path: root/ELECTRIC_MACHINERY_by_Fitzgerald_Kingsley_and_Umans/chapter5.ipynb

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   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 5: Synchronous Machines"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 5.1, Page number: 254"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import math\n",
      "import cmath\n",
      "\n",
      "#Varaible Declaration:\n",
      "pf=0.95                                 #Lagging power factor\n",
      "Vl=460                                  #Terminal voltage(V)\n",
      "I=120                                   #Terminal current(A)\n",
      "If=47                                   #Field current(A)\n",
      "X=1.68j                                 #Line syncchronous reactance(ohm)\n",
      "\n",
      "\n",
      "#Calculation:\n",
      "#Choosing motor reference direction:\n",
      "Va=Vl/math.sqrt(3)\n",
      "theta=math.acos(0.95)\n",
      "Ia=I*cmath.exp(-theta*1j)\n",
      "Eaf=Va-X*Ia\n",
      "wc=120*math.pi\n",
      "Laf=math.sqrt(2)*abs(Eaf)/(wc*If)\n",
      "P=3*Va*Ia*pf\n",
      "\n",
      "#Results:\n",
      "print \"Generated emf:\",round(abs(Eaf),1),\"V line to line\"\n",
      "print \"Fied to armature mutual inductance:\",round(Laf*1000,1),\"mH\"\n",
      "print \"Three phase power:\",round(abs(P/1000),1),\"kW or\",round(abs(P)/746),\"hp\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Generated emf: 278.8 V line to line\n",
        "Fied to armature mutual inductance: 22.3 mH\n",
        "Three phase power: 90.8 kW or 122.0 hp\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 5.2, Page number: 255"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import cmath \n",
      "from math import *\n",
      "\n",
      "#Variable Declaration:\n",
      "Pin=90.6*10**3                              #Input power(kW)\n",
      "Va=265.6                                    #Terninal voltage(V)\n",
      "X=1.68j                                     #Synchronous reactance(ohm)\n",
      "Laf=22.3*10**-3                             #Mutual inductance(H)\n",
      "wc=120*pi                                   #Angular frequency(rad/sec)\n",
      "\n",
      "\n",
      "#Calculations:\n",
      "Ia=Pin/(3*Va)\n",
      "Eaf=Va-X*Ia\n",
      "delta=degrees(cmath.phase(Eaf))\n",
      "I=sqrt(2)*Eaf/(wc*Laf)\n",
      "\n",
      "\n",
      "#Results:\n",
      "print\"The phase angle,delta:\",round(delta,1),\"degrees\"\n",
      "print\"Required field current:\",round(abs(I),2),\"A\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The phase angle,delta: -35.7 degrees\n",
        "Required field current: 55.04 A\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 5.3, Page number: 257"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "from math import *\n",
      "\n",
      "#Variable declaration:\n",
      "Eafl=13.8*10**3                             #Open circuit voltage(V)\n",
      "If1=318                                     #Field current(A)\n",
      "If2=263                              #Field current after extrapolation(A)\n",
      "wc=120*pi                            #Angular frequency(Hz)\n",
      "\n",
      "#Calculations:\n",
      "Eaf=Eafl/sqrt(3)\n",
      "La1=sqrt(2)*Eaf/(wc*If1)\n",
      "La2=sqrt(2)*Eaf/(wc*If2)\n",
      "\n",
      "#Results:\n",
      "print \"Saturated Laf1:\",round(La1*1000,0),\"mH\"    \n",
      "print \"Unsaturated Laf1:\",round(La2*1000,0),\"mH\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Saturated Laf1: 94.0 mH\n",
        "Unsaturated Laf1: 114.0 mH\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 5.4, Page number: 262"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "from math import *\n",
      "\n",
      "#Variable declaration:\n",
      "Ia=[118, 152]                     #Armature current from SC Characteristics(A)\n",
      "If=[2.20, 2.84]                     #Field current from SC Characteristics(A)\n",
      "Vll=220                             #Line-to-line Voltage(V)\n",
      "V=202                               #Line-to-line air voltage(V) \n",
      "P=45*10**3                          #Power roted to motor(W)   \n",
      "Is_sc=1                             #per unit rated current(A)\n",
      "\n",
      "#Calculations:\n",
      "Va_ag=V/sqrt(3)                 #At field current of 2.20A,at air gap,(V)\n",
      "Ia_ag=Ia[0]\n",
      "Xs_u=Va_ag/Ia_ag\n",
      "Ia_rated=P/(sqrt(3)*Vll)\n",
      "Xa_g=Va_ag/1\n",
      "Xs_u_pu=Va_ag/Is_sc\n",
      "Xs=Vll/(Ia[1]*sqrt(3))\n",
      "Ia_pu=Ia[1]/Ia[0]\n",
      "SCR=If[1]/If[0]\n",
      "Xs=1/SCR\n",
      "\n",
      "\n",
      "\n",
      "#Results:\n",
      "print \"'All quantities are in per unit values'\"\n",
      "print\"Unsaturated value of synchronous reactance:\",round(Xs_u,3),\"ohm\"\n",
      "print \"Satureted value of synchronous reactance: \",round(Xs,3),\"ohm\"\n",
      "print\"Short circuit ratio:\",round(SCR,3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "'All quantities are in per unit values'\n",
        "Unsaturated value of synchronous reactance: 0.988 ohm\n",
        "Satureted value of synchronous reactance:  0.775 ohm\n",
        "Short circuit ratio: 1.291\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 5.5, Page number: 265"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "\n",
      "#Variable declaration:\n",
      "P_rated=45*10**3                        #Rated power(KV)\n",
      "Pl=1.80*10**3                           #Short circuit load loss(W)\n",
      "Ia_pu=1                                    #Per unit armature current\n",
      "Ia=118                                  #rated armature current(A)\n",
      "Ra_dc=0.0335                            #Dc resistance(ohm/phase)\n",
      "\n",
      "\n",
      "#Calculations:\n",
      "Pl_pu=Pl/P_rated    \n",
      "Ra_eff1=Pl_pu/Ia_pu**2                      #in per unit basis\n",
      "Ra_eff2=Pl/(3*(Ia)**2)\n",
      "\n",
      "#Results:\n",
      "print \"Armature resistance in per unit:\",round(Ra_eff1,3),\"per unit\" \n",
      "print \"Armature resistance in ohms/phase:\", round(Ra_eff2,3),\"ohms/phase\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Armature resistance in per unit: 0.04 per unit\n",
        "Armature resistance in ohms/phase: 0.043 ohms/phase\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 5.6, Page number: 269"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "%matplotlib inline\n",
      "import cmath\n",
      "import math\n",
      "from pylab import *\n",
      "\n",
      "\n",
      "#Variable declaration:\n",
      "Veq=1.0                                 #Externalsupply(p.u)                                    \n",
      "Eaf=1.0                                 #Internal voltage(p.u)\n",
      "Xeq=0.23                                #Eqv.resistance of external system(p.u)\n",
      "Xs=1.35                                #Saturated synchronous reactance(p.u)\n",
      "\n",
      "\n",
      "#Calculations:\n",
      "#for part (a):\n",
      "P_max=Eaf*Veq/(Xs+Xeq)\n",
      "\n",
      "\n",
      "#for part (b):\n",
      "delta=[0]*500\n",
      "Ia=[0]*500\n",
      "Va=[0]*500\n",
      "degree=[0]*500\n",
      "for n in range(1,101,1):\n",
      "    delta[n-1]=(pi/2)*(n-1)/100\n",
      "    Ia[n-1] = (Eaf *exp(1j*delta[n-1]) - Veq)/(1j*(Xs + Xeq))\n",
      "    Va[n-1] = abs(Veq + 1j*Xeq*Ia[n-1])\n",
      "    degree[n-1]=180*delta[n-1]/pi\n",
      "plot(degree,Va,'r.')\n",
      "xlabel('Power angle,delta(degrees)')\n",
      "ylabel('Terminal voltage(per unit)')\n",
      "title('Terminal voltage vs. power angle for part (b)')\n",
      "show()\n",
      "#for part (c):\n",
      "Vterm=1.0\n",
      "P=[0]*500\n",
      "deltat=[0]*500\n",
      "Ia=[0]*500\n",
      "Eaf=[0]*500\n",
      "\n",
      "for n in range(1,101,1):\n",
      "    P[n-1]=(n-1)/100\n",
      "    deltat[n-1]=math.asin(P[n-1]*Xeq/(Vterm*Veq))\n",
      "    Ia[n-1]=(Vterm*exp(1j*deltat[n-1])-Veq)/(1j*Xeq)\n",
      "    Eaf[n-1]=abs(Vterm+1j*(Xs+Xeq)*Ia[n-1])\n",
      "plot(P,Eaf,'r.')\n",
      "xlabel('Power [per unit]')\n",
      "ylabel('Eaf [per unit]')\n",
      "title('Eaf vs. power for part (c)')\n",
      "show()\n",
      "\n",
      "\n",
      "\n",
      "#Results:\n",
      "print \"(a) Maximum power supplied to external system:\",round(P_max,2),\"p.u\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
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69aqv6EMDAIDu1G5CkJWVrZeVla1n5rlcrhT6EAAA3j/tJgRXV9fYTZs2fVVT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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x34638d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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zy9hstiQsLGxPcnLyDNkyAwcOvEXXOOrr600tLS3vySYFAADoeUpvuz1t2rSj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\ncv4f7PGByn7cLZQAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x3463890>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(a) Maximum power supplied to external system: 0.63 p.u\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 5.7, Page number: 272"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "from math import *\n",
      "\n",
      "#Variable declaration:\n",
      "P_rated=2000*746/3                     #per phase rated power of motor(W)\n",
      "Xsm=1.95                                #Synchronous reactance(ohm)\n",
      "Vl=2300                                #Line to line voltage(V)\n",
      "f=60                                   #Angular frequency(Hz)\n",
      "p=30                                   #No. of poles\n",
      "Xsg=2.65                               #Synchronous reactance of generator(ohm)\n",
      "\n",
      "\n",
      "#Calculations:\n",
      "#for part (a):\n",
      "Vp=2300/sqrt(3)\n",
      "Ip=P_rated/Vp\n",
      "Eafm=sqrt(Vp**2+(Ip*Xsm)**2)\n",
      "Pm=3*Vp*Eafm/Xsm                             #Max power delivered to motor(W)\n",
      "ws=2*2*pi*f/p\n",
      "Tmax=Pm/ws                                  #MAx torque of motor(Nm)\n",
      "\n",
      "\n",
      "#for part (b):\n",
      "Eafg=sqrt(Vp**2+(Ip*Xsg)**2)\n",
      "Pm2=3*Eafm*Eafg/(Xsg+Xsm)                   #Max power delivered to motor(W)\n",
      "Tmax2=Pm2/ws                                #Max torque(Nm)\n",
      "\n",
      "\n",
      "\n",
      "#Results:\n",
      "print\"(a) Max power  :\",round(Pm/1000,0),\"kW,3-ph\"\n",
      "print\"    Max torque :\",round(Tmax/1000,1),\"kNm\"\n",
      "print \"(b) Max power :\", round(Pm2/1000,0),\"kW,3-ph\"\n",
      "print \"    Max torque:\", round(Tmax2/1000,1),\"Nm\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(a) Max power  : 3096.0 kW,3-ph\n",
        "    Max torque : 123.2 kNm\n",
        "(b) Max power : 1639.0 kW,3-ph\n",
        "    Max torque: 65.2 Nm\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 5.8, Page number: 279"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "from math import *\n",
      "\n",
      "\n",
      "#Variable declaration:\n",
      "P=45                                    #Power rated(KVA)\n",
      "Va=220                                  #Terminal voltage(V)\n",
      "Pin=45                                  #Power input to the armature(KVA)\n",
      "If=5.50                                 #field current(A)\n",
      "Rf=35.5                                 #Field winding resistance(ohm)\n",
      "Ra=0.0399                               #Armature dc resistance(ohm/phase)\n",
      "Xal=0.215                               #Leakage reactance of motor(ohm)\n",
      "pf=0.80                                 #Lagging power factor \n",
      "Pc=1.8                                  #Core loss(kW)\n",
      "Pw=0.91                                 #Friction & windage losses(kW)\n",
      "Ps=0.37                                 #Stray load loss(kW)\n",
      "\n",
      "\n",
      "#Calculations:\n",
      "Ia=P*10**3/(sqrt(3)*Va)\n",
      "P1=If**2*Rf/10**3                            #Loss in field winding(kW)\n",
      "P2=3*Ia**2*Ra/10**3                          #Loss in armature(kW)\n",
      "Pl=(Pc+Pw+Ps+P1+P2)\n",
      "Pi=Pin*pf+P1\n",
      "Po=Pi-Pl\n",
      "eff=(Po/Pi)*100\n",
      "\n",
      "#Results:\n",
      "print \"Efficiency of the synchronous machine:\",round(eff,1),\"%\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Efficiency of the synchronous machine: 84.3 %\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 5.9, Page number: 287"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import math\n",
      "import cmath\n",
      "\n",
      "#Variable declaration:\n",
      "Xd=1                              #Direct axis synchronus reactance(p.u)\n",
      "Xq=0.60                           #Quadrature axis synchronous reactance(p.u)\n",
      "Va=1                              #Terminal voltage(p.u)\n",
      "pf=0.8                              #Lagging power factor\n",
      "Ia=0.8-1j*math.sin(math.acos(0.8))       #Line current(p.u)\n",
      "\n",
      "\n",
      "#Calculations:\n",
      "phy=-math.acos(pf)\n",
      "E=Va+1j*Xq*Ia\n",
      "delta=cmath.phase(E)\n",
      "Id=abs(Ia)*math.sin(delta-phy)*cmath.exp(1j*(-pi/2+delta))\n",
      "Iq=abs(Ia)*math.cos(delta-phy)*cmath.exp(1j*delta)\n",
      "Eaf=Va+Xd*Id*1j+Xq*Iq*1j\n",
      "\n",
      "\n",
      "#Results:\n",
      "print \"Generated voltage:\",round(abs(Eaf),2),\"p.u Volt\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Generated voltage: 1.78 p.u Volt\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 5.11, Page number: 291"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from pylab import *\n",
      "import cmath\n",
      "from sympy import *\n",
      "\n",
      "#Variable declaration:\n",
      "P_rated=2000*746                  #Rated power of motor(W)\n",
      "Xs=1.95                           #Synchronous reactance(ohm/phase)\n",
      "Xd=1.95                           #Direct axis synchronous reactance(ohm/ph)\n",
      "Xq=1.40                         #Quadrature axis synchronous reactance(ohm/ph)\n",
      "pf=1                            #Power factor of the machine\n",
      "Vl=2300                         #Line to line voltage(V)\n",
      "\n",
      "#Calculatons:\n",
      "Va=float(Vl/sqrt(3))              #volt\n",
      "Ia=float(P_rated/(Va*3))          #ampere\n",
      "E1=Va-1j*Ia*Xq                      #From phasor diagram\n",
      "delta=cmath.phase(E1)             #power angle\n",
      "Id=Ia*sin(abs(delta))             #direct axis current(A)\n",
      "Eaf=abs(E1)+Id*(Xd-Xq)\n",
      "r=symbols('r')\n",
      "def P(r):                           #Process for finding maximum power\n",
      "    return Eaf*Va*sin(r)/Xd + Va**2*(Xd-Xq)*sin(2*r)/(2*Xd*Xq)\n",
      "P1=diff(P(r),r)\n",
      "#On differentiation,\n",
      "#P1 = 1023732.58489791*cos(r) + 355250.305250306*(2*(cos(r))**2-1)\n",
      "l = solve(1023732.58489791*cos(r) + 355250.305250306*(2*(cos(r))**2-1),r)\n",
      "P_max = (P(round(l[0],5)))\n",
      "\n",
      "\n",
      "#Results:\n",
      "print \"Maximum mechanical power:\",math.ceil(3*P_max/10**3),\"kW,3-phase\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Maximum mechanical power: 3236.0 kW,3-phase\n"
       ]
      }
     ],
     "prompt_number": 1
    }
   ],
   "metadata": {}
  }
 ]
}