path: root/Electronic_Measurements_and_Instrumentation_by_Er.R.K.Rajput/Chapter_6.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 6:Instrument Transformers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example:6.1,Page No:367"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "actual tranformation ratio = 240.77\n",
      "phase angle = 4.57 ° \n",
      "maximum flux density in core = 0.0938 Wb/m**2\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "#variable declaration\n",
    "Np     =  1;                      #number of primary turns\n",
    "Ns     =  240;                    #number of secondary turns\n",
    "Is     =  5;                      #secondary current in A\n",
    "Re     =  1.2;                    #external burden in Ω  \n",
    "mmf    =  96;                     #magnetomotive force in AT\n",
    "Ac     =  1200*10**-6;            #cross section area mm**2\n",
    "f      = 50;                      #frequency in Hz\n",
    "\n",
    "#calculation\n",
    "Kt   =  Ns/float(Np);                           #turns ratio\n",
    "Es   =  Is*Re;                                  #voltage induced in secondary winding in V\n",
    "Im   =  mmf/float(Np);                          #secondary current in A\n",
    "Ip   = math.sqrt(((Kt*Is)**2)+((Im)**2));       #primary current in A\n",
    "Kact = Ip/float(Is);                            #actual transformation ratio \n",
    "x    = Im/float(Kt*Is);                         #tangential component\n",
    "theta = math.atan(x);                           #phase angle \n",
    "phimax = Es/float(4.44*f*Ns);\n",
    "Bmax   = phimax/float(Ac);\n",
    "\n",
    "#result\n",
    "print'actual tranformation ratio = %3.2f'%Kact;\n",
    "print'phase angle = %3.2f'%((theta*180)/float(math.pi)),'° ';\n",
    "print'maximum flux density in core = %3.4f'%Bmax,'Wb/m**2';\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example:6.2,Page No:368"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ratio error at full load = -0.0450 %\n",
      "phase angle  = 5.116677 degrees(equal to (3 minutes 4 seconds))\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "#variable declaration\n",
    "I0      = 1;                  #exciting current in  A\n",
    "Knom    = 200;               #current transformer ratio \n",
    "Re      = 1.1;               #non inductive resistance in Ω  \n",
    "p       = 0.45;              #power factor \n",
    "delta   = 0;\n",
    "Is      = 5;               #rated secondary winding current in A\n",
    "\n",
    "#calculations\n",
    "alpha  = 90-(((math.acos(p))*180)/float(math.pi));\n",
    "Kt     = Knom                                                          #since no turn compenasation\n",
    "y      = math.sin(((delta+alpha)*math.pi)/float(180));\n",
    "Kact   = Kt+((I0/float(Is))*(y));                                      #actual transformation ratio\n",
    "r      = ((Knom-Kact)/float(Kact))*100;                                #ratio error\n",
    "k      =math.cos(((delta+alpha)*math.pi)/float(180));\n",
    "theta  = (180/math.pi)*((I0*k)/float(Kt*Is));                          #phase angle degreess\n",
    "\n",
    "#calculation\n",
    "print'ratio error at full load = %3.4f'%r,'%';\n",
    "print'phase angle  = %f'%(theta*100),'degrees(equal to (3 minutes 4 seconds))';\n",
    "\n",
    "\n",
    "            "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example:6.3,Page No:369"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "flux in the core = 1.5766e-04 wb\n",
      "ratio error = -3.846 %\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "#variuable declaration\n",
    "Knom   = 200;                #nominal ratio\n",
    "Np     = 1;                  #number of primary turns\n",
    "R      = 1.4;                #secondary impendance in Ω  \n",
    "L      = 1.4;                #iron loss in W\n",
    "I      = 5;                  #current in A\n",
    "d      = 0;                  #load angle when burden is pure resistive \n",
    "mmf    = 80;                 #magnetomotive force in A\n",
    "f      = 50;\n",
    "\n",
    "#calculations\n",
    "Kt       = Knom;                                                    #turns ratio\n",
    "Ns       = Kt*Np;                                                   #number of secondary turns\n",
    "Es       = I*R;                                                     #secondary induced voltage in V\n",
    "phimax  = Es/float(4.44*f*Ns);                                      #flux in core Wb\n",
    "Ep       = Es/float(Kt);                                            #primary induced voltage in V\n",
    "Iw       = L/float(Ep);                                             #loss component of exciting current in A\n",
    "Im       = mmf/float(Np);                                           #magnetising current\n",
    "Kact     = Kt+(((Im*math.sin(d))+(Iw*math.cos(d)))/float(Is));      #actual ratio \n",
    "r        =  (Knom-Kact)/float(Kact);                                #ratio error in %\n",
    "r1       = r*100;\n",
    "\n",
    "#result\n",
    "print'flux in the core = %3.4e'%phimax,'wb';\n",
    "print'ratio error = %3.3f'%r1,'%';\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example:6.4,Page No:370"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ratio error = -5.57 %\n",
      "phase angle =2.01 °\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "#variable declaration\n",
    "Np     = 1;                       #number of primary turns\n",
    "Ns     =  250;                    #number of secondary turns\n",
    "Rp     =  1.4;                    #resistance of secondary circuit in Ω\n",
    "Xs     =  1.1;                    #reactance of secondary circuit in Ω\n",
    "Is     =  5;                      #current in secondary winding in A\n",
    "mmf    =  80;                     #magnetomotive force in A\n",
    "L      = 1.1;                     #iron loss in W\n",
    "\n",
    "#calculations\n",
    "Kt      = Ns/float(Np);                                              #turns ratio\n",
    "Knom    = Kt; \n",
    "Rs      = math.sqrt((Rp**2)+(Xs**2));                                #secondary  circuit impedance\n",
    "cosd    = Rp/float(Rs);      \n",
    "sind    = Xs/float(Rs);\n",
    "Es      = Is*Rs;                                                     #secondary induced voltage in V\n",
    "Ep      =  Es/float(Ns);                                             #primary induced voltage in V\n",
    "Iw      = L/float(Ep);                                               #loss of component reffering to primary winding in A\n",
    "Im      = mmf/float(Np);                                             #magnetising current in A\n",
    "Kact    = Kt+(((Im*sind)+(Iw*cosd))/float(Is));                      #actual transformation ratio\n",
    "r       =  ((Knom-Kact)/float(Kact))*100;                            #ratio error in %\n",
    "theta   = (180/math.pi)*(((Im*cosd)-(Iw*sind))/float(Kt*Is));       #phase angle degreess\n",
    "\n",
    "#result\n",
    "print'ratio error = %3.2f'%r,'%';\n",
    "print'phase angle =%3.2f'%theta,'°';\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example:6.5,Page No:371"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "actual ratio = 317.10\n",
      "primary current =  1585.49 A\n",
      "reduction in secondary winding turns =  17\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "#variable declaration\n",
    "Np   = 1;                           #number of primary windings\n",
    "Ns   = 300;                         #umber of secondary windings\n",
    "Re   = 1;                           #ammeter ressistance in Ω\n",
    "Xe   = 0.55;                        #reactance in Ω\n",
    "Rs   = 0.3;                         #resistance if secondary winding in Ω\n",
    "Xs   = 0.25;                        #reactance of secondary winding in Ω\n",
    "mmf  = 90;                          # mmf for magnetisation\n",
    "mmfc = 45;                          #mmf for core loss \n",
    "Is   = 5;                           #current in A\n",
    "\n",
    "#calculations\n",
    "R   = Rs+Re;                        #total secondarycircuit resistance in Ω\n",
    "X   = Xs+Xe;                        #total secondarycircuit reactance in Ω\n",
    "delta  = math.atan(X/float(R));     #secondary circuit phase angle \n",
    "c      = math.cos(delta);\n",
    "s      = math.sin(delta);\n",
    "Kt     = Ns/float(Np);              #turn ratio \n",
    "Im     = mmf/float(Np);             #magnetising current in A\n",
    "Iw     = mmfc/float(Np);            #loss component in A\n",
    "Kact   = Kt+(((Im*math.sin(delta))+(Iw*math.cos(delta)))/float(Is));  #actual ratio\n",
    "Ip     = Kact*Is;                   #primary current A\n",
    "Knom   = Kt;\n",
    "y      = (((Im*math.sin(delta))+(Iw*math.cos(delta)))/float(Is));\n",
    "Kt1    = (Knom)-(y);\n",
    "Ns1    = Kt1*Np;                    #secondary winding turns\n",
    "r      = Ns-Ns1;                    #reduction in secondary winding turns\n",
    "\n",
    "#result\n",
    "print'actual ratio = %3.2f'%Kact;\n",
    "print'primary current =  %3.2f'%Ip,'A';\n",
    "print'reduction in secondary winding turns = %3.0f'%r;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example:6.6,Page No:372"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "actual ratio 101.12 °\n",
      "phase angle 0.641 °\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "#variable declaration\n",
    "Np    = 1;                            #number of primary windings\n",
    "Ns    = 100;                         #number of secondary windings\n",
    "Knom  = 100;                         #nominal ratio\n",
    "Re    = 1.45;                         #external burden non inductive in Ω\n",
    "Rs    = 0.25;                         #winding resistance in Ω\n",
    "I0    = 1.8;                          #current in A\n",
    "l     = 38.4;                         #lagging angle with secondary voltage reversed in °\n",
    "Is    =  1;                           #current in secondary winding in A\n",
    "delta  = 0;\n",
    "\n",
    "\n",
    "#calculations\n",
    "Kt      = Ns/float(Np);                        #turn ratio\n",
    "Rt      = Re+Rs;                               #totaal secondary circuit resistance in Ω\n",
    "alpha   = 90-l;\n",
    "x       = math.cos(((delta+alpha)*math.pi)/float(180));\n",
    "Kact    = Kt+((I0/float(Is))*x);                        #actual ratio\n",
    "y       = math.cos(((delta+alpha)*math.pi)/float(180));\n",
    "theta   = (180/float(math.pi))*((I0*y/float(Kt*Is)));     #phase angle in °\n",
    "\n",
    "#result\n",
    "print'actual ratio %3.2f'%Kact,'°';\n",
    "print'phase angle %3.3f'%theta,'°';\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example:6.7,Page No:373"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ratio error -0.87 %\n",
      "phase angle 0.1948\n",
      "ratio error 0.08 %\n",
      "phase angle 0.5386 °\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "#variable declaration\n",
    "Np       = 1;                  #number of primary windings\n",
    "Ns       = 200;                #number of secondary winding\n",
    "Kt       = 200;                #actual ratio\n",
    "Im       = 8;                  #magnetising current  in A\n",
    "Iw       = 5;                  #loss component in A\n",
    "cosphi   = 0.8;                # leading by\n",
    "Knom     = 200;                #transformer is rated \n",
    "cosphi1  = 0.8;                #lagging by\n",
    "Is       = 5;                  #current in A\n",
    "\n",
    "#calculations\n",
    "sinphi   = math.sqrt((1**2)-(cosphi**2));\n",
    "Kact     = Kt+(((Im*sinphi)+(Iw*cosphi))/float(Is));               #actual ratio\n",
    "er       = ((Knom-Kact)/float(Kact))*100;                           #error ratio\n",
    "theta    = (180/float(math.pi))*(((Im*cosphi)-(Iw*sinphi))/float(Kt*Is));  #phase angle\n",
    "sinphi1  = -math.sqrt((1**2)-(cosphi1**2));\n",
    "Kact1    = Kt+(((Im*sinphi1)+(Iw*cosphi1))/float(Is));               #actual ratio\n",
    "er1      = ((Knom-Kact1)/float(Kact1))*100;                          #ratio error\n",
    "theta1   = (180/float(math.pi))*(((Im*cosphi1)-(Iw*sinphi1))/float(Kt*Is));    #phase angle\n",
    "\n",
    "#result\n",
    "print'ratio error %3.2f'%er,'%';\n",
    "print'phase angle %3.4f'%theta;\n",
    "print'ratio error %3.2f'%er1,'%';\n",
    "print'phase angle %3.4f'%theta1,'°';\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "#Example:6.8,Page No:373"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ratio error -0.86 %\n",
      "phase angle 0.4074\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "#variable declaration\n",
    "Np       = 1;                  #number of primary windings\n",
    "Ns       = 99;                #number of secondary winding\n",
    "Rs       = 0.4;               #secondary winding resistance in Ω\n",
    "Xs       = 0.35;               #secondary winding reactance in Ω\n",
    "Knom     = 100;                #ratio \n",
    "mmf      = 6;                   #magnetising mmf in AT\n",
    "lmmf     = 8;                   #loss mmf in AT\n",
    "V        = 20;                  #voltage in VA\n",
    "\n",
    "\n",
    "#calculations\n",
    "Kt       = Ns/float(Np);                #actual ratio\n",
    "Im       = mmf/float(Np);               #magnetising current in A\n",
    "Iw       = lmmf/float(Np);              #loss component in A\n",
    "Re       = V/float(Is**2);               #external reistance burden in Ω\n",
    "R        = Rs+Re;                       #resistance of total seccondary circuit in Ω\n",
    "#reactance is zero \n",
    "Xe       = 0;\n",
    "X        = Xs+Xe;                       #reactance of total secondary circcuit burden in Ω\n",
    "delta    = ((math.atan(X/float(R))*180)/float(math.pi));       #phase angle\n",
    "c        = math.cos((delta*math.pi)/float(180));\n",
    "s        = math.sin((delta*math.pi)/float(180));\n",
    "Kact     = Kt+(((Im*s)+(Iw*c))/float(Is));   #actual ratio\n",
    "er       = ((Knom-Kact)/float(Kact))*100;                           #error ratio\n",
    "theta    = (180/float(math.pi))*(((Im*c)-(Iw*s))/float(Kt*Is));    #phase angle\n",
    "\n",
    "#result\n",
    "print'ratio error %3.2f'%er,'%';\n",
    "print'phase angle %3.4f'%theta;\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "#Example:6.9,Page No:374"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ratio error -1.198 %\n",
      "phase angle 0.6531 °\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "#variable declaration\n",
    "Knom   = 20;               #nominal ratio of 100/5A\n",
    "V      = 20;               #rated load in VA\n",
    "Il     = 0.18;             #iron loss in W\n",
    "Im     =  1.4;             #magnetising current in A\n",
    "x      = 4;                #ratio of reactance to resistance \n",
    "Ip     = 100;              #primary currnt widing in A\n",
    "Is     = 5;                #current in secondary winding in A\n",
    "\n",
    "#calculations\n",
    "Kt       = Knom;                                                 #assuming the value of Kt\n",
    "Ep       = V/float(Ip);                                          #voltage across primary winding in V\n",
    "Iw       = Il/float(Ep);                                         #loss current of exciting current in A\n",
    "delta    = ((math.atan(1/float(x))*180)/float(math.pi));         #phase angle\n",
    "c        = math.cos((delta*math.pi)/float(180));\n",
    "s        = math.sin((delta*math.pi)/float(180));\n",
    "Kact     = Kt+(((Im*s)+(Iw*c))/float(Is));                          #actual ratio\n",
    "er       = ((Knom-Kact)/float(Kact))*100;                           #error ratio\n",
    "theta    = (180/float(math.pi))*(((Im*c)-(Iw*s))/float(Kt*Is));     #phase angle\n",
    "\n",
    "#result\n",
    "print'ratio error %3.3f'%er,'%';\n",
    "print'phase angle %3.4f'%theta,'°';\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#Example:6.10,Page No:382"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "phase angle error  at no load -0.00156 °\n",
      "Note:printing mistake in textbook,theta value  is printed wrong\n",
      "burden load in VA 15.34 V A\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "#variable declaration\n",
    "Kt   = 10;              #ratio of 1000/100volts potentia meter \n",
    "Rp    = 86.4;          #primary resistance in Ω\n",
    "Rs    = 0.78;          #secondary resistance in Ω\n",
    "Xp    = 62.5;          #primary reactance in Ω\n",
    "Xs    = 102;           #total equivalent reactance in Ω\n",
    "I0    = 0.03;          #no-load current in A\n",
    "cosphi   = 0.42;          #power factor \n",
    "cosgamma  = 1;          #since power factor = 1\n",
    "Vs        = 100;          #voltage in V\n",
    "\n",
    "\n",
    "#calculations\n",
    "\n",
    "sinphi   = math.sqrt(1-(cosphi**2));\n",
    "Im       = I0*sinphi;                          #magnetising current in A\n",
    "Iw       = I0*cosphi;                          #loss current in A\n",
    "\n",
    "#theta    = ((((Is/Kt)*((X*cosgamma)-(Rp*singamma)))+(Iw*Xp)-(Im*Rp))/float(Kt*Vs));\n",
    "#since Is  =0 \n",
    "\n",
    "theta   = (((Iw*Xp)-(Im*Rp))/float(Kt*Vs));\n",
    "singamma = math.sqrt(1-(cosgamma**2));\n",
    "\n",
    "#burden in VA,theta1 = 0,thus ((((Is/Kt)*((X*cosgamma)-(Rp*singamma)))+(Iw*Xp)-(Im*Rp))/float(Kt*Vs))=0\n",
    "#(((Is/Kt)*((X*cosgamma)-(Rp*singamma)))+(Iw*Xp)-(Im*Rp)) =0\n",
    "#Is/Kt   = ((Im*Rp)-(Iw*Xp)))/float(((X*cosgamma)-(Rp*singamma)))\n",
    "#assume x = ((X*cosgamma)-(Rp*singamma)),y = (Iw*Xp)-(Im*Rp)\n",
    "#Is     = Kt*(y/x)\n",
    "\n",
    "x        = ((Xs*cosgamma)-(Rp*singamma));\n",
    "y        = (Im*Rp)-(Iw*Xp);\n",
    "Is       =   Kt*(y/float(x));       #current in A\n",
    "l        = Vs*Is;                   # burden load in VA \n",
    "\n",
    "#result\n",
    "print'phase angle error  at no load %3.5f'%theta,'°';\n",
    "print'Note:printing mistake in textbook,theta value  is printed wrong';\n",
    "print'burden load in VA %3.2f'%l,'V A'\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#Example:6.11,Page No:383"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ratio error -0.7937 %\n",
      "phase angle -0.3438 °\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "#variable declartion\n",
    "Kt      = 60.476;                 #turns ratio  3810/63 tranformer\n",
    "Vs      = 63;                     #secondary voltage in V\n",
    "Rs      = 2;                      #series resistance in Ω\n",
    "Xs      = 1;                      #reactance in Ω\n",
    "R       = 100;                    #resistance in Ω\n",
    "X       = 200;                    #reactance in Ω\n",
    "\n",
    "#calculations\n",
    "\n",
    "delta    = ((math.atan(X/float(R))*180)/float(math.pi));         #phase angle\n",
    "Z        = math.sqrt((R**2)+(X**2));                           #agnitude of impedance\n",
    "\n",
    "#Kact     = Kt+(((Rs*c)+(Xs*s))/float(Vs/float(Is))); \n",
    "#Vs/float(Is) = Z\n",
    "\n",
    "c        = math.cos((delta*math.pi)/float(180));\n",
    "s        = math.sin((delta*math.pi)/float(180));\n",
    "x        =(Rs*c)+(Xs*s);\n",
    "y        = ((x*Kt)/float(Z));\n",
    "Kact     = Kt+y;                                                #actual ratio\n",
    "Knom     = Kt;                                                   #nominal ration      \n",
    "er       = ((Knom-Kact)/float(Kact))*100;                        #error ratio\n",
    "theta    = (180/float(math.pi))*(((Xs*c)-(Rs*s))/float(Z));      #phase angle\n",
    "\n",
    "\n",
    "\n",
    "#result\n",
    "print'ratio error %3.4f'%er,'%';\n",
    "print'phase angle %3.4f'%theta,'°';\n"
   ]
  }
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