path: root/DC_Machines_and_Synchronous_Machines/ch6.ipynb

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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 6 : Synchronization and Parallel Operation of Alternators"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      " \n",
      "Example 6.2  Page no : 31"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "# Variables\n",
      "X_d = 0.7 \n",
      "X_q = 0.4  \t\t\t#direct and quadrature axis synchronous reactance p.u.\n",
      "R_a = 0\n",
      "phi = math.acos(0.8)  \t\t\t#Lag\n",
      "\n",
      "V_t = 1. \t\t\t#assumed rated terminal Voltage \n",
      "I_a = 1. \t\t\t#Full-load armature current\n",
      "\n",
      "# Calculations\n",
      "psi = math.atan(  (V_t*math.sin(phi)+I_a*X_q)/(V_t*math.cos(phi)+I_a*R_a)            )\n",
      "delta = psi-phi\n",
      "I_d = I_a*math.sin(psi)\n",
      "I_q = I_a*math.cos(psi)\n",
      "E_f = V_t*math.cos(delta)+I_d*X_d+I_q*R_a\n",
      "\n",
      "# Results\n",
      "print 'Total e.m.f induced on open circuit is %.4f p.u.'%(E_f)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Total e.m.f induced on open circuit is 1.5149 p.u.\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.3 Page no :  35"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "import cmath\n",
      "\n",
      "#note that a new function p2z has been defined below for direct representation of complex numbers in polar form\n",
      "def  p2z(RRRR,Theeeta):\n",
      "        return  RRRR*cmath.exp((math.pi*Theeeta/180.)*1j);\n",
      "\n",
      "# Variables\n",
      "Z1 = complex(0,3) \t\t\t#impedance of alternator 1\n",
      "Z2 = complex(0,4) \t\t\t#impedance of alternator 2\n",
      "Z = 6.       #load\n",
      "\n",
      "E1 = p2z(220,0) \t\t\t#induced emf vector on no load\n",
      "E2 = p2z(220,10)\t\t\t#induced emf vector on no load\n",
      "\n",
      "# Calculations and Results\n",
      "I1 = ((E1-E2)*Z+E1*Z2)/(Z*(Z1+Z2)+Z1*Z2)\n",
      "I2 = ((E2-E1)*Z+E2*Z1)/(Z*(Z1+Z2)+Z1*Z2)\n",
      "\n",
      "phi1 = math.degrees(math.atan(I1.imag/I1.real))  \t\t\t#Phasemag returns the angle of complex number in degrees\n",
      "phi2 = math.degrees(math.atan(I2.imag/I2.real))  \t\t\t#Phasemag returns the angle of complex number in degrees\n",
      "\n",
      "I = I1+I2\n",
      "V = I*Z \t\t\t#Terminal voltage\n",
      "print 'i) Terminal voltage is %.1f volts at %.2f degrees'%(abs(V),math.degrees(math.atan(V.imag/V.real)))\n",
      "print 'ii) Currents are %.2f A at %.2f degrees and %.2f A at %.2f degrees      \\\n",
      "\\nTotal current is %.2f A at %.2f degrees  '%(abs(I1),math.degrees(math.atan(I1.imag/I1.real)),\\\n",
      "                                              abs(I2),math.degrees(math.atan(I2.imag/I2.real)),\\\n",
      "                                              abs(I),math.degrees(math.atan(I.imag/I.real)))\n",
      "\n",
      "P1 = abs(V)*abs(I1)*math.cos(math.radians(phi1))\n",
      "P2 = abs(V)*abs(I2)*math.cos(math.radians(phi2))\n",
      "print 'iii)Power delivered is %.2f watts and %.2f watts'%(P1,P2)\n",
      "\n",
      "# note : rounding off error."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "i) Terminal voltage is 210.7 volts at -11.66 degrees\n",
        "ii) Currents are 14.91 A at -17.71 degrees and 20.36 A at -7.24 degrees      \n",
        "Total current is 35.12 A at -11.66 degrees  \n",
        "iii)Power delivered is 2992.46 watts and 4257.11 watts\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.4  Page no :  54"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "# Variables\n",
      "V_l = 10000.\n",
      "V_ph = V_l/math.sqrt(3)\n",
      "VA = 10.*10**6\n",
      "I_FL = VA/(V_l*math.sqrt(3)) \t\t\t#Current at full laod\n",
      "IX_s = (20./100)*V_ph \t\t\t#product of I and X_s\n",
      "\n",
      "# Calculations\n",
      "X_s = IX_s/I_FL\n",
      "N_s = 1500.\n",
      "f = 50.\n",
      "P = 120*f/N_s \t\t\t#poles\n",
      "\n",
      "delta_dash_mech = math.pi/180 \t\t\t#phase print lacement in degree mechanical\n",
      "delta_dash_elec = delta_dash_mech*(P/2)  \t\t\t#P/2 is pole pairs(and not poles)\n",
      "E = V_ph \t\t\t#math.since alternator is on no-load\n",
      "P_SY = delta_dash_elec*E**2/X_s  \t\t\t#Synchronous Power\n",
      "P_SY_3ph = P_SY*3 \t\t\t#For 3 phases\n",
      "\n",
      "# Results\n",
      "print 'Synchronising Power of armature is %.3f kW.\\\n",
      "\\nSynchronising Power for 3 phase is %.3f kW'%(P_SY*10**-3,P_SY_3ph*10**-3)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Synchronising Power of armature is 581.776 kW.\n",
        "Synchronising Power for 3 phase is 1745.329 kW\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.5 Page no :  55"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "import cmath\n",
      "\n",
      "#note that a new function p2z has been defined below for direct representation of complex numbers in polar form\n",
      "\n",
      "def  p2z(RRRR,Theeeta):\n",
      "    return  RRRR*cmath.exp(1j*math.pi*Theeeta/180.);\n",
      "\n",
      "# Variables\n",
      "V_L = 6.6*10**3\n",
      "V_ph = V_L/math.sqrt(3)\n",
      "VA = 3.*10**6\n",
      "I_FL = VA/(V_L*math.sqrt(3)) \t\t\t#full load current \n",
      "P = 8.\n",
      "f = 50. \t\t\t#poles and frequency\n",
      "\n",
      "X_s = complex(0,2.9)\t\t\t#X_s = 2.9\n",
      "delta_dash_mech = math.pi/180\n",
      "delta_dash_elec = delta_dash_mech*(P/2)  \t\t\t#P/2 is pole pairs(and not poles)\n",
      "\n",
      "# Calculations and Results\n",
      "#part(i)\n",
      "E = V_ph\n",
      "P_SY = delta_dash_elec*E**2/abs(X_s)  \t\t\t#Synchronous Power per phase\n",
      "P_SY_3ph = P_SY*3 \t\t\t#For 3 phases\n",
      "print 'i)   Synchronising power at no load is %.3f kW'%(P_SY*10**-3)\n",
      "print '   Total Synchronising power at no load is %.2f kW'%(P_SY_3ph*10**-3)\n",
      "\n",
      "N_s = 120*f/P \t\t\t#in rpm\n",
      "n_s = (N_s)/60 \t\t\t#in rps\n",
      "T_SY = P_SY_3ph/(2*math.pi*n_s)\n",
      "print 'Synchronous torque per mechanical degree of phase print lacement is %.2f * 10**3 N-m'%(T_SY*10**-3)\n",
      "\n",
      "#part(ii)\n",
      "phi = math.acos(math.radians(0.85))\n",
      "I = p2z(I_FL,0)\n",
      "V = p2z(V_ph,phi)\n",
      "\n",
      "E = V+I*X_s\n",
      "#E leads I by phasemag(E). V leads I by phasemag(V)\n",
      "\n",
      "delta = (math.pi/180)* (math.atan(E.imag/E.real)-math.atan(V.imag/V.real) ) \t\t\t#power angle in radians\n",
      "P_SY2 = abs(E)*abs(V)*math.cos(delta)*math.sin(delta_dash_elec)/abs(X_s)\n",
      "\n",
      "P_SY_total_2 = 3*P_SY2\n",
      "#n_s = T_SY/(P_SY/(2*math.pi) )       \t\t\t#because T_SY = P_SY/(2*math.pi*n_s)\n",
      "print 'ii)Total Synchronising power is %.0f kW'%(P_SY_total_2*10**-3)\n",
      "\n",
      "T_SY2 = P_SY_total_2/(2*math.pi*n_s)\n",
      "print 'Synchronising torque is %.2f * 10**3 N-m'%(T_SY2/1000)\n",
      "\n",
      "# note : book answer is wrong.\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "i)   Synchronising power at no load is 349.547 kW\n",
        "   Total Synchronising power at no load is 1048.64 kW\n",
        "Synchronous torque per mechanical degree of phase print lacement is 13.35 * 10**3 N-m\n",
        "ii)Total Synchronising power is 1074 kW\n",
        "Synchronising torque is 13.68 * 10**3 N-m\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.6  Page no :  57"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "import cmath\n",
      "\n",
      "#note that a new function p2z has been defined below for direct representation of complex numbers in polar form\n",
      "def  p2z(RRRR,Theeeta):\n",
      "    return  RRRR*cmath.exp(1j*math.pi*Theeeta/180.)\n",
      "\n",
      "# Variables\n",
      "V_l = 10.*10**3\n",
      "V_ph = V_l/math.sqrt(3)\n",
      "R_a = 0.4\n",
      "Z = complex(R_a,6)\n",
      "I_a = p2z(300,-math.acos(math.radians(0.8)))\n",
      "E = V_ph+I_a*Z\n",
      "\n",
      "# Calculations\n",
      "phi = math.acos(0.8)\n",
      "alternator_op_ph = V_ph*abs(I_a)*math.cos(phi) \t\t\t#Power delivered to infinite bus per phase\n",
      "\n",
      "#Power deliered to the altrernator  =  Power delivewred to bus bar +  I**2*R losses in armature\n",
      "alternator_power =  alternator_op_ph+ abs(I_a)**2*R_a\n",
      "\n",
      "#this power developed remains constant.change pf to 1 and calculate corresponding armature current\n",
      "#alternator_power = V_ph*I_a1*math.cos(phi1)+I_a1**2*0.4\n",
      "#solve the quadratic equation  0.4 I_a1**2+5773.50 I_a1- 1421640  = 0\n",
      "I_a1 = (-1*V_ph+math.sqrt(V_ph**2-4*R_a*-1*alternator_power))/(2*R_a)\n",
      "\n",
      "#also as follows \n",
      "E1 = V_ph+I_a1*Z\n",
      "decrease = 100*(abs(E)-abs(E1))/abs(E)\n",
      "\n",
      "# Results\n",
      "print 'Percentage decrease in induced e.m.f is %.1f percent'%(decrease)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Percentage decrease in induced e.m.f is 2.6 percent\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.7 Page no :  58"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "#Line PQ for Altermnator 1 and PR for alternaator 2.AB is at frequency x from P where total load is 3000 kW\n",
      "\n",
      "# Variables\n",
      "QC = 2000.\n",
      "PS = 2.5\n",
      "#PC = x\n",
      "TR = 2000.\n",
      "PT = 2.\n",
      "\n",
      "# Calculations and Results\n",
      "#using similarity of triangles PAC and PQS\n",
      "AC_by_PC = (QC/PS)\t\t\t# because (AC/QC) = (PC/PS)\n",
      "#using similarity of triangles PCB and PTR\n",
      "CB_by_PC = (TR/PT) \t\t\t# because (CB/TR) = (PC/PT)\n",
      "\n",
      "AC_by_x = AC_by_PC   \t\t\t#which implies AC = 12.5*x\n",
      "CB_by_x = CB_by_PC  \t\t\t#which implies CB = 16.67*x\n",
      "\n",
      "AC_plus_CB = 3000.  \t\t\t#total load at the frequency at P is 30 kW\n",
      "x =  AC_plus_CB/(AC_by_x + CB_by_x)\n",
      "AC = AC_by_x * x\n",
      "CB = CB_by_x * x  \n",
      "frequency = 50-x\n",
      "print 'Loads shared by alternator 1 and 2 are %.2f kW and %.2f kW respectively'%(AC,CB)\n",
      "\n",
      "#construction for max load: RT is extended to cut PQ at X.\n",
      "QS = 2000.\n",
      "RT = 2000. \t\t\t#see figure\n",
      "XT = QS*(PT/PS)\n",
      "RX = RT+XT  \t\t\t#maximum load\n",
      "\n",
      "print 'Maximum load is %.0f kW'%(RX)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Loads shared by alternator 1 and 2 are 1333.33 kW and 1666.67 kW respectively\n",
        "Maximum load is 3600 kW\n"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.8 Page no :  60"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "# Variables\n",
      "P_out = 1500.*10**3\n",
      "V_L = 11000.\n",
      "phi = math.acos(0.8)\n",
      "I_L = P_out/(math.sqrt(3)*V_L*math.cos(phi))\n",
      "\n",
      "I_L_actv = I_L*math.cos(phi)   \t\t\t#wattful or active component of current\n",
      "I_L_reactive = I_L*math.sin(phi) \t\t\t#wattless or reactive component of current\n",
      "\n",
      "# Calculations and Results\n",
      "I_each = I_L/2  \t\t\t#in identical conditions\n",
      "I_arm1 = 45. \t\t\t#given\n",
      "I_1_reactive = math.sqrt(I_arm1**2-39.364**2 )  \t\t\t#from the power triangle \n",
      "I_2_reactive = 59.046-21.80\n",
      "I_a_2 = math.sqrt( 39.364**2 + I_2_reactive**2 )  \t\t\t#required armature current of 2nd alternator\n",
      "print 'Required armature current of second alternator is %.4f A'%(I_a_2)\n",
      "#power factors of 2 machines\n",
      "cos_phi1 = 39.364/45 \n",
      "cos_phi2 = 39.364/54.1921\n",
      "\n",
      "print 'Power factors are %.4f lagging and %.4f lagging'%(cos_phi1,cos_phi2)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Required armature current of second alternator is 54.1921 A\n",
        "Power factors are 0.8748 lagging and 0.7264 lagging\n"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.9 Page no : 61"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "#Line AB for Altermnator 1 and AC for alternator 2.AF is at frequency x measured from A where total load is 3000 kW\n",
      "# Variables\n",
      "BO = 2000.\n",
      "AO = 5.\t\t\t#AF = x\n",
      "DC = 2000.\n",
      "AD = 3.\n",
      "#AF = x\n",
      "\n",
      "# Calculations\n",
      "#using similarity of triangles AEF and ABO\n",
      "EF_by_AF = (BO/AO)\t\t\t# because (EF/BO) = (AF/AO)\n",
      "#using similarity of triangles AFG and ADC\n",
      "FG_by_AF = (DC/AD) \t\t\t#because (FG/DC) = (AF/AD)\n",
      "\n",
      "EF_by_x = EF_by_AF   \t\t\t#which implies EF = 400*x\n",
      "FG_by_x = FG_by_AF   \t\t\t#which implies FG = 666.67*x\n",
      "\n",
      "EF_plus_FG = 3000  \t\t\t#total load at the frequency at P is 3000 kW\n",
      "x =  EF_plus_FG/(EF_by_x + FG_by_x)\n",
      "EF = (BO/AO)*x\n",
      "FG = (DC/AD)*x  \n",
      "\n",
      "# Results\n",
      "print 'Loads shared by machine 1 and 2 are %.0f kW and %.0f kW respectively'%(EF,FG)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Loads shared by machine 1 and 2 are 1125 kW and 1875 kW respectively\n"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.10 Page no :  63"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "import cmath\n",
      "\n",
      "#note that a new function p2z has been defined below for direct representation of complex numbers in polar form\n",
      "\n",
      "def  p2z(RRRR,Theeeta):\n",
      "    return  RRRR*cmath.exp(1j*math.pi*Theeeta/180.);\n",
      "\n",
      "# Variables\n",
      "V_l = 6000.\n",
      "V_ph = V_l/math.sqrt(3)\n",
      "VA = 2000.*10**3\n",
      "I_FL = VA/(V_l*math.sqrt(3))\n",
      "X_s = complex(0,6) \t\t\t#synchronous reactance\n",
      "P = 8.\n",
      "f = 50.\n",
      "\n",
      "delta_mech = math.pi/180 \t\t\t#phase print lacemant in degree mechanical \n",
      "#phase print lacemant in degree electrical\n",
      "delta_elec = delta_mech*(P/2)  \t\t\t#P/2 is pole pairs(and not poles)\n",
      "\n",
      "phi = math.acos(math.radians(0.8))\n",
      "V = p2z(V_ph,phi)\n",
      "E = V+I_FL*X_s\n",
      "#E leads I by phasemag(E). V leads I by phasemag(V)\n",
      "\n",
      "# Calculations and Results\n",
      "delta = (math.pi/180)* (math.atan(E.imag/E.real)-(math.atan(V.imag/V.real ) ) ) \t\t\t#power angle in radians\n",
      "P_SY = abs(E)*abs(V)*math.cos(delta)*math.sin(delta_elec)/abs(X_s) \t\t\t#Synchronising power\n",
      "P_SY_total = 3*P_SY \t\t\t#totla Synchronising power \n",
      "print 'Total Synchronising power is %.3f kW'%(10**-3*P_SY_total)\n",
      "\n",
      "N_s = 120*f/P \t\t\t#in rpm\n",
      "n_s = (N_s)/60 \t\t\t#in rps\n",
      "T_SY = P_SY_total/(2*math.pi*n_s)\n",
      "print 'Synchronising torque is %.0f N-m'%(T_SY)\n",
      "\n",
      "# note : book answer it seems wrong."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Total Synchronising power is 444.753 kW\n",
        "Synchronising torque is 5663 N-m\n"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.11  Page no : 64"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "import cmath\n",
      "\n",
      "#note that a new function p2z has been defined below for direct representation of complex numbers in polar form\n",
      "def  p2z(RRRR,Theeeta):\n",
      "    return  RRRR*cmath.exp(1j*math.pi*Theeeta/180.);\n",
      "\n",
      "# Variables\n",
      "V_l = 3300.\n",
      "V_ph = V_l/math.sqrt(3)\n",
      "VA = 3*10.**6\n",
      "I_FL = VA/(V_l*math.sqrt(3))\n",
      "IX_s = (25./100)*V_ph \t\t\t#product of I and X_s\n",
      "X_s = complex(0,IX_s/I_FL) \t\t\t#synchronous reactance\n",
      "N_s = 1000. \t\t\t#in rpm\n",
      "P = 6.\n",
      "f = 50.\n",
      "\n",
      "# Calculations and Results\n",
      "delta_dash_mech = math.pi/180\n",
      "delta_dash_elec = delta_dash_mech*(P/2)  \t\t\t#P/2 is pole pairs(and not poles)\n",
      "\n",
      "I = I_FL\n",
      "phi = math.acos(math.radians(0.8))\n",
      "V = p2z(V_ph,phi)\n",
      "E = V+I*X_s\n",
      "#E leads I by phasemag(E). V leads I by phasemag(V)\n",
      "\n",
      "delta = (math.pi/180)* (math.atan(E.imag/E.real)-math.atan(V.imag/V.real) ) \t\t\t#power angle in radians\n",
      "P_SY = abs(E)*abs(V)*math.cos(delta)*math.sin(delta_dash_elec)/abs(X_s) \t\t\t#Synchronising power per phase\n",
      "print 'Synchronising power is %.3f kW'%(10**-3*P_SY)\n",
      "P_SY_total = 3*P_SY \t\t\t#Total Synchronising power\n",
      "\n",
      "N_s = 120*f/P \t\t\t#in rpm\n",
      "n_s = (N_s)/60 \t\t\t#in rps\n",
      "T_SY = P_SY_total/(2*math.pi*n_s)\n",
      "print 'Synchronising torque is %.0f N-m'%(T_SY)\n",
      "\n",
      "print 'Answer mismatches due to approximation'\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Synchronising power is 217.160 kW\n",
        "Synchronising torque is 6221 N-m\n",
        "Answer mismatches due to approximation\n"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.12 Page no : 65"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "# Variables\n",
      "V_l = 3300.\n",
      "V_ph = V_l/math.sqrt(3)\n",
      "VA = 3*10.**6\n",
      "I_FL = VA/(V_l*math.sqrt(3))\n",
      "IX_s = (20./100)*V_ph \t\t\t#product of I and X_s\n",
      "X_s = complex(0,IX_s/I_FL) \t\t\t#synchronous reactance\n",
      "N_s = 1000.\n",
      "P = 6.\n",
      "f = 50.\n",
      "\n",
      "delta_dash_mech = math.pi/180 \t\t\t#phase print lacement in degree mechanical\n",
      "#phase print lacement in degree electrical\n",
      "delta_dash_elec = delta_dash_mech*(P/2)  \t\t\t#P/2 is pole pairs(and not poles)\n",
      "\n",
      "# Calculations and Results\n",
      "E = V_ph\n",
      "Z_s = X_s \t\t\t#math.since R = 0\n",
      "P_SY = abs(E)*abs(V_ph)*delta_dash_elec/abs(Z_s) \t\t\t#Synchronising power per phase\n",
      "print 'Synchronising power is %.3f kW'%(10**-3*P_SY)\n",
      "P_SY_total = 3*P_SY \t\t\t#Total Synchronising power\n",
      "print '3 phase Synchronising power is %.3f kW'%(10**-3*P_SY_total)\n",
      "\n",
      "N_s = 120*f/P \t\t\t#in rpm\n",
      "n_s = (N_s)/60 \t\t\t#in rps\n",
      "T_SY = P_SY_total/(2*math.pi*n_s)\n",
      "print 'Synchronising torque is %.0f N-m'%(T_SY)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Synchronising power is 261.799 kW\n",
        "3 phase Synchronising power is 785.398 kW\n",
        "Synchronising torque is 7500 N-m\n"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.13 Page no :  66"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "# Variables\n",
      "V_L = 11.*10**3\n",
      "V_ph = V_L/math.sqrt(3)\n",
      "VA = 700.*10**3\n",
      "I_FL = VA/(math.sqrt(3)*V_L) \t\t\t#full load current\n",
      "IR_a = (1.5/100)*V_ph \t\t\t#product of I and R_a\n",
      "R_a = IR_a/I_FL\n",
      "IX_s = (14./100)*V_ph \t\t\t# product of I and X_s\n",
      "X_s = IX_s/I_FL \t\t\t#synchronous reactance\n",
      "\n",
      "# Calculations\n",
      "#at full load and 0.8 pf\n",
      "I = I_FL\n",
      "phi = math.acos(0.8)\n",
      "V_ph = complex(V_ph*math.cos(phi),V_ph*math.sin(phi))  \t\t\t#just introduced the angle\n",
      "E_ph = math.sqrt(    (abs(V_ph)*math.cos(phi)+ IR_a)**2+   (abs(V_ph)*math.sin(phi)+ IX_s)**2     )\n",
      "\n",
      "Poles = 4.\n",
      "f = 50. \t\t\t#poles and frequency\n",
      "delta = math.asin( (abs(V_ph)*math.sin(phi)+IX_s)/E_ph)  -phi\n",
      "delta_dash_mech = (math.pi/180) \t\t\t#print lacement in degree mechanical\n",
      "\t\t\t#print lacement in degree electrical\n",
      "delta_dash_elec = delta_dash_mech*(Poles/2)\n",
      "P_SY = abs(E_ph)*abs(V_ph)*math.cos(delta)*math.sin(delta_dash_elec)/X_s   \t\t\t#Synchronising power per phase \n",
      "P_SY_total = 3*P_SY  \t\t\t#total Synchronising power\n",
      "\n",
      "ns = 120*f/(60*Poles)  \t\t\t#in r.p.s\n",
      "T_SY = P_SY_total/(2*math.pi*ns)   \t\t\t#Synchronising torque \n",
      "\n",
      "# Results\n",
      "print 'Synchronising power is %.2fkW'%(P_SY_total/1000)\n",
      "print 'Synchronising torque is %.2f N-m'%(T_SY)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Synchronising power is 191.25kW\n",
        "Synchronising torque is 1217.53 N-m\n"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.14 Page no :  68"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "# Variables\n",
      "V_l = 9.*10**3\n",
      "V_ph = V_l/math.sqrt(3)\n",
      "VA = 5.5*10**6\n",
      "I_FL = VA/(V_l*math.sqrt(3))\n",
      "IX_s = (25./100)*V_ph \t\t\t#product of I and X_s\n",
      "X_s = complex(0,IX_s/I_FL) \t\t\t#synchronous reactance\n",
      "N_s = 1500. \t\t\t#in rpm\n",
      "n_s = N_s/60 \t\t\t#in rps\n",
      "f = 50.\n",
      "P = 120.*f/N_s \t\t\t#frequency and pole\n",
      "\n",
      "# Calculations\n",
      "delta_dash_mech = math.pi/180 \t\t\t#print lacemnt in degree mechanical \n",
      "#print lacemnt in degree electrical\n",
      "delta_dash_elec = delta_dash_mech*(P/2)  \t\t\t#P/2 is pole pairs(and not poles)\n",
      "\n",
      "E = V_ph\n",
      "P_SY = abs(E)*abs(V_ph)*delta_dash_elec/abs(X_s) \t\t\t#Synchronising power per phase\n",
      "P_SY_total = 3*P_SY \t\t\t#Total Synchronising power\n",
      "\n",
      "T_SY = P_SY_total/(2*math.pi*n_s)\n",
      "\n",
      "# Results\n",
      "print 'Synchronising torque is %.2f N-m'%(T_SY)\n",
      "print 'Answer mismatches due to approximation'\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Synchronising torque is 4888.89 N-m\n",
        "Answer mismatches due to approximation\n"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.15  Page no :  69"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "# Variables\n",
      "V_L = 6.*10**3\n",
      "V_ph = V_L/math.sqrt(3)\n",
      "VA = 2000.*10**3\n",
      "I_FL = VA/(math.sqrt(3)*V_L)  \n",
      "I = I_FL\n",
      "\n",
      "# Calculations\n",
      "X_s = 1.2\n",
      "R_a = 0.01 \t\t\t#both per unit\n",
      "IR_a = (1/100)*V_ph \t\t\t#product of I and R_a\n",
      "R_a = IR_a/I_FL\n",
      "IX_s = (120/100)*V_ph \t\t\t#product of I and X_s\n",
      "#IX_s = (12/100)*V_ph   \t\t\t# this is the mistake made in the textbook\n",
      "X_s = IX_s/I_FL\n",
      "\n",
      "#at full load and 0.8 pf\n",
      "phi = math.acos(0.8)\n",
      "#V_ph = complex(V_ph*math.cos(phi)V_ph*math.sin(phi))  \t\t\t#just introduced the angle\n",
      "E_ph = math.sqrt(    (abs(V_ph)*math.cos(phi)+ IR_a)**2+   (abs(V_ph)*math.sin(phi)+ IX_s)**2     )\n",
      "Poles = 8\n",
      "f = 50\n",
      "\n",
      "delta = math.asin( (abs(V_ph)*math.sin(phi)+IX_s)/E_ph)  -phi\n",
      "delta_dash_mech = (math.pi/180) \t\t\t#print lacemnt in degree mechanical \n",
      "#print lacemnt in degree electrical\n",
      "delta_dash_elec = delta_dash_mech*(Poles/2)\n",
      "P_SY = abs(E_ph)*abs(V_ph)*math.cos(delta)*math.sin(delta_dash_elec)/X_s   \t\t\t#Synchronising power per phase\n",
      "P_SY_total = 3*P_SY  \t\t\t#total Synchronising power\n",
      "\n",
      "ns = 120*f/(60*Poles)  \t\t\t#in r.p.s\n",
      "T_SY = P_SY_total/(2*math.pi*ns)   \t\t\t#Synchronising torque \n",
      "\n",
      "# Results\n",
      "print 'Synchronising power is %.2f kW'%(P_SY_total/1000)\n",
      "print 'Synchronising torque is %.2f N-m'%(T_SY)\n",
      "\n",
      "print 'Note that answer obtained doesnt match with textbook due to the following reasons: \\\n",
      "\\niIX_s is considered wrong in textbook.It should have been 4156.92instead of 415.692  To verify this use commented statement of IX_s line 13and notice that it matches with textbook ans then' \n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Synchronising power is 223.22 kW\n",
        "Synchronising torque is 2960.56 N-m\n",
        "Note that answer obtained doesnt match with textbook due to the following reasons: \n",
        "iIX_s is considered wrong in textbook.It should have been 4156.92instead of 415.692  To verify this use commented statement of IX_s line 13and notice that it matches with textbook ans then\n"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.16  Page no :  71"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "# Variables\n",
      "E = 11.*10**3/math.sqrt(3)\n",
      "I_sc = 1000.\n",
      "Pole = 2.\n",
      "f = 50.\n",
      "delta_dash_mech = 1*math.pi/180 \t\t\t#print lacemnt in degree mechanical \n",
      "\n",
      "# Calculations\n",
      "#print lacemnt in degree electrical \n",
      "delta_dash_elec = delta_dash_mech*(Pole/2)\n",
      "P_SY = E*I_sc*delta_dash_mech \t\t\t#Synchronising power per phase\n",
      "P_SY_total = P_SY*3 \t\t\t#total Synchronising power\n",
      "\n",
      "ns = 120*f/(60*Pole)  \t\t\t#in r.p.s\n",
      "T_SY = P_SY_total/(2*math.pi*ns)   \t\t\t#Synchronising torque \n",
      "\n",
      "# Results\n",
      "print 'Synchronising power is %.2f kW'%(P_SY_total/1000)\n",
      "print 'Synchronising torque is %.2f N-m'%(T_SY)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Synchronising power is 332.53 kW\n",
        "Synchronising torque is 1058.48 N-m\n"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.17 Page no :  72"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "#Line PQ for Altermnator 1 and PR for alternaator 2.AB is at frequency x from P where total load is 30 MW\n",
      "# Variables\n",
      "QT = 25.\n",
      "PT = 2.\n",
      "#PC = x\n",
      "SR = 25.\n",
      "PS = 1.5\n",
      "\n",
      "# Calculations\n",
      "#using similarity of triangles PAC and PQT\n",
      "AC_by_PC = (QT/PT)\t\t\t# because (AC/QT) = (PC/PT)\n",
      "#using similarity of triangles PCB and PSR\n",
      "CB_by_PC = (SR/PS)\n",
      "\n",
      "AC_by_x = AC_by_PC   \t\t\t#which implies AC = 12.5*x\n",
      "CB_by_x = CB_by_PC  \t\t\t#which implies CB = 16.67*x\n",
      "\n",
      "AC_plus_CB = 30  \t\t\t#total load at the frequency at P is 30 MW\n",
      "x =  AC_plus_CB/(AC_by_x + CB_by_x)\n",
      "AC = 12.5*x\n",
      "CB = 16.67*x  \n",
      "frequency = 50-x\n",
      "\n",
      "# Results\n",
      "print 'Loads shared by alternator 1 and 2 are %.2f MW and %.2f MW respectively'%(AC,CB)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Loads shared by alternator 1 and 2 are 12.86 MW and 17.15 MW respectively\n"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.18  Page no :  73"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "import cmath\n",
      "\n",
      "#note that a new function p2z has been defined below for direct representation of complex numbers in polar form\n",
      "def  p2z(RRRR,Theeeta):\n",
      "    return  RRRR*cmath.exp(1j*math.pi*Theeeta/180.);\n",
      "\n",
      "# Variables\n",
      "load_total = 1600.*10**3\n",
      "pf = 1/math.sqrt(2)  \t\t\t#lag\n",
      "V_L = 6600.\n",
      "\n",
      "# Calculations\n",
      "I_L = p2z(load_total/(math.sqrt(3)*V_L*pf),-1*math.acos(math.radians(pf)) )\n",
      "I_1 = p2z(90,-1*math.acos(math.radians(0.8)))\n",
      "I_2 = I_L-I_1\n",
      "phi = abs(math.atan(I_2.imag/I_2.real))\n",
      "I_a = abs(I_2)\n",
      "R_a = 1.05\n",
      "X_s = 5 \t\t\t#resistance and synchronous reactance per phase\n",
      "V_ph = V_L/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",
      "E_line = math.sqrt(3)*E_ph\n",
      "\n",
      "# Results\n",
      "print 'Excitation of second alternator is %.2f V '%(E_line)\n",
      "print ' The corresponding field current from the graph is about 310 A'\n",
      "print 'Note: The answer obtained will differ from textbook answer because of higher degree of accuracy while storing I_2 and the improper rounding off of I_2 in the textbook'\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Excitation of second alternator is 6884.65 V \n",
        " The corresponding field current from the graph is about 310 A\n",
        "Note: The answer obtained will differ from textbook answer because of higher degree of accuracy while storing I_2 and the improper rounding off of I_2 in the textbook\n"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.19 Page no : 75"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "# Variables\n",
      "V_L = 10.*10**3\n",
      "V_ph = V_L/math.sqrt(3)\n",
      "VA = 5.*10**6\n",
      "I_FL = VA/(math.sqrt(3)*V_L) \t\t\t#full-load current\n",
      "IX_s = (20./100)*V_ph \t\t\t#product of I and X_s\n",
      "X_s = IX_s/I_FL \t\t\t#synchronous reactance\n",
      "P = 4.\n",
      "\n",
      "# Calculations\n",
      "delta_dash_mech = 1*(math.pi/180) \t\t\t#print lacement in degree mechanical \n",
      "#print lacement in degree electrical\n",
      "delta_dash_elec = delta_dash_mech*(P/2)\n",
      "E = V_ph  \t\t\t#at no load\n",
      "P_SY =  delta_dash_elec*E**2/X_s  \t\t\t#Synchronising power per phase\n",
      "P_SY_total = P_SY*3  \t\t\t#Total Synchronising power\n",
      "\n",
      "# Results\n",
      "print 'Synchronising power per phase is %.2fkW \\\n",
      "\\nTotal Synchronising power is %.2fkW '%(P_SY/1000,P_SY_total/1000)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Synchronising power per phase is 290.89kW \n",
        "Total Synchronising power is 872.66kW \n"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.20 Page no : 76"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "# Variables\n",
      "Power_total = 1.414 \t\t\t#per unit\n",
      "V_L = 1. \t\t\t#per unit\n",
      "phi_t = math.acos(0.707)\n",
      "I_L_T = Power_total/(math.sqrt(3)*V_L*math.cos(phi_t))  \t\t\t#Total current\n",
      "\n",
      "# Calculations\n",
      "#Current supplied by each alternator\n",
      "I_1 = I_L_T/2\n",
      "I_2 = I_1\n",
      "V_ph = V_L/math.sqrt(3)\n",
      "\n",
      "phi = math.acos(0.707)\n",
      "R_a = 0\n",
      "X_s = 0.6 \t\t\t#resistacne and synchronous reactance\n",
      "E_ph = math.sqrt(  (V_ph*math.cos(phi)+ I_1*R_a)**2 + (V_ph*math.sin(phi)+I_1*X_s)**2          )\n",
      "delta =  math.atan((I_1*X_s+V_ph*math.sin(phi)) / (V_ph*math.cos(phi))) - phi    \t\t\t#power angle\n",
      "\n",
      "# Results\n",
      "print 'EMF is %.4f p.u. and power angle is %.2f degrees '%(E_ph,delta*180/math.pi)\n",
      "print 'Following assumptions were made :'\n",
      "print '1.Terminal or bus bar voltage at ppoint of connection is constant'\n",
      "print '2.The alternators are identical and are initially equally excited'\n",
      "print '3.The power supplied by prime movers is adjusted so that each machine carries half the load represented by external impedance Z = R+ j 2pifL %( where R and L are constant'\n",
      "print '4.The stator resistance is negligible'\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "EMF is 0.8580 p.u. and power angle is 16.58 degrees \n",
        "Following assumptions were made :\n",
        "1.Terminal or bus bar voltage at ppoint of connection is constant\n",
        "2.The alternators are identical and are initially equally excited\n",
        "3.The power supplied by prime movers is adjusted so that each machine carries half the load represented by external impedance Z = R+ j 2pifL %( where R and L are constant\n",
        "4.The stator resistance is negligible\n"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.21 Page no : 77"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "# Variables\n",
      "V_l = 480.\n",
      "X_d = 0.1\n",
      "X_q = 0.075\n",
      "R_a = 0. \t\t\t#armature resistance and synchronous reactance of direct quadrature axis\n",
      "I_l = 1200.\n",
      "I_ph = I_l/math.sqrt(3)\n",
      "V_ph = V_l\n",
      "V_t = V_l\n",
      "I_a = I_ph\n",
      "\n",
      "# Calculations\n",
      "phi = math.acos(0.8)\n",
      "psi = math.atan(  (V_t*math.sin(phi)+I_a*X_q)/(V_t*math.cos(phi)+I_a*R_a)            )\n",
      "delta = psi-phi \n",
      "\n",
      "I_d = I_a*math.sin(psi)\n",
      "I_q = I_a*math.cos(psi)\n",
      "E_f = V_t*math.cos(delta)+I_d*X_d+I_q*R_a\n",
      "\n",
      "# Results\n",
      "print 'Excitation e.m.f is %.f V '%(E_f)\n",
      "\n",
      "# note : rounding off error."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Excitation e.m.f is 524 V \n"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.22  Page no :  78"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "# Variables\n",
      "VA = 3.5*10**6\n",
      "P = 32.        \t\t\t#Poles\n",
      "Power = 2.5*10**6 \t\t\t#In watts\n",
      "V_l = 6.6*10**3\n",
      "phi = math.acos(0.8)\n",
      "I_l = Power/(V_l*math.cos(phi)*math.sqrt(3))\n",
      "X_d = 9.6\n",
      "X_q = 6.\n",
      "R_a = 0. \t\t\t#armature resistance and synchronous reactance of direct quadrature axis\n",
      "\n",
      "# Calculations\n",
      "V_t = V_l/math.sqrt(3)\n",
      "psi = math.atan(  (V_t*math.sin(phi)+I_l*X_q)/(V_t*math.cos(phi)+I_l*R_a)            )\n",
      "delta = psi-phi\n",
      "I_s = I_l\n",
      "I_d = I_s*math.sin(psi)\n",
      "I_q = I_s*math.cos(psi)\n",
      "E_f = V_t*math.cos(delta)+I_d*X_d+I_q*R_a\n",
      "regulation = 100*(E_f-V_t)/V_t\n",
      "\n",
      "# Results\n",
      "print 'percentage regulation is %.2f percent'%(regulation)\n",
      "print 'Excitation emf =  %.0f V'%(E_f)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "percentage regulation is 50.85 percent\n",
        "Excitation emf =  5748 V\n"
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.23 Page no :  79"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "# Variables\n",
      "X_d = 7.6\n",
      "X_q = 4.5\n",
      "R_a = 0.15 \t\t\t#armature resistance and synchronous reactance of directquadrature \n",
      "axisV_l = 13.8*10**3\n",
      "V_l = 13.8*10**3\n",
      "V_t = V_l/math.sqrt(3)\n",
      "phi = math.acos(0.8)\n",
      "VA = 25*10**6\n",
      "I_a = VA/(math.sqrt(3)*V_l)\n",
      "psi = math.atan(  (V_t*math.cos(phi)+I_a*X_q)/(V_t*math.sin(phi)+I_a*R_a)            )\n",
      "\n",
      "# Calculations\n",
      "delta = psi-phi\n",
      "I_s = I_a\n",
      "I_d = I_s*math.sin(psi)\n",
      "I_q = I_s*math.cos(psi)\n",
      "\n",
      "E_f = V_t*math.cos(delta)+I_d*X_d+I_q*R_a\n",
      "regulation = 100*(E_f-V_t)/V_t\n",
      "\n",
      "# Results\n",
      "print 'percentage regulation is %.2f percent'%(regulation)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "percentage regulation is 79.30 percent\n"
       ]
      }
     ],
     "prompt_number": 39
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.24 Page no :  80"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "# Variables\n",
      "X_d = 1.\n",
      "X_q = 0.6\n",
      "R_a = 0. \t\t\t#armature resistance and synchronous reactance of direct quadrature axis\n",
      "phi = math.acos(0.8) \t\t\t#lag\n",
      "V_t = 1.\n",
      "I_a = 1. \t\t\t#full load\n",
      "psi = math.atan(  (V_t*math.sin(phi)+I_a*X_q)/(V_t*math.cos(phi)+I_a*R_a)            )\n",
      "\n",
      "# Calculations\n",
      "delta = psi-phi\n",
      "I_s = I_a\n",
      "I_d = I_a*math.sin(psi)\n",
      "I_q = I_a*math.cos(psi)\n",
      "\n",
      "E_f = V_t*math.cos(delta)+I_d*X_d+I_q*R_a\n",
      "regulation = 100*(E_f-V_t)/V_t\n",
      "\n",
      "# Results\n",
      "print 'percentage regulation is %.2f percent'%(regulation)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "percentage regulation is 77.50 percent\n"
       ]
      }
     ],
     "prompt_number": 40
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.25 Page no :  81"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "# Variables\n",
      "I_a = 10.\n",
      "phi = 20. \t\t\t#lag and degrees\n",
      "V_t = 400.\n",
      "X_d = 10.\n",
      "X_q = 6.5\n",
      "R_a = 0. \t\t\t#armature resistance and synchronous reactance of direct quadrature axis\n",
      "\n",
      "# Calculations\n",
      "psi = math.atan((V_t*math.sin(math.radians(phi))+I_a*X_q)/(V_t*math.cos(math.radians(phi))+I_a*R_a))\n",
      "delta = math.degrees(psi)-phi\n",
      "I_d = math.degrees(I_a*math.sin(math.radians(psi)))\n",
      "I_q = (I_a*math.cos(psi))\n",
      "\n",
      "# Results\n",
      "print 'Load angle is %.2f degrees '%(delta)\n",
      "print 'I_d and I_q are %.4f A and %.4f A respectively '%(I_d,I_q  )\n",
      "\n",
      "# note : rounding off error."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Load angle is 8.23 degrees \n",
        "I_d and I_q are 4.9272 A and 8.8105 A respectively \n"
       ]
      }
     ],
     "prompt_number": 53
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.26 Page no : 81"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "X_d = 0.8\n",
      "X_q = 0.5\n",
      "R_a = 0.02 \t\t\t#armature resistance and synchronous reactance of direct quadrature axis\n",
      "\n",
      "\t\t\t#case(i)  lag\n",
      "phi = math.acos(0.8)\n",
      "V_t = 1\n",
      "I_a = 1\t\t\t#full-load\n",
      "psi = math.atan(  (V_t*math.sin(phi)+I_a*X_q)/(V_t*math.cos(phi)+I_a*R_a)            )\n",
      "delta = psi-phi\n",
      "\n",
      "I_d = I_a*math.sin(psi)\n",
      "I_q = I_a*math.cos(psi)\n",
      "\n",
      "E_f = V_t*math.cos(delta)+I_d*X_d+I_q*R_a\n",
      "regulation = 100*(E_f-V_t)/V_t\n",
      "print 'percentage regulation at 0.8 pf lag is %.2f percent'%(regulation)\n",
      "\n",
      "\t\t\t#case(ii)  lead\n",
      "phi2 = -1*math.acos(0.8) \t\t\t#minus sign because of leading pf\n",
      "psi2 = math.atan(  (V_t*math.sin(phi2)+I_a*X_q)/(V_t*math.cos(phi2)+I_a*R_a)            )\n",
      "delta2 = psi2-phi2\n",
      "\n",
      "I_d2 = I_a*math.sin(psi2)\n",
      "I_q2 = I_a*math.cos(psi2)\n",
      "\n",
      "E_f2 = V_t*math.cos(delta2)+I_d2*X_d+I_q2*R_a\n",
      "regulation2 = 100*(E_f2-V_t)/V_t\n",
      "print 'percentage regulation at 0.8 pf lead is %.f percent'%(regulation2)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "percentage regulation at 0.8 pf lag is 61.25 percent\n",
        "percentage regulation at 0.8 pf lead is -21 percent\n"
       ]
      }
     ],
     "prompt_number": 55
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.27 Page no : 83"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "from numpy import *\n",
      "\n",
      "# Variables\n",
      "kW = array([800,500,1000,600])\n",
      "cosphi = array([1,0.9,0.8,0.9])\n",
      "tanphi = tan(arccos(cosphi))\n",
      "kVAR = kW*tanphi\n",
      "\n",
      "# Calculations\n",
      "kW_total = kW[0]+kW[1]+kW[2]+kW[3]\n",
      "kVAR_total = kVAR[0]+kVAR[1]+kVAR[2]+-1*kVAR[3] \t\t\t#4th case is leading \n",
      "\n",
      "phi_c = math.atan(kVAR_total/kW_total)  \t\t\t#total power factor angle\n",
      "phi_1 = math.acos(0.95)\t\t\t#pf of machine 1\n",
      "kW_1 = 1000 \t\t\t#active component of machine 1\n",
      "kVAR_1 = kW_1*math.tan(phi_1) \t\t\t#reactive component of machine 1\n",
      "kW_2 = kW_total - kW_1 \t\t\t#active component of machine 1\n",
      "kVAR_2 = kVAR_total-kVAR_1 \t\t\t#reactive component of machine 2\n",
      "\n",
      "phi_2 = math.atan(kVAR_2/kW_2) \n",
      "pf_2 = math.cos(phi_2) \t\t\t#power factor of machine 2\n",
      "\n",
      "# Results\n",
      "print 'Output of second alternator =  %.0f kW'%(kW_2)\n",
      "print 'power factor of machine 2  =  %.2f and lagging'%(pf_2)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Output of second alternator =  1900 kW\n",
        "power factor of machine 2  =  0.98 and lagging\n"
       ]
      }
     ],
     "prompt_number": 56
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.28 Page no : 84"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "from numpy import *\n",
      "\n",
      "# Variables\n",
      "kW = array([250,300,150])\n",
      "cosphi = array([0.9,0.75,0.8]) \t\t\t#all lagging\n",
      "tanphi = tan(arccos(cosphi))\n",
      "kVAR = kW*tanphi\n",
      "\n",
      "# Calculations\n",
      "kW_total = kW[0]+kW[1]+kW[2]\n",
      "kVAR_total = kVAR[0]+kVAR[1]+kVAR[2] \n",
      "\n",
      "phi_1 = math.acos(0.8)\t\t\t#pf of machine 1\n",
      "kW_1 = 100 \t\t\t#active component of machine 1\n",
      "kVAR_1 = kW_1*math.tan(phi_1) \t\t\t#reactive component of machine 1\n",
      "kW_2 = kW_total - kW_1 \t\t\t#active component of machine 1\n",
      "kVAR_2 = kVAR_total-kVAR_1 \t\t\t#reactive component of machine 2\n",
      "phi_2 = math.atan(kVAR_2/kW_2) \n",
      "pf_2 = math.cos(phi_2) \t\t\t#power factor of machine 2\n",
      "\n",
      "# Results\n",
      "print 'Output of second alternator =  %.0f kW'%(kW_2)\n",
      "print 'power factor of machine 2  =  %.4f and lagging'%(pf_2)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Output of second alternator =  600 kW\n",
        "power factor of machine 2  =  0.8172 and lagging\n"
       ]
      }
     ],
     "prompt_number": 57
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.29 Page no :  85"
     ]
    },
    {
     "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",
      "V_t = V_ph\n",
      "X_d = 9.6\n",
      "X_q = 6.\n",
      "R_a = 0. \t\t\t#armature resistance and synchronous reactance of direct quadrature axis\n",
      "VA = 3.5*10**6\n",
      "I_L = VA/(math.sqrt(3)*V_L)\n",
      "\n",
      "# Calculations\n",
      "P = 2.5*10**6\n",
      "phi = math.acos(0.8)\n",
      "I_a = P/(math.sqrt(3)*V_L*math.cos(phi))\n",
      "psi = math.atan(  (V_t*math.sin(phi)+ I_a*X_q)/(V_t*math.cos(phi)+ I_a*R_a)     )\n",
      "\n",
      "delta = psi-phi\n",
      "I_d = I_a*math.sin(psi)\n",
      "I_q = I_a*math.cos(phi)\n",
      "\n",
      "E_f = V_t*math.cos(delta)+I_d*X_d+I_q*R_a\n",
      "regulation = 100*(E_f-V_t)/V_t\n",
      "P_max = (V_ph**2/2)*((X_d-X_q)/(X_d*X_q))*(math.sin(2*delta))\n",
      "\n",
      "# Results\n",
      "print 'percentage voltage regulation is %.2f percent'%(regulation)\n",
      "print 'Power under open circuit is %.1f kW per phase'%(P_max/1000)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "percentage voltage regulation is 50.85 percent\n",
        "Power under open circuit is 231.1 kW per phase\n"
       ]
      }
     ],
     "prompt_number": 58
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.30  Page no :  86"
     ]
    },
    {
     "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",
      "VA = 3.*10**6\n",
      "I_FL = VA/(math.sqrt(3)*V_L)\n",
      "IX_s = (25./100)*V_ph \t\t\t#product of I and X_s\n",
      "X_s = complex(0,IX_s/I_FL)\n",
      "N_s = 1000 \t\t\t#in r.p.m\n",
      "\n",
      "\n",
      "# Calculations\n",
      "Poles = 6.\n",
      "f = 50.\n",
      "delta_dash_mech = (math.pi/180) \t\t\t#print lacement in degree mechanical\n",
      "#print lacement in degree electrical\n",
      "delta_dash_elec = delta_dash_mech*(Poles/2)\n",
      "\n",
      "I = I_FL\n",
      "phi = math.acos(0.8)\n",
      "V = complex(V_ph*math.cos(phi),V_ph*math.sin(phi))\n",
      "E =  V+ I*X_s\n",
      "\n",
      "delta = (math.pi/180)*math.atan(E.imag/E.real)-phi   \t\t\t#E leads I by (math.pi/180)*phasemag(E) and V leads I by phi radians \n",
      "P_SY = abs(E)*abs(V_ph)*math.cos(delta)*math.sin(delta_dash_elec)/abs(X_s)   \t\t\t#Synchronising power per phase \n",
      "P_SY_total = 3*P_SY  \t\t\t#total Synchronising power\n",
      "\n",
      "ns = 120*f/(60*Poles)  \t\t\t#in r.p.m\n",
      "T_SY = P_SY_total/(2*math.pi*ns)   \t\t\t#Synchronising torque \n",
      "\n",
      "# Results\n",
      "print 'Synchronising power per phase is %.3f kW'%(P_SY/1000)\n",
      "print 'Synchronising torque is %.0f N-m'%(T_SY)\n",
      "print 'Answer mismatches due to improper approximation'\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Synchronising power per phase is 197.555 kW\n",
        "Synchronising torque is 5660 N-m\n",
        "Answer mismatches due to improper approximation\n"
       ]
      }
     ],
     "prompt_number": 60
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.31  Page no :  87"
     ]
    },
    {
     "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",
      "VA = 3.*10**6\n",
      "I_FL = VA/(math.sqrt(3)*V_L)\n",
      "IX_s = (20./100)*V_ph \t\t\t#product of I and X_s\n",
      "X_s = complex(0,IX_s/I_FL)\n",
      "N_s = 1000. \t\t\t#in r.p.m\n",
      "Poles = 6.\n",
      "f = 50.\n",
      "\n",
      "# Calculations\n",
      "delta_dash_mech = (math.pi/180) \t\t\t#print lacement in degree mechanical\n",
      "#print lacement in degree electrical \n",
      "delta_dash_elec = delta_dash_mech*(Poles/2)\n",
      "\n",
      "#E = V as the alternator is on no-load and X_s = Z_s\n",
      "P_SY = abs(V_ph)**2*(delta_dash_elec)/abs(X_s)   \t\t\t#Synchronising power per phase\n",
      "P_SY_total = 3*P_SY  \t\t\t#total Synchronising power\n",
      "\n",
      "ns = 120*f/(60*Poles)  \t\t\t#in r.p.s\n",
      "T_SY = P_SY_total/(2*math.pi*ns)   \t\t\t#Synchronising torque \n",
      "\n",
      "# Results\n",
      "print 'Synchronising power per phase is %.3f kW'%(P_SY/1000)\n",
      "print 'Total Synchronising power is %.3f kW'%(P_SY_total/1000)\n",
      "print 'Synchronising torque is %.0f N-m'%(T_SY)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Synchronising power per phase is 261.799 kW\n",
        "Total Synchronising power is 785.398 kW\n",
        "Synchronising torque is 7500 N-m\n"
       ]
      }
     ],
     "prompt_number": 61
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.32 Page no :  88"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "# Variables\n",
      "V_L = 11.*10**3\n",
      "V_ph = V_L/math.sqrt(3)\n",
      "VA = 700.*10**3\n",
      "I_FL = VA/(math.sqrt(3)*V_L)\n",
      "IX_s = (14./100)*V_ph \t\t\t#product of I and X_s\n",
      "X_s = IX_s/I_FL\n",
      "#X_s = complex(0,IX_s/I_FL)\n",
      "IR_a = (1.5/100)*V_ph \t\t\t#product of I and R_a\n",
      "R_a = IR_a/I_FL\n",
      "\n",
      "\n",
      "# Calculations\n",
      "I = I_FL\n",
      "phi = math.acos(0.8)\n",
      "V = complex(V_ph*math.cos(phi),V_ph*math.sin(phi))\n",
      "E_ph = math.sqrt(  (V_ph*math.cos(phi)+IR_a)**2 +(V_ph*math.sin(phi)+IX_s)**2    )\n",
      "delta = math.asin((V_ph*math.sin(phi)+IX_s)/E_ph)   -phi\n",
      "\n",
      "Poles = 4.\n",
      "f = 50.\n",
      "delta_dash_mech = (math.pi/180) \t\t\t#phase print lacemnt in degree mechanical\n",
      "delta_dash_elec = delta_dash_mech*(Poles/2)\t\t\t#phase print lacemnt in degree electrical\n",
      "\n",
      "P_SY = abs(V_ph)*abs(E_ph)*math.cos(delta)*math.sin(delta_dash_elec)/abs(X_s)   \t\t\t#Synchronising power per phase\n",
      "P_SY_total = 3*P_SY  \t\t\t#total Synchronising power\n",
      "\n",
      "ns = 120*f/(60*Poles)  \t\t\t#in r.p.s\n",
      "T_SY = P_SY_total/(2*math.pi*ns)   \t\t\t#Synchronising torque \n",
      "\n",
      "# Results\n",
      "print 'Synchronising power per phase is %.3f kW'%(P_SY/1000)\n",
      "print 'Synchronising power is %.3f kW ; '%(P_SY/1000)\n",
      "print 'Total Synchronising power is %.3f kW'%(P_SY_total/1000)\n",
      "print 'Synchronising torque is %.2f N-m'%(T_SY)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Synchronising power per phase is 63.750 kW\n",
        "Synchronising power is 63.750 kW ; \n",
        "Total Synchronising power is 191.249 kW\n",
        "Synchronising torque is 1217.53 N-m\n"
       ]
      }
     ],
     "prompt_number": 62
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.33 Page no : 91"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "import cmath\n",
      "\n",
      "#note that a new function p2z has been defined below for direct representation of complex numbers in polar form\n",
      "def  p2z(RRRR,Theeeta):\n",
      "    return  RRRR*cmath.exp(1j*math.pi*Theeeta/180.);\n",
      "\n",
      "# Variables\n",
      "Z1 = complex(0,2)\n",
      "Z2 = complex(0,3)\n",
      "Z = 6.\n",
      "E1 = p2z(230,0)\n",
      "E2 = p2z(230,10)\n",
      "\n",
      "# Calculations\n",
      "I1 = ((E1-E2)*Z+E1*Z2)/(Z*(Z1+Z2)+Z1*Z2)\n",
      "I2 = ((E2-E1)*Z+E2*Z1)/(Z*(Z1+Z2)+Z1*Z2)\n",
      "\n",
      "phi1 = math.atan(I1.imag/I1.real)  \t\t\t#Phasemag returns the angle of complex number in degrees\n",
      "phi2 = math.atan(I2.imag/I2.real)  \t\t\t#Phasemag returns the angle of complex number in degrees\n",
      "\n",
      "I = I1+I2\n",
      "V = I*Z \t\t\t#Terminal voltage\n",
      "\n",
      "# Results\n",
      "print 'i) Terminal voltage is %.2f volts at %.1f degrees'%(abs(V),math.degrees(math.atan(V.imag/V.real)))\n",
      "print 'ii) Currents are %.2f A at %.0f degrees and %.2f A at %.2f degrees     \\\n",
      "\\nTotal current is %.2f A at %.1f degrees  '%(abs(I1),math.degrees(math.atan(I1.imag/I1.real)),abs(I2),\\\n",
      "                                              math.degrees(math.atan(I2.imag/I2.real)),abs(I) \\\n",
      "                                              ,math.degrees(math.atan(I.imag/I.real)))\n",
      "\n",
      "P1 = abs(V)*abs(I1)*math.cos(math.radians(phi1))\n",
      "P2 = abs(V)*abs(I2)*math.cos(math.radians(phi2))\n",
      "print 'iii)Power delivered %.2f watts and  %.2f watts'%(P1,P2)\n",
      "\n",
      "# note : rounding off error. kindly check the calculations\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "i) Terminal voltage is 224.71 volts at -7.3 degrees\n",
        "ii) Currents are 14.74 A at -14 degrees and 22.88 A at -3.03 degrees     \n",
        "Total current is 37.45 A at -7.3 degrees  \n",
        "iii)Power delivered 3311.43 watts and  5141.03 watts\n"
       ]
      }
     ],
     "prompt_number": 65
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.34  Page no : 91"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "# Variables\n",
      "X_d = 0.8\n",
      "X_q = 0.5  \t\t\t#both per unit\n",
      "R_a = 0. \t\t\t#assumed\n",
      "phi = math.acos(0.8)\n",
      "V_t = 1.\t\t\t#pu\n",
      "I_a = 1. \t\t\t#full-load\n",
      "\n",
      "# Calculations\n",
      "psi = math.atan(  (V_t*math.sin(phi)+I_a*X_q)/(V_t*math.cos(phi)+I_a*R_a)            )\n",
      "delta = psi-phi\n",
      "I_d = I_a*math.sin(psi)\n",
      "I_q = I_a*math.cos(psi)\n",
      "E_f = V_t*math.cos(delta)+I_d*X_d+I_q*R_a\n",
      "\n",
      "# Results\n",
      "print 'Open circuit voltage is %.3f p.u.'%(E_f)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Open circuit voltage is 1.603 p.u.\n"
       ]
      }
     ],
     "prompt_number": 66
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.35 Page no : 92"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "from numpy import *\n",
      "\n",
      "# Variables\n",
      "V_L = 6600.\n",
      "I_L = 110.\n",
      "phi_1 = math.acos(0.9) \t\t\t#lagging\n",
      "kW = array([400,1000,400,300])*10**3\n",
      "cosphi = array([1,0.71,0.8,0.9])\n",
      "tanphi = tan(arccos(cosphi))\n",
      "kVAR = kW*tanphi\n",
      "\n",
      "# Calculations\n",
      "kW_total = kW[0]+kW[1]+kW[2]+kW[3]\n",
      "kVAR_total = kVAR[0]+kVAR[1]+kVAR[2]+kVAR[3]\n",
      "\n",
      "phi_c = math.atan(kVAR_total/kW_total)  \t\t\t#total power factor angle\n",
      "load_1 = math.sqrt(3)*V_L*I_L*math.cos(phi_1)\n",
      "\n",
      "kW_1 = load_1 \t\t\t#active component of machine 1\n",
      "kVAR_1 = kW_1*math.tan(phi_1) \t\t\t#reactive component of machine 1\n",
      "kW_2 = kW_total - kW_1 \t\t\t#active component of machine 1\n",
      "kVAR_2 = kVAR_total-kVAR_1 \t\t\t#reactive component of machine 2\n",
      "\n",
      "phi_2 = math.atan(kVAR_2/kW_2) \n",
      "pf_2 = math.cos(phi_2) \t\t\t#power factor of machine 2\n",
      "\n",
      "# Results\n",
      "print 'Output of second alternator =  %.2f kW'%(kW_2/1000)\n",
      "print 'Power factor of machine 2  =  %.4f and lagging'%(pf_2)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Output of second alternator =  968.28 kW\n",
        "Power factor of machine 2  =  0.7366 and lagging\n"
       ]
      }
     ],
     "prompt_number": 67
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.36  Page no :  93"
     ]
    },
    {
     "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 = 2.*10**6\n",
      "phi = math.acos(0.8)\n",
      "I_FL = VA/(math.sqrt(3)*V_L)\n",
      "phi_1 = math.acos(0.8)\n",
      "IX_s = (20./100)*V_ph \t\t\t#product of I and X_s\n",
      "\n",
      "# Calculations\n",
      "X_s = IX_s/I_FL\n",
      "I_1 = I_FL\n",
      "BC = I_1*math.cos(phi_1)*X_s\n",
      "AB = I_1*math.sin(phi_1)*X_s    \n",
      "OA = V_ph\n",
      "OC = math.sqrt( (OA+AB)**2+(BC)**2 ) \n",
      "E_1 = OC\n",
      "E_2 = 1.25*E_1\n",
      "OE = E_2\n",
      "DE = BC\n",
      "AD = math.sqrt(OE**2-DE**2) -OA           \t\t\t#because OE = math.sqrt( (OA+AD)**2 + (DE)**2  )\n",
      "\n",
      "I_2sinphi2 = AD/X_s\n",
      "I_2cosphi2 = I_1*math.cos(phi)\n",
      "I_2 = math.sqrt( (I_2cosphi2)**2 + (I_2sinphi2)**2  )\n",
      "phi2 = math.atan( I_2sinphi2/ I_2cosphi2 )\n",
      "new_pf = math.cos(phi2)\n",
      "\n",
      "# Results\n",
      "print 'Machine current is %.2f A '%(I_2)\n",
      "print 'Power factor is  %.4f lagging'%(new_pf)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Machine current is 228.62 A \n",
        "Power factor is  0.3673 lagging\n"
       ]
      }
     ],
     "prompt_number": 68
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.37  Page no :  95"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "#note that a new function p2z has been defined below for direct representation of complex numbers in polar form\n",
      "def  p2z(RRRR,Theeeta):\n",
      "    return  RRRR*exp(1j*math.pi*Theeeta/180.);\n",
      "\n",
      "\n",
      "# Variables\n",
      "P_out = 3000.*10**3\n",
      "V_L = 6.6*10**3\n",
      "V_ph = V_L/math.sqrt(3)\n",
      "phi = math.acos(0.8)\n",
      "I_L = p2z(P_out/(math.sqrt(3)*V_L*math.cos(phi)),-1*(180/math.pi)*phi)\n",
      "\n",
      "# Calculations\n",
      "P_out1 = P_out/2\n",
      "I_L1 = 150  \t\t\t#given\n",
      "phi_L1 = math.acos(    P_out1/(math.sqrt(3)*V_L*I_L1)  )\n",
      "I_L1 = p2z(I_L1,-1*(180/math.pi)*phi_L1)\n",
      "\n",
      "I_L2 = I_L-I_L1\n",
      "pf_2 = math.cos(math.atan(I_L2.imag/I_L2.real))\n",
      "Z_1 = complex(0.5,10)\n",
      "I_1 = I_L1\n",
      "E_1 = V_ph + I_1*Z_1\n",
      "delta_1 =  math.atan(E_1.imag/E_1.real)   \t\t\t#load angle of alternator 1\n",
      "E_1L = math.sqrt(3)*E_1\n",
      "\n",
      "Z_2 = complex(0.4,12)\n",
      "I_2 = I_L2\n",
      "E_2 = V_ph + I_2*Z_2\n",
      "delta_2 = (math.pi/180)*math.atan(E_2.imag/E_2.real)    \t\t\t#load angle of alternator 2\n",
      "\n",
      "# Results\n",
      "print 'Part i) Currents are %.0f A at %.1f degrees and %.1f A at %.1f degrees\\nTotal current is %.0f at %.2f' %(abs(I_L1),\\\n",
      "                            math.degrees(math.atan(I_L1.imag/I_L1.real)),abs(I_L2),\\\n",
      "                            math.degrees(math.atan(I_L2.imag/I_L2.real)),abs(I_L),math.degrees(math.atan(I_L.imag/I_L.real)))\n",
      "print 'Part ii)Power factor is %.4f and lagging'%(math.cos(phi_L1))\n",
      "print 'Part iii)emf are %.2f V at %.2f degrees and %.4f V at %.0f degrees'%(abs(E_1),\\\n",
      "                            math.degrees(math.atan(E_1.imag/E_1.real)),abs(E_2),math.degrees(math.atan(E_2.imag/E_2.real)))\n",
      "print 'Part iv)Power angles are %.2f degrees and %.0f degrees '%(180/math.pi*delta_1,(180/math.pi)*delta_2)\n",
      "\n",
      "# note : rounding off error. kindly check the calculations\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Part i) Currents are 150 A at -29.0 degrees and 180.6 A at -43.4 degrees\n",
        "Total current is 328 at -36.87\n",
        "Part ii)Power factor is 0.8748 and lagging\n",
        "Part iii)emf are 4776.46 V at 15.49 degrees and 5565.7081 V at 16 degrees\n",
        "Part iv)Power angles are 15.49 degrees and 0 degrees \n"
       ]
      }
     ],
     "prompt_number": 73
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.38  Page no :  97"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "# Variables\n",
      "Z1 = complex(0.2,2)\n",
      "Z2 = Z1\n",
      "ZL = complex(3,4)\n",
      "Z = ZL\n",
      "E1 = complex(2000,0)\n",
      "E2 = complex(2200,100)\n",
      "\n",
      "# Calculations\n",
      "I1 = ((E1-E2)*Z+E1*Z2)/(Z*(Z1+Z2)+Z1*Z2)\n",
      "I2 = ((E2-E1)*Z+E2*Z1)/(Z*(Z1+Z2)+Z1*Z2)\n",
      "\n",
      "IL = I1+I2\n",
      "V = IL*Z \t\t\t#Terminal voltage\n",
      "\n",
      "phi1 = math.atan(V.imag/V.real)-math.atan(I1.imag/I1.real)  \t\t\t#Phasemag returns the angle of complex number in degrees\n",
      "phi2 = math.atan(V.imag/V.real)-math.atan(I2.imag/I2.real)  \t\t\t#Phasemag returns the angle of complex number in degrees\n",
      "\n",
      "Pout1 = math.sqrt(3)*math.sqrt(3)*abs(V)*abs(I1)*math.cos(math.radians(phi1))\n",
      "Pout2 = math.sqrt(3)*math.sqrt(3)*abs(V)*abs(I2)*math.cos(math.radians(phi2))\n",
      "\n",
      "# Results\n",
      "print 'Power delivered is %.2f kW and %.2f kW at power-factors %.4f lag and %.4f lag respectively'%(Pout1/1000,Pout2/1000,math.cos(math.radians(phi1)),math.cos(math.radians(phi2)))\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Power delivered is 658.24 kW and 1253.92 kW at power-factors 0.9999 lag and 0.9999 lag respectively\n"
       ]
      }
     ],
     "prompt_number": 74
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.39  Page no :  99"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "# Variables\n",
      "f = 50.\n",
      "P = 12.\n",
      "V_L = 6600.\n",
      "V_ph = V_L/math.sqrt(3)\n",
      "VA = 2000.*10**3\n",
      "I_FL = VA/(math.sqrt(3)*V_L)\n",
      "\n",
      "# Calculations\n",
      "IX_s = (25./100)*V_ph \t\t\t#product of I and X_s\n",
      "X_s = complex(0,IX_s/I_FL)\n",
      "N_s = 12*f/P \t\t\t#in rpm\n",
      "delta_dash_mech = (math.pi/180) \t\t\t#phase print lacemnt in degree mechanical\n",
      "delta_dash_elec = delta_dash_mech*(P/2) \t\t\t#phase print lacemnt in degree electrical\n",
      "\n",
      "phi = math.acos(0.8) \t\t\t#lag\n",
      "I = complex(I_FL*math.cos(-1*phi),I_FL*math.sin(-1*phi))\n",
      "V = V_ph\n",
      "E = V + I*X_s\n",
      "delta = math.atan(E.imag/E.real)*(math.pi/180)\n",
      "P_SY = abs(E)*abs(V)*math.cos(delta)*math.sin(delta_dash_elec)/abs(X_s)\n",
      "P_SY_total = 3*P_SY\n",
      "\n",
      "# Results\n",
      "print 'Synchronising power is %.2f kW'%(P_SY/1000)\n",
      "print 'Total Synchronising power is %.2f kW'%(P_SY_total/1000)\n",
      "\n",
      "# note : rounding off error. kindly check."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Synchronising power is 325.36 kW\n",
        "Total Synchronising power is 976.09 kW\n"
       ]
      }
     ],
     "prompt_number": 76
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.40  Page no :  101"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "# Variables\n",
      "V_L = 22000.\n",
      "V_ph = V_L/math.sqrt(3)\n",
      "power = 230.*10**6\n",
      "phi = math.acos(1.)\n",
      "I_FL = power/(math.sqrt(3)*V_L*math.cos(phi))\n",
      "I_1 = I_FL\n",
      "X_s = 1.2\n",
      "\n",
      "# Calculations\n",
      "E_1 = math.sqrt( V_ph**2 + (I_1*X_s)**2 )\n",
      "E_2 = 1.3*E_1\n",
      "AC =   math.sqrt( E_2**2-(I_1*X_s)**2  )   -V_ph     \t\t\t# because E**2 = (V_ph+AC)**2+(I_1*X_s)**2\n",
      "I2X_S = AC\n",
      "\n",
      "I_2cosphi2 = I_1  \t\t\t#because phi_2 = math.acos(I_1/I_2) \t\t\t#from ACD\n",
      "I_2sinphi2 = AC/X_s\n",
      "I_2 = math.sqrt( (I_2cosphi2)**2 + (I_2sinphi2)**2  )\n",
      "phi2 = math.atan( I_2sinphi2/ I_2cosphi2 )\n",
      "new_pf = math.cos(phi2)\n",
      "\n",
      "# Results\n",
      "print 'Machine current is %.2f A '%(I_2)\n",
      "print 'Power factor is  %.4f and lagging'%(new_pf)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Machine current is 7274.58 A \n",
        "Power factor is  0.8297 and lagging\n"
       ]
      }
     ],
     "prompt_number": 77
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.41  Page no :  102"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "import cmath\n",
      "\n",
      "#note that a new function p2z has been defined below for direct representation of complex numbers in polar form\n",
      "def  p2z(RRRR,Theeeta):\n",
      "\treturn RRRR*cmath.exp(1j*math.pi*Theeeta/180.);\n",
      "\n",
      "# Variables\n",
      "P_out = 1500.*10**3\n",
      "V_L = 3.3*10**3\n",
      "phi = math.acos(0.8)\n",
      "I_L = p2z(P_out/(math.sqrt(3)*V_L*math.cos(phi)),-1*math.acos(math.radians(0.8)))\n",
      "\n",
      "I_L1_magnitude = 150.  \t\t\t#given\n",
      "P_out1 = (3.*10**6)/2 \t\t\t#because load is EQUALLY shared between 2 alternators\n",
      "pf_L1 = P_out1/(math.sqrt(3)*2*V_L*I_L1_magnitude)  \t\t\t#operating pf of alternator 1\n",
      "phi1 = math.acos(math.radians(pf_L1))\n",
      "I_L1 = p2z(I_L1_magnitude,-1*phi1)\n",
      "I_L2 = I_L-I_L1   \t\t\t#because I_L = I_L1 + I_L2\n",
      "pf_L2 = math.cos(math.atan(I_L2.imag/I_L2.real))\n",
      "\n",
      "# Calculations\n",
      "V_ph = 6.6*10**3/math.sqrt(3)\n",
      "Z_1 = complex(0.5,10)\n",
      "I_1 = I_L1\n",
      "E_1 =  V_ph + I_1*Z_1\n",
      "delta_1 = math.atan(E_1.imag/E_1.real)  \t\t\t#load angle of alternator 1\n",
      "I_2 = I_L2\n",
      "\n",
      "Z_2 = complex(0.4,12)\n",
      "E_2 =  V_ph + I_2*Z_2\n",
      "delta_2 = math.atan(E_2.imag/E_2.real) \t\t\t#load angle of alternator 1\n",
      "\n",
      "# Results\n",
      "print 'for machine 1current is %.0f A at %.2f degrees \\nPower factor of %.4f laginduced emf \\\n",
      "        of %.2f V \\nload angle of %.2f degrees'%(abs(I_L1),math.degrees(math.atan(I_L1.imag/I_L1.real)),pf_L1,abs(E_1),delta_1)\n",
      "print 'for machine 2current is %.1f A at %.1f degrees\\nPower factor of %.4f laginduced emf \\\n",
      "        of %.2f V\\nload angle of %.0f degrees'%(abs(I_L2),math.degrees(math.atan(I_L2.imag/I_L2.real)),pf_L2,abs(E_2),math.degrees(delta_2))\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "for machine 1current is 150 A at -1.56 degrees \n",
        "Power factor of 0.8748 laginduced emf         of 4202.06 V \n",
        "load angle of 0.36 degrees\n",
        "for machine 2current is 178.0 A at -1.6 degrees\n",
        "Power factor of 0.9996 laginduced emf         of 4480.49 V\n",
        "load angle of 28 degrees\n"
       ]
      }
     ],
     "prompt_number": 81
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.42  Page no :  104"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "# Variables\n",
      "V_l = 230\n",
      "VA = 5*10**3\n",
      "X_d = 12\n",
      "X_q = 7\n",
      "R_a = 0 \t\t\t#armature resistance and synchronous reactance of direct quadrature axis\n",
      "phi = math.acos(1)\n",
      "\n",
      "# Calculations\n",
      "I_l = VA/(V_l*math.sqrt(3))\n",
      "V_ph = V_l/math.sqrt(3)\n",
      "V_t = V_ph\n",
      "I_a = I_l\n",
      "\n",
      "psi = math.atan(  (V_t*math.sin(phi)+I_a*X_q)/(V_t*math.cos(phi)+I_a*R_a)            )\n",
      "delta = psi-phi\n",
      "I_d = I_a*math.sin(psi)\n",
      "I_q = I_a*math.cos(psi)\n",
      "E_f = V_t*math.cos(delta)+I_d*X_d+I_q*R_a\n",
      "\n",
      "# Results\n",
      "print 'Excitation voltage is %.3f V '%(E_f)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Excitation voltage is 193.852 V \n"
       ]
      }
     ],
     "prompt_number": 82
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 6.43  Page no :  104"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "# Variables\n",
      "V_l = 6.6*10**3\n",
      "V_t = V_l/math.sqrt(3)\n",
      "X_d = 23.2\n",
      "X_q = 14.5\n",
      "R_a = 0. \t\t\t#armature resistance and synchronous reactance of direct quadrature axis\n",
      "VA = 1800.*10**3\n",
      "phi = math.acos(0.8) \t\t\t#lag\n",
      "\n",
      "# Calculations and Results\n",
      "I_a = VA/(V_l*math.sqrt(3))\n",
      "\n",
      "psi = math.atan(  (V_t*math.sin(phi)-I_a*X_q)/(V_t*math.cos(phi)-I_a*R_a)  ) \t\t\t#minus sign in numerator and denomenator for motors\n",
      "delta = psi+phi\n",
      "I_d = I_a*math.sin(psi)\n",
      "I_q = I_a*math.cos(psi)\n",
      "E_f = V_t*math.cos(delta)-I_d*X_d-I_q*R_a\n",
      "print 'Excitation emf  =  %.4f V'%(E_f)\n",
      "#P_m =  ( V_t*E_f*math.sin(delta)/X_d  ) + ((1/X_q)-(1/X_d))*0.5*math.sin(2*delta)*V_t**2\n",
      "#P_m = 0.4996*math.cos(delta)+0.1877*math.sin(2*delta)\n",
      "#for maximum power output differenciate and equate to zero\n",
      "\n",
      "delta_max = 63.4 \t\t\t#degree\n",
      "\n",
      "P_m_max = ((1/X_q)-(1/X_d))*0.5*math.sin(math.radians(2*delta_max))*V_t**2   \t\t\t#Maximuum load supplied with E_f = 0\n",
      "print 'Maximum load the motor can supply is %.4f MW per phase '%(P_m_max*10**-6      )\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Excitation emf  =  3042.2721 V\n",
        "Maximum load the motor can supply is 0.1503 MW per phase \n"
       ]
      }
     ],
     "prompt_number": 83
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}