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+{
+ "metadata": {
+  "name": "",
+  "signature": "sha256:ae2b9384b1b13f79321d75082b020b6a54688771e761bc6446ad00de14bf068e"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+  {
+   "cells": [
+    {
+     "cell_type": "heading",
+     "level": 1,
+     "metadata": {},
+     "source": [
+      "Chapter 5 : Methods for Calculating Regulation of Alternator"
+     ]
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 5.1 page no : 12"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math \n",
+      "\n",
+      "# Variables\n",
+      "P = 1000.*10**3 \t\t\t#load power\n",
+      "phi = math.acos(math.radians(0.8)) \t\t\t#power factor lagging angle\n",
+      "V_L = 11.*10**3 \t\t\t#rated terminal voltae\n",
+      "R_a = 0.4 \t\t\t#armature resistance per phase\n",
+      "X_s = 3.\t\t\t#synchronous reactance per phase\n",
+      "\n",
+      "# Calculations\n",
+      "I_L = P/(math.sqrt(3)*V_L*math.cos(math.radians(phi)))\n",
+      "I_aph = I_L \t\t\t#for star connected load\n",
+      "I_a = I_L\t\t\t#current through armature\n",
+      "V_ph = V_L/math.sqrt(3) \t\t\t#rated terminal volatge phase value\n",
+      "\n",
+      "E_ph =  math.sqrt(  (V_ph*math.cos(math.radians(phi))+I_a*R_a)**2+(V_ph*math.sin(math.radians(phi))+I_a*X_s)**2   )  \t\t\t#emf generated phase value\n",
+      "E_line = E_ph*math.sqrt(3) \t\t\t#line value of emf generated\n",
+      "regulation = 100*(E_ph-V_ph)/V_ph  \t\t\t#pecentage regulation\n",
+      "\n",
+      "# Results\n",
+      "print 'Line value of e.m.f generated is %.2f kV  \\nRegulation is %.3f percent'%(E_line*10**-3,regulation)\n",
+      "\n",
+      "# note : book answer is wrong.\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Line value of e.m.f generated is 11.05 kV  \n",
+        "Regulation is 0.428 percent\n"
+       ]
+      }
+     ],
+     "prompt_number": 3
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 5.2 Page no : 14"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math \n",
+      "\n",
+      "# Variables\n",
+      "VA = 1200.*10**3\n",
+      "V_L = 6600.\n",
+      "R_a = 0.25 \t\t\t#armature resistance per phase\n",
+      "X_s = 5.\t\t\t#synchronous reactance per phase\n",
+      "\n",
+      "# Calculations and Results\n",
+      "I_L = VA/(math.sqrt(3)*V_L)\n",
+      "I_aph = I_L \t\t\t#for star connected load\n",
+      "I_a = I_L\n",
+      "V_ph = V_L/math.sqrt(3)\n",
+      "\n",
+      "#Part(i)\n",
+      "phi1 = math.acos(0.8)\t\t\t#and lagging\n",
+      "E_ph1 =  math.sqrt(  (V_ph*math.cos(phi1)+I_a*R_a)**2+(V_ph*math.sin(phi1)+I_a*X_s)**2   )\n",
+      "regulation = 100*(E_ph1-V_ph)/V_ph  \t\t\t#percentage regulation\n",
+      "print 'i)Regulation at 0.8 lagging pf is %.2f percent'%(regulation)\n",
+      "#Part(ii)\n",
+      "phi2 = math.acos(0.8)\t\t\t#and leading\n",
+      "E_ph2 =  math.sqrt(  (V_ph*math.cos(phi2)+I_a*R_a)**2+(V_ph*math.sin(phi2)-I_a*X_s)**2   )\n",
+      "regulation2 = 100*(E_ph2-V_ph)/V_ph \t\t\t#percentage regulation\n",
+      "print 'ii)Regulation at 0.8 leading pf is %.f percent'%(regulation2)\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "i)Regulation at 0.8 lagging pf is 9.33 percent\n",
+        "ii)Regulation at 0.8 leading pf is -7 percent\n"
+       ]
+      }
+     ],
+     "prompt_number": 5
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 5.3 Page no : 17"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math \n",
+      "\n",
+      "# Variables\n",
+      "#full load\n",
+      "V_L_FL = 1100.\n",
+      "V_ph_FL = V_L_FL/math.sqrt(3)\n",
+      "\n",
+      "# Calculations\n",
+      "#no load\n",
+      "V_L_NL = 1266\n",
+      "E_line = V_L_NL\n",
+      "E_ph = E_line/math.sqrt(3)\n",
+      "regulation = 100*(E_ph-V_ph_FL)/V_ph_FL\n",
+      "\n",
+      "# Results\n",
+      "print 'Regulation at full load is %.2f percent'%(regulation)\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Regulation at full load is 15.09 percent\n"
+       ]
+      }
+     ],
+     "prompt_number": 6
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 5.4 Page no : 23"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math \n",
+      "\n",
+      "# Variables\n",
+      "V_L = 866.\n",
+      "VA = 100.*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_aph = I_L\t\t\t#full load and star connected alternator\n",
+      "V_ph = V_L/math.sqrt(3)\n",
+      "\n",
+      "# Calculations\n",
+      "#Graph is plotted and V_oc_ph and I_asc_Ph is obtained for \n",
+      "#SCC for I_asc = 66.67 A\n",
+      "I_f = 2.4  # A\n",
+      "#OCC for I_f = 2.4 A\n",
+      "V_oc_ph = 240    # V\n",
+      "\n",
+      "#for measruemnt of impedance\n",
+      "V_oc_ph = 240 \t\t\t#for I_f = 2.4..From o.c.c graph\n",
+      "I_asc_ph = 66.67 \t\t\t#for I_f = 2.4...From s.c.c graph\n",
+      "Z_s = V_oc_ph/I_asc_ph\n",
+      "R_a = 0.15\n",
+      "X_s = math.sqrt( Z_s**2-R_a**2 )\n",
+      "\n",
+      "V_ph_FL = 500.\n",
+      "phi = math.acos(0.8)  \t\t\t#lagging pf\n",
+      "E_ph = math.sqrt((V_ph_FL*math.cos(phi)+I_aph*R_a)**2+(V_ph_FL*math.sin(phi)+I_aph*X_s)**2)\n",
+      "regulation = 100*(E_ph-V_ph)/V_ph\n",
+      "\n",
+      "# Results\n",
+      "print 'Full-load regulation at 0.8 lagging pf is %.2f percent '%(regulation )\n",
+      "\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Full-load regulation at 0.8 lagging pf is 35.57 percent \n"
+       ]
+      }
+     ],
+     "prompt_number": 7
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 5.5  Page no : 25"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math \n",
+      "\n",
+      "# Variables\n",
+      "V_OC_line = 230.\n",
+      "I_asc = 12.5  \t\t\t# when I_f = 0.38\n",
+      "V_OC_ph = V_OC_line/math.sqrt(3)\n",
+      "Z_s = V_OC_ph/I_asc \n",
+      "\n",
+      "R_a = 1.8/2  \t\t\t#1.8 is between terminals..0.9 is per phase\n",
+      "X_s = math.sqrt(Z_s**2-R_a**2)\n",
+      "\n",
+      "I_a = 10.\t\t\t# when regulation is needed\n",
+      "V_L = 230.\n",
+      "V_ph = V_L/math.sqrt(3)\n",
+      "\n",
+      "# Calculations and Results\n",
+      "#Part(i)\n",
+      "phi1 = math.acos(0.8) \t\t\t#and lagging\n",
+      "E_ph1 = math.sqrt((V_ph*math.cos(phi1)+I_a*R_a)**2+(V_ph*math.sin(phi1)+I_a*X_s)**2)\n",
+      "regulation1 = 100*(E_ph1-V_ph)/V_ph\n",
+      "print 'Regulation for 10 A at 0.8 lagging pf is %.2f percent'%(regulation1)\n",
+      "#Part(ii)\n",
+      "phi2 = math.acos(0.8) \t\t\t#and leading\n",
+      "E_ph2 = math.sqrt((V_ph*math.cos(phi2)+I_a*R_a)**2+(V_ph*math.sin(phi2)-I_a*X_s)**2)\n",
+      "regulation2 = 100*(E_ph2-V_ph)/V_ph\n",
+      "print 'Regulation for 10 A at 0.8 leading pf is %.2f percent'%(regulation2)\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Regulation for 10 A at 0.8 lagging pf is 64.47 percent\n",
+        "Regulation for 10 A at 0.8 leading pf is -11.01 percent\n"
+       ]
+      }
+     ],
+     "prompt_number": 8
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 5.6  Page no :  31"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math \n",
+      "\n",
+      "# Variables\n",
+      "phi = math.acos(0.8)\n",
+      "VA = 1000.*10**3\n",
+      "V_L = 1905.\n",
+      "V_ph = V_L/math.sqrt(3)\n",
+      "R_a = 0.2\t\t\t#Armature reactance per phase\n",
+      "\n",
+      "# Calculations and Results\n",
+      "#Part(i)\n",
+      "#Ampere-turn method\n",
+      "I_L = VA/(math.sqrt(3)*V_L)\n",
+      "I_aph = I_L\n",
+      "V_dash = V_ph+I_aph*R_a*math.cos(phi)\t\t\t#V_dash is a dummy quantity and has no significance..it's used only for mapping correcponding current\n",
+      "F_o = 32 \t\t\t#F_o corresponds to voltage V_dash = 1148.5 from O.C.C graph\n",
+      "F_AR = 27.5 \t\t\t#Field current required to circulate full-load short circuit current of 303.07A.From SCC F_AR = 27.5\n",
+      "F_R  =  math.sqrt(    F_o**2 + F_AR**2-2*F_o*F_AR*math.cos(phi+math.pi/2) )\t\t\t#using Comath.sine rule\n",
+      "\n",
+      "# for F_R = 53.25 E_ph = 1490 V from O.C.C\n",
+      "E_ph = 1490.\n",
+      "regulation1 = 100*(E_ph-V_ph)/V_ph\n",
+      "print 'Regulation on full-load by ampere-turn method is %.2f percent'%(regulation1)\n",
+      "\n",
+      "#Part (ii)\n",
+      "#Synchronous Impedance method\n",
+      "\n",
+      "I_sc = I_L\n",
+      "I_aph2 = I_sc\n",
+      "I_f = 27.5\n",
+      "\n",
+      "V_OC_ph = 1060. \t\t\t#corresponding to I-f = 27.5 in the graph\n",
+      "Z_s = V_OC_ph/I_aph2\n",
+      "X_s = math.sqrt(Z_s**2-R_a**2)\n",
+      "\n",
+      "E_ph2 =  math.sqrt( (V_ph*math.cos(phi)+I_aph2*R_a)**2+(V_ph*math.sin(phi)+I_aph2*X_s)**2 )   \t\t\t#from phasor diagram\n",
+      "regulation2 = 100*(E_ph2-V_ph)/V_ph\n",
+      "print 'Regulation on full-load by synchronous impedance method is %.2f percent'%(regulation2)\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Regulation on full-load by ampere-turn method is 35.47 percent\n",
+        "Regulation on full-load by synchronous impedance method is 78.09 percent\n"
+       ]
+      }
+     ],
+     "prompt_number": 9
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 5.7  Page no :  39"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math \n",
+      "\n",
+      "# Variables\n",
+      "#case(i)\n",
+      "V_L = 440.\n",
+      "V_ph = V_L/math.sqrt(3)\n",
+      "phi = math.acos(0.8)\n",
+      "\n",
+      "#armature resistance drop from the graph\n",
+      "#RS = 1.1 cm and scale  = 50 V/cm\n",
+      "arm_leak_resis =  1.1*50    \t\t\t#armature leakage resistance\n",
+      "\n",
+      "OB = V_ph*math.cos(phi)\n",
+      "AB = V_ph*math.sin(phi) + arm_leak_resis\n",
+      "E_1ph =  math.sqrt( OB**2+AB**2   )\n",
+      "\n",
+      "F_f1 = 6.1  \t\t\t#corresponding value from OCC\n",
+      "F_AR = 3.1*1\n",
+      "\n",
+      "# Calculations and Results\n",
+      "F_R =  math.sqrt( F_f1**2 + F_AR**2 -2*F_f1*F_AR*math.cos(math.radians(90+math.acos(math.radians(0.8)))))\n",
+      "E_ph = 328. \t\t\t#voltage corresponding to F_R = 8.33 A from OCC graph\n",
+      "regulation1 =  100*(E_ph - V_ph)/V_ph\n",
+      "print 'i)Regulation for 0.8 pf lagging is %.2f percent '%(regulation1)\n",
+      "\n",
+      "#case(ii)\n",
+      "\n",
+      "OC = V_ph*math.cos(phi)\n",
+      "BC = V_ph*math.sin(phi) - arm_leak_resis\n",
+      "E_1ph =  math.sqrt( OC**2+BC**2   )\n",
+      "\n",
+      "F_f1 = 6.1  \t\t\t#corresponding value from OCC\n",
+      "F_R =  math.sqrt(   F_f1**2 + F_AR**2 -2*F_f1*F_AR*math.cos(math.radians(90-math.acos(math.radians(0.8)))))\n",
+      "E_ph = 90 \t\t\t#volatge corresponding to F_R = 3.34 A from OCC graph\n",
+      "regulation2 =  100*(E_ph - V_ph)/V_ph\n",
+      "print 'ii)Regulation for 0.8 pf leading is %.2f percent '%(regulation2)\n",
+      "print 'The answer in part ii doesnt match with textbook because of calculation mistake done in last step in the textbook'\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "i)Regulation for 0.8 pf lagging is 29.12 percent \n",
+        "ii)Regulation for 0.8 pf leading is -64.57 percent \n",
+        "The answer in part ii doesnt match with textbook because of calculation mistake done in last step in the textbook\n"
+       ]
+      }
+     ],
+     "prompt_number": 10
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 5.8 Page no : 44"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math \n",
+      "\n",
+      "# Variables\n",
+      "P = 1200.*10**3\n",
+      "V_line = 12000.\n",
+      "R_a = 2.\n",
+      "X_s = 35.\t\t\t#armature resistance and synchronous reactance\n",
+      "phi = math.acos(0.8)\n",
+      "\n",
+      "# Calculations\n",
+      "I_L = P/(math.sqrt(3)*V_line*math.cos(phi))\n",
+      "I_a = I_L\n",
+      "V_ph = V_line/math.sqrt(3)\n",
+      "E_ph = math.sqrt((V_ph*math.cos(phi)+I_a*R_a)**2+(V_ph*math.sin(phi)+I_a*X_s)**2)\n",
+      "regulation = 100*(E_ph-V_ph)/V_ph\n",
+      "\n",
+      "# Results\n",
+      "print 'Regulation at 0.8 lag power factor is %.2f percent'%(regulation)\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Regulation at 0.8 lag power factor is 26.66 percent\n"
+       ]
+      }
+     ],
+     "prompt_number": 11
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 5.9 Page no : 45"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math \n",
+      "\n",
+      "# Variables\n",
+      "V_L = 11000.  \n",
+      "V_ph =  V_L/math.sqrt(3)\n",
+      "VA = 1000.*1000\n",
+      "I_L = VA/(V_L*math.sqrt(3))\n",
+      "\n",
+      "V_OC_ph = 433/math.sqrt(3)\n",
+      "I_asc_ph = I_L\n",
+      "\n",
+      "Z_s = V_OC_ph /I_asc_ph  \t\t\t#ohms per phase\n",
+      "R_a = 0.45 \t\t\t#ohms per phase\n",
+      "X_s = math.sqrt(Z_s**2-R_a**2)\n",
+      "\n",
+      "# Calculations and Results\n",
+      "#part(i)\n",
+      "phi = math.acos(0.8) \t\t\t#lagging\n",
+      "E_ph  =  math.sqrt((V_ph*math.cos(phi)+I_L*R_a)**2 +(V_ph*math.sin(phi)+ I_L*X_s)**2)\n",
+      "regulation = 100*(E_ph-V_ph)/V_ph\n",
+      "print 'Voltage regulation at 0.8 pf lagging is %f percent'%(regulation)\n",
+      "\n",
+      "#part(ii)\n",
+      "phi = math.acos(0.8) \t\t\t#leading\n",
+      "E_ph2  =  math.sqrt((V_ph*math.cos(phi)+I_L*R_a)**2 +(V_ph*math.sin(phi)- I_L*X_s)**2)\n",
+      "regulation2 = 100*(E_ph2-V_ph)/V_ph\n",
+      "print 'Voltage regulation at 0.8 pf lagging is %f percent'%(regulation2)\n",
+      "print 'Answer mismatches due to improper approximation'\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Voltage regulation at 0.8 pf lagging is 2.690067 percent\n",
+        "Voltage regulation at 0.8 pf lagging is -1.996182 percent\n",
+        "Answer mismatches due to improper approximation\n"
+       ]
+      }
+     ],
+     "prompt_number": 12
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 5.10 Page no :  46"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math \n",
+      "\n",
+      "# Variables\n",
+      "VA = 125.*10**3\n",
+      "V_L = 400.\n",
+      "V_ph = V_L/math.sqrt(3)\n",
+      "I_L = VA/(math.sqrt(3)*V_L)\n",
+      "I_aph = I_L\n",
+      "\n",
+      "# Calculations\n",
+      "I_f = 4.\n",
+      "I_asc = I_aph/2 \t\t\t#for half load.. refer to graph\n",
+      "V_OC_line = 140.\n",
+      "V_OC_ph = V_OC_line/math.sqrt(3)\n",
+      "I_asc_ph = I_asc\n",
+      "Z_s =  V_OC_ph/I_asc_ph\n",
+      "R_a = 0.1\n",
+      "X_s = math.sqrt(Z_s**2-R_a**2) \t\t\t#armature resistance and synchronous reactance\n",
+      "\n",
+      "phi = math.acos(0.8)\n",
+      "E_ph  =  math.sqrt((V_ph*math.cos(phi)+I_asc*R_a)**2 +(V_ph*math.sin(phi)- I_asc*X_s)**2)\n",
+      "regulation = 100*(E_ph-V_ph)/V_ph\n",
+      "\n",
+      "# Results\n",
+      "print 'Voltage regulation at 0.8 pf leading for half load is %.2f percent'%(regulation)\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Voltage regulation at 0.8 pf leading for half load is -12.39 percent\n"
+       ]
+      }
+     ],
+     "prompt_number": 13
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 5.11  Page no :  48"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math \n",
+      "from numpy import roots\n",
+      "\n",
+      "# Variables\n",
+      "V_OC_line = 575.\n",
+      "V_OC_ph = V_OC_line/math.sqrt(3)\n",
+      "I_asc_line = 75.\n",
+      "I_asc_ph   = I_asc_line \n",
+      "I_aph = I_asc_ph\n",
+      "I_L = I_aph\n",
+      "\n",
+      "Z_s =  V_OC_ph/I_asc_ph\n",
+      "R_a = 2.16/2\n",
+      "X_s  =   math.sqrt(Z_s**2 - R_a**2)\n",
+      "\n",
+      "# Calculations and Results\n",
+      "#on full load\n",
+      "E_ph = 6100.\n",
+      "phi = math.acos(0.8) \t\t\t#leading\n",
+      "\n",
+      "#using E_ph  =  math.sqrt((V_ph*math.cos(phi)+I_a*R_a)**2 +(V_ph*math.sin(phi)- I_a*X_s)**2)\n",
+      "p = [1, -256.68, -3.71*10**7]\n",
+      "ans = roots(p)\n",
+      "V_ph = ans[0] \t\t\t#second root is ignored as its -ve\n",
+      "V_L = V_ph*math.sqrt(3)\n",
+      "print 'Rated terminal voltage between the lines is %.3f V '%(V_L)\n",
+      "VA_rating = math.sqrt(3)*V_L*I_L\n",
+      "print 'kVA rating of the alternator is %.f kVA'%(VA_rating*10**-3)\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Rated terminal voltage between the lines is 10774.515 V \n",
+        "kVA rating of the alternator is 1400 kVA\n"
+       ]
+      }
+     ],
+     "prompt_number": 15
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 5.12  Page no :  49"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math \n",
+      "from numpy import roots\n",
+      "\n",
+      "# Variables\n",
+      "V_L = 6600.\n",
+      "V_ph = V_L/math.sqrt(3)\n",
+      "VA = 1500.*10**3\n",
+      "I_L = VA/(math.sqrt(3)*V_L)\n",
+      "I_aph = I_L\n",
+      "\n",
+      "# Calculations and Results\n",
+      "R_a = 0.5\n",
+      "X_s = 5\t\t\t#armature resistance and synchronous reactance\n",
+      "phi = math.acos(0.8)\n",
+      "E_ph  =  math.sqrt((V_ph*math.cos(phi)+I_aph*R_a)**2 +(V_ph*math.sin(phi)+ I_aph*X_s)**2)\n",
+      "print 'Induced EMF per phase is %f V'%(E_ph)\n",
+      "\n",
+      "#full load \n",
+      "phi = math.acos(1)\n",
+      "#using E_ph  =  math.sqrt((V_ph*math.cos(phi)+I_a*R_a)**2 +(V_ph*math.sin(phi)- I_a*X_s)**2)\n",
+      "p = [1, 131.215, -1.791*10**7]\n",
+      "ans = roots(p)\n",
+      "V_ph = ans[1] \t\t\t#first root is ignored as it is -ve\n",
+      "print 'Terminal voltage per phase is %f V'%(V_ph)\n",
+      "\n",
+      "# note : rounding off error."
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Induced EMF per phase is 4284.243828 V\n",
+        "Terminal voltage per phase is 4166.921808 V\n"
+       ]
+      }
+     ],
+     "prompt_number": 16
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 5.13  Page no :  50"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math \n",
+      "\n",
+      "# Variables\n",
+      "V_ph = 2000.\n",
+      "R_a = 0.8\n",
+      "I_sc = 100.\n",
+      "V_OC = 500.\n",
+      "I_f = 2.5\n",
+      "Z_s = V_OC/I_sc\n",
+      "X_s =  math.sqrt(Z_s**2 - R_a**2 )\n",
+      "I_aFL = 100.\n",
+      "I_a = I_aFL\n",
+      "\n",
+      "# Calculations and Results\n",
+      "#part(i)\n",
+      "phi = math.acos(1)\n",
+      "E_ph  =  math.sqrt((V_ph*math.cos(phi)+I_a*R_a)**2 +(V_ph*math.sin(phi)+ I_a*X_s)**2)\n",
+      "regulation = 100*(E_ph-V_ph)/V_ph\n",
+      "print 'i)Voltage regulation is %.2f percent'%(regulation)\n",
+      "\n",
+      "#part(ii)\n",
+      "phi2 = math.acos(0.8)\n",
+      "E_ph2  =  math.sqrt((V_ph*math.cos(phi2)+I_a*R_a)**2 +(V_ph*math.sin(phi2)- I_a*X_s)**2)\n",
+      "regulation2 = 100*(E_ph2-V_ph)/V_ph\n",
+      "print 'ii)Voltage regulation is %.2f percent'%(regulation2)\n",
+      "\n",
+      "#part(iii)\n",
+      "phi3 = math.acos(0.71)\n",
+      "E_ph3  =  math.sqrt((V_ph*math.cos(phi3)+I_a*R_a)**2 +(V_ph*math.sin(phi3)+ I_a*X_s)**2)\n",
+      "regulation3 = 100*(E_ph3-V_ph)/V_ph\n",
+      "print 'iii)Voltage regulation is %.2f percent'%(regulation3)\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "i)Voltage regulation is 6.89 percent\n",
+        "ii)Voltage regulation is -8.88 percent\n",
+        "iii)Voltage regulation is 21.11 percent\n"
+       ]
+      }
+     ],
+     "prompt_number": 17
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 5.14 Page no :  51"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math \n",
+      "\n",
+      "# Variables\n",
+      "VA = 1000.*1000\n",
+      "V_L = 4600. \n",
+      "V_ph = V_L/math.sqrt(3)\n",
+      "I_L = VA/(math.sqrt(3)*V_L)\n",
+      "I_aph_FL = I_L\n",
+      "I_aph = I_aph_FL\n",
+      "I_sc = (150./100)* I_aph_FL\n",
+      "V_OC_line = 1744\n",
+      "V_OC_ph =  V_OC_line/math.sqrt(3)\n",
+      "\n",
+      "# Calculations\n",
+      "Z_s = V_OC_ph / I_sc\n",
+      "R_a = 1\n",
+      "X_s = math.sqrt(Z_s**2-R_a**2)\n",
+      "\n",
+      "phi = math.acos(0.8 ) \t\t\t#lagging\n",
+      "E_ph  =  math.sqrt((V_ph*math.cos(phi)+I_aph*R_a)**2 +(V_ph*math.sin(phi)+ I_aph*X_s)**2)\n",
+      "regulation = 100*(E_ph-V_ph)/V_ph\n",
+      "\n",
+      "# Results\n",
+      "print 'Voltage regulation at full load 0.8 pf is %.2f percent'%(regulation)\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Voltage regulation at full load 0.8 pf is 19.89 percent\n"
+       ]
+      }
+     ],
+     "prompt_number": 18
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 5.15 Page no :  52"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math \n",
+      "\n",
+      "\n",
+      "#part(i)    Ampere turn method\n",
+      "# Variables\n",
+      "F_O = 37.5\n",
+      "F_AR = 20.\n",
+      "V_L = 6600.\n",
+      "V_ph = V_L/math.sqrt(3)\n",
+      "\n",
+      "# Calculations and Results\n",
+      "#lagging\n",
+      "phi = math.acos(0.8) \n",
+      "F_R =  math.sqrt((F_O+F_AR*math.sin(phi) )**2 + (F_AR*math.cos(phi))**2 ) \n",
+      "#E_ph corresponding to F_R can be obtained by plotting open circuit characteristics\n",
+      "E_ph = 4350\n",
+      "regulation = 100*(E_ph-V_ph)/V_ph\n",
+      "print 'i)By Ampere-turn method or MMF methodFull-load regulation at 0.8 lagging pf is %.2f percent'%(regulation)\n",
+      "#leading\n",
+      "phi = math.acos(0.8) \n",
+      "F_R =  math.sqrt((F_O-F_AR*math.sin(phi) )**2 + (F_AR*math.cos(phi))**2 ) \n",
+      "#E_ph corresponding to F_R can be obtained by plotting open circuit characteristics\n",
+      "E_ph = 3000\n",
+      "regulation = 100*(E_ph-V_ph)/V_ph\n",
+      "print 'Full-load regulation at 0.8 leading pf is %.2f percent'%(regulation)\n",
+      "\n",
+      "#EMF method\n",
+      "V_OC_ph = 100\n",
+      "V_ph = 100\n",
+      "I_sc =  100*(F_O/F_AR)   \t\t\t#times the rated value\n",
+      "Z_s = V_OC_ph/I_sc\n",
+      "F_O =  100\n",
+      "F_AR =  Z_s*100\n",
+      "\n",
+      "#lagging\n",
+      "phi = math.acos(0.8)\n",
+      "F_R =   math.sqrt((F_O+F_AR*math.sin(phi) )**2 + (F_AR*math.cos(phi))**2 ) \n",
+      "regulation = 100*(F_R-V_ph)/V_ph\n",
+      "print 'iiSynchronous impedance method or EMF method'\n",
+      "print 'Full-load regulation at 0.8 lagging pf is %.2f percent'%(regulation)\n",
+      "#leading\n",
+      "phi = math.acos(0.8)\n",
+      "F_R =   math.sqrt((F_O-F_AR*math.sin(phi) )**2 + (F_AR*math.cos(phi))**2 ) \n",
+      "regulation = 100*(F_R-V_ph)/V_ph\n",
+      "print 'Full-load regulation at 0.8 leading pf is %.2f percent'%(regulation)\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "i)By Ampere-turn method or MMF methodFull-load regulation at 0.8 lagging pf is 14.16 percent\n",
+        "Full-load regulation at 0.8 leading pf is -21.27 percent\n",
+        "iiSynchronous impedance method or EMF method\n",
+        "Full-load regulation at 0.8 lagging pf is 38.72 percent\n",
+        "Full-load regulation at 0.8 leading pf is -19.72 percent\n"
+       ]
+      }
+     ],
+     "prompt_number": 19
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 5.16 Page no :  56"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math \n",
+      "\n",
+      "# Variables\n",
+      "V_L = 6000.\n",
+      "V_ph = V_L/math.sqrt(3)\n",
+      "I_ph_X_Lph  =  0.9*500  \t\t\t#leakage reactance drop in volts  =  0.9 cm * 500 V/cm\n",
+      "phi =  math.acos(0.8) \t\t\t#lagging\n",
+      "\n",
+      "# Calculations\n",
+      "E_1ph = math.sqrt( (V_ph*math.cos(phi))**2 + (V_ph*math.sin(phi)+I_ph_X_Lph)**2 )   \t\t\t#From triangle OAB\n",
+      "F_f1  =  26 \t\t\t#from OCC\n",
+      "F_AR =  2.9*5  \t\t\t#2.9cm * 5 A/cm\n",
+      "\n",
+      "F_R  =    math.sqrt(F_f1**2 + F_AR**2 -2*F_AR*F_f1*math.cos(phi+ (math.pi/2)) )\n",
+      "\n",
+      "# Results\n",
+      "print 'Required field current is %.2f A'%(F_R)\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Required field current is 36.59 A\n"
+       ]
+      }
+     ],
+     "prompt_number": 20
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 5.17 Page no :  58"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math \n",
+      "\n",
+      "# Variables\n",
+      "V_L = 400.\n",
+      "V_ph = V_L/math.sqrt(3)\n",
+      "VA = 40.*10**3\n",
+      "I_L = VA/(math.sqrt(3)*V_L) \n",
+      "I_aph = I_L\n",
+      "\n",
+      "# Calculations and Results\n",
+      "I_aph_X_Lph  =  0.65*50  \t\t\t#leakage reactance drop in volts  =  2.4 cm * 500 V/cm\n",
+      "X_Lph =  I_aph_X_Lph/ I_aph\n",
+      "print 'Armature leakage reactance is %.3f ohms'%(X_Lph)\n",
+      "phi = math.acos(0.8)  \t\t\t#lagging\n",
+      "E_ph  =  math.sqrt((V_ph*math.cos(phi))**2 +(V_ph*math.sin(phi)+ I_aph_X_Lph)**2)\n",
+      "F_f1 = 15.6 \t\t\t#as obtained from OCC corresponding to this E_ph\n",
+      "\n",
+      "F_AR =  2.3*3  \t\t\t#2.3cm * 3 A/cm\n",
+      "print 'Armature reaction is %.1f '%(F_AR)\n",
+      "F_R  =    math.sqrt(F_f1**2 + F_AR**2 -2*F_AR*F_f1*math.cos(phi+ (math.pi/2)) )  \t\t\t#math.comath.sine rule to Triangle OAB\n",
+      "E_ph = 267.5  \t\t\t#corresponding to F_R from open circiut characteristics\n",
+      "regulation = 100*(E_ph-V_ph)/V_ph\n",
+      "print 'Voltage regulation at 0.8 pf lagging is %.1f percent'%(regulation)\n",
+      "\n",
+      "\n",
+      "#Note:This answer doesnt match with textbook as it has been reciprocated in textbook\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Armature leakage reactance is 0.563 ohms\n",
+        "Armature reaction is 6.9 \n",
+        "Voltage regulation at 0.8 pf lagging is 15.8 percent\n"
+       ]
+      }
+     ],
+     "prompt_number": 21
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 5.18 Page no :  60"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math \n",
+      "\n",
+      "# Variables\n",
+      "VA = 10.*10**3\n",
+      "V_L = 11.*10**3\n",
+      "V_ph = V_L/math.sqrt(3)\n",
+      "I_ph_X_Lph  =  2.4*500  \t\t\t#leakage reactance drop in volts  =  2.4 cm * 500 V/cm\n",
+      "\n",
+      "# Calculations\n",
+      "I_ph_R_aph  = VA/(math.sqrt(3)*V_L)\n",
+      "phi = math.acos(0.8)\n",
+      "E_ph  =  math.sqrt((V_ph*math.cos(phi)+I_ph_R_aph)**2 +(V_ph*math.sin(phi)+ I_ph_X_Lph)**2)\n",
+      "F_f1 = 109 \t\t\t#obtained from open circuit characteristics corresponding to calculated E_ph\n",
+      "F_AR =  2.8*10  \t\t\t#2.8cm * 10 A/cm\n",
+      "F_R  =    math.sqrt(F_f1**2 + F_AR**2 -2*F_AR*F_f1*math.cos(phi+ (math.pi/2)) )  \t\t\t#math.comath.sine rule to Triangle OAB\n",
+      "E_ph = 7700.  \t\t\t#corresponding to F_R from open circiut characteristics\n",
+      "\n",
+      "regulation = 100*(E_ph-V_ph)/V_ph\n",
+      "\n",
+      "# Results\n",
+      "print 'Voltage regulation at full-load 0.8 pf lagging is %.2f percent'%(regulation)\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Voltage regulation at full-load 0.8 pf lagging is 21.24 percent\n"
+       ]
+      }
+     ],
+     "prompt_number": 22
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 5.19  Page no : 63"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math \n",
+      "from numpy import roots\n",
+      "\n",
+      "# Variables\n",
+      "VA = 2000.*1000\n",
+      "V_L = 11000.\n",
+      "V_ph = V_L/math.sqrt(3)\n",
+      "R_a = 0.3\n",
+      "X_s = 5. \t\t\t#armature resistance and synchronous reactance\n",
+      "\n",
+      "# Calculations\n",
+      "#case (i)\n",
+      "phi = math.acos(0.8) \t\t\t#lagging\n",
+      "I_L = VA/(math.sqrt(3)*V_L)  \n",
+      "I_a = I_L\n",
+      "E_ph  =  math.sqrt((V_ph*math.cos(phi)+I_a*R_a)**2 +(V_ph*math.sin(phi)+ I_a*X_s)**2)\n",
+      "\n",
+      "#using E_ph  =  math.sqrt((V_ph*math.cos(phi)+I_aph*R_a)**2 +(V_ph*math.sin(phi)+ I_aph*X_s)**2)\n",
+      "#we get  V_ph**2 -579.4455 V_ph -44653301.91 = 0\n",
+      "p = [1, -579.4455, -44653301.91]\n",
+      "ans = roots(p)\n",
+      "V_ph = ans[0]    \t\t#second root is ignored as its -ve\n",
+      "print 'Terminal voltage is %.4f V'%(V_ph)\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Terminal voltage is 6978.3131 V\n"
+       ]
+      }
+     ],
+     "prompt_number": 23
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 5.20 Page no : 64"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math \n",
+      "from numpy import roots\n",
+      "\n",
+      "# Variables\n",
+      "R_a = 0.6\n",
+      "X_s = 6. \t\t\t#armature resistance and synchronous reactance per phase\n",
+      "E_L = 6599.\n",
+      "E_ph = E_L/math.sqrt(3)\n",
+      "I_L = 180.\n",
+      "I_a = I_L\n",
+      "\n",
+      "# Calculations and Results\n",
+      "#part(i)\n",
+      "# using E_ph  =  math.sqrt((V_ph*math.cos(phi)+I_a*R_a)**2 +(V_ph*math.sin(phi)+ I_a*X_s)**2) and solving for V_ph\n",
+      "p = [1 ,1135.83, -13338836.49]\n",
+      "ans = roots(p)\n",
+      "V_ph = ans[1]\n",
+      "V_L = V_ph*math.sqrt(3)\n",
+      "regulation = 100*(E_ph-V_ph)/V_ph\n",
+      "\n",
+      "phi = math.acos(0.9)\n",
+      "theta = math.atan((I_a*X_s+V_ph*math.sin(phi) )/(E_ph))\n",
+      "delta = theta-phi\n",
+      "print 'i)0.9 laggingTerminal voltage is %.2f VVoltage regulation is %.2f percentLoad angle is %.2f degrees'%(V_ph*math.sqrt(3),regulation,delta*180/math.pi)\n",
+      "\n",
+      "#part(ii)\n",
+      "phi_2 = math.acos(0.8)\n",
+      "p = [1, -941.53, -11399574.87]\n",
+      "ans = roots(p) \n",
+      "V_ph = ans[0] \t\t\t#second root is ignored as its -ve\n",
+      "V_L = V_ph*math.sqrt(3)\n",
+      "regulation2 = 100*(E_ph-V_ph)/V_ph\n",
+      "delta_2  =  math.asin( (math.tan(phi)*(V_ph*math.cos(phi_2)+I_a*R_a) -I_a*X_s )/E_ph   )\n",
+      "print 'ii)0.8 leadingTerminal voltage is %.2f VVoltage regulation is %.2f percentLoad angle is %.2f degrees'%(V_L,regulation2,delta_2*180/math.pi)\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "i)0.9 laggingTerminal voltage is 5418.22 VVoltage regulation is 21.79 percentLoad angle is 6.83 degrees\n",
+        "ii)0.8 leadingTerminal voltage is 6719.93 VVoltage regulation is -1.80 percentLoad angle is 7.17 degrees\n"
+       ]
+      }
+     ],
+     "prompt_number": 24
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 5.21 Page no :  66"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math \n",
+      "\n",
+      "# Variables\n",
+      "V_ph = 2000.\n",
+      "R_a = 0.8\n",
+      "I_sc = 100.\n",
+      "I_a = I_sc\n",
+      "V_OC = 500.\n",
+      "I_f = 2.5\n",
+      "Z_s = V_OC/I_sc\n",
+      "\n",
+      "X_s = math.sqrt(Z_s**2- R_a**2)\n",
+      "I_a_FL = 100.\n",
+      "\n",
+      "# Calculations and Results\n",
+      "#Part(i)\n",
+      "phi1 = math.acos(1) \t\t\t#and lagging\n",
+      "E_ph1 = math.sqrt((V_ph*math.cos(phi1)+I_a*R_a)**2+(V_ph*math.sin(phi1)+I_a*X_s)**2)\n",
+      "regulation1 = 100*(E_ph1-V_ph)/V_ph\n",
+      "print 'Regulation at upf is %.2f percent'%(regulation1)\n",
+      "\n",
+      "#Part(ii)\n",
+      "phi2 = math.acos(0.8) \n",
+      "E_ph2 = math.sqrt((V_ph*math.cos(phi2)+I_a*R_a)**2+(V_ph*math.sin(phi2)-I_a*X_s)**2)\n",
+      "regulation2 = 100*(E_ph2-V_ph)/V_ph\n",
+      "print 'Regulation at 0.8 leading pf is %.2f percent'%(regulation2)\n",
+      "\n",
+      "#Part(iii)\n",
+      "phi3 = math.acos(0.71) \n",
+      "E_ph3 = math.sqrt((V_ph*math.cos(phi3)+I_a*R_a)**2+(V_ph*math.sin(phi3)+I_a*X_s)**2)\n",
+      "regulation3 = 100*(E_ph3-V_ph)/V_ph\n",
+      "print 'Regulation at 0.71 lagging pf is %.2f percent'%(regulation3)\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Regulation at upf is 6.89 percent\n",
+        "Regulation at 0.8 leading pf is -8.88 percent\n",
+        "Regulation at 0.71 lagging pf is 21.11 percent\n"
+       ]
+      }
+     ],
+     "prompt_number": 25
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 5.22 Page no : 68"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math \n",
+      "\n",
+      "# Variables\n",
+      "V = 600.\n",
+      "VA = 60.*10**3\n",
+      "I_sc = 210.\n",
+      "V_oc = 480.\n",
+      "I_f = 10.\n",
+      "R_a = 0.2\n",
+      "\n",
+      "I = VA/V        \t\t\t#VA = V*I and alternator is math.single phase\n",
+      "I_a = I\n",
+      "\n",
+      "# Calculations and Results\n",
+      "Z_s = V_oc/I_sc  \t\t\t#Synchronous Impedance\n",
+      "X_s = math.sqrt(Z_s**2-R_a**2) \t\t\t#SYnchronous reactance\n",
+      "print 'Synchronous impedances is %f ohms and synchronous reactance is %f ohms'%(Z_s,X_s)\n",
+      "\n",
+      "#PART (i)\n",
+      "phi1 = math.acos(0.8) \t\t\t#and lagging\n",
+      "E1 = math.sqrt((V*math.cos(phi1)+I_a*R_a)**2+(V*math.sin(phi1)+I_a*X_s)**2) \t\t\t#plus sign for lagging power factor\n",
+      "regulation1 = 100*(E1-V)/V\n",
+      "print 'Regulation at 0.8 lagging pf is %.2f percent '%(regulation1 )\n",
+      "\n",
+      "#PART (ii)\n",
+      "phi2 = math.acos(1) \n",
+      "E2 = math.sqrt((V*math.cos(phi2)+I_a*R_a)**2+(V*math.sin(phi2)+I_a*X_s)**2) \n",
+      "regulation2 = 100*(E2-V)/V\n",
+      "print 'Regulation at UNITY pf is %.2f percent '%(regulation2 )\n",
+      "\n",
+      "#PART (iii)\n",
+      "phi3 = math.acos(0.6) \t\t\t#and leading \n",
+      "E3 = math.sqrt((V*math.cos(phi3)+I_a*R_a)**2+(V*math.sin(phi3)-I_a*X_s)**2) \t\t\t#minus sign for leading power factor\n",
+      "regulation3 = 100*(E3-V)/V\n",
+      "print 'Regulation at 0.6 leading pf is %.2f percent '%(regulation3 )\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Synchronous impedances is 2.285714 ohms and synchronous reactance is 2.276947 ohms\n",
+        "Regulation at 0.8 lagging pf is 28.60 percent \n",
+        "Regulation at UNITY pf is 10.08 percent \n",
+        "Regulation at 0.6 leading pf is -23.98 percent \n"
+       ]
+      }
+     ],
+     "prompt_number": 26
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 5.23 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",
+      "I_a = 100.\n",
+      "I_f = 5.\n",
+      "V_OC_line = 900. \n",
+      "V_OC_ph = V_OC_line/math.sqrt(3) \n",
+      "R_a = 0.8 \t\t\t#armature resistance\n",
+      "I_aph = I_a\n",
+      "Z_s = V_OC_ph/I_aph\n",
+      "X_s = math.sqrt(Z_s**2-R_a**2) \t\t\t#synchronous reactance\n",
+      "\n",
+      "# Calculations and Results\n",
+      "#Part(i)\n",
+      "phi1 = math.acos(0.8) \t\t\t#and lagging\n",
+      "E_ph1 = math.sqrt((V_ph*math.cos(phi1)+I_a*R_a)**2+(V_ph*math.sin(phi1)+I_a*X_s)**2)\n",
+      "regulation1 = 100*(E_ph1-V_ph)/V_ph\n",
+      "print 'Regulation at 0.8 lagging is %.2f percent'%(regulation1)\n",
+      "\n",
+      "#Part(ii)\n",
+      "phi2 = math.acos(0.8)  \t\t\t#and leading\n",
+      "E_ph2 = math.sqrt((V_ph*math.cos(phi2)+I_a*R_a)**2+(V_ph*math.sin(phi2)-I_a*X_s)**2)\n",
+      "regulation2 = 100*(E_ph2-V_ph)/V_ph\n",
+      "print 'Regulation at 0.8 leading pf is %.2f percent'%(regulation2)\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Regulation at 0.8 lagging is 21.03 percent\n",
+        "Regulation at 0.8 leading pf is -9.55 percent\n"
+       ]
+      }
+     ],
+     "prompt_number": 27
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 5.24  Page no : 70"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math \n",
+      "\n",
+      "# Variables\n",
+      "V_L = 13500.\n",
+      "R_a = 1.5 \n",
+      "X_s = 30. \t\t\t#armature resistance and synchronous reactance\n",
+      "V_ph = V_L/math.sqrt(3)\n",
+      "\n",
+      "# Calculations and Results\n",
+      "#CASE 1\n",
+      "phi1 = math.acos(0.8)\n",
+      "P_out = 1280*10**3\n",
+      "I_L =  P_out/ (math.sqrt(3)*V_L*math.cos(phi1) )    \t\t\t#because P_out = math.sqrt(3)*V_L*I_L*math.cos(phi)\n",
+      "\n",
+      "I_a = I_L\n",
+      "E_ph = math.sqrt((V_ph*math.cos(phi1)+I_a*R_a)**2+(V_ph*math.sin(phi1)+I_a*X_s)**2)\n",
+      "regulation = 100*(E_ph-V_ph)/V_ph\n",
+      "print 'Regulation at 0.8 lagging power factor is %.2f percent'%(regulation)\n",
+      "\n",
+      "#Case 2\n",
+      "phi2 = math.acos(1)\n",
+      "I_L =  P_out/ (math.sqrt(3)*V_L*math.cos(phi2) )    \t\t\t#because P_out = math.sqrt(3)*V_L*I_L*math.cos(phi)\n",
+      "\n",
+      "I_a = I_L\n",
+      "E_ph = math.sqrt((V_ph*math.cos(phi2)+I_a*R_a)**2+(V_ph*math.sin(phi2)+I_a*X_s)**2)\n",
+      "regulation2 = 100*(E_ph-V_ph)/V_ph\n",
+      "print 'Regulation at unity power factor is %.2f percent'%(regulation2)\n",
+      "\n",
+      "#case 3\n",
+      "phi3 = math.acos(0.8)\n",
+      "I_L =  P_out/ (math.sqrt(3)*V_L*math.cos(phi3) )    \t\t\t#because P_out = math.sqrt(3)*V_L*I_L*math.cos(phi)\n",
+      "I_a = I_L\n",
+      "E_ph = math.sqrt((V_ph*math.cos(phi3)+I_a*R_a)**2+(V_ph*math.sin(phi3)-I_a*X_s)**2)\t\t\t# minus sign in the second bracket beacuse of leading pf\n",
+      "regulation3 = 100*(E_ph-V_ph)/V_ph\n",
+      "print 'Regulation at 0.8 leading power factor is %.2f percent'%(regulation3)\n",
+      "\n",
+      "# note : rounding off error"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Regulation at 0.8 lagging power factor is 18.60 percent\n",
+        "Regulation at unity power factor is 3.23 percent\n",
+        "Regulation at 0.8 leading power factor is -11.99 percent\n"
+       ]
+      }
+     ],
+     "prompt_number": 29
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 5.26  Page no :  72"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math \n",
+      "\n",
+      "# Variables\n",
+      "V_L = 11.*10**3\n",
+      "VA_rating = 10.**6\n",
+      "R_a = 2.2 \t\t\t#alternator resistance\n",
+      "phi = math.acos(0.8)\n",
+      "\n",
+      "# Calculations\n",
+      "I_L = VA_rating/(math.sqrt(3)*V_L)\t\t\t#VA = math.sqrt(3)V_L*I_L\n",
+      "I_a = I_L\n",
+      "V_ph = V_L/math.sqrt(3)\n",
+      "regulation = 24.\n",
+      "\n",
+      "E_ph =  ((regulation/100)+1)*V_ph    \t\t\t# because regulation = 100*(E_ph-V_ph)/V_ph\n",
+      "#using E_ph = math.sqrt((V_ph*math.cos(phi)+I_a*R_a)**2+(V_ph*math.sin(phi)+I_a*X_s)**2)\n",
+      "X_s = (math.sqrt(E_ph**2-((V_ph*math.cos(phi)+I_a*R_a)**2))-V_ph*math.sin(phi))*(1/I_a)\n",
+      "\n",
+      "phi1 = math.acos(0.8)\n",
+      "E_ph = math.sqrt((V_ph*math.cos(phi1)+I_a*R_a)**2+(V_ph*math.sin(phi1)-I_a*X_s)**2)\n",
+      "regulation1 = 100*(E_ph-V_ph)/V_ph\n",
+      "\n",
+      "# Results\n",
+      "print 'Regulation at 0.8 leading power factor is %.2f percent'%(regulation1)\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Regulation at 0.8 leading power factor is -13.90 percent\n"
+       ]
+      }
+     ],
+     "prompt_number": 31
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 5.27  Page no :  73"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math \n",
+      "\n",
+      "# Variables\n",
+      "V_L = 220.\n",
+      "VA = 100.*10**3\n",
+      "R_a = 0.1 \t\t\t#effective resistacne of alternator\n",
+      "X_a = 0.5 \t\t\t#leakage reactance\n",
+      "X_ar = 2*X_a\n",
+      "\n",
+      "Z_s = complex(R_a,X_a+X_ar)\n",
+      "\n",
+      "# Calculations and Results\n",
+      "#Part(1)\n",
+      "phi = math.acos(0.4)\n",
+      "V_ph = V_L/math.sqrt(3)\n",
+      "I_L = VA/(math.sqrt(3)*V_L)\t\t\t#VA = math.sqrt(3)*V_L*I_L\n",
+      "I_a = I_L\n",
+      "E_ph = math.sqrt((V_ph*math.cos(phi)+I_a*R_a)**2+(V_ph*math.sin(phi)+I_a*(X_a+X_ar))**2)\n",
+      "print 'i)Required noload voltage is %.3f V'%(E_ph)\n",
+      "\n",
+      "#Part(2)\n",
+      "V_ph2 = 0\n",
+      "E_ph2 = math.sqrt((V_ph2*math.cos(phi)+I_a*R_a)**2+(V_ph2*math.sin(phi)+I_a*(X_a+X_ar))**2)\n",
+      "print 'ii)Required noload voltage is %.3f V'%(E_ph2)\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "i)Required noload voltage is 515.848 V\n",
+        "ii)Required noload voltage is 394.522 V\n"
+       ]
+      }
+     ],
+     "prompt_number": 32
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 5.28 Page no : 74"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math \n",
+      "\n",
+      "# Variables\n",
+      "V_L = 2000.\n",
+      "V_ph = V_L/math.sqrt(3)\n",
+      "VA = 1000.*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_aph = I_L\n",
+      "\n",
+      "I_f = 28.5\t\t\t#for this I_aph = 288.67513 as obtained from SCC graph\n",
+      "V_oc_ph = 1060.\t\t\t#for I_f = 28.5 as obtained fromOCC graph\n",
+      "Z_s = V_oc_ph/I_aph\n",
+      "R_a = 0.2 \t\t\t#armature effective resistance\n",
+      "X_s = math.sqrt( Z_s**2-R_a**2 )\n",
+      "\n",
+      "# Calculations and Results\n",
+      "#Part(i)\n",
+      "phi1 = math.acos(0.8)\t\t\t#lagging\n",
+      "E_ph1 = math.sqrt((V_ph*math.cos(phi1)+I_aph*R_a)**2+(V_ph*math.sin(phi1)+I_aph*X_s)**2)\n",
+      "regulation1 = 100*(E_ph1-V_ph)/V_ph\n",
+      "print \"i)Full-load percentage regulation at 0.8 pf lagging is %.2f percent\"%(regulation1)\n",
+      "\n",
+      "#Part(ii)\n",
+      "phi2 = math.acos(0.8)\t\t\t#leading\n",
+      "E_ph2 = math.sqrt((V_ph*math.cos(phi2)+I_aph*R_a)**2+(V_ph*math.sin(phi2)-I_aph*X_s)**2)\n",
+      "regulation2 = 100*(E_ph2-V_ph)/V_ph\n",
+      "print \"ii)Full-load percentage regulation at 0.8 pf leading is %.2f percent\"%(regulation2)\n",
+      "print 'Note that the answer mismatches because of calculation mistake done in the last step of part 1'\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "i)Full-load percentage regulation at 0.8 pf lagging is 73.86 percent\n",
+        "ii)Full-load percentage regulation at 0.8 pf leading is -9.29 percent\n",
+        "Note that the answer mismatches because of calculation mistake done in the last step of part 1\n"
+       ]
+      }
+     ],
+     "prompt_number": 33
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 5.29 Page no : 76"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math \n",
+      "\n",
+      "# Variables\n",
+      "V_L = 3300.\n",
+      "VA = 200.*10**3\n",
+      "R_a = 0.6\n",
+      "X_s = 6.\t\t\t#armature resistance and synchronous reactance\n",
+      "\n",
+      "# Calculations\n",
+      "I_L = VA/(math.sqrt(3)*V_L)\t\t\t#VA = math.sqrt(3)V_L*I_L\n",
+      "I_a = I_L\n",
+      "V_ph = V_L/math.sqrt(3)\n",
+      "phi = math.acos(0.8)\n",
+      "E_ph = math.sqrt((V_ph*math.cos(phi)+I_a*R_a)**2+(V_ph*math.sin(phi)+I_a*X_s)**2)\n",
+      "\n",
+      "regulation = 100*(E_ph-V_ph)/V_ph\n",
+      "\n",
+      "# Results\n",
+      "print 'Regulation at 0.8 lagging power factor is %.3f percent'%(regulation)\n",
+      "print ' Note : Regulation is positive for lagging power factor loads'\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Regulation at 0.8 lagging power factor is 7.802 percent\n",
+        " Note : Regulation is positive for lagging power factor loads\n"
+       ]
+      }
+     ],
+     "prompt_number": 34
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 5.30 Page no : 77"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math \n",
+      "\n",
+      "# Variables\n",
+      "V_L = 2300.   \n",
+      "V_ph =  V_L/math.sqrt(3)\n",
+      "f = 50.\n",
+      "R_a = 0.2 \t\t\t#armature resistance\n",
+      "I_sc = 150.\n",
+      "V_OC_line = 780.   \n",
+      "V_OC_ph = V_OC_line/math.sqrt(3)\n",
+      "\n",
+      "Z_s =  V_OC_ph/I_sc\n",
+      "X_s  =   math.sqrt(Z_s**2 - R_a**2)\n",
+      "I_aph = 25 \n",
+      "I_aFL = I_aph\n",
+      "\n",
+      "# Calculations and Results\n",
+      "#part(i)\n",
+      "phi =  math.acos(0.8)  \t\t\t#lag\n",
+      "E_ph  =  math.sqrt((V_ph*math.cos(phi)+I_aph*R_a)**2 +(V_ph*math.sin(phi)+ I_aph*X_s)**2)\n",
+      "regulation = 100*(E_ph-V_ph)/V_ph\n",
+      "print 'Voltage regulation at 0.8 pf lagging is %.3f percent'%(regulation)\n",
+      "\n",
+      "#part(ii)\n",
+      "phi2 =  math.acos(0.8)  \t\t\t#lead\n",
+      "E_ph2  =  math.sqrt((V_ph*math.cos(phi2)+I_aph*R_a)**2 +(V_ph*math.sin(phi2)- I_aph*X_s)**2 )\n",
+      "regulation2 = 100*(E_ph2-V_ph)/V_ph\n",
+      "print 'Voltage regulation at 0.8 pf leading is %.3f percent'%(regulation2)\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Voltage regulation at 0.8 pf lagging is 3.774 percent\n",
+        "Voltage regulation at 0.8 pf leading is -2.967 percent\n"
+       ]
+      }
+     ],
+     "prompt_number": 35
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [],
+     "language": "python",
+     "metadata": {},
+     "outputs": []
+    }
+   ],
+   "metadata": {}
+  }
+ ]
+}
\ No newline at end of file