path: root/Fundamentals_of_Electrical_Drives/Chapter7_1.ipynb

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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 7: Synchronous Motor and Brushless dc Motor Drives"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example no:7.1,Page no:247"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import cmath\n",
      "\n",
      "#variable declaration\n",
      "#ratings of the synchronous motor\n",
      "Pm1=500*1000   # power rating in W\n",
      "f=50           # frequency in HZ\n",
      "Vl=3.3*1000    # line voltage in V\n",
      "pf=0.8         # power factor lagging\n",
      "P=4            # number of poles\n",
      "I=10           # field current in A\n",
      "Xs=15          # reactance of the windings in ohm\n",
      "Rs=0           # resistance of the windings in ohm\n",
      "Wms=50*math.pi # synchronous speed in rad/sec\n",
      "Pm=Pm1/2       # power at half the rated torque when the losses are neglected\n",
      "\n",
      "#calculation\n",
      "V=Vl/math.sqrt(3)  #phase voltage\n",
      "Is=Pm1/(math.sqrt(3)*Vl*pf)   #rated current\n",
      "rad=math.acos(pf)\n",
      "\n",
      "Is=cmath.rect(Is,-rad)        #rated current in vector form\n",
      "V=cmath.rect(V,0)             #rated phase voltage in rectangular form\n",
      "E=V-Is*1j*Xs                  #back emf\n",
      "\n",
      "#(i) when field current has not changed\n",
      "sin_delta=Pm*Xs/(3*abs(V)*abs(E))  \n",
      "delta=math.asin(sin_delta)                 #angle delta\n",
      "Is=(V-cmath.rect(abs(E),-delta))/(1j*Xs)   #armature current\n",
      "Is1=cmath.polar(Is)\n",
      "x=math.degrees(Is1[1])           #where x=Is which is the required armature current           \n",
      "power_factor=math.cos(Is1[1])    #power factor \n",
      "\n",
      "#(ii) At unity power factor and rated torque\n",
      "cos_phi=1\n",
      "Is=Pm1/(3*V)         #since Pm1=3*V*Is\n",
      "E1=V-Is*1j*Xs\n",
      "If=abs(E1)/abs(E)*I  #field current\n",
      "\n",
      "#(iii) At the field current of 12.5 A\n",
      "If1=12.5      #field current \n",
      "E2=If1/I*abs(E)\n",
      "Is=math.sqrt(E2**2-abs(V)**2)/Xs  #since E2=abs(V-Is*1j*Xs)\n",
      "Pm=3*abs(V)*Is*cos_phi            #power output at the given field current\n",
      "T=Pm/Wms                          #required torque\n",
      "\n",
      "#results\n",
      "print\"i)armature current :\",round(Is1[0],2),round(x),\"\u00b0\",\"A\"\n",
      "print\"  power factor\",round(power_factor,2),\"lagging\"\n",
      "print\"\\nii)field current at unity power factor at rated torque:\",round(If,2),\"A\"\n",
      "print\"\\niii)Required torque is:\",round(T,1),\"N-m\"\n",
      "print\"Note: there is a slight difference in the answer due to the decimal place\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "i)armature current : 52.76 -34.0 \u00b0 A\n",
        "  power factor 0.83 lagging\n",
        "\n",
        "ii)field current at unity power factor at rated torque: 14.43 A\n",
        "\n",
        "iii)Required torque is: 1507.2 N-m\n",
        "Note: there is a slight difference in the answer due to the decimal place\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example no:7.2,Page no:249"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "from __future__ import division\n",
      "import cmath\n",
      "\n",
      "#variable declaration\n",
      "#ratings of the synchronous motor is same as that of Example-7.1\n",
      "Pm1=500*1000   # power rating in W\n",
      "f=50           # frequency in HZ\n",
      "Vl=3.3*1000    # line voltage in V\n",
      "pf=0.8         # power factor lagging\n",
      "P=4            # number of poles\n",
      "I=10           # field current in A\n",
      "Xs=15          # reactance of the windings in ohm\n",
      "Rs=0           # resistance of the windings in ohm\n",
      "Pm=Pm1/2       # power at half the rated torque when the losses are neglected\n",
      "\n",
      "#calculation\n",
      "Wms=50*math.pi     # synchronous speed in rad/sec\n",
      "V=Vl/math.sqrt(3)  # phase voltage\n",
      "Is=Pm1/(math.sqrt(3)*Vl*pf)  #rated current\n",
      "rad=math.acos(pf)\n",
      "\n",
      "Is=cmath.rect(Is,-rad)       #rated current in vector form\n",
      "V=cmath.rect(V,0) \n",
      "E=V-Is*1j*Xs                 #back emf\n",
      "\n",
      "#(i) at rated current and unity power factor\n",
      "E1=V-abs(Is)*1j*Xs\n",
      "delta=cmath.phase(E1)       #phase angle of E1\n",
      "Pm=3*abs(V)*abs(E1)*math.sin(delta)/Xs   #mechanical power developed\n",
      "T=Pm/Wms                #braking torque\n",
      "If=abs(E1)/abs(E)*I     #field current\n",
      "\n",
      "#(ii) at field current of 15A and 500kW output\n",
      "If1=15           #field current\n",
      "Pm=-500*1000    #output power \n",
      "E2=If1/I*abs(E)\n",
      "sin_delta=Pm*Xs/(3*abs(V)*abs(E2))  \n",
      "delta=math.asin(sin_delta)               #angle delta\n",
      "Is=(cmath.rect(E2,abs(delta))-V)/(1j*Xs) #armature current\n",
      "Is=cmath.polar(Is)\n",
      "x=(Is[1])*180/math.pi        #phase angle of Is\n",
      "power_factor=math.cos(Is[1]) #power factor\n",
      "\n",
      "\n",
      "#results\n",
      "print\"i)braking torque :\",round(T,1),\"N-m\"\n",
      "print\"  Field current\",round(If,2),\"A\"\n",
      "print\"\\nii)armature current :\",round(Is[0],2),round(x,2),\"\u00b0\",\"A\"\n",
      "print\"   power factor\",round(power_factor,3),\"lagging\"\n",
      "print\"\\nNote :There is a slight difference in the answers due to the decimal place\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "i)braking torque : -3978.9 N-m\n",
        "  Field current 15.68 A\n",
        "\n",
        "ii)armature current : 87.78 -4.79 \u00b0 A\n",
        "   power factor 0.997 lagging\n",
        "\n",
        "Note :There is a slight difference in the answers due to the decimal place\n"
       ]
      }
     ],
     "prompt_number": 66
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example no:7.3,Page no:257"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "from __future__ import division\n",
      "import cmath\n",
      "from sympy import *\n",
      "\n",
      "#variable declaration\n",
      "#ratings of the synchronous motor\n",
      "Pm1=6*10**6     # power rating in W\n",
      "f=50           # frequency in HZ\n",
      "Vl=11*1000     # line voltage in V\n",
      "pf=0.9         # power factor leading\n",
      "P=6            # number of poles\n",
      "I=10           # rated field current in A\n",
      "Xs=9           # reactance of the windings in ohm\n",
      "Rs=0           # resistance of the windings in ohm\n",
      "N=120*f/P      # synchronous speed\n",
      "\n",
      "#calculation\n",
      "V=Vl/math.sqrt(3)           #phase voltage\n",
      "Is=Pm1/(math.sqrt(3)*Vl*pf)  #rated current\n",
      "rad=math.acos(pf)\n",
      "\n",
      "#(i)to find torque and field current at rated armature current\n",
      "#   at 750 rpm and 0.8 leading power factor\n",
      "Is=cmath.rect(Is,rad)       #rated current in vector form\n",
      "V=cmath.rect(V,0)\n",
      "E=V-Is*1j*Xs                #back emf\n",
      "\n",
      "N1=750          #speeed in rpm\n",
      "pf1=0.8         #given leading power factor\n",
      "f1=N1/N*f       #required frequency\n",
      "V1=abs(V)*f1/f  #required voltage\n",
      "Xs1=Xs*f1/f     #required field resistance\n",
      "E1=V1-Xs1*1j*cmath.rect(abs(Is),math.acos(pf1))   #rated back emf  in complex form \n",
      "E1_polar=cmath.polar(E1)                          #rated back emf in rectangular form        \n",
      "#at rated field current and 750 rpm\n",
      "E2=abs(E)*N1/N             #back emf at the given speed N1           \n",
      "If=abs(E1)/E2*f            #field current at the given speed N1     \n",
      "Pm=3*abs(V1)*abs(Is)*pf1   #power input at the given speed N1\n",
      "Wm1=2*math.pi*N1/60        #angular motor speed in rad/s\n",
      "T=Pm/Wm1\n",
      "\n",
      "#(ii) at half the rated motor torque and 1500 rpm and rated field current\n",
      "Pm=6*10**6       #rated power rating in W\n",
      "N1=1500          #speeed in rpm\n",
      "f1=N1/N*f        #required frequency\n",
      "Xs1=f1/f*Xs      #required field resistance\n",
      "E1=abs(E)*f1/f   #back emf at rated field current \n",
      "\n",
      "Wms = Symbol('Wms')           #rated speed in rad/sec\n",
      "T_rated = Symbol('T_rated')   #rated torque\n",
      "Wms=Pm/T_rated\n",
      "Wms_=N1/N*Wms\n",
      "Pm_= (0.5*T_rated)*Wms_       #required power developed at N1=1500 rpm \n",
      "\n",
      "sin_delta=Pm_*Xs1/(3*abs(V)*abs(E1))       #since Pm=3*abs(V)*abs(E1)*math.sin(delta)/Xs  \n",
      "delta=math.asin(sin_delta)                 #angle delta\n",
      "Is=(abs(V)-cmath.rect(E1,-delta))/(1j*Xs1) #armature current\n",
      "Is1=cmath.polar(Is)                         #aramture current in rectangular form\n",
      "x1=math.degrees(Is1[1])\n",
      "power_factor1=math.cos(Is1[1])               #power factor\n",
      " \n",
      "#(iii) at 750 rpm and rated field current from part(i)\n",
      "N1=750         #speeed in rpm\n",
      "pf1=0.8        #given leading power factor\n",
      "f1=N1/N*f      #required frequency at N1=750 rpm\n",
      "V1=abs(V)*f1/f #required voltage at N1=750 rpm\n",
      "Xs1=Xs*f1/f    #required field resistance\n",
      "E2=abs(E)*N1/N    \n",
      "\n",
      "Pm=-4.2*10**6 #braking power output\n",
      "sin_delta=Pm*Xs1/(3*abs(V1)*abs(E2))       #since Pm=3*abs(V)*abs(E1)*math.sin(delta)/Xs  \n",
      "delta=math.asin(sin_delta)                 #angle delta\n",
      "Is=(cmath.rect(E2,abs(delta))-V1)/(1j*Xs1) #armature current \n",
      "Is2=cmath.polar(Is)                         #aramture current in rectangular form\n",
      "x2=math.degrees(Is2[1]) \n",
      "power_factor2=math.cos(Is2[1]) #power factor\n",
      "\n",
      "#(iv)from part (ii) at 1500 rpm and from part(iii) the armature current of 349.9 A is taken\n",
      "Is=Pm1/(math.sqrt(3)*Vl*pf)        #armature current as given from (i)\n",
      "N1=1500           #speeed in rpm\n",
      "f1=N1/N*f         #required frequency at N1=1500 rpm\n",
      "Xs1=f1/f*Xs       #required field resistance\n",
      "E1=abs(E)*f1/f    #at rated field current \n",
      "E2=V-1j*Xs1*Is\n",
      "E2=cmath.polar(E2)\n",
      "\n",
      "If1=E2[0]/abs(E1)*f   #required field current\n",
      "Pm=3*abs(V)*E2[0]*math.sin(abs(E2[1]))/Xs1   #power input\n",
      "Wm1=2*math.pi*N1/60   #motor speed in rad/sec\n",
      "T1=Pm/Wm1\n",
      "\n",
      "#results\n",
      "print\"\\ni)Required torque is:\",round(T,1),\"N-m\"\n",
      "print\"  Field current :\",round(If,2),\"A\"\n",
      "print\"\\nii)armature current :\",round(Is1[0],1),round(x1,2),\"\u00b0\",\"A\"\n",
      "print\"   power factor :\",round(power_factor1,1),\"leading\"\n",
      "print\"\\niii)armature current :\",round(Is2[0],2),round(x2,2),\"\u00b0\",\"A\"\n",
      "print\"    power factor :\",round(power_factor2,3),\"lagging\"\n",
      "print\"\\niv)Field current :\",round(If1,2),\"A\"\n",
      "print\"   Required torque is:\",round(T1),\"N-m\"\n",
      "print\"\\nNote :There is a slight difference in the answers due to the decimal place\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "i)Required torque is: 50929.6 N-m\n",
        "  Field current : 52.37 A\n",
        "\n",
        "ii)armature current : 475.5 60.21 \u00b0 A\n",
        "   power factor : 0.5 leading\n",
        "\n",
        "iii)armature current : 334.62 -28.55 \u00b0 A\n",
        "    power factor : 0.878 lagging\n",
        "\n",
        "iv)Field current : 32.07 A\n",
        "   Required torque is: 42441.0 N-m\n",
        "\n",
        "Note :There is a slight difference in the answers due to the decimal place\n"
       ]
      }
     ],
     "prompt_number": 60
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example no:7.4,Page no:265"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "from __future__ import division\n",
      "import cmath\n",
      "\n",
      "#variable declaration\n",
      "#ratings of the synchronous motor\n",
      "Pm=8*10**6     # power rating in W\n",
      "f=50           # frequency in HZ\n",
      "Vl=6600        # line voltage in V\n",
      "pf=1           # unity power factor \n",
      "P=6            # number of poles\n",
      "I=10           # rated field current in A\n",
      "Xs=2.8         # reactance of the windings in ohm\n",
      "Rs=0           # resistance of the windings in ohm\n",
      "Rd=0.1         # Dc link inductor resistance\n",
      "alpha=140      # constant firing angle in degrees \n",
      "\n",
      "#calculation\n",
      "N=120*f/P                   #synchronous speed\n",
      "V=Vl/math.sqrt(3)           #phase voltage\n",
      "Is=Pm/(math.sqrt(3)*Vl*pf)  #rated current\n",
      "\n",
      "Id=math.pi/math.sqrt(6)*Is  #Dc line current\n",
      "phi=180-alpha  #phase angle between Is and V in degrees\n",
      "\n",
      "#(i) when motor operates at rated current and 500rpm\n",
      "N1=500     #motor speed in rpm\n",
      "f1=N1/N*f  #frequency at N1\n",
      "V1=f1/f*V  #voltge at N1\n",
      "Pm1=3*V1*Is*math.cos(math.radians(phi)) #power developed by the motor\n",
      "#for the 3-phase load commutated inverter\n",
      "Vdl=(3*math.sqrt(6)/math.pi)*V1*math.cos(math.radians(alpha))\n",
      "Vds=-Vdl+Id*Rd\n",
      "cos_alpha_s=Vds/(3*math.sqrt(6)/math.pi*V)\n",
      "alpha_s=math.acos(cos_alpha_s)  #in radian\n",
      "alpha_s1=math.degrees(alpha_s)   #in degrees\n",
      "\n",
      "#(ii) regenerative braking at 500rpm and at rated motor current\n",
      "alpha=0  #firing angle\n",
      "#when firng angle is zero then power factor is unity\n",
      "pf=1\n",
      "\n",
      "Pm2=3*V1*Is*pf   #power developed by the motor\n",
      "Ps=Pm2-Id**2*Rd  #power supplied to the source\n",
      "Vdl=(3*math.sqrt(6)/math.pi)*V1*math.cos(math.radians(alpha))\n",
      "Vds=-Vdl+Id*Rd\n",
      "cos_alpha_s=Vds/(3*math.sqrt(6)/math.pi*V)\n",
      "alpha_s=math.acos(cos_alpha_s)   #in radian\n",
      "alpha_s2=math.degrees(alpha_s)   #in degrees\n",
      "\n",
      "#results\n",
      "print\"i)power developed by the motor is:\",round(Pm1/10**6,3),\"MW\"\n",
      "print\"  Source side converter firing angle is\",round(alpha_s1,2),\"\u00b0\"\n",
      "print\"\\nii)power supplied to the source is:\",round(Ps/10**6,3),\"MW\"\n",
      "print\"  Source side converter firing angle is\",round(alpha_s2,2),\"\u00b0\"\n",
      "#answer for firing angle in the book is wrong"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "i)power developed by the motor is: 3.064 MW\n",
        "  Source side converter firing angle is 66.85 \u00b0\n",
        "\n",
        "ii)power supplied to the source is: 3.919 MW\n",
        "  Source side converter firing angle is 119.34 \u00b0\n"
       ]
      }
     ],
     "prompt_number": 65
    }
   ],
   "metadata": {}
  }
 ]
}