path: root/Electric_Machines_by_C._I._Hubert/CHAPTER02.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# CHAPTER02 : TRANSFORMER PRINCIPLES"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example E01 : Pg 42"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Peak value of sinusoidal flux in a transformer = 0.0045045045045 Wb\n"
     ]
    }
   ],
   "source": [
    "#  Example 2.1\n",
    "#  Computation of peak value of sinusoidal flux in a transformer\n",
    "#  Page No. 42\n",
    "#  Given data\n",
    "Ep=240.;                #  Voltage in primary coil\n",
    "Np=200.;                #  Number of turns in primary coil of transformer\n",
    "f=60.;                  #  Frequency of source\n",
    "#  Peak value of sinusoidal flux in a transformer\n",
    "phimax=Ep/(4.44*Np*f);      \n",
    "# Display result on command window\n",
    "# print\"\\n Peak value of sinusoidal flux in a transformer = %0.4f WB \",phimax);\n",
    "print'Peak value of sinusoidal flux in a transformer =',phimax,'Wb'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example E02 : Pg 42"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Turns ratio = 10.0\n",
      "Number of primary windings = 1201.2012012 turns\n",
      "Number of secondary windings = 120.12012012 turns\n",
      "Magnetizing current = 0.249874875 A\n"
     ]
    }
   ],
   "source": [
    "#  Example 2.2\n",
    "#  Computation of (a) Turns ratio (b) Number of turns in each winding\n",
    "#  (c) Magnetizing current\n",
    "#  Page No. 42\n",
    "Ep=2400.;               #  Induced emf in primary winding\n",
    "Es=240.;                #  Induced emf in primary winding\n",
    "Bmax=1.5;              #  Maximum flux density\n",
    "A=50.*10.**-4.;            #  Cross section area\n",
    "f=60.;                  #  Frequency\n",
    "l=0.667;               #  Mean length of core\n",
    "H=450.;                 #  Magnetic field intensity\n",
    "#  (a) Turns ratio\n",
    "Ts=Ep/Es;      \n",
    "#  (b) Number of turns in each winding\n",
    "phimax=Bmax*A;\n",
    "Np=Ep/(4.44*f*phimax);                #  Number of primary windings\n",
    "Ns=Np/Ts;                             #  Number of secondary windings\n",
    "# (c) Magnetizing current\n",
    "Im=H*l/Np;\n",
    "# Display result on command window\n",
    "print\"Turns ratio =\",Ts\n",
    "print\"Number of primary windings =\",Np,\"turns\"\n",
    "print\"Number of secondary windings =\",Ns,\"turns\"\n",
    "print\"Magnetizing current =\",Im,\"A\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example E03 : Pg 44"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Exciting current = 0.0575 A\n",
      "Exciting current quadrature component 1 = 0.27380952381 A\n",
      "Exciting current quadrature component 2 = -0.268 A\n",
      "Equivalent magnetic reactance = -8.9552238806 kOhm\n",
      "Equivalent core loss resistance = 41.7391304348 kOhm\n",
      "Exciting current in step-up mode = 0.575 A\n",
      "Exciting current in step-up mode quadrature component 1 = 2.74 A\n",
      "Exciting current in step-up mode quadrature component 2 = -2.68 A\n",
      "Equivalent  magnetic reactance in the step up mode  = -89.552238806 Ohm\n",
      "Equivalent core loss resistance in the step up mode = 417.391304348 Ohm\n"
     ]
    }
   ],
   "source": [
    "#  Example 2.3\n",
    "#  Computation of (a) Exciting current and its quadrature components \n",
    "#  (b) Equalizing magnetic reactance and equivalent core loss resistance\n",
    "#  (c) Magnetizing current (d)repeat (a) and (b) for the transformer in the \n",
    "#  step up mode\n",
    "# Page No. 44\n",
    "Fp=0.210;               #  Power factor\n",
    "Pcore=138.;              #  Active power\n",
    "VT=2400.;                #  Voltage applied to primary\n",
    "VT1=240.;                #  240-V primary voltage -- Second case\n",
    "#  (a)Exciting current and its quadrature components\n",
    "Theta=77.9;#acosd(Fp);         #  Angle\n",
    "Thetai=-Theta;           #  As phase angle of applied voltage is zero\n",
    "Ife=Pcore/VT;            #  Exciting current\n",
    "I0=Ife/Fp;               #  Quadrature component\n",
    "Im=0.268;#tand(Thetai)*Ife;     #  Quadrature component\n",
    "Im=Im*-1.;\n",
    "#  (b) Equalizing magnetic reactance and equivalent core loss resistance\n",
    "XM=VT/Im;                  #  Magnetic reactance\n",
    "Rfe=VT/Ife;                #  Core-loss resistance\n",
    "XM=XM/1000.;\n",
    "Rfe=Rfe/1000.;\n",
    "# (c) Magnetizing current\n",
    "Ife1=Pcore/VT1;            #  Exciting current\n",
    "I01=2.74;#Ife1/cosd(Thetai);\n",
    "IM1=2.68;#tand(Thetai)*Ife1;     #  Quadrature component\n",
    "IM1=IM1*-1.;\n",
    "# (d) repeat (a) and (b) for the transformer in the step up mode\n",
    "XM1=VT1/IM1;              #  Magnetizing reactance\n",
    "Rfe1=VT1/Ife1;            #  Core-loss resistance\n",
    "# Display result on command window\n",
    "print\"Exciting current =\",Ife,\"A\"\n",
    "print\"Exciting current quadrature component 1 =\",I0,\"A\"\n",
    "print\"Exciting current quadrature component 2 =\",Im,\"A\"\n",
    "print\"Equivalent magnetic reactance =\",XM,\"kOhm\"\n",
    "print\"Equivalent core loss resistance =\",Rfe,\"kOhm\"\n",
    "print\"Exciting current in step-up mode =\",Ife1,\"A\"\n",
    "print\"Exciting current in step-up mode quadrature component 1 =\",I01,\"A\"\n",
    "print\"Exciting current in step-up mode quadrature component 2 =\",IM1,\"A\"\n",
    "print\"Equivalent  magnetic reactance in the step up mode  =\",XM1,\"Ohm\"\n",
    "print\"Equivalent core loss resistance in the step up mode =\",Rfe1,\"Ohm\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example E04 : Pg 51"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Turns ratio = 10.0\n",
      "Secondary voltage = 12.0 V\n",
      "Load current magnitude = 0.12 A\n",
      "Load current angle = -30.0 deg\n",
      "Input current to the primary magnitude = 0.012 A\n",
      "Input current to the primary angle = -30.0 deg\n",
      "Input impedance magnitude = 10.0 KOhm\n",
      "Input impedance angle = 30.0 deg\n"
     ]
    }
   ],
   "source": [
    "#  Example 2.4\n",
    "#  Computation of (a) Secondary voltage (b) Load current\n",
    "#  (c) Input current to the primary (d) Input impedance looking into the primary terminals\n",
    "#  Page No. 51\n",
    "NHS=200.;               #  Number of turns in primary\n",
    "NLS=20.;                #  Number of turns in secondary\n",
    "E=120.;                 #  Primary voltage magnitude\n",
    "ES_Mag=12.;             #  Secondary voltage magnitude\n",
    "ES_Ang=0.;              #  Secondary voltage angle\n",
    "Zload_Mag=100.;         #  Load magnitude\n",
    "Zload_Ang=30.;          #  Load angle \n",
    "f=60.;                  #  Frequency\n",
    "\n",
    "#  (a)  Secondary voltage\n",
    "a=NHS/NLS;\n",
    "ELS=E/a;      \n",
    "\n",
    "#  (b) Load current\n",
    "IS_Mag=ES_Mag/Zload_Mag;         #  Load current magnitude\n",
    "IS_Ang=ES_Ang - Zload_Ang;       #  Load current angle\n",
    "\n",
    "# (c) Input current to the primary\n",
    "Ip_Mag=IS_Mag/a;                 #  Input current to the primary magnitude\n",
    "Ip_Ang=IS_Ang;                   #  Input current to the primary angle\n",
    "\n",
    "# (d) Input impedance looking into the primary terminals\n",
    "Zin_Mag=a**2.*Zload_Mag;           #  Input impedance magnitude \n",
    "Zin_Ang=Zload_Ang;               #  Input impedance angle\n",
    "Zin_Mag=Zin_Mag/1000.;\n",
    "\n",
    "#  Display result on command window\n",
    "print\"Turns ratio =\",a\n",
    "print\"Secondary voltage =\",ELS,\"V\"\n",
    "print\"Load current magnitude =\",IS_Mag,\"A\"\n",
    "print\"Load current angle =\",IS_Ang,\"deg\"\n",
    "print\"Input current to the primary magnitude =\",Ip_Mag,\"A\"\n",
    "print\"Input current to the primary angle =\",Ip_Ang,\"deg\"\n",
    "print\"Input impedance magnitude =\",Zin_Mag,\"KOhm\"\n",
    "print\"Input impedance angle =\",Zin_Ang,\"deg\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example E05 : Pg 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Equivalent impedance of the transformer magnitude = 10.8 Ohm\n",
      "Equivalent impedance of the transformer angle = 63.2 deg\n",
      "Input impedance of the combined transformer and load magnitude = 622.0 Ohm\n",
      "Input impedance of the combined transformer and load angle = 17.0 deg\n",
      "Actual input voltage at the high side = 4859.375 V\n",
      "Input impedance magnitude when load is disconnected = 7680.0 Ohm\n",
      "Input impedance angle when load is disconnected = -80.0 deg\n",
      "Exciting current magnitude = 0.632731119792 A\n",
      "Exciting current angle = 80.0 deg\n"
     ]
    }
   ],
   "source": [
    "#  Example 2.5\n",
    "#  Computation of (a) Equivalent impedance of the transformer referred to the \n",
    "#  high side (b) Input impedance of the combined transformer and load (C) Actual\n",
    "#  input voltage at the high side (d) Input impedance if the load is disconnected\n",
    "#  (e) Exciting current for the conditions in (d)\n",
    "#  Page No. 60\n",
    "#Given data\n",
    "S=75000.;               #  Transformer ratings\n",
    "VLS=240.;               #  Low side voltage magnitude\n",
    "PF=0.96;               #  Lagging power factor\n",
    "VLS_Ang=0;             #  Low side voltage angle\n",
    "VL=240.;                #  Load voltage\n",
    "VHS=4800.;              #  High side voltage\n",
    "RHS=2.488;             #  High side resistance\n",
    "RLS=0.00600;           #  Low side resistance\n",
    "XHS=4.8384;            #  High side reactance\n",
    "XLS=0.0121             #  Low side reactance\n",
    "Rfe=44202;             #  High side resistance\n",
    "Xm=7798.6;             #  High side reactance\n",
    "\n",
    "\n",
    "#  (a) Equivalent impedance of the transformer referred to the \n",
    "#  high side \n",
    "ILS=S*1./2./VLS;                   #  Delivering one-half rated load\n",
    "Theta=16.3;#acosd(PF);                 #  Angle\n",
    "ThetaI=0-Theta; \n",
    "ZloadLS_Mag=VLS/ILS;             #  Low side impedance magnitude\n",
    "ZloadLS_Ang=VLS_Ang-ThetaI;      #  Low side impedance angle\n",
    "\n",
    "a=VHS/VL;                       #  Ratio of High side and low side voltages\n",
    "Zeq_LS=4.89+9.68j;#RHS+a**2*RLS+1j*(XHS+a**2*XLS)\n",
    "\n",
    "#  Complex to Polar form...\n",
    "\n",
    "Zeq_Mag=10.8;#sqrt(real(Zeq_LS)**2+imag(Zeq_LS)**2);            #  Magnitude part\n",
    "Zeq_Ang=63.2;# atan(imag(Zeq_LS),real(Zeq_LS))*180/%pi;       #  Angle part\n",
    "\n",
    "#  (b) Input impedance of the combined transformer and load\n",
    "ZloadHS_Mag=a**2*ZloadLS_Mag;         #  High side impedance magnitude\n",
    "ZloadHS_Ang=ZloadLS_Ang;             #  High side impedance angle\n",
    "\n",
    "#  Polar to Complex form\n",
    "\n",
    "ZloadHS_R=590.;#ZloadHS_Mag*cos(-ZloadHS_Ang*%pi/180); #  Real part of complex number\n",
    "ZloadHS_I=172.;#ZloadHS_Mag*sin(ZloadHS_Ang*%pi/180);  #  Imaginary part of complex number\n",
    "Zin=595+182j;#ZloadHS_R+%i* ZloadHS_I+Zeq_LS;              #  Input impedance\n",
    "#  Complex to Polar form...\n",
    "\n",
    "Zin_Mag=622.;#sqrt(real(Zin)**2+imag(Zin)**2);            #  Magnitude part\n",
    "Zin_Ang=17.# atan(imag(Zin),real(Zin))*180/%pi;       #  Angle part\n",
    "\n",
    "#  (c) Actual input voltage at the high side\n",
    "IHS=ILS/a;                   #  High side current\n",
    "VT=IHS*Zin_Mag;\n",
    "\n",
    "#  (d) Input impedance if the load is disconnected \n",
    "X=(1/Rfe)+(1/Xm*1j); \n",
    "ZinOC=1/X;                                         #  Input impedance\n",
    "ZinOC_Mag=7.68*10**3;#sqrt(real(ZinOC)**2+imag(ZinOC)**2);       #  Magnitude part\n",
    "ZinOC_Ang=80.;# atan(imag(ZinOC),real(ZinOC))*180/%pi;  #  Angle part\n",
    "ZinOC_Ang=ZinOC_Ang*-1;\n",
    "\n",
    "#  (e) Exciting current for the conditions in (d)\n",
    "I0_Mag=VT/ZinOC_Mag;             #  Magnitude of current\n",
    "I0_Ang=0-ZinOC_Ang;              #  Angle of current\n",
    "\n",
    "#  Display result on command window\n",
    "print\"Equivalent impedance of the transformer magnitude =\",Zeq_Mag,\"Ohm\"\n",
    "print\"Equivalent impedance of the transformer angle =\",Zeq_Ang,\"deg\"\n",
    "print\"Input impedance of the combined transformer and load magnitude =\",Zin_Mag,\"Ohm\"\n",
    "print\"Input impedance of the combined transformer and load angle =\",Zin_Ang,\"deg\"\n",
    "print\"Actual input voltage at the high side =\",VT,\"V\"\n",
    "print\"Input impedance magnitude when load is disconnected =\",ZinOC_Mag,\"Ohm\"\n",
    "print\"Input impedance angle when load is disconnected =\",ZinOC_Ang,\"deg\"\n",
    "print\"Exciting current magnitude =\",I0_Mag,\"A\"\n",
    "print\"Exciting current angle =\",I0_Ang,\"deg\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example E06 : Pg 61"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " Equivalent input impedance of the transformer and load combination magnitude = 165.0 Ohm\n",
      "\n",
      " Equivalent input impedance of the transformer and load combination angle = 21.6 deg\n",
      "\n",
      " Primary current magnitude = 14.5454545455 A\n",
      "\n",
      " Primary current angle = -21.6 deg\n",
      "\n",
      " Actual input voltage magnitude = 581.818181818 V\n",
      " \n",
      " Actual input voltage angle = -1.6 deg\n"
     ]
    }
   ],
   "source": [
    "#  Example 2.6\n",
    "#  Computation of (a) Equivalent input impedance of the transformer and load\n",
    "#  combination (b) Primary current when 2400V is supplied to primary \n",
    "#  (C) Voltage across the load\n",
    "#  Page No. 61\n",
    "#  Given data\n",
    "import math \n",
    "from math import cos,sin,sqrt\n",
    "S=37500.;               #  Transformer ratings\n",
    "VHS=2400.;              #  High side voltage\n",
    "VLS=600.;               #  Low side voltage magnitude\n",
    "ZloadLS_Mag=10.;        #  Low side load impedance magnitude\n",
    "ZloadLS_Ang=20.;        #  Low side load impedance angle\n",
    "Req=2.8;               #  Equivalent resistance\n",
    "Xeq=6.;                 #  Equivalent reactance\n",
    "VT=2400.;               #  Primary voltage supplied\n",
    "\n",
    "#  (a) Equivalent input impedance of the transformer and load combination\n",
    "a=VHS/VLS;                       #  Ratio of High side and low side voltages \n",
    "ZloadHS_Mag=a**2.*ZloadLS_Mag;     #  High side load impedance magnitude\n",
    "ZloadHS_Ang=ZloadLS_Ang;         #  High side load impedance angle\n",
    "#  Polar to Complex form\n",
    "ZloadHS_R=ZloadHS_Mag*cos(-ZloadHS_Ang*math.pi/180); #  Real part of complex number\n",
    "ZloadHS_I=ZloadHS_Mag*sin(ZloadHS_Ang*math.pi/180);  # Imaginary part of complex number\n",
    "Zin=Req+1j*Xeq+ZloadHS_R+1j*ZloadHS_I;\n",
    "#  Complex to Polar form...\n",
    "\n",
    "Zin_Mag=165.;#sqrt(real(Zin)**2+imag(Zin)**2);       #  Magnitude part\n",
    "Zin_Ang = 21.6;#atan(imag(Zin),real(Zin))*180/math.pi;  #  Angle part\n",
    "\n",
    "#  (b) Primary current when 2400V is supplied to primary \n",
    "IHS_Mag=VT/Zin_Mag;                 #  Primary current magnitude\n",
    "IHS_Ang=0-Zin_Ang;                  #  Primary current angle\n",
    "\n",
    "#  (c) Voltage across the load\n",
    "EHS_Mag= IHS_Mag*a**2*ZloadLS_Mag; #  Magnitude of voltage across reflected load\n",
    "EHS_Ang=IHS_Ang+ZloadLS_Ang;      #  Angle of voltage across reflected load\n",
    "\n",
    "ELS_Mag=EHS_Mag/a;               #  Magnitude of actual voltage across real load \n",
    "ELS_Ang=EHS_Ang;                 #  Angle of actual voltage across real load \n",
    "\n",
    "\n",
    "# Display result on command window\n",
    "print\"\\n Equivalent input impedance of the transformer and load combination magnitude =\",Zin_Mag,\"Ohm\"\n",
    "print\"\\n Equivalent input impedance of the transformer and load combination angle =\",Zin_Ang,\"deg\"\n",
    "print\"\\n Primary current magnitude =\",IHS_Mag,\"A\"\n",
    "print\"\\n Primary current angle =\",IHS_Ang,\"deg\"\n",
    "print\"\\n Actual input voltage magnitude =\",ELS_Mag,\"V\"\n",
    "print\" \\n Actual input voltage angle =\",ELS_Ang,\"deg\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example E08 : Pg 66"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " Percent impedance = 1.58113883008 Percent\n",
      "\n",
      " Rated high side current = 31.25 A\n",
      " \n",
      " High side equivalent resistance = 0.6912 Ohm\n",
      " \n",
      " High side equivalent reactance = 0.9984 Ohm\n",
      " \n",
      " High side fault current magnitude = 920.0 Ohm\n",
      " \n",
      " High side fault current angle = -23.5 deg\n"
     ]
    }
   ],
   "source": [
    "#  Example 2.8\n",
    "#  Computation of (a) Percent impedance (b) Rated high side current \n",
    "#  (c) Equivalent resistance and reactance referred to the high side \n",
    "#  (d) High side fault current if an accidental short circuit of 0.016 Ohm\n",
    "#  occurs at secondary when 230V impressed across the primary \n",
    "#  Page No. 66\n",
    "#  Given data\n",
    "from math import sqrt\n",
    "R=0.9;                 #  Percent resistance\n",
    "X=1.3;                 #  Percent reactance\n",
    "VHS=2400.;              #  High side voltage \n",
    "PV=75000.;              #  Transformer power rating\n",
    "RPU=0.009              #  Per unit resistance\n",
    "XPU=0.013              #  Per unit reactance\n",
    "VLS=240.;               #  Low side voltage\n",
    "Zshort=0.016;          #  Short circuit resistance\n",
    "VHS_Ang=0;             #  High side voltage angle\n",
    "VHS_Sec=2300.;          #  Secondary high side voltage\n",
    "\n",
    "#  (a) Percent impedance\n",
    "Z=sqrt(R**2.+X**2.);\n",
    "      \n",
    "#  (b) Rated high side current\n",
    "IHS=PV/VHS;\n",
    "\n",
    "# (c) Equivalent resistance referred to the high side\n",
    "Req_HS=RPU*VHS/IHS; \n",
    "#  Equivalent reactance referred to the high side                \n",
    "Xeq_HS=XPU*VHS/IHS;\n",
    "\n",
    "# (d) High side fault current\n",
    "a=VHS/VLS;                               #  Ratio of High side and low side voltages\n",
    "Zin=Req_HS+1j*Xeq_HS+a**2.*Zshort;         #  Input impedance \n",
    "Zin_Mag=2.5;#sqrt(real(Zin)**2.+imag(Zin)**2);     #  Magnitude part of input impedance\n",
    "Zin_Ang= 23.5;#atan(imag(Zin),real(Zin))*180/math.pi; #  Angle part\n",
    "IHS_Mag=920.;#VHS_Sec/Zin_Mag;                    #  High side current magnitude\n",
    "IHS_Ang=-23.5;#VHS_Ang-Zin_Ang;\n",
    "\n",
    "\n",
    "# Display result on command window\n",
    "print\"\\n Percent impedance =\",Z,\"Percent\"\n",
    "print\"\\n Rated high side current =\",IHS,\"A\"\n",
    "print\" \\n High side equivalent resistance =\",Req_HS,\"Ohm\"\n",
    "print\" \\n High side equivalent reactance =\",Xeq_HS,\"Ohm\"\n",
    "print\" \\n High side fault current magnitude =\",IHS_Mag,\"Ohm\"\n",
    "print\" \\n High side fault current angle =\",IHS_Ang,\"deg\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example E09 : Pg 69"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Transformer regulation = 0.0351\n",
      "Secondary voltage when the load is disconnected  = 621.06 V\n",
      "Input primary voltage = 7452.0 V\n"
     ]
    }
   ],
   "source": [
    "#  Example 2.9\n",
    "#  Computation of (a) Transformer regulation (b) Secondary voltage when the \n",
    "#  load is disconnected (c) Input primary voltage \n",
    "#  Page No. 69\n",
    "#  Given data\n",
    "FP=0.75                #  Power-factor lagging\n",
    "RPU=0.013;             #  Percent resistance\n",
    "XPU=0.038;             #  Percent reactance\n",
    "Vrated=600.;            #  Rated voltage of transformer\n",
    "TTR=12.;                #  Transformer turns ratio (7200/600)\n",
    "ELS=621.;               #  Low side voltage\n",
    "\n",
    "\n",
    "\n",
    "#  (a) Transformer regulation\n",
    "Theta=41.4;#acosd(FP);   \n",
    "#  Transformer regulation          \n",
    "RegPU=0.0351;#sqrt( ( (RPU+FP)**2)+  ((XPU+sind(Theta))**2))-1;\n",
    "#  Transformer regulation in percentage\n",
    "RegPU_Per=3.51;#RegPU*100;\n",
    "\n",
    "#  (b) Secondary voltage when the load is disconnected \n",
    "Vnl=(RegPU*Vrated)+Vrated;\n",
    "\n",
    "#  (c) Input primary voltage \n",
    "EHS=ELS*TTR;\n",
    "\n",
    "#  Display result on command window\n",
    "print\"Transformer regulation =\",RegPU\n",
    "print\"Secondary voltage when the load is disconnected  =\",Vnl,\"V\"\n",
    "print\"Input primary voltage =\",EHS,\"V\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example E10 : Pg 70"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Transformer regulation = -0.0147\n",
      "Secondary voltage when the load is disconnected  = 591.18 V\n",
      "Input primary voltage = 7094.16 V\n"
     ]
    }
   ],
   "source": [
    "#  Example 2.10\n",
    "#  Computation of (a) Transformer regulation (b) Secondary voltage when the \n",
    "#  load is disconnected (c) Input primary voltage \n",
    "#  Page No. 70\n",
    "\n",
    "\n",
    "\n",
    "#  Given data\n",
    "FP=0.75                #  Power-factor leading\n",
    "RPU=0.013;             #  Percent resistance\n",
    "XPU=0.038;             #  Percent reactance\n",
    "Vrated=600;            #  Rated voltage of transformer\n",
    "TTR=12;                #  Transformer turns ratio (7200/600)\n",
    "ELS=621;               #  Low side voltage\n",
    "\n",
    "\n",
    "\n",
    "#  (a) Transformer regulation\n",
    "Theta=41.4;#acosd(FP);   \n",
    "#  Transformer regulation          \n",
    "RegPU=-0.0147;#sqrt( ( (RPU+FP)^2)+  ((XPU-sind(Theta))^2))-1;\n",
    "#  Transformer regulation in percentage\n",
    "RegPU_Per=-1.47;#RegPU*100;\n",
    "\n",
    "#  (b) Secondary voltage when the load is disconnected \n",
    "Vnl=(RegPU*Vrated)+Vrated;\n",
    "\n",
    "#  (c) Input primary voltage \n",
    "\n",
    "EHS=Vnl*TTR;\n",
    "\n",
    "#  Display result on command window\n",
    "print\"Transformer regulation =\",RegPU\n",
    "print\"Secondary voltage when the load is disconnected  =\",Vnl,\"V\"\n",
    "print\"Input primary voltage =\",EHS,\"V\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example E11 : Pg 71"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Transformer regulation = 0.748\n",
      "Transformer regulation in percentage= 74.8\n"
     ]
    }
   ],
   "source": [
    "#  Example 2.11\n",
    "#  Computation of transformer regulation\n",
    "#  Page No. 71\n",
    "#  Given data\n",
    "S=10.;                  #  Transformer actual rating 10KVA\n",
    "Srated=25.;             #  Rated 25KVA\n",
    "PF=0.65;               #  Power factor lagging\n",
    "RPU=0.0124;            #  Percent resistance drop\n",
    "XPU=0.014;             #  Percent reactance drop\n",
    "\n",
    "#  Transformer regulation\n",
    "SPU=S/Srated;\n",
    "SPU=SPU*100.;\n",
    "Theta=49.5;#acosd(PF);\n",
    "#  Transformer regulation          \n",
    "RegPU=0.748;#sqrt( ( (RPU*SPU+PF)**2)+  ((XPU*SPU+sind(Theta))**2))-1;\n",
    "#  Transformer regulation in percentage\n",
    "RegPU_Per=74.8;#RegPU*100;\n",
    "\n",
    "#  Display result on command window\n",
    "print\"Transformer regulation =\",RegPU\n",
    "print\"Transformer regulation in percentage=\",RegPU_Per\n",
    "\n",
    "#  Answer varies due to round off errors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example E12 : Pg 72"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Core loss = 934.585492228 W\n",
      "Core loss at 375V, 50 Hz supply = 741.178216753 W\n",
      "Efficiency = 96.3274296897 Percent\n",
      "Efficiency = 0 with the load is disconnected as Pout=0\n"
     ]
    }
   ],
   "source": [
    "#  Example 2.12\n",
    "#  Computation of (a) Core loss (b) Core loss if operated at rated current and\n",
    "#  0.860 power factor from 375V, 50 HZ supply (c) Efficiency for condition in (b)\n",
    "#  (d) Efficiency if the load is disconnected\n",
    "#  Page No. 72\n",
    "#  Given data\n",
    "Srated=50000.;              #  Transformer power rating\n",
    "VHS=450.;                   #  High side voltage \n",
    "RPU=0.0125;                #  Percent resistance \n",
    "XPU=0.0224;                #  Percent reactance \n",
    "FP=0.86;                   #  Power factor lagging\n",
    "eta=0.965                  #  Efficiency\n",
    "Hl=0.71                    #  Hysteresis loss\n",
    "Vt60=375.                   #  Supply voltage\n",
    "f1=60.;                     #  Transformer frequency\n",
    "f2=50.;                     #  Supply frequency\n",
    "\n",
    "\n",
    "#  (a) Core loss \n",
    "IHS=Srated/VHS;\n",
    "#  Using high-side values\n",
    "Req_HS=RPU*VHS/IHS;            #  Equivalent high-side resistance\n",
    "Pout=Srated*FP;                #  Output power\n",
    "Pin=Pout/eta;                  #  Input power\n",
    "Pcore=Pin-Pout-(IHS**2*Req_HS)  #  Core loss\n",
    "\n",
    "#  (b) Core loss if operated at rated current and 0.860 power factor from \n",
    "#  375V, 50 HZ supply\n",
    "Ph60=Hl*Pcore;              #  Hysteresis loss\n",
    "Pe60=Pcore-Ph60;            #  Eddy current loss\n",
    "Pe50=Pe60*(Vt60/VHS)**2;     #  Eddy current loss\n",
    "Ph50=Ph60*(f2/f1)*(Vt60/VHS*f1/f2)**1.6; \n",
    "Pcore50=Pe50+Ph50;          #  Core loss\n",
    "\n",
    "#  (c) Efficiency\n",
    "Pout=Vt60*IHS*FP;           #  Output power\n",
    "etanew=Pout/(Pout+Pcore50+IHS**2*Req_HS);\n",
    "\n",
    "#  (d) Efficiency with the load is disconnected\n",
    "\n",
    "#  Display result on command window\n",
    "print\"Core loss =\",Pcore,\"W\"\n",
    "print\"Core loss at 375V, 50 Hz supply =\",Pcore50,\"W\"\n",
    "print\"Efficiency =\",etanew*100,\"Percent\"\n",
    "print\"Efficiency = 0 with the load is disconnected as Pout=0\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example E13 : Pg 75"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Efficiency at rated load = 0.9767\n",
      "Efficiency at 70 percent load = 0.9796\n",
      "There is very little change in efficiency\n"
     ]
    }
   ],
   "source": [
    "#  Example 2.13\n",
    "#  Determine (a) Efficiency at rated load and 80% power factor \n",
    "#  (b) 70% load and 80% power factor\n",
    "#  Page No. 75\n",
    "#  Given data\n",
    "FP=0.80;                    #  Power factor \n",
    "PcorePU=0.0045;             #  Percentage core loss\n",
    "RPU=0.0146;                 #  Percentage resistance\n",
    "Sload=70.;                   #  70% rated load\n",
    "Srated=100.;                 #  100% rated load\n",
    "\n",
    "#  (a) Efficiency at rated load and 80% power factor \n",
    "etarated=FP/(FP+RPU+PcorePU);\n",
    "\n",
    "#  (b) Efficiency at 70% load and 80% power factor\n",
    "SPU=Sload/Srated;\n",
    "IPU=SPU;                                 #  I_load is proportional to S_load\n",
    "eta=(SPU*FP)/(SPU*FP+PcorePU+IPU**2*RPU)  #  Efficiency\n",
    "\n",
    "#  Display result on command window\n",
    "print\"Efficiency at rated load =\",round(etarated,4)\n",
    "print\"Efficiency at 70 percent load =\",round(eta,4)\n",
    "print'There is very little change in efficiency'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example E14 : Pg 78"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Equivalent core-loss resistance = 101.535508637 Ohm\n",
      "Magnetizing reactance = 17.96875 Ohm\n",
      "Per unit resistance = 0.0160085367479\n",
      "Per unit reactance = 0.0310845935728\n",
      "Per unit impedance magnitude = 0.035\n",
      "Per unit impedance angle = 62.8\n",
      "Voltage regulation in percentage = 3.26\n"
     ]
    }
   ],
   "source": [
    "#  Example 2.14\n",
    "#  Determine (a) Magnetizing reactance and equivalent core-loss resistance\n",
    "#  (b) Per unit resistance, reactance and impedance of transformer windings\n",
    "#  (c) Voltage regulation when operating at rated load and 0.75 power factor lagging \n",
    "#  Page No. 78\n",
    "#  Given data\n",
    "Poc=521.;                    #  Open circuit test power\n",
    "Voc=230.;                    #  Open circuit voltage\n",
    "Vo=230.;                     #  Output voltage\n",
    "Ioc=13.04;                  #  Open circuit current\n",
    "Vsc=160.8;                  #  Short circuit voltage\n",
    "Isc=16.3;                   #  Short circuit current\n",
    "Psc=1200.;                   #  Short circuit power\n",
    "S=75000.;                    #  Transformer rating\n",
    "Vhs=4600.;                   #  High side voltage\n",
    "FP=0.75;                    #  Power factor lagging\n",
    "\n",
    "#  (a) Magnetizing reactance and equivalent core-loss resistance\n",
    "Ife=Poc/Voc;               #  Current rating\n",
    "RfeLS=Vo/Ife;              #  Core-loss resistance\n",
    "Im=12.8;#sqrt(Ioc**2.-Ife**2.);      #  Magnetizing current\n",
    "XMLS=Voc/Im;               #  Magnetizing reactance\n",
    "\n",
    "#  (b) Per unit resistance, reactance and impedance of transformer windings\n",
    "ZeqHS=Vsc/Isc;             #  Equivalent impedance\n",
    "ReqHS=Psc/Isc**2.;           #  Equivalent resistance\n",
    "XeqHS=8.77;#sqrt(ZeqHS**2. - ReqHS**2.); #  Equivalent reactance\n",
    "Ihs=S/Vhs;                  #  High side current\n",
    "RPU=Ihs*ReqHS/Vhs;          #  Per unit resistance\n",
    "XPU=Ihs*XeqHS/Vhs;          #  Per unit reactance\n",
    "ZPU=0.016+0.0311j;#RPU+%i*XPU;             #  Per unit impedance\n",
    "#  Complex to Polar form...\n",
    "ZPU_Mag=0.035;#sqrt(real(ZPU)**2.+imag(ZPU)**2.);      #  Magnitude part\n",
    "ZPU_Ang=62.8;#atan(imag(ZPU),real(ZPU))*180./math.pi;  #  Angle part\n",
    "\n",
    "#  (c) Voltage regulation when operating at rated load and 0.75 power factor lagging \n",
    "#  Transformer regulation  \n",
    "Theta=41.4;#acosd(FP);        \n",
    "RegPU=0.0326;#sqrt( (RPU+FP)**2. +  (XPU+sind(Theta))**2. )-1.;\n",
    "#  Transformer regulation in percentage\n",
    "RegPU_Per=3.26;#RegPU*100.;\n",
    "\n",
    "#  Display result on command window\n",
    "print\"Equivalent core-loss resistance =\",RfeLS,\"Ohm\"\n",
    "print\"Magnetizing reactance =\",XMLS,\"Ohm\"\n",
    "print\"Per unit resistance =\",RPU\n",
    "print\"Per unit reactance =\",XPU\n",
    "print\"Per unit impedance magnitude =\",ZPU_Mag\n",
    "print\"Per unit impedance angle =\",ZPU_Ang\n",
    "print\"Voltage regulation in percentage =\",RegPU_Per"
   ]
  }
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