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diff --git a/Electric_Machines_by_C._I._Hubert/CHAPTER03.ipynb b/Electric_Machines_by_C._I._Hubert/CHAPTER03.ipynb new file mode 100644 index 00000000..06d165ad --- /dev/null +++ b/Electric_Machines_by_C._I._Hubert/CHAPTER03.ipynb @@ -0,0 +1,578 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# CHAPTER03 : TRANSFORMER CONNECTIONS OPERATION AND SPECIALITY TRANSFORMERS" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E01 : Pg 98" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Load current = 8.0 A\n", + "Incoming line current = 2.0 A\n", + "Transformed current = 6.0 A\n", + "Apparent power conducted = 1200.0 VA\n", + "Apparent power transformed = 3600.0 VA\n" + ] + } + ], + "source": [ + "# Example 3.1\n", + "# Computation of (a) Load current (b) Incoming line current\n", + "# (c) Transformed current (d) Apparent power conducted and apparent power transformed\n", + "# Page No. 98\n", + "# Given data\n", + "NHS=400.; # Number of turns in the high side\n", + "NLS=0.25*400.; # Number of turns in the low side\n", + "VHS=2400.; # Voltage at the high side\n", + "S=4800.; # Supply voltage\n", + "\n", + "# (a) Load current\n", + "a=NHS/NLS; # Transformer turn ratio \n", + "VLS=VHS/a; # Low side voltage \n", + "ILS=S/VLS; # Load current\n", + "\n", + "# (b) Incoming line current\n", + "IHS=ILS/a; \n", + "\n", + "# (c) Transformed current\n", + "ITR=ILS-IHS;\n", + "\n", + "# (d) Apparent power conducted and apparent power transformed\n", + "\n", + "SCOND=IHS*VLS; # Apparent power conducted\n", + "STRANS=ITR*VLS; # Apparent power transformed \n", + "\n", + "\n", + "# Display result on command window\n", + "print\"Load current =\",ILS,\"A\"\n", + "print\"Incoming line current =\",IHS,\"A\"\n", + "print\"Transformed current =\",ITR,\"A\"\n", + "print\"Apparent power conducted =\",SCOND,\"VA\"\n", + "print\"Apparent power transformed =\",STRANS,\"VA\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E02 : Pg 100" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Rated primary current = 41.6666666667 A\n", + "Rated secondary current = 4.16666666667 A\n", + "Apparent power rating = 110.0 KVA\n" + ] + } + ], + "source": [ + "# Example 3.2\n", + "# Computation of (a) Rated primary and secondary currents when connected as \n", + "# autotransformer (b) Apparent power rating when connected as an autotransformer\n", + "# Page No. 100\n", + "# Given data\n", + "S=10000.; # Supply voltage\n", + "VLS=240.; # Voltage at the low side\n", + "VHS=2400.; # Voltage at the high side\n", + "Sw=10.; # Power rating\n", + "# (a) Rated primary and secondary currents when connected as autotransformer \n", + "ILSWINDING=S/VLS; # Rated primary current\n", + "IHSWINDING=S/VHS; # Rated secondary current\n", + "# (b) Apparent power rating when connected as an autotransformer\n", + "a=VHS/VLS; # Magnetic drop across R1\n", + "Sat=(a+1)*Sw; \n", + "# Display result on command window\n", + "print\"Rated primary current =\",ILSWINDING,\"A\"\n", + "print\"Rated secondary current =\",IHSWINDING,\"A\"\n", + "print\"Apparent power rating =\",Sat,\"KVA\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E03 : Pg 102" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Actual output voltage supplied to the air conditioner is = 233.2 V\n", + "Actual output voltage assuming utilization voltage as 246 V is = 230.617793194 V\n" + ] + } + ], + "source": [ + "# Example 3.3\n", + "# Computation of (a) Buck boost transformer parameters \n", + "# (b) Repeating the same assuming utilization voltage as 246V\n", + "# Page No. 102\n", + "# Given data\n", + "S=10000.; # Supply voltage\n", + "VLS=212.; # Voltage at the low side\n", + "VHSNEW=246.; # New voltage at the high side\n", + "a1=1.100; \n", + "a11=1.0667;\n", + "# (a) Buck boost transformer parameters \n", + "VHS=a1*VLS;\n", + "# (b) Repeating the same assuming utilization voltage as 246V\n", + "VLSNEW=VHSNEW/a11; \n", + "# Display result on command window\n", + "print\"Actual output voltage supplied to the air conditioner is =\",VHS,\"V\"\n", + "print\"Actual output voltage assuming utilization voltage as 246 V is =\",VLSNEW,\"V\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E04 : Pg 104" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Circulating current magnitude = 65.6 A\n", + "Circulating current angle = -68.0 deg\n", + "Circulating current as a percent of the rated current = 30.176 Percent\n", + "Percent difference in secondary voltage = 2.22222222222 Percent\n" + ] + } + ], + "source": [ + "# Example 3.4\n", + "# Determine (a) Circulating current in the paralleled secondaries \n", + "# (b) Circulating current as a percent of the rated current of transformer A \n", + "# (c) Percent difference in secondary voltage that caused the circulating current\n", + "# Page No. 104\n", + "# Given data\n", + "S=100000.; # Transformer A and B rating \n", + "VLSA=460.; # Voltage at the low side of transformer A\n", + "VLSB=450.; # Voltage at the low side of transformer A\n", + "RPUA=0.0136; # Percent resistance of transformer A\n", + "XPUA=0.0350; # Percent reactance of transformer A\n", + "RPUB=0.0140; # Percent resistance of transformer B\n", + "XPUB=0.0332; # Percent reactance of transformer B\n", + "# (a) Circulating current in the paralleled secondaries \n", + "IA= S/VLSA; # Rated low side current for transformer A\n", + "IB= S/VLSB; # Rated low side current for transformer B\n", + "ReqA=RPUA*VLSA/IA; # Equivalent resistance of transfomer A\n", + "ReqB=RPUB*VLSB/IB; # Equivalent resistance of transfomer B\n", + "XeqA=XPUA*VLSA/IA; # Equivalent reactance of transfomer A\n", + "XeqB=XPUB*VLSB/IB; # Equivalent reactance of transfomer B\n", + "# Impedance of the closed loop formed by two secondaries is\n", + "Zloop=0.0571+0.14j;#ReqA+%i*XeqA+ReqB+%i*XeqB; \n", + "# Complex to Polar form...\n", + "Zloop_Mag=0.152;#sqrt(real(Zloop)**2+imag(Zloop)**2); # Magnitude part\n", + "Zloop_Ang=68.;#atan(imag(Zloop),real(Zloop))*180/%pi; # Angle part\n", + "Icirc_Mag=65.6;#(VLSA-VLSB)/Zloop_Mag; # Circulating current magnitude\n", + "Icirc_Ang=-68.;#0- Zloop_Ang; # Circulating current angle\n", + "\n", + "# (b) Circulating current as a percent of the rated current of transformer A\n", + "IcircA=Icirc_Mag*100/IA;\n", + "# (c) Percent difference in secondary voltage that caused the circulating current\n", + "PD=(VLSA-VLSB)*100/VLSB;\n", + "# Display result on command window\n", + "print\"Circulating current magnitude =\",Icirc_Mag,\"A\"\n", + "print\"Circulating current angle =\",Icirc_Ang,\"deg\"\n", + "print\"Circulating current as a percent of the rated current =\",IcircA,\"Percent\"\n", + "print\"Percent difference in secondary voltage =\",PD,\"Percent\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E05 : Pg 107" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Rated high side current of transformer A = 31.25 A\n", + "Rated high side current of transformer B = 83.3333333333 A\n", + "Percent of total bank current drawn by transformer A = 3070.0 Percent\n", + "Percent of total bank current drawn by transformer B = 6980.0 Percent\n", + "Maximum load that can be handled by the bank = 101.791530945 A\n" + ] + } + ], + "source": [ + "# Example 3.5\n", + "# Determine (a) Rated high side current of each transformer (b) Percent of the\n", + "# total bank-current drawn by each transformer (c) Maximum load that can be \n", + "# handled by the bank without overloading by one of the transformer\n", + "# Page No. 107\n", + "# Given data\n", + "SA=75000.; # Transformer A rating\n", + "SB=200000.; # Transformer B rating\n", + "VHSA=2400.; # Voltage at the high side of transformer A\n", + "VHSB=2400.; # Voltage at the high side of transformer B\n", + "RPUA=1.64; # Percent resistance of transformer A\n", + "XPUA=3.16; # Percent reactance of transformer A\n", + "RPUB=1.10; # Percent resistance of transformer B\n", + "XPUB=4.03; # Percent reactance of transformer B\n", + "# (a) Rated high side current of each transformer\n", + "IArated=SA/VHSA; # High side rated current transformer A\n", + "IBrated=SB/VHSB; # High side rated current transformer B\n", + "# (b) Percent of the total bank-current drawn by each transformer\n", + "ZAper=1.64+3.16j;#RPUA+%i*XPUA; # Percent impadance for transformer A\n", + "# Complex to Polar form...\n", + "ZAper_Mag=3.56;#sqrt(real(ZAper)**2+imag(ZAper)**2); # Magnitude part\n", + "ZAper_Ang=62.6;#atan(imag(ZAper),real(ZAper))*180/%pi; # Angle part\n", + "\n", + "ZBper=1.1+4.03j;#RPUB+%i*XPUB; # Percent impadance for transformer B\n", + "# Complex to Polar form...\n", + "ZBper_Mag=4.18;#sqrt(real(ZBper)**2+imag(ZBper)**2); # Magnitude part\n", + "ZBper_Ang=74.7;#atan(imag(ZBper),real(ZBper))*180/%pi; # Angle part\n", + "\n", + "ZAbase=VHSA/IArated; # Base impedance of transformer A\n", + "ZBbase=VHSB/IBrated; # Base impedance of transformer A\n", + "\n", + "ZeqA_Mag=ZAbase*ZAper_Mag/100; # Magnitude of equivalent impedance A\n", + "ZeqA_Ang=ZAper_Ang; # Angle of equivalent impedance A\n", + "\n", + "ZeqB_Mag=ZBbase*ZBper_Mag/100; # Magnitude of equivalent impedance B\n", + "ZeqB_Ang=ZBper_Ang; # Angle of equivalent impedance B\n", + "\n", + "YeqA_Mag=0.366;#1/ZeqA_Mag; # Magnitude of equivalent admittance A\n", + "YeqA_Ang=-62.6;#0-ZeqA_Ang; # Angle of equivalent admittance A\n", + "\n", + "# Polar to Complex form\n", + "YeqA_R=0.168;#YeqA_Mag*cos(-YeqA_Ang*%pi/180); # Real part of complex number\n", + "YeqA_I=-0.325;#YeqA_Mag*sin(YeqA_Ang*%pi/180); # Imaginary part of complex number\n", + "\n", + "YeqB_Mag=0.831;#1/ZeqB_Mag; # Magnitude of equivalent admittance B\n", + "YeqB_Ang=-74.7;#0-ZeqB_Ang; # Angle of equivalent admittance B\n", + "\n", + "# Polar to Complex form\n", + "\n", + "YeqB_R=0.219;#YeqB_Mag*cos(-YeqB_Ang*%pi/180); # Real part of complex number\n", + "YeqB_I=-0.802;#YeqB_Mag*sin(YeqB_Ang*%pi/180); # Imaginary part of complex number\n", + "YP=0.387+1.13j;#(YeqA_R - %i* YeqA_I)+(YeqB_R - %i* YeqB_I); # Parallel admittance\n", + "\n", + " # Complex to Polar form...\n", + "YP_Mag=1.19;#sqrt(real(YP)**2+imag(YP)**2); # Magnitude part\n", + "YP_Ang=71.;#atan(imag(YP),real(YP))*180/%pi; # Angle part\n", + "\n", + "IA=30.7;#YeqA_Mag/YP_Mag; # Transformer A load\n", + "IB=69.8;#YeqB_Mag/YP_Mag; # Transformer A load\n", + "IA=IA*100.;\n", + "IB=IB*100.;\n", + "\n", + "# (c) Maximum load that can be handled by the bank without overloading by \n", + "# one of the transformer\n", + "Ibank=IArated/0.307;\n", + "\n", + "# Display result on command window\n", + "\n", + "print\"Rated high side current of transformer A =\",IArated,\"A\"\n", + "print\"Rated high side current of transformer B =\",IBrated,\"A\"\n", + "print\"Percent of total bank current drawn by transformer A =\",IA,\"Percent\"\n", + "print\"Percent of total bank current drawn by transformer B =\",IB,\"Percent\"\n", + "print\"Maximum load that can be handled by the bank =\", Ibank,\"A\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E06 : Pg 109" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Percent of total bank current drawn by transformer A = 55.1594746717 Percent\n", + "Percent of total bank current drawn by transformer B = 44.8405253283 Percent\n" + ] + } + ], + "source": [ + "# Example 3.6\n", + "# Determine the percent of the total bank-current drawn by each transformer \n", + "# Page No. 109\n", + "# Given data\n", + "ZaPU_R=0.0158; # Transformer A impedance real part\n", + "ZaPU_I=0.0301; # Transformer A impedance imaginary part\n", + "ZbPU_R=0.0109; # Transformer B impedance real part\n", + "ZbPU_I=0.0398; # Transformer B impedance imaginary part\n", + "SB=200000.; # Transformer B rating\n", + "VHSA=2400.; # Voltage at the high side of transformer A\n", + "VHSB=2400.; # Voltage at the high side of transformer B\n", + "RPUA=1.64; # Percent resistance of transformer A\n", + "XPUA=3.16; # Percent reactance of transformer A\n", + "RPUB=1.10; # Percent resistance of transformer B\n", + "XPUB=4.03; # Percent reactance of transformer B\n", + "\n", + "\n", + "\n", + "# Base impedance of transformer A\n", + "ZaPU=0.0158 + 0.0301j;#ZaPU_R+%i*ZaPU_I;\n", + "# Complex to Polar form...\n", + "ZaPU_Mag=0.034;#sqrt(real(ZaPU)**2+imag(ZaPU)**2); # Magnitude part\n", + "ZaPU_Ang=62.3;#atan(imag(ZaPU),real(ZaPU))*180/%pi; # Angle part\n", + "\n", + "# Base impedance of transformer B\n", + "ZbPU=0.0109+0.0398j;#ZbPU_R+%i*ZbPU_I;\n", + "# Complex to Polar form...\n", + "ZbPU_Mag=0.0413;#sqrt(real(ZbPU)**2+imag(ZbPU)**2); # Magnitude part\n", + "ZbPU_Ang=74.7;#atan(imag(ZbPU),real(ZbPU))*180/%pi; # Angle part\n", + "\n", + "# Admittance of transformer A\n", + "YaPU_Mag=29.4;#1/ZaPU_Mag; # Magnitude of equivalent admittance A\n", + "YaPU_Ang=-62.3;#0-ZaPU_Ang; # Angle of equivalent admittance A\n", + "\n", + "# Polar to Complex form\n", + "\n", + "YaPU_R=13.7;#YaPU_Mag*cos(-YaPU_Ang*%pi/180); # Real part of complex number\n", + "YaPU_I=-26;#YaPU_Mag*sin(YaPU_Ang*%pi/180); # Imaginary part of complex number\n", + "\n", + "# Admittance of transformer B\n", + "YbPU_Mag=24.2;#1/ZbPU_Mag; # Magnitude of equivalent admittance B\n", + "YbPU_Ang=-74.7;#0-ZbPU_Ang; # Angle of equivalent admittance B\n", + "# Polar to Complex form\n", + "\n", + "YbPU_R=6.4;#YbPU_Mag*cos(-YbPU_Ang*%pi/180); # Real part of complex number\n", + "YbPU_I=-23.4;#YbPU_Mag*sin(YbPU_Ang*%pi/180); # Imaginary part of complex number\n", + "\n", + "# Parallel admittance\n", + "YP=20.1+49.4j;#(YaPU_R-%i*YaPU_I)+(YbPU_R-%i*YbPU_I);\n", + "# Complex to Polar form...\n", + "YP_Mag=53.3;#sqrt(real(YP)**2+imag(YP)**2); # Magnitude part\n", + "YP_Ang=67.9;#atan(imag(YP),real(YP))*180/%pi; # Angle part\n", + "\n", + "IA=YaPU_Mag/YP_Mag*100; # Percent current drawn by transformer A \n", + "IB=100-IA; \n", + "\n", + "# Display the result on the command window\n", + "print\"Percent of total bank current drawn by transformer A =\",IA,\"Percent\"\n", + "print\"Percent of total bank current drawn by transformer B =\",IB,\"Percent\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E07 : Pg 113" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Bank ratio = 17.3333333333\n", + "Transformer ratio = 10.007404666\n", + "Rated line current for the high side = 20.8179183602 A\n", + "Rated phase current for the high side = 20.8179183602 A\n", + "Rated line current for the low side = 360.843918244 A\n", + "Rated phase current for the low side = 208.333333333 A\n" + ] + } + ], + "source": [ + "# Example 3.7\n", + "# Computation of (a) Bank ratio (b) Transformer ratio (c) Rated line and phase \n", + "# currents for the high side (d) Rated line and phase currents for the low side\n", + "# Page No. 113\n", + "# Given data\n", + "import math \n", + "VLINEHS=4160.; # Number of turns in the high side\n", + "VLINELS=240.; # Number of turns in the low side\n", + "VHS=2400.; # Voltage at the high side\n", + "S=4800.; # Supply voltage\n", + "Vline=150000.; # Transformer rating\n", + "\n", + "# (a) Bank ratio\n", + "bankratio=VLINEHS/VLINELS; \n", + "\n", + "# (b) Transformer ratio\n", + "Vphasep= VLINEHS/ math.sqrt(3); # For wye primary\n", + "Vphases=VLINELS # For secondary\n", + "TR=Vphasep/Vphases; # Transformer ratio \n", + "\n", + "# (c) Rated line and phase currents for the high side \n", + "Ilinew=Vline/(math.sqrt(3)*VLINEHS);\n", + "Iphasew=Ilinew;\n", + "\n", + "# (d) Rated line and phase currents for the low side\n", + "Ilined=Vline/(math.sqrt(3)*VLINELS); \n", + "Iphased=Ilined/math.sqrt(3);\n", + "\n", + "\n", + "# Display result on command window\n", + "print\"Bank ratio =\",bankratio\n", + "print\"Transformer ratio =\",TR\n", + "print\"Rated line current for the high side =\",Ilinew,\"A\"\n", + "print\"Rated phase current for the high side =\",Iphasew,\"A\"\n", + "print\"Rated line current for the low side =\",Ilined,\"A\"\n", + "print\"Rated phase current for the low side =\",Iphased,\"A\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E08 : Pg 117" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Capacity of the bank when operating open-delta is = 43.275 kVA\n" + ] + } + ], + "source": [ + "# Example 3.8\n", + "# Determine the maximum allowable power that the open-delta bank handle \n", + "# without overheating\n", + "# Page No. 117\n", + "# Given data\n", + "S=25.;# Transformer rating\n", + "# Capacity of the delta-delta bank is\n", + "Cddb=S*3;\n", + "# Capacity of the bank when operating open-delta is\n", + "Cob=Cddb*0.577;\n", + "# Display result on command window\n", + "print\"Capacity of the bank when operating open-delta is =\",Cob,\"kVA\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E09 : Pg 117" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Minimum power rating required for each transformer = 32.075014955 kVA\n" + ] + } + ], + "source": [ + "# Example 3.9\n", + "# Determine the minimum power rating required for each transformer\n", + "# Page No. 117\n", + "# Given data\n", + "import math\n", + "P=50000.; # Transformer power rating\n", + "Eline=120.; # Line voltage\n", + "FP=0.9 # Power factor lagging\n", + "VL=120.;\n", + "#Line current is\n", + "Iline=P/(math.sqrt(3.)*Eline*FP);\n", + "#Minimum power rating required for each transformer\n", + "Pmin=VL*Iline/1000.;\n", + "#Display result on command window\n", + "print\"Minimum power rating required for each transformer =\",Pmin,\"kVA\"" + ] + } + ], + "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 +} |