path: root/ELECTRIC_MACHINERY_by_Fitzgerald_Kingsley_and_Umans/chapter9.ipynb

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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 9: Single- and Two-Phase Motors"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 9.1, Page number: 459"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "from sympy import *\n",
      "import math\n",
      "\n",
      "#Variable declaration:\n",
      "Zmain=4.5+3.7j                              #main winding impedance(ohm)\n",
      "Zaux=9.5+3.5j                               #auxilliary winding impedance(ohm)\n",
      "f=60                                        #frequency(Hz)\n",
      "\n",
      "\n",
      "#Calculations:\n",
      "phy_main=math.degrees(math.atan(Zmain.imag/Zmain.real))\n",
      "phy=phy_main-90\n",
      "w=2*pi*60\n",
      "Xc=symbols('Xc')\n",
      "a=solve((3.5+Xc)/9.5-math.tan(math.radians(float(phy))), Xc)\n",
      "C=-1/(w*a[0])\n",
      "\n",
      "\n",
      "#Results:\n",
      "print \"The starting capacitance:\",round(float(C)*10**6,0), \"uF\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The starting capacitance: 176.0 uF\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 9.2, Page number: 467"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import cmath\n",
      "from math import *\n",
      "\n",
      "\n",
      "#Variable Declaration:\n",
      "R1_m=2.02                                   #resistance of main winding(ohm)\n",
      "X1_m=2.79                                   #resistance of main\n",
      "R2_m= 4.12                                  #Rotor resistance ref. to stator(ohm)\n",
      "X2_m=2.12                                   #Rotor reactance ref. to stator(ohm)\n",
      "Xm=66.8                                     #Magnetising reactance(ohm)\n",
      "s=0.05                                      #slip\n",
      "Pcu=24                                       #copper loss(W)\n",
      "Pw=13                                       #friction & windage loss(W)\n",
      "V=110                                       #line-to-line voltage(V)\n",
      "p=4                                         #no.of poles\n",
      "fc=60                                       #frequency(Hz)\n",
      "\n",
      "#Calculations:\n",
      "X22=X2_m+Xm\n",
      "Q2_m=X22/R2_m\n",
      "Rf=(Xm**2/X22)*(1/(s*Q2_m+1/(s*Q2_m)))\n",
      "Xf=(X2_m*Xm/X22)+Rf/(s*Q2_m)\n",
      "Zf=Rf+1j*Xf                             #forward field impedance(ohm)\n",
      "\n",
      "Rb=R2_m*(Xm/X22)**2/(2-s)\n",
      "Xb=(X2_m*Xm/X22)+Rb/((2-s)*Q2_m)\n",
      "Zb=Rb+1j*Xb                             #bachward field impedance\n",
      "Zt=0.5*(Zf+Zb)+R1_m+1j*X1_m\n",
      "I=V/abs(Zt)                             #Stator current(A)\n",
      "pf=cos(cmath.phase(Zt))                 #power factor\n",
      "Pin=V*I*pf\n",
      "Pg_f=I**2*0.5*Rf                        #power absorbed by forward field(W)\n",
      "Pg_b=I**2*0.5*Rb                        #power absorbed by backward field(W)\n",
      "Pmech=(1-s)*(Pg_f-Pg_b)\n",
      "Pshaft=Pmech-(Pcu+Pw)\n",
      "ws=(2/p)*120*pi\n",
      "ns=(120/p)*fc\n",
      "n=(1-s)*ns                              #Rotor speed(rpm)\n",
      "wm=(1-s)*ws\n",
      "Tshaft=Pshaft/wm                         #shaft torque(Nm)\n",
      "eff=Pshaft/Pin\n",
      "\n",
      "#Results:\n",
      "print \"Stator current:\",round(I),\"A\", \"\\nPower factor:\",round(pf,3)\n",
      "print \"Power output:\",round(Pshaft),\"W\", \"\\nSpeed:\",n,\"rpm\"\n",
      "print \"Shaft torque:\",round(Tshaft,3),\"Nm\",\"Efficiency\",round(eff*100),\"%\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Stator current: 4.0 A \n",
        "Power factor: 0.621\n",
        "Power output: 147.0 W \n",
        "Speed: 1710.0 rpm\n",
        "Shaft torque: 0.823 Nm Efficiency 60.0 %\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 9.3, Page number: 474"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import math\n",
      "import cmath\n",
      "\n",
      "\n",
      "#Variable declaration:\n",
      "f=60                                        #freq(Hz)\n",
      "omeag=2*pi*f\n",
      "s=0.05                                      #slip\n",
      "R1=0.534                                    #resistance of main winding(ohm)\n",
      "X1=2.45\n",
      "Xm=70.1\n",
      "R2=0.956\n",
      "X2=2.96\n",
      "Valpha=230\n",
      "Vbeta=210*cmath.exp(1j*80*pi/180)\n",
      "\n",
      "#Calculations:\n",
      "Vf = 0.5*(Valpha - 1j*Vbeta)\n",
      "Vb = 0.5*(Valpha + 1j*Vbeta)\n",
      "Zf=R1+1j*X1+1j*Xm*(R2/s+1j*X2)/(R2/s+1j*(X2+Xm))\n",
      "If=Vf/Zf\n",
      "Zb=R1+1j*X1+1j*Xm*(R2/(2-s)+1j*X2)/(R2/(2-s)+1j*(X2+Xm))\n",
      "Ib = Vb/Zb\n",
      "Ialpha=If+Ib\n",
      "Ibeta=1j*(If-Ib)\n",
      "Pgf=2*((Vf*(If.conjugate())).real-R1*abs(If)**2)\n",
      "Pgb=2*((Vb*(Ib.conjugate())).real-R1*abs(Ib)**2)\n",
      "Pmech=(1-s)*(Pgf-Pgb)\n",
      "\n",
      "\n",
      "#Results:\n",
      "print \"(a) Positive seq components:\", round(Vf.real,1)+1j*round(Vf.imag,1),\"V\"\n",
      "print\"    Negative seq. components:\", round(Vb.real,1)+1j*round(Vb.imag,1),\"V\"\n",
      "\n",
      "print\"\\n(b) Positive stator currents:\",round(If.real,1)+1j*round(If.imag,1),\"A\"\n",
      "print\"    Negative stator currnets:\",round(Ib.real,1)+1j*round(Ib.imag,1),\"A\"\n",
      "\n",
      "print\"\\n(c) Positive currents:\",round(Ialpha.real,1)+1j*round(Ialpha.imag,1),\"A\"\n",
      "print\"    Negative currnets:\",round(Ibeta.real,1)+1j*round(Ibeta.imag,1),\"A\"\n",
      "\n",
      "print \"\\n(d) Power to forward field:\",round(Pgf,0),\"W\"\n",
      "print \"    Power to backward field:\",round(Pgb,0),\"W\"\n",
      "print \"    Pmech:\",round(Pmech,0),\"W\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(a) Positive seq components: (218.4-18.2j) V\n",
        "    Negative seq. components: (11.6+18.2j) V\n",
        "\n",
        "(b) Positive stator currents: (9.3-6.3j) A\n",
        "    Negative stator currnets: (3.7-1.5j) A\n",
        "\n",
        "(c) Positive currents: (13-7.8j) A\n",
        "    Negative currnets: (4.8+5.6j) A\n",
        "\n",
        "(d) Power to forward field: 4149.0 W\n",
        "    Power to backward field: 15.0 W\n",
        "    Pmech: 3928.0 W\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 9.5, Page number: 483"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "%matplotlib inline\n",
      "import cmath\n",
      "from math import *\n",
      "from matplotlib.pyplot import *\n",
      "\n",
      "#Variable declaration:\n",
      "Lmain=0.0806                           #main winding inductance(H)\n",
      "Rmain = 0.58                           #main winding resistance(ohm)\n",
      "Laux = 0.196                           #auxilliary winding inductance(H)\n",
      "Raux = 3.37                            #auxilliary winding resistance(ohm)\n",
      "Lr=4.7*10**-6                          #rotor inductance(H)\n",
      "Rr=37.6*10**-6                         #rotor resistance(ohm)\n",
      "Lmain_r=0.588*10**-3                   #main inductance ref. to rotor(H)\n",
      "Laux_r = 0.909*10**-3                  #aux inductance ref. to rotor(H)\n",
      "p=2                                    #poles\n",
      "Vo=230                                 #terminal voltage(V)\n",
      "w=120*pi                               #angular frequency(Hz)\n",
      "C=35*10**-6\n",
      "Prot=40                                #Windage losses(W)\n",
      "Pcore=105                              #Core loss(W)\n",
      "n=3500                                 #rpm\n",
      "\n",
      "\n",
      "#calculations and Results:\n",
      "Xc=-1/(w*C)\n",
      "speed=[0]*102\n",
      "for cal in range(1,3,1):\n",
      "    if cal==1:\n",
      "        mmax=2\n",
      "    else:\n",
      "        mmax=102\n",
      "    for m in range(1,mmax,2):\n",
      "        if cal==1:\n",
      "            speed[m-1]=3500\n",
      "        else:\n",
      "            speed[m-1]=3599*(m-1)/100\n",
      "        \n",
      "        ns=(2/p)*3600\n",
      "        s=(ns-speed[m-1])/ns\n",
      "\n",
      "#for part (a):\n",
      "        Kplus=s*w/(2*(Rr+1j*s*w*Lr))\n",
      "        Kminus=(2-s)*w/(2*(Rr+1j*(2-s)*w*Lr))\n",
      "        A1=Lmain-1j*Lmain_r**2*(Kplus+Kminus)\n",
      "        A2=Lmain_r*Laux_r*(Kplus-Kminus)\n",
      "        A3=Laux-1j*Laux_r**2*(Kplus+Kminus)\n",
      "        M=[[0]*2,[0]*2]\n",
      "        M[0][0]=Rmain + 1j*w*A1\n",
      "        M[0][1] = 1j*w*A2;\n",
      "        M[1][0] = -1j*w*A2;\n",
      "        M[1][1] = Raux + 1j*Xc+ 1j*w*A3\n",
      "        V=[[Vo],[-Vo]]\n",
      "        M1=inv(M)\n",
      "        I=dot(M1,V)\n",
      "        Imain=I[0][0]\n",
      "        Iaux=I[1][0]\n",
      "        Is=Imain-Iaux\n",
      "        magImain=abs(Imain)\n",
      "        angleImain=math.degrees(cmath.phase(Imain))\n",
      "        magIaux=abs (Iaux)\n",
      "        angleIaux=math.degrees(cmath.phase(Iaux))\n",
      "        magIs=abs(Is)\n",
      "        angleIs=math.degrees(cmath.phase(Is))\n",
      "        Vcap=Iaux*Xc\n",
      "        magVcap=abs(Vcap)\n",
      "        \n",
      "    #for part (b):\n",
      "        Tmech=[0]*102\n",
      "        Pshaft=[0]*102\n",
      "        Tmechl = (Kplus-Kminus).conjugate()\n",
      "        Tmechl=Tmechl*(Lmain_r**2*Imain*((Imain).conjugate())+Laux_r**2*Iaux*((Iaux).conjugate()))\n",
      "        Tmech2 = 1j*Lmain_r*Laux_r*((Kplus+Kminus).conjugate())\n",
      "        Tmech2 = Tmech2*((Imain).conjugate()*Iaux-Imain*((Iaux).conjugate()));\n",
      "        Tmech[m-1] = (p/2)*(Tmechl+Tmech2).real\n",
      "        Pshaft=((2/p)*(1-s)*w*Tmech[m-1])-Prot\n",
      "        \n",
      "    #for part (c):\n",
      "        Pmech=[0]*102\n",
      "        Pmain = (Vo*(Imain.conjugate())).real\n",
      "        Paux = (-Vo*(Iaux.conjugate())).real\n",
      "        Pin = Pmain+Paux+Pcore\n",
      "        eta = Pshaft/Pin;\n",
      "        if cal==1:\n",
      "            print \"part (a):\"\n",
      "            print  \"\\nImain=\",round(magImain,1),\"A  at an angle\",round(angleImain,1),\"degrees\"\n",
      "            print  \"\\nImain=\",round(magIaux,1),\"A  at an angle\",round(angleIaux,1),\"degrees\"\n",
      "            print  \"\\nImain=\",round(magIs,1),\"A  at an angle\",round(angleIs,1),\"degrees\"\n",
      "            print  \"\\nVcap=\",round(magVcap,0),\"V\"\n",
      "            print \"\\npart (b):\"\n",
      "            print \"\\nTmech=\",round(Tmech[0],2),\"Nm\"\n",
      "            print \"\\nPshaft=\",round(Pshaft),\"W\"\n",
      "            print \"\\npart (c):\"\n",
      "            print \"\\nPmain=\",round(Pmain,0),\"W\"\n",
      "            print \"\\nPaux=\",round(Paux,0),\"W\"\n",
      "            print \"\\nPin=\",round(Pin,0),\"W\"\n",
      "            print \"\\nEfficiency=\",round(eta*100,1),\"%\"\n",
      "        else:\n",
      "            \n",
      "            plot(speed,Tmech,'g.')\n",
      "            xlabel('speed (rpm)')\n",
      "            ylabel('Tmech (Nm)')\n",
      "            title('Electromagnetic torque vs speed')\n",
      "    show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "part (a):\n",
        "\n",
        "Imain= 15.9 A  at an angle -37.6 degrees\n",
        "\n",
        "Imain= 5.2 A  at an angle -150.8 degrees\n",
        "\n",
        "Imain= 18.5 A  at an angle -22.7 degrees\n",
        "\n",
        "Vcap= 394.0 V\n",
        "\n",
        "part (b):\n",
        "\n",
        "Tmech= 9.75 Nm\n",
        "\n",
        "Pshaft= 3532.0 W\n",
        "\n",
        "part (c):\n",
        "\n",
        "Pmain= 2893.0 W\n",
        "\n",
        "Paux= 1043.0 W\n",
        "\n",
        "Pin= 4041.0 W\n",
        "\n",
        "Efficiency= 87.4 %\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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KagsAyoHkACoNtQUA5cC0Eqg01BYAWgc1B9BIqC0AvBnUHEAjobYAoFqQHEAl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\nAABACpIDAABI+T9crBvDDQoKmwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x2854950>"
       ]
      }
     ],
     "prompt_number": 4
    }
   ],
   "metadata": {}
  }
 ]
}