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diff --git a/Electric_Power_Distribution_System_Engineering_by_T._Gonen/ch3.ipynb b/Electric_Power_Distribution_System_Engineering_by_T._Gonen/ch3.ipynb new file mode 100755 index 00000000..fb811a30 --- /dev/null +++ b/Electric_Power_Distribution_System_Engineering_by_T._Gonen/ch3.ipynb @@ -0,0 +1,898 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:e3360cc86683c7a5706db81b033b8664f6c6abe93730acff7b5ab6cc3ddee4ce" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 3 : Application of Distribution Transformers" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.1 Page No : 118" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "S = 25.*(10**3); #Rating of the transformer in VA\n", + "#Values in per unit\n", + "Rt = 0.014; #Resismath.tance of Transformer\n", + "Xt = 0.012; #Reacmath.tance of transformer\n", + "Vh = 7200; #High Voltage End in V\n", + "Vx = 120; # Low Voltage End in V\n", + "Rb = (Vh**2)/S; #Base Value of Resismath.tance\n", + "#Accroding to Lloyd's Formula\n", + "\n", + "# Calculations\n", + "Zhx12 = (1.5*Rt)+(1j*1.2*Xt); #Impedance referred to HV side when the winding x2x3 is shorted\n", + "\n", + "n = Vh/Vx; #Turns Ratio\n", + "\n", + "Zhx13 = Rt+(1j*Xt); #Use of Entire low voltage winding\n", + "\n", + "#Impedances of the required terms in pu\n", + "A = (2*Zhx13)-Zhx12;\n", + "B = ((2*Zhx12)-(2*Zhx13))/(n**2);\n", + "C = B;\n", + "\n", + "#Angle of Impedances\n", + "ta = math.degrees(math.atan(A.imag/A.real));\n", + "tb = math.degrees(math.atan(B.imag/B.real));\n", + "\n", + "# Results\n", + "print 'The Circuit impedances on the high voltage side is %g/_%g ohm'%(abs(A*Rb),ta)\n", + "print 'Each of the Circuit impedances on the low voltage side is %g/_%g ohm'%(abs(B*Rb),tb)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The Circuit impedances on the high voltage side is 24.6366/_53.9017 ohm\n", + "Each of the Circuit impedances on the low voltage side is 0.0085248/_18.9246 ohm\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.2 Page No : 119" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "from numpy import exp\n", + "\n", + "# Variables\n", + "#Impedances from the previous example\n", + "Zh = 24.6437*exp(1j*53.9*math.pi/180);\n", + "Zl = 8.525*(10**-3)*exp(1j*18.9*math.pi/180);\n", + "#Voltages\n", + "Vh = 7200.; #High End\n", + "Vx = 120.; # Low End\n", + "S = 25.*1000; #Transformer Rating in VA\n", + "N = Vh/Vx; #Turns Ratio\n", + "\n", + "# Calculations\n", + "#R of service drop is zero #Line to Neutral Currents\n", + "IfLVn = Vx/(Zl+((1/(N**2))*Zh)); #Secondary Fault Current\n", + "IfHVn = IfLVn/N; #Primary Fault Current\n", + "\n", + "#R of service drop is zero #Line to Line Currents\n", + "Nl = Vh/(2*Vx); #New Truns Ratio\n", + "IfLVl = 2*Vx/((2*Zl)+((1/(Nl**2))*Zh)); #Secondary Fault Current\n", + "IfHVl = IfLVl/Nl; #Primary Fault Current\n", + "\n", + "# Results\n", + "print 'a) The Magnitude of Line to Neutral Fault Currentson HV and LV when R of service drop\\\n", + " is zero are %g A and %g A respectively'%(abs(IfHVn),abs(IfLVn))\n", + "print 'b) The Magnitude of Line to Line Fault Currentson HV and LV when R of service drop is zero are\\\n", + " %g A and %g A respectively'%(abs(IfHVl),abs(IfLVl))\n", + "print 'c) The Minimum Allowable interrupting capacity for circuit breaker isconnected to the LV is %g A'%(abs(IfLVn))\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "a) The Magnitude of Line to Neutral Fault Currentson HV and LV when R of service drop is zero are 136.353 A and 8181.2 A respectively\n", + "b) The Magnitude of Line to Line Fault Currentson HV and LV when R of service drop is zero are 188.283 A and 5648.5 A respectively\n", + "c) The Minimum Allowable interrupting capacity for circuit breaker isconnected to the LV is 8181.2 A\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.3 Page No : 121" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "from sympy import solve,Symbol\n", + "from numpy import exp\n", + "\n", + "# Variables\n", + "Vx = 120.; #Low End Voltage\n", + "#When Service drop is Zero\n", + "IfLVn = 8181.7*exp(-1*1j*34.3*math.pi/180); #Line to Neutral Vault Current\n", + "IfLVl = 5649*exp(-1*1j*40.6*math.pi/180); #Line to Line Fault Current\n", + "\n", + "Ral4 = 2.58; # #4 AWG Aluminium Conductor Resismath.tance per mile\n", + "Ralinf = 1.03; # #1/0 AWG Aluminium Conductor Resismath.tance per mile\n", + "\n", + "# Calculations\n", + "#Impedances when Service drop is zero, suffix l denotes line to line\n", + "#Suffix n denotes line to neutral\n", + "Zl0 = (2*Vx)/IfLVl;\n", + "Zn0 = (Vx)/IfLVn;\n", + "\n", + "#When there is R service drop\n", + "#Magnitudes of Line to Line and Line to Earth fault currents are equal\n", + "\n", + "R = Symbol('R'); #Variable Value\n", + "#Effective Impedances\n", + "Zl = Zl0+(2*R);\n", + "Zn = Zn0+(2*R);\n", + "#Fault Currents\n", + "Ifl = 2*Vx/Zl;\n", + "Ifn = Vx/Zn;\n", + "#print Ifl[1]\n", + "#Magnitudes of Currents\n", + "MIfl = abs(240.)/abs(Ifl.subs(R,3));\n", + "MIfn = abs(Ifn.subs(R,2))/abs(Ifn.subs(R,3));\n", + "DI = MIfl-MIfn;\n", + "X = - 1.5781966 + 240*R #DI.subs(R,2); #Polynomial Equation to find 'R'\n", + "R = solve(X)[0]; #Numerical Value\n", + "\n", + "#The Magnitude of R found is Wrong in the Textbook\n", + "\n", + "#Length of service drop cable\n", + "SDL4 = R/Ral4;\n", + "SDLinf = R/Ralinf;\n", + "\n", + "# Results\n", + "print 'a) The Value of Service drop in the Cable is %g ohm'%(R)\n", + "print 'b The Length of service drop cable for:'\n", + "print 'i) #4 AWG Conductor is %g miles'%(SDL4) \n", + "print 'ii) #1/0 AWG Conductor is %g miles'%(SDLinf) \n", + "\n", + "#Length is printed in Miles\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "a) The Value of Service drop in the Cable is 0.00657582 ohm\n", + "b The Length of service drop cable for:\n", + "i) #4 AWG Conductor is 0.00254877 miles\n", + "ii) #1/0 AWG Conductor is 0.00638429 miles\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.4 Page No : 122" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Variables\n", + "#Transformer Ratings in kVA\n", + "Sr1 = 250.; \n", + "Sr2 = 500.;\n", + "\n", + "#percentage impedances\n", + "Zr1 = 2.4;\n", + "Zr2 = 3.1;\n", + "\n", + "# Calculations\n", + "#Ratio of Maximum Loads\n", + "R = Sr1*Zr2/(Sr2*Zr1);\n", + "\n", + "#If 500 kVA is chosen as the full load transformer, Transformer 1 becomes overloaded\n", + "SL1 = Sr1; #To Avoid OverLoading of transformer 1\n", + "\n", + "SL2 = SL1/R; #Maximum Load on transformer 2\n", + "\n", + "Tl = SL1+SL2; #Total Load without overloading\n", + "\n", + "# Results\n", + "print 'The Maximum Load Carried without overloading any of the transformer is %g kVA'%(Tl)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The Maximum Load Carried without overloading any of the transformer is 637.097 kVA\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.5 Page No : 127" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "#Considering Van as reference voltage\n", + "SL3phi = 200*(10**3); #Load to be powered\n", + "pf3 = 0.8; #Power Factor of three phase load\n", + "t3 = math.acos(pf3); #Power FActor Angle for three phase load\n", + "pf1 = 0.9; #Power Factor of math.single phase load\n", + "t1 = math.acos(pf1); #Power Factor angle of math.single phase load\n", + "SL1 = 80.*(10**3); #Single Phase Light Load\n", + "Vll = 240.; #Secondary Voltage\n", + "#Rating of Single Phase Transformers between individual lines\n", + "Sbc = 100.*(10**3);\n", + "Sab = 75.*(10**3);\n", + "Sca = Sab;\n", + "#Angles of Three phase voltages \n", + "ta = 0.;\n", + "tb = -120.;\n", + "tc = 120.;\n", + "#Angles of three line currents\n", + "tai = ta-t3;\n", + "tbi = tb-t3;\n", + "tci = tc-t3;\n", + "\n", + "# Calculations\n", + "I = SL3phi/(math.sqrt(3)*Vll); #Magnitude of Current\n", + "#3 Phase Line Currents\n", + "Ia3 = I*exp(1j*math.pi*tai/180);\n", + "Ib3 = I*exp(1j*math.pi*tbi/180);\n", + "Ic3 = I*exp(1j*math.pi*tci/180);\n", + "\n", + "MIbc = SL1/Vll; #Magnitude Single Phase Current\n", + "\n", + "tbc = -90; #Lagging Van #Angle of Vbc\n", + "tbci = tbc-t1; #Angle of Current Ibc\n", + "Ibc = MIbc*exp(1j*math.pi*tbci/180);\n", + "\n", + "#Load Currents\n", + "Ia = Ia3;\n", + "Ta = math.degrees(math.atan(Ia.imag/Ia.real));\n", + "Ib = Ib3+Ibc;\n", + "Tb = math.degrees(math.atan(Ib.imag/Ib.real));\n", + "Ic = Ic3-Ibc; #Current is wrong in the textbook\n", + "Tc = math.degrees(math.atan(Ic.imag/Ic.real));\n", + "\n", + "#Current Flowing in the secondary winding of the transformers 1,2 and 3\n", + "Iac = ((Ic/Sbc)-(Ia/Sab))/((1/Sab)+(1/Sbc)+(1/Sca));\n", + "T1 = math.degrees(math.atan(Iac.imag/Iac.real)); #Angle of the above current\n", + "Iba = ((Ia/Sca)-(Ib/Sbc))/((1/Sab)+(1/Sbc)+(1/Sca));\n", + "T2 = math.degrees(math.atan(Iba.imag/Iba.real)); #Angle of the above current\n", + "Icb = ((Ib/Sab)-(Ic/Sca))/((1/Sab)+(1/Sbc)+(1/Sca));\n", + "T3 = math.degrees(math.atan(Icb.imag/Icb.real)); #Angle of the above current\n", + "\n", + "#Kilovoltampere Load on each transformer\n", + "SLab = Vll*abs(Iba)/1000;\n", + "SLbc = Vll*abs(Icb)/1000;\n", + "SLca = Vll*abs(Iac)/1000;\n", + "\n", + "Vlls = Vll; #Secondary Voltage\n", + "Vllp = 7620; #Primary Voltage\n", + "n = Vllp/Vlls; #Turns Ratio\n", + "\n", + "#Primary Currents of the transformer\n", + "IAC = Iac/n;\n", + "IBA = Iba/n;\n", + "ICB = Icb/n;\n", + "\n", + "#Primary Current in each each phase wire\n", + "IA = IAC-IBA;\n", + "TA = math.degrees(math.atan(IA.imag/IA.real)); #Angle of the above current\n", + "IB = IBA-ICB;\n", + "TB = math.degrees(math.atan(IB.imag/IB.real)); #Angle of the above current\n", + "IC = ICB-IAC;\n", + "TC = math.degrees(math.atan(IC.imag/IC.real)); #Angle of the above current\n", + "\n", + "# Results\n", + "print 'a The Line Currents flowing in secondary phase wire :'\n", + "print 'A phase is %g/_%g A'%(abs(Ia),Ta)\n", + "print 'B phase is %g/_%g A'%(abs(Ib),Tb)\n", + "print 'C phase is %g/_%g A'%(abs(Ic),Tc)\n", + "print 'b The Current flowing in secondary winding of each transformer:'\n", + "print 'AC is %g/_%g A'%(abs(Iac),T1)\n", + "print 'AB is %g/_%g A'%(abs(Iba),T2)\n", + "print 'BC is %g/_%g A'%(abs(Icb),T3)\n", + "print 'c The Load on Each Transformer is:'\n", + "print '1 : %g kVA'%(SLca)\n", + "print '2 : %g kVA'%(SLab)\n", + "print '3 : %g kVA'%(SLbc)\n", + "print 'd The Current flowing in primary winding of each transformer:'\n", + "print 'AC is %g/_%g A'%(abs(IAC),T1)\n", + "print 'AB is %g/_%g A'%(abs(IBA),T2)\n", + "print 'BC is %g/_%g A'%(abs(ICB),T3)\n", + "print 'e The Line Currents flowing in primary phase wire :'\n", + "print 'A phase is %g/_%g A'%(abs(IA),TA)\n", + "print 'B phase is %g/_%g A'%(abs(IB),TB)\n", + "print 'C phase is %g/_%g A'%(abs(IC),TC)\n", + "\n", + "#Ic is calculation is wrong, the author has added Ibc instead of subtracting, so if you change - into + in line 45, you get the answer as in the textbook\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "a The Line Currents flowing in secondary phase wire :\n", + "A phase is 481.125/_-0.643501 A\n", + "B phase is 787.293/_71.6504 A\n", + "C phase is 787.977/_-72.7823 A\n", + "b The Current flowing in secondary winding of each transformer:\n", + "AC is 316/_-40.9814 A\n", + "AB is 315.535/_39.7662 A\n", + "BC is 545.454/_89.442 A\n", + "c The Load on Each Transformer is:\n", + "1 : 75.84 kVA\n", + "2 : 75.7283 kVA\n", + "3 : 130.909 kVA\n", + "d The Current flowing in primary winding of each transformer:\n", + "AC is 9.95276/_-40.9814 A\n", + "AB is 9.9381/_39.7662 A\n", + "BC is 17.1796/_89.442 A\n", + "e The Line Currents flowing in primary phase wire :\n", + "A phase is 15.1536/_-0.643501 A\n", + "B phase is 24.7966/_71.6504 A\n", + "C phase is 24.8182/_-72.7823 A\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.6 Page No : 140" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "#Considering Van as reference voltage\n", + "SL3phi = 100.*(10**3); #Load to be powered\n", + "pf3 = 0.8; #Power Factor of three phase load\n", + "t3 = math.acos(pf3); #Power FActor Angle for three phase load\n", + "pf1 = 0.9; #Power Factor of math.single phase load\n", + "t1 = math.acos(pf1); #Power Factor angle of math.single phase load\n", + "SL1 = 50.*(10**3); #Single Phase Light Load\n", + "Vll = 240.; #Secondary Voltage\n", + "#Angles of Three phase voltages \n", + "ta = 0.;\n", + "tb = -120.;\n", + "tc = 120.;\n", + "#Angles of three line currents\n", + "tai = ta-t3;\n", + "tbi = tb-t3;\n", + "tci = tc-t3;\n", + "\n", + "# Calculations\n", + "I = SL3phi/(math.sqrt(3)*Vll); #Magnitude of Current\n", + "#3 Phase Line Currents\n", + "Ia3 = I*exp(1j*math.pi*tai/180);\n", + "Ib3 = I*exp(1j*math.pi*tbi/180);\n", + "Ic3 = I*exp(1j*math.pi*tci/180);\n", + "\n", + "MI1 = SL1/Vll; #Magnitude Single Phase Current\n", + "\n", + "t1v = 30; #Leading Van #Angle of Vbc\n", + "t1i = t1v-t1; #Angle of Current Ibc\n", + "I1 = MI1*exp(1j*math.pi*t1i/180);\n", + "\n", + "#Load Currents\n", + "Ia = Ia3+I1;\n", + "Ta = math.degrees(math.atan(Ia.imag/Ia.real));\n", + "Ib = Ib3-I1;\n", + "Tb = -180+(math.degrees(math.atan(Ib.imag/Ib.real)));\n", + "Ic = Ic3; #Current is wrong in the textbook\n", + "Tc = math.degrees(math.atan(Ic.imag/Ic.real));\n", + "\n", + "#Current flowing in the secondary of the transformer\n", + "Iba = Ia;\n", + "T2 = math.degrees(math.atan(Iba.imag/Iba.real)); #Angle of the above current\n", + "Icb = Ic;\n", + "T3 = 180+(math.degrees(math.atan(Icb.imag/Icb.real))); #Angle of the above current\n", + "\n", + "#Load on Each Transformer\n", + "SLba = Vll*abs(Iba)/1000;\n", + "SLcb = Vll*abs(Icb)/1000;\n", + "\n", + "Vlls = Vll; #Secondary Voltage\n", + "Vllp = 7620; #Primary Voltage\n", + "n = Vllp/Vlls; #Turns Ratio\n", + "\n", + "#Primary Currents of the transformer\n", + "IA = Iba/n;\n", + "TA = math.degrees(math.atan(IA.imag/IA.real)); #Angle of the above current\n", + "IB = Icb/n;\n", + "TB = T3; #Angle of the above current\n", + "IN = IA+IB; #Neutral Current\n", + "TN = math.degrees(math.atan(IN.imag/IN.real)); #Angle of the above current\n", + "\n", + "# Results\n", + "print 'a The Line Currents flowing in secondary phase wire :'\n", + "print 'A phase is %g/_%g A'%(abs(Ia),Ta)\n", + "print 'B phase is %g/_%g A'%(abs(Ib),Tb)\n", + "print 'C phase is %g/_%g A'%(abs(Ic),Tc)\n", + "print 'b The Current flowing in secondary winding of each transformer:'\n", + "print 'AB is %g/_%g A'%(abs(Iba),T2)\n", + "print 'BC is %g/_%g A'%(abs(Icb),T3)\n", + "print 'c The Load on Each Transformer is:'\n", + "print '1 : %g kVA'%(SLba)\n", + "print '2 : %g kVA'%(SLcb)\n", + "print 'd The Line Currents flowing in primary phase wire :'\n", + "print 'AB is %g/_%g A'%(abs(IA),TA)\n", + "print 'CB is %g/_%g A'%(abs(IB),TB)\n", + "print 'The Neutral Current is %g/_%g'%(abs(IN),TN)\n", + "\n", + "#Note the mistake in the Textbook for the calulation for Neutral Current\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "a The Line Currents flowing in secondary phase wire :\n", + "A phase is 433.486/_13.3432 A\n", + "B phase is 433.874/_-134.453 A\n", + "C phase is 240.563/_-60.6435 A\n", + "b The Current flowing in secondary winding of each transformer:\n", + "AB is 433.486/_13.3432 A\n", + "BC is 240.563/_119.356 A\n", + "c The Load on Each Transformer is:\n", + "1 : 104.037 kVA\n", + "2 : 57.735 kVA\n", + "d The Line Currents flowing in primary phase wire :\n", + "AB is 13.6531/_13.3432 A\n", + "CB is 7.57678/_119.356 A\n", + "The Neutral Current is 13.6653/_45.5475\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.8 Page No : 152" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "\n", + "# Variables\n", + "Vll = 480.; #Line to Line Voltage\n", + "Vln = 277.; #Line to neutral Voltage\n", + "\n", + "# Calculations\n", + "#From the Phasor Diagram from the result file\n", + "Vab = Vll*exp(1j*0); #Vab is taken as reference\n", + "Vabh = 50*Vab/100;\n", + "VAB = 4160.;\n", + "VABh = 50*VAB/100; \n", + "VH1H2o = math.sqrt((VAB**2)-(VABh**2));\n", + "VH1H2t = (VABh);\n", + "Vx1x2o = 1*math.sqrt((Vab**2)-(Vabh**2))/3;\n", + "Vx2x3o = 2*math.sqrt((Vab**2)-(Vabh**2))/3;\n", + "VH2H3t = (VABh);\n", + "Vx1x2t = Vabh;\n", + "Vx2x3t = Vabh;\n", + "\n", + "# Results\n", + "print 'a The Phasor diagram is shown in the result file attached to the code'\n", + "print 'b) Vab is %g/_%g V'%(abs(Vab),Vab.imag/Vab.real)\n", + "print 'c The Magnitudes of the following rated winding voltages'\n", + "print 'i) The Voltage VH1H2 on transformer 1 : %g V'%(VH1H2o)\n", + "print 'ii) The Voltage Vx1x2 on transformer 1 : %g V'%(Vx1x2o)\n", + "print 'iii) The Voltage Vx2x3 on transformer 1 : %g V'%(Vx2x3o)\n", + "print 'iv) The Voltage VH1H2 on transformer 2 : %g V'%(VH1H2t)\n", + "print 'v) The Voltage VH2H3 on transformer 2 : %g V'%(VH2H3t)\n", + "print 'vi) The Voltage Vx1x2 on transformer 2 : %g V'%(Vx1x2t)\n", + "print 'vii) The Voltage Vx1x2 on transformer 2 : %g V'%(Vx2x3t)\n", + "print 'd i NO ii NO iii YES'\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "a The Phasor diagram is shown in the result file attached to the code\n", + "b) Vab is 480/_0 V\n", + "c The Magnitudes of the following rated winding voltages\n", + "i) The Voltage VH1H2 on transformer 1 : 3602.67 V\n", + "ii) The Voltage Vx1x2 on transformer 1 : 138.564 V\n", + "iii) The Voltage Vx2x3 on transformer 1 : 277.128 V\n", + "iv) The Voltage VH1H2 on transformer 2 : 2080 V\n", + "v) The Voltage VH2H3 on transformer 2 : 2080 V\n", + "vi) The Voltage Vx1x2 on transformer 2 : 240 V\n", + "vii) The Voltage Vx1x2 on transformer 2 : 240 V\n", + "d i NO ii NO iii YES\n" + ] + }, + { + "output_type": "stream", + "stream": "stderr", + "text": [ + "-c:16: ComplexWarning: Casting complex values to real discards the imaginary part\n", + "-c:17: ComplexWarning: Casting complex values to real discards the imaginary part\n", + "-c:31: ComplexWarning: Casting complex values to real discards the imaginary part\n", + "-c:32: ComplexWarning: Casting complex values to real discards the imaginary part\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.9 Page No : 154" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "from numpy import exp\n", + "\n", + "# Variables\n", + "R = 2.77; #Resismath.tance of the balanced load\n", + "#From Phasor Diagram in Result file\n", + "Vab = 480*exp(1j*0); #Reference Voltage\n", + "MVn = abs(Vab)/math.sqrt(3); #Magnitude of line to neutral voltages\n", + "#Angles of Three phase voltages \n", + "ta = -30.;\n", + "tb = -150.;\n", + "tc = 90.;\n", + "\n", + "# Calculations\n", + "#Angles of Winding according to the Line Currents\n", + "tx3x2 = 30; #Leading\n", + "tx1x2 = -30; #Lagging\n", + "\n", + "I = MVn/R; #Magnitude of current\n", + "\n", + "#Low Voltage Current Phasors\n", + "Ia = I*exp(1j*math.pi*ta/180);\n", + "Ib = I*exp(1j*math.pi*tb/180);\n", + "Ic = I*exp(1j*math.pi*tc/180);\n", + "pfT = math.cos(math.radians(ta-ta)); #Angle of Ia is same as phase voltage #Resismath.tance load\n", + "\n", + "# Results\n", + "print 'a The Low voltage current phasors are:'\n", + "print 'A is %g/_%g A'%(abs(Ia),ta)\n", + "print 'B is %g/_%g A'%(abs(Ib),tb)\n", + "print 'C is %g/_%g A'%(abs(Ic),tc)\n", + "print 'b The Phasor Diagram is the ''b'' diagram of in the result file'\n", + "print 'c) The Power Factor of the Transformer is %g'%(pfT)\n", + "print 'd) Power Factor as seen by winding x3x2 of transformer 2 is %g leading'%(math.cos(math.radians(tx3x2)))\n", + "print 'e) Power Factor as seen by winding x1x2 of transformer 2 is %g lagging'%(math.cos(math.radians(tx1x2)))\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "a The Low voltage current phasors are:\n", + "A is 100.046/_-30 A\n", + "B is 100.046/_-150 A\n", + "C is 100.046/_90 A\n", + "b The Phasor Diagram is the b diagram of in the result file\n", + "c) The Power Factor of the Transformer is 1\n", + "d) Power Factor as seen by winding x3x2 of transformer 2 is 0.866025 leading\n", + "e) Power Factor as seen by winding x1x2 of transformer 2 is 0.866025 lagging\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.10 Page No : 156" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "from numpy import exp\n", + "\n", + "#'o' and 't' represent transformer one and two respectively\n", + "# Variables\n", + "#Objective is to find the Factor which has to be multiplied to get VA rating\n", + "Vll = 1.; #Assumption Made\n", + "#From the Phasor Diagram from the result file\n", + "Vab = Vll*exp(1j*0); #Vab is taken as reference\n", + "Vabh = 50.*Vab/100;\n", + "Vx1x2o = 1*math.sqrt((Vab**2)-(Vabh**2))/3;\n", + "Vx2x3o = 2*math.sqrt((Vab**2)-(Vabh**2))/3;\n", + "Vx1x2t = Vabh;\n", + "Vx2x3t = Vabh;\n", + "\n", + "#Let I be unity\n", + "I = 1;\n", + "\n", + "# Calculations\n", + "#VA Ratings of the respective windings\n", + "Sx1x2o = Vx1x2o*I;\n", + "Sx2x3o = Vx2x3o*I;\n", + "Sx1x2t = Vx1x2t*I;\n", + "Sx2x3t = Vx2x3t*I;\n", + "\n", + "#Total VA rating of transformer\n", + "S1 = Sx1x2o+Sx2x3o;\n", + "S2 = Sx1x2t+Sx2x3t;\n", + "\n", + "#Ratio of total rating to maximum rating\n", + "Rt = (S1+S2)/(math.sqrt(3)*Vll*I);\n", + "\n", + "# Results\n", + "print 'a) The voltampere raing of x1x2 of transformer 1 is %g*VI VA'%(Sx1x2o)\n", + "print 'b) The voltampere raing of x1x2 of transformer 1 is %g*VI VA'%(Sx2x3o)\n", + "print 'c) The Total Output from transformer 1 is %g*VI VA'%(S1)\n", + "print 'd) The voltampere raing of x1x2 of transformer 2 is %g*VI VA'%(Sx1x2t)\n", + "print 'e) The voltampere raing of x1x2 of transformer 2 is %g*VI VA'%(Sx2x3t)\n", + "print 'f) The Total Output from transformer 2 is %g*VI VA'%(S2)\n", + "print 'g) The Total Rating to the Maximum Continous Output is %g'%(Rt)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "a) The voltampere raing of x1x2 of transformer 1 is 0.288675*VI VA\n", + "b) The voltampere raing of x1x2 of transformer 1 is 0.57735*VI VA\n", + "c) The Total Output from transformer 1 is 0.866025*VI VA\n", + "d) The voltampere raing of x1x2 of transformer 2 is 0.5*VI VA\n", + "e) The voltampere raing of x1x2 of transformer 2 is 0.5*VI VA\n", + "f) The Total Output from transformer 2 is 1*VI VA\n", + "g) The Total Rating to the Maximum Continous Output is 1.07735\n" + ] + }, + { + "output_type": "stream", + "stream": "stderr", + "text": [ + "-c:11: ComplexWarning: Casting complex values to real discards the imaginary part\n", + "-c:12: ComplexWarning: Casting complex values to real discards the imaginary part\n", + "-c:37: ComplexWarning: Casting complex values to real discards the imaginary part\n", + "-c:38: ComplexWarning: Casting complex values to real discards the imaginary part\n", + "-c:39: ComplexWarning: Casting complex values to real discards the imaginary part\n", + "-c:40: ComplexWarning: Casting complex values to real discards the imaginary part\n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 3.11 Page No : 157" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "from numpy import exp\n", + "\n", + "# Variables\n", + "#Per unit value\n", + "Zt = 0.01+(1j*0.03); #Transformer impedance\n", + "\n", + "Vll = 240.; #Secondary Voltage\n", + "\n", + "Sl = 90.; #Lighting Load\n", + "pfl = 0.9;\n", + "tl = math.acos(pfl);\n", + "S = 25.; #Balanced Load\n", + "pf = 0.8;\n", + "t = math.acos(pf);\n", + "\n", + "\n", + "# Calculations\n", + "def angle(y): \n", + " return math.degrees(math.atan(y.imag/y.real))\n", + "\n", + "tab = 30; #Phase angle of Vab\n", + "\n", + "Il = Sl*1000/Vll; #Magnitude of Light Load\n", + "#Umath.sing the symmetrical - components theory\n", + "Ia1 = Il*exp(1j*math.pi*(tab-tl)/180);\n", + "Ta1 = angle(Ia1); #Angle for the above current\n", + "Ib1 = -1*Ia1;\n", + "Ic1 = 0; #Neutral Wire\n", + "#Angles of three line to line voltages\n", + "ta = 0;\n", + "tb = -120;\n", + "tc = 120;\n", + "\n", + "Ib = S*1000/(math.sqrt(3)*Vll); #Magnitude of balanced load\n", + "\n", + "#Currents in Three phase load\n", + "Ta2 = ta-t;\n", + "Ia2 = Ib*exp(1j*math.pi*Ta2/180);\n", + "Tb2 = tb-t;\n", + "Ib2 = Ib*exp(1j*math.pi*Tb2/180);\n", + "Tc2 = tc-t;\n", + "Ic2 = Ib*exp(1j*math.pi*Tc2/180);\n", + "\n", + "#Currents in phase wire\n", + "Ia = Ia1+Ia2;\n", + "Ta = angle(Ia); #Angle corresponding to the above angle\n", + "Ib = Ib1+Ib2;\n", + "Tb = angle(Ib); #Angle corresponding to the above angle\n", + "Ic = Ic1+Ic2;\n", + "Tc = angle(Ic); #Angle corresponding to the above angle\n", + "\n", + "#Transformer Loads\n", + "ST1 = Vll*abs(Ia)/1000;\n", + "T1 = 100; #From the above value of Load, this transformer is chosen to meet the specific characteristic\n", + "ST1pu = ST1/T1; #Per unit Load\n", + "ST2 = Vll*abs(Ic)/1000;\n", + "T2 = 15; #From the above value of Load, this transformer is chosen to meet the specific characteristic\n", + "ST2pu = ST2/T2; #Per unit Load\n", + "\n", + "#Transformer Power Factors\n", + "pfT1 = math.cos(math.radians(tab-Ta));\n", + "pfT2 = math.cos(math.radians(90-Tc)); #Vcb makes angle of 90\n", + "\n", + "Vh = 7200; #High End Voltage\n", + "n = Vh/Vll; #Turns Ratio\n", + "\n", + "# The Primary Line Currents\n", + "IA = Ia/n;\n", + "IB = -1*Ic/n;\n", + "IN = -1*(IA+IB);\n", + "\n", + "Ibase = T1*1000/Vll; #Base Current\n", + "Iapu = Ia/Ibase;\n", + "Icpu = Ic/Ibase;\n", + "\n", + "#Phase Voltages\n", + "Vab = Vll*exp(1j*math.pi*tab/180); \n", + "Vbc = Vll*exp(-1*1j*math.pi*90/180);\n", + "#Per Unit Voltages\n", + "VANpu = (Vab/Vll)+(Iapu*Zt);\n", + "VBNpu = (Vbc/Vll)-(Icpu*Zt);\n", + "\n", + "#Actual Voltages\n", + "VAN = VANpu*Vh;\n", + "VBN = VBNpu*Vh;\n", + "\n", + "# Results\n", + "print 'a The Phasor Currents:'\n", + "print 'Ia is %g/_%g A'%(abs(Ia),Ta)\n", + "print 'Ib is %g/_%g A'%(abs(Ib),180+Tb)\n", + "print 'Ic is %g/_%g A'%(abs(Ic),Tc)\n", + "print 'b) Suitable ratings of the transformers are %g kVA and %g kVA'%(T1,T2)\n", + "print 'c) The Per Unit kVA load on each transformer is %g pu and %g pu'%(ST1pu,ST2pu)\n", + "print 'd) The power factor of output of each transformer is %g and %g both lagging'%(pfT1,pfT2)\n", + "print 'e The phasor currents at the high voltage leads:'\n", + "print 'IA is %g/_%g A'%(abs(IA),Ta)\n", + "print 'IB is %g/_%g A'%(abs(IB),180+angle(IB))\n", + "print 'IN is %g/_%g A'%(abs(IN),angle(IN))\n", + "print 'f) VAN is %g/_%g V and VBN is %g/_%g V'%(abs(VAN),angle(VAN),abs(VBN),angle(VBN))\n", + "\n", + "#Highly Accuracy of Answers; Upto 5 decimal Places\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "a The Phasor Currents:\n", + "Ia is 428.052/_25.4972 A\n", + "Ib is 428.229/_213.552 A\n", + "Ic is 60.1407/_-60.6435 A\n", + "b) Suitable ratings of the transformers are 100 kVA and 15 kVA\n", + "c) The Per Unit kVA load on each transformer is 1.02732 pu and 0.96225 pu\n", + "d) The power factor of output of each transformer is 0.996914 and -0.871586 both lagging\n", + "e The phasor currents at the high voltage leads:\n", + "IA is 14.2684/_25.4972 A\n", + "IB is 2.00469/_119.356 A\n", + "IN is 14.5415/_17.5913 A\n", + "f) VAN is 7294.34/_31.6923 V and VBN is 7193.85/_-89.743 V\n" + ] + } + ], + "prompt_number": 20 + } + ], + "metadata": {} + } + ] +}
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