.\n", + "V_ph = V_L/math.sqrt(3)\n", + "E_b = 460.\n", + "E_bph = E_b/math.sqrt(3)\n", + "input_power = 3.75*10**3\n", + "Z_s = complex(1,8) \t\t\t#synchronous impedance\n", + "angle = math.degrees(math.atan(Z_s.imag/Z_s.real))\n", + "\n", + "theta = math.degrees(angle) \t\t\t#phasemag returns angle in degree ,not radians\n", + "I_L_cos_phi = input_power/(math.sqrt(3)*V_L)\n", + "\n", + "# Calculations and Results\n", + "#Applying math.comath.sine rule to triangle OAB and solving further\n", + "#math.tan(phi)**2 + 458.366*math.tan(phi) -450.65 = 0 \n", + "p = [1,458.366-450.65]\n", + "tan_phi = roots(p)\n", + "\n", + "phi = math.atan(tan_phi[0]) \t\t\t#ignoring negative value\n", + "print 'Required power factor is %.4f leading'%(cos(phi))\n", + "I_L = I_L_cos_phi /math.cos(phi)\n", + "print 'Required current is %.4f A'%(I_L)\n", + "\n", + "# roots() python gives some different answer. Kindly check." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Required power factor is 0.1285 leading\n", + "Required current is 42.1134 A\n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.14 Page no : 60" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "#subscript 1 indicates induction motor 1\n", + "P_1 = 350.\n", + "phi_1 = math.acos(0.7071) \t\t\t#lagging\n", + "Q_1 = P_1*math.tan(phi_1)\t\t\t#from power triangle\n", + "\n", + "#subscript 2 indicates induction motor 2\n", + "P_2 = 190.\n", + "\n", + "# Calculations\n", + "#subscript T indicates total\n", + "P_T = P_1+P_2\n", + "phi_T = math.acos(0.9) \t\t\t#lagging\n", + "Q_T = P_T*math.tan(phi_T)\n", + "\n", + "Q_2 = Q_T-Q_1\n", + "kva_rating = math.sqrt(P_2**2+ Q_2**2)\n", + "\n", + "# Results\n", + "print 'kVA rating of synchronous motor is %.2f kVA'%(kva_rating)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "kVA rating of synchronous motor is 209.59 kVA\n" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.15 Page no : 61" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "V_L = 400.\n", + "V_ph = V_L/math.sqrt(3)\n", + "Pole = 6.\n", + "f = 50.\n", + "R_a = 0.2\n", + "X_s = 3. \t\t\t#armature reactance and synchronous reactance\n", + "Z_s = complex(R_a,X_s)\t\t\t#synchronous impedance\n", + "theta = math.atan(Z_s.imag/Z_s.real) # calculates angle in radians\n", + "\n", + "N_s = 120*f/Pole \t\t\t#synchronous speed\n", + "\n", + "# Calculations\n", + "#subscript 1` refers to load 1\n", + "I_a1 = 20.\n", + "phi_1 = math.acos(1)\n", + "E_R1 = I_a1* abs(Z_s)\n", + "E_bph = math.sqrt( E_R1**2 + V_ph**2 - 2*E_R1*V_ph*math.cos(phi_1+theta) )\n", + "\n", + "#subscript 2` refers to load 2\n", + "I_a2 = 60.\n", + "E_R2 = I_a2* abs(Z_s)\n", + "phi_2 = math.acos ((E_R2**2 + V_ph**2 -E_bph**2 )/(2*E_R2*V_ph)) -theta \t\t\t#new power factor\n", + "\n", + "input_power = math.sqrt(3)*V_L*I_a2*math.cos(phi_2)\n", + "cu_loss = 3*I_a2**2*R_a\n", + "P_m = input_power-cu_loss\n", + "T_g = P_m /(2*math.pi*N_s/60) \t\t\t#gross mechanical power developed\n", + "\n", + "# Results\n", + "print 'Gross torque developed is %.4f N-m and new power factor is %.4f lagging'%(T_g,cos(phi_2))\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Gross torque developed is 357.1971 N-m and new power factor is 0.9518 lagging\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.16 Page no : 63" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "V_L = 3300.\n", + "V_ph = V_L/math.sqrt(3)\n", + "E_bph = V_ph\n", + "Z_s = complex(0.5,5) \t\t\t#synchronous impedance\n", + "angle = math.degrees(math.atan(Z_s.imag/Z_s.real))\n", + "\n", + "theta = (math.pi/180)*angle \t\t\t#phasemag returns angle in degrees, not radians\n", + "P = 8.\n", + "f = 50. \t\t\t#pole and frequency\n", + "delta_mech = 3. \t\t\t#mechanical angle in degrees by which rotor is behind\n", + "delta_elec = (P/2)*delta_mech \t\t\t#delta mech converted to electrical degrees\n", + "E_Rph = math.sqrt( E_bph**2 + V_ph**2 -2*E_bph*V_ph*math.cos(math.radians(delta_elec) )) \n", + "I_aph = E_Rph/abs(Z_s)\n", + "\n", + "#from the phasor diagram \n", + "phi = theta- math.asin( math.sin(math.radians(delta_elec))*E_bph/E_Rph )\n", + "pf = math.cos(phi)\n", + "print 'power factor of the motor is %.5f lagging'%(pf)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "power factor of the motor is 0.99999 lagging\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.17 Page no : 64" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "V_L = 400.\n", + "V_ph = V_L/math.sqrt(3)\n", + "E_bph = V_ph\n", + "P = 4.\n", + "f = 50.\t\t\t#Pole and frequency\n", + "delta_mech = 4*(math.pi/180) \t\t\t#mechanical angle in degrees by which rotor is behind\n", + "delta_elec = delta_mech *(P/2) \t\t\t#delta_mech convertd to electrical degrees\n", + "Z_s = complex(0,2) \t\t\t#synchronous impedance\n", + "\n", + "# Calculations\n", + "#referring to phasor diagram\n", + "BC = E_bph*math.sin(delta_elec)\n", + "AB = E_bph\n", + "OA = V_ph\n", + "\n", + "AC = math.sqrt(AB**2-BC**2)\n", + "OC = OA-AC\n", + "phi = math.atan(OC/BC)\n", + "OB = math.sqrt(OC**2 + BC**2)\n", + "I_a = OB/abs(Z_s)\n", + "\n", + "# Results\n", + "print 'Armature current drawn by the motor is %.4f A'%(I_a)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Armature current drawn by the motor is 16.1096 A\n" + ] + } + ], + "prompt_number": 23 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.18 Page no : 65" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "V_L = 400.\n", + "V_ph = V_L/math.sqrt(3)\n", + "input_power = 5472.\n", + "Z_s = complex(0,10) \t\t\t#synchronous impedance\n", + "I_L_cosphi = input_power/(math.sqrt(3)*V_L) \t\t\t#product of I_L & math.cos(phi)\n", + "BC = 10*I_L_cosphi\n", + "AB = V_ph\n", + "OA = V_ph\n", + "\n", + "# Calculations\n", + "#from Triangle ABC in phasor diagram\n", + "AC = math.sqrt(AB**2- BC**2)\n", + "OC = OA - AC\n", + "\n", + "\t\t\t#from Triangle OCB \n", + "OB = math.sqrt( OC**2+ BC**2 )\n", + "E_Rph = OB\n", + "I_L = E_Rph/abs(Z_s)\n", + "\n", + "phi = math.atan(OC/BC)\n", + "pf = math.cos(phi)\n", + "delta = math.atan(BC/AC) \t\t\t#load angle\n", + "\n", + "# Results\n", + "print 'Power factor is %.4f lagging'%(pf)\n", + "print 'Load angle is %.0f degrees'%(delta*180/math.pi)\n", + "print 'Armature current is %.3f A'%(I_L)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Power factor is 0.9848 lagging\n", + "Load angle is 20 degrees\n", + "Armature current is 8.020 A\n" + ] + } + ], + "prompt_number": 24 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.19 Page no : 67" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "V_L = 6600.\n", + "V_ph = V_L/math.sqrt(3)\n", + "Z_s = complex(2,20) \t\t\t#synchronous impedance\n", + "angle = math.degrees(math.atan(Z_s.imag/Z_s.real))\n", + "\n", + "theta = (math.pi/180) * angle \t\t\t#phasemag returns angle in degrees not radians\n", + "P_1 = 1000*10**3\n", + "P_2 = 1500*10**3\n", + "phi_1 = math.acos(0.8) \t\t\t#leading\n", + "\n", + "# Calculations\n", + "I_L1 = P_1/(math.sqrt(3)*V_L*math.cos(phi_1))\n", + "I_a1ph = I_L1\n", + "E_R1ph = I_a1ph*abs(Z_s)\n", + "E_bph = math.sqrt( V_ph**2 + E_R1ph** -2*V_ph*E_R1ph*math.cos(theta+phi_1) )\n", + "I_a2_cosphi_2 = P_2/(math.sqrt(3)*V_L)\n", + "\n", + "#Refer to the phasor diagram and solving for I_y\n", + "#404I_y**2 -152399.968 I_y -4543000 = 0\n", + "p = [404, -152399.968, -4543000]\n", + "ans = roots(p)\n", + "I_y = abs(ans[1]) \t\t\t#becuase root 1 is too high and root is -ve\n", + "\n", + "I_a2 = complex(I_a2_cosphi_2,I_y)\n", + "phi_2 = math.degrees(math.atan(I_a2.imag/I_a2.real))\n", + "\n", + "print 'Required power factor is %.3f leading'%(math.cos(math.radians(phi_2)))\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Required power factor is 0.978 leading\n" + ] + } + ], + "prompt_number": 25 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.20 Page no : 69" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "V_L = 2300.\n", + "V_ph = V_L/math.sqrt(3)\n", + "I_L = 200.\n", + "I_a = I_L\n", + "Z_s = complex(0.2,2.2) \t\t\t#synchronous impedance\n", + "theta = math.atan(Z_s.imag/Z_s.real)\n", + "phi = math.acos(0.5)\n", + "\n", + "# Calculations\n", + "E_Rph = I_a*abs(Z_s)\n", + "E_bph = math.sqrt( E_Rph**2 + V_ph**2 - 2*E_Rph*V_ph*math.cos(phi+theta) ) \n", + "\n", + "# Results\n", + "print 'Generated EMF per phase is %.3f V'%(E_bph)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Generated EMF per phase is 1708.045 V\n" + ] + } + ], + "prompt_number": 26 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.21 Page no : 69" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "V_L = 3300.\n", + "V_ph = V_L/math.sqrt(3)\n", + "E_bline = 3800.\n", + "E_bph = E_bline/math.sqrt(3)\n", + "\n", + "R_a = 2.\n", + "X_s = 18. \t\t\t#armature resistance and synchronous reactance\n", + "Z_s = complex(R_a,X_s) \t\t\t#synchronous impedance\n", + "theta = math.atan(Z_s.imag/Z_s.real)\n", + "\n", + "#part(i)\n", + "P_m_max = (E_bph*V_ph/abs(Z_s))- (E_bph**2/abs(Z_s))*math.cos(theta) \t\t\t#maximum total mechanical power\n", + "print 'i)Maximum total mechanical power that the motor can develop is %.2f W per phase'%(P_m_max )\n", + "#part(ii)\n", + "delta = theta \t\t\t#for max P_m\n", + "E_Rph = math.sqrt( E_bph**2 + V_ph**2 -2*E_bph*V_ph*math.cos(delta) ) \n", + "I_aph = E_Rph/abs(Z_s)\n", + "print 'ii)Current at maximum power developed is %.1f A'%(I_aph)\n", + "cu_loss_total = 3*I_aph**2*R_a \t\t\t#total copper loss\n", + "P_m_max_total = 3*P_m_max \t\t\t#total maximum total mechanical power\n", + "P_in_total = P_m_max_total+ cu_loss_total \t\t\t#total input power\n", + "\n", + "pf = P_in_total/(math.sqrt(3)*V_L*I_aph)\n", + "print ' Power factor at maximum power developed is %.3f leading'%(pf)\n", + "\n", + "# note : rounding off error." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "i)Maximum total mechanical power that the motor can develop is 201452.30 W per phase\n", + "ii)Current at maximum power developed is 151.4 A\n", + " Power factor at maximum power developed is 0.857 leading\n" + ] + } + ], + "prompt_number": 28 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.22 Page no : 71" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "#subscript 1 refers to load 1\n", + "I_1 = 18.\n", + "phi_1 = math.acos(0.8)\n", + "V_L = 440.\n", + "S_1 = math.sqrt(3)*I_1*V_L /1000 \t\t\t#kVA for load 1\n", + "P_1 = S_1*math.cos(phi_1)\n", + "Q_1 = S_1*math.sin(phi_1)\n", + "\n", + "# Calculations\n", + "P_out = 6.\n", + "eta_motor = 88./100\n", + "P_2 = P_out/eta_motor\n", + "\n", + "P_T = P_1+P_2\n", + "phi_T = math.acos(1) \t\t\t#total power factor angle\n", + "Q_T = P_T*math.tan(phi_T)\n", + "\n", + "Q_2 = Q_T - Q_1 \t\t\t#kVAR supplied by motor\n", + "#this will have a negative sign just indicating its leading nature \n", + "phi_2 = math.atan(abs(Q_2)/P_2)\n", + "pf = math.cos(phi_2) \t\t\t#leading\n", + "S_2 = P_2/math.cos(phi_2) \t\t\t#kVA input to the motor\n", + "\n", + "# Results\n", + "print 'kVA input to the motor is %.3f kVA '%(S_2)\n", + "print 'Power factor when driving a 6kW mechanical load is %.4f leading'%(pf)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "kVA input to the motor is 10.688 kVA \n", + "Power factor when driving a 6kW mechanical load is 0.6379 leading\n" + ] + } + ], + "prompt_number": 29 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.23 Page no : 72" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "output_power = 8.*10**3\n", + "V_L = 400.\n", + "V_ph = V_L/math.sqrt(3)\n", + "R_a = 0.\n", + "X_s = 8.\t\t\t#armature resistance and syncronous reactance\n", + "Z_s = complex(R_a,X_s) \t\t\t#synchronous impedance\n", + "theta = math.atan(Z_s.imag) \t\t\t# returns angle in radians \n", + "eta = 88./100\n", + "input_power = output_power/eta\n", + "\n", + "# Calculations and Results\n", + "#minimum current occurs at max power factors\n", + "phi = math.acos(1)\n", + "I_a_min = input_power/(math.sqrt(3)*V_L*math.cos(phi)) \t\t\t#required minimum current \n", + "print 'Minimum current is %.3f A'%(I_a_min)\n", + "E_R = I_a_min * abs(Z_s)\n", + "E_bph = math.sqrt( E_R**2 + V_ph**2 - 2*E_R*V_ph*math.cos(phi+theta) ) \n", + "print 'Induced EMF at full-load is %.3f V'%(E_bph)\n", + "\n", + "# note : rounding off error." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Minimum current is 13.122 A\n", + "Induced EMF at full-load is 241.534 V\n" + ] + } + ], + "prompt_number": 31 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.24 Page no : 73" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "R_a = 0.8\n", + "X_s = 5.\n", + "Z_s = complex(R_a,X_s) \t\t\t#armature resistance and syncronous reactance\n", + "theta = math.atan(Z_s.imag/Z_s.real) \t\t\t# returns angle in radians \n", + "alpha = (math.pi/2) - theta\n", + "V_t = 3300/math.sqrt(3)\n", + "P_e_in = 800./(3) \t\t\t#per phase\n", + "phi = math.acos(0.8) \t\t\t#leading\n", + "Q_e_in = -P_e_in*math.tan(phi)\n", + "\n", + "# Calculations\n", + "# using the following equation\n", + "# P_e_in = V_t**2*R_a/(abs(Z_s))**2 + V_t*E_b*math.sin(delta-alpha)/abs(Z_S)\n", + "# Q_e_in = V_t**2*X_s/(abs(Z_s))**2 - V_t*E_b*math.cos(delta-alpha)/abs(Z_S)\n", + "E_b_sin_delta_minus_9 = 407.2\n", + "E_b_cos_delta_minus_9 = 2413.6\n", + "#solving further\n", + "delta = math.atan(E_b_sin_delta_minus_9/E_b_cos_delta_minus_9 ) + 9\n", + "E_b = E_b_sin_delta_minus_9/math.sin(math.radians(delta-9))\n", + "\n", + "P_e_in_new = 1200*10**3/3\n", + "# using the following equation again\n", + "# P_e_in = V_t**2*R_a/(abs(Z_s))**2 + V_t*E_b*math.sin(delta-alpha)/abs(Z_S)\n", + "# Q_e_in = V_t**2*X_s/(abs(Z_s))**2 - V_t*E_b*math.cos(delta-alpha)/abs(Z_S)\n", + "\n", + "alpha = delta - math.asin(math.radians(P_e_in_new - V_t**2*R_a/(abs(Z_s))**2 ) / (V_t*E_b/abs(Z_s)))\n", + "Q_e_in_new = V_t**2*X_s/(abs(Z_s))**2 - V_t*E_b*math.cos(math.radians(delta - alpha))/abs(Z_s)\n", + "\n", + "pf = math.cos ( math.atan(abs(Q_e_in_new/P_e_in_new)))\n", + "\n", + "# Results\n", + "print 'New power factor is %.2f leading '%(pf)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "New power factor is 0.01 leading \n" + ] + } + ], + "prompt_number": 33 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.25 Page no : 74" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "V_L = 6.6*10**3\n", + "V_ph = V_L/math.sqrt(3)\n", + "P_in = 900.*10**3\n", + "R_a = 0.\n", + "X_s = 20. \t\t\t#armature resistance and synchronous reactance \n", + "Z_s = complex(R_a,X_s) \t\t\t#synchronous impedance\n", + "theta = math.atan(Z_s.imag) \t\t\t# returns angle in radians \n", + "E_b_L = 8.6*10**3\n", + "E_bph = E_b_L/math.sqrt(3) \n", + "\n", + "# Calculations\n", + "#refer to phasor diagram\n", + "OA = V_ph\n", + "AB = E_bph \t\t\t#OB = E_Rph\n", + "\n", + "I_a_cosphi = P_in/(math.sqrt(3)*V_L) \t\t\t#I_a*math.cos(phi)\n", + "BC = I_a_cosphi*abs(Z_s) \t\t\t#BC is a vector in phasor diagram\n", + "\n", + "OC = math.sqrt(AB**2 -BC**2 )- OA \t\t\t#from phasor diagram\n", + "I_a_sinphi = OC/abs(Z_s) \t\t\t#product of I_a and math.sin(phi)\n", + "phi = math.atan (I_a_sinphi/I_a_cosphi)\n", + "I_a = I_a_cosphi/math.cos(phi) \t\t\t#product of I_a and math.cos(phi)\n", + "\n", + "# Results\n", + "print 'Motor current is %.3f A'%(I_a)\n", + "print 'Power factor of motor is %f leading'%(cos(phi))\n", + "print 'Note:There is slight mismatch in answer due to the approximation made during I_a* sinphi calculation'\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Motor current is 90.643 A\n", + "Power factor of motor is 0.868564 leading\n", + "Note:There is slight mismatch in answer due to the approximation made during I_a* sinphi calculation\n" + ] + } + ], + "prompt_number": 34 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.26 Page no : 75" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "\n", + "# Variables\n", + "#subscipt 1 refers to factory load\n", + "P_1 = 1800.\n", + "phi_1 = math.acos(0.6) \t\t\t#lagging\n", + "Q_1 = P_1*math.tan(phi_1)\n", + "\n", + "#Subscript 2 refers to synchronous condenser\n", + "P_2 = 0.\n", + "\n", + "# Calculations\n", + "#Subscript T refers to combination of condenser and factory load\n", + "P_T = P_1+P_2\n", + "phi_T = math.acos(0.95) \t\t\t#lagging\n", + "Q_T = P_T*math.tan(phi_T)\n", + "\n", + "kva_rating = math.sqrt(P_T**2+ Q_T**2)\n", + "\n", + "Q_2 = Q_T - Q_1\n", + "\n", + "# Results\n", + "print 'i)kVA rating of synchronous condender is %.3f kVA Minus sign indicates leading nature'%(Q_2)\n", + "print 'ii)kVA rating of total factory is %.4f kVA'%(kva_rating)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "i)kVA rating of synchronous condender is -1808.369 kVA Minus sign indicates leading nature\n", + "ii)kVA rating of total factory is 1894.7368 kVA\n" + ] + } + ], + "prompt_number": 35 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.27 Page no : 77" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "I_1 = 35.\n", + "phi_1 = math.acos(0.8)\n", + "V_L = 440.\n", + "S_1 = math.sqrt(3)*I_1*V_L /1000 \t\t\t#in kVA\n", + "\n", + "\n", + "# Calculations\n", + "P_1 = S_1*math.cos(phi_1)\n", + "Q_1 = S_1*math.sin(phi_1)\n", + "\n", + "P_out = 12. \t\t\t#motor load\n", + "eta_motor = 85./100\n", + "P_2 = P_out/eta_motor\n", + "\n", + "P_T = P_1 + P_2\n", + "phi_T = math.acos(1)\n", + "Q_T = P_T * math.tan(phi_T)\n", + "\n", + "\n", + "Q_2 = Q_T - Q_1 \t\t\t#kVA supplied by motor\n", + "#negative sign of Q_2 indicates its leading nature\n", + "phi_2 = math.atan(abs(Q_2)/P_2)\n", + "S_2 = P_2/math.cos(phi_2)\n", + "\n", + "# Results\n", + "print 'Power factor when motor supplies 12kW load is %.4f leading'%(math.cos(phi_2))\n", + "print 'kVA input to the motor is %.3f kVA'%(S_2)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Power factor when motor supplies 12kW load is 0.6615 leading\n", + "kVA input to the motor is 21.341 kVA\n" + ] + } + ], + "prompt_number": 36 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.28 Page no : 78" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "V_L = 400\n", + "V_ph = V_L/math.sqrt(3)\n", + "Z_s = complex(0.5,4) \t\t\t#synchronous impedance\n", + "theta = math.atan(Z_s.imag/Z_s.real) \t\t\t# returns angle in radians \n", + "\n", + "I_aph = 60.\n", + "phi = math.acos(0.866) \t\t\t#leading\n", + "power_losses = 2*10**3\n", + "\n", + "# Calculations\n", + "E_bph = math.sqrt( (I_aph*abs(Z_s))**2 + (V_ph)**2 - 2*(I_aph*abs(Z_s))*(V_ph)*math.cos(phi+theta) ) \n", + "delta = theta \t\t\t#for P_m_max\n", + "P_m_max = (E_bph*V_ph/abs(Z_s))- (E_bph**2/abs(Z_s))*math.cos(delta)\n", + "P_m_max_total = 3 * P_m_max\n", + "P_out_max = P_m_max_total- power_losses\n", + "\n", + "# Results\n", + "print 'Maximum power output is %.4f kW'%(P_out_max*10**-3)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Maximum power output is 51.3899 kW\n" + ] + } + ], + "prompt_number": 37 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.29 Page no : 79" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "V_L = 6.6*10**3\n", + "V_ph = V_L/math.sqrt(3)\n", + "I_L = 50.\n", + "I_aph = I_L\n", + "Z_s = complex(1.5,8) \t\t\t#synchronous impedance\n", + "theta = math.atan(Z_s.imag/Z_s.real) \t\t\t# returns angle in radians \n", + "E_Rph = I_aph*abs(Z_s)\n", + "\n", + "# Calculations and Results\n", + "#part(i)\n", + "phi = math.acos(0.8)\n", + "P_in = math.sqrt(3)*V_L*I_L*math.cos(phi) \t\t\t#for both lag and lead supplied power will be the same\n", + "print 'i)Power supplied to the motor is %.3f kW'%(P_in*10**-3)\n", + "#part(ii)\n", + "E_bph_lag = math.sqrt( E_Rph**2 + V_ph**2 - 2*E_Rph*V_ph*math.cos(theta-phi) ) \t\t\t#for lagging power factor\n", + "#Note that E_bph_lag > V_ph\n", + "print 'ii)Induced EMF for 0.8 power factor lag is %.3f V'%(E_bph_lag)\n", + "E_bph_lead = math.sqrt( E_Rph**2 + V_ph**2 - 2*E_Rph*V_ph*math.cos(theta+phi) ) \t\t\t#for leading power factor\n", + "#Note that E_bph_lead < V_ph\n", + "print ' Induced EMF for 0.8 power factor lead is %.3f V'%(E_bph_lead)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "i)Power supplied to the motor is 457.261 kW\n", + "ii)Induced EMF for 0.8 power factor lag is 3521.267 V\n", + " Induced EMF for 0.8 power factor lead is 4007.170 V\n" + ] + } + ], + "prompt_number": 38 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.30 Page no : 80" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "V_L = 400.\n", + "V_ph = V_L/math.sqrt(3)\n", + "P_out = 7.5*735.5\n", + "eta = 85./100 \t\t\t#efficiency\n", + "R_a = 0.\n", + "X_s = 10. \t\t\t#armature resistance and synchronous reactance\n", + "Z_s = complex(R_a,X_s)\t\t\t#synchronous impedance\n", + "theta = math.atan(Z_s.imag) \t\t\t# returns angle in radians \n", + "\n", + "# Calculations and Results\n", + "P_in = P_out/eta\n", + "phi = math.acos(1) \t\t\t#for mimimum current power factor is maximum\n", + "I_L = P_in/(math.sqrt(3)*V_L*math.cos(phi)) \n", + "I_aph = I_L\n", + "print 'Minimum current is %.3f A at full load condition '%(I_L)\n", + "\n", + "E_Rph = I_aph*abs(Z_s)\n", + "E_bph = math.sqrt( E_Rph**2 + V_ph**2 - 2*E_Rph*V_ph*math.cos(phi+theta) ) \n", + "print 'and corresponding EMF is %.4f V'%(E_bph)\n", + "\n", + "# note : rounding off error.\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Minimum current is 9.367 A at full load condition \n", + "and corresponding EMF is 240.4216 V\n" + ] + } + ], + "prompt_number": 40 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.31 Page no : 80" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "V_L = 3.3*10**3\n", + "V_ph = V_L/math.sqrt(3)\n", + "V_t = V_ph\n", + "Pole = 24.\n", + "f = 50. \t\t\t#Pole and frequency\n", + "P = 1000.*10**3\n", + "R_a = 0\n", + "X_s = 3.24 \t\t\t#armature resistance and synchronous reactance\n", + "Z_s = complex(R_a,X_s) \t\t\t#synchronous impedance\n", + "theta = math.atan(Z_s.imag) \t\t\t# returns angle in radians \n", + "phi = math.acos(1)\n", + "I_aph = P/(math.sqrt(3)*V_L*math.cos(phi))\n", + "\n", + "# Calculations\n", + "E_Rph = I_aph*abs(Z_s)\n", + "E_bph = math.sqrt( E_Rph**2 + V_ph**2 - 2*E_Rph*V_ph*math.cos(phi+theta) ) \n", + "\n", + "P_m_max = 3*(E_bph*V_ph/abs(Z_s)) \t\t\t#maximum power that can be delivered\n", + "N_s = 120*f/Pole \t\t\t#synchronous speed\n", + "T_max = P_m_max /(2*math.pi*N_s/60) \t\t\t#maximum torque that can be developed\n", + "\n", + "# Results\n", + "print 'Maximum power and torque the motor can deliver is %.3f kW and %.2f *10**3 Nm respectively'%(P_m_max*10**-3,T_max/1000)\n", + "\n", + "# rounding off error." + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Maximum power and torque the motor can deliver is 3211.633 kW and 122.68 *10**3 Nm respectively\n" + ] + } + ], + "prompt_number": 42 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
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