{ "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": { "collapsed": false }, "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" ] } ], "metadata": { "kernelspec": { "display_name": "Python [Root]", "language": "python", "name": "Python [Root]" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.12" } }, "nbformat": 4, "nbformat_minor": 0 }