{ "metadata": { "name": "", "signature": "sha256:f7ea291c8e2293a8fc339d930ac29424b99d2f3c6350ea4ec55a2d06cfae4c2d" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 3 : Transformers" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.1 Page No : 196" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Given Data\n", "kVA = 500.; #rating\n", "V1 = 11000.; #primary voltage in volts\n", "V2 = 400.; #secondary voltage in volts\n", "N2 = 100.; #number of turns in secondary winding\n", "f = 50.; #frequency in hertz\n", "\n", "# Calculations and Results\n", "N1 = (V1*N2)/V2; #number of turns in primary winding\n", "print \"number of turns in primary winding, N1 = %dturns\"%(N1)\n", "I1 = (kVA*1000)/V1;\n", "I2 = (kVA*1000)/V2\n", "print \"primary current, I1 = %fA\"%(I1)\n", "print \"secondary current, I2 = %fA\"%(I2)\n", "E1 = V1;\n", "phi = E1/(4.44*f*N1)\n", "print \"maximium flux in the core = %fWb\"%(phi)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "number of turns in primary winding, N1 = 2750turns\n", "primary current, I1 = 45.454545A\n", "secondary current, I2 = 1250.000000A\n", "maximium flux in the core = 0.018018Wb\n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.2 Page No : 196" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Given Data\n", "V1 = 6600.; #primary voltage in volts\n", "V2 = 230.; #secondary voltage in volts\n", "f = 50.; #frequency in hertz\n", "Bm = 1.1; #flux density in Wb/m**2\n", "\n", "# Calculations and Results\n", "A = (25*25*10**(-4)); #area of the core in m**2\n", "phi = Bm*A\n", "print \"flux = %fWb\"%(phi)\n", "E1 = V1;\n", "E2 = V2;\n", "N1 = E1/(4.44*f*phi);\n", "N2 = E2/(4.44*f*phi);\n", "print \"number of turns in primary winding, N1 = %dturns\"%(N1)\n", "print \"number of turns in secondary winding, N2 = %dturns\"%(N2)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "flux = 0.068750Wb\n", "number of turns in primary winding, N1 = 432turns\n", "number of turns in secondary winding, N2 = 15turns\n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.3 Page No : 197" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Given Data\n", "V1 = 230.; #primary voltage in volts\n", "f = 50.; #frequency in hertz\n", "N1 = 100.; #number of primary turns\n", "N2 = 400.; #number of secondary turns\n", "\n", "# Calculations and Results\n", "A = 250.*10**(-4); #cross section area of core in m**2\n", "print (\"since at no-load E2 = V2\")\n", "E2 = (V1*N2)/N1;\n", "print \"induced secondary winding, E2 = %dV\"%(E2);\n", "phi = E2/(4.44*f*N2);\n", "Bm = phi/A;\n", "print \"Maximium flux density in the core = %fWb/m**2\"%(Bm)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "since at no-load E2 = V2\n", "induced secondary winding, E2 = 920V\n", "Maximium flux density in the core = 0.414414Wb/m**2\n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.4 Page No : 197" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Given Data\n", "kVA = 40.; #rating of the transformer\n", "V1 = 2000.; #primary side voltage in volts\n", "V2 = 250.; #secondary side voltage in volts\n", "R1 = 1.15; #primary resistance in ohms\n", "R2 = 0.0155; #secondary resistance in ohms\n", "\n", "# Calculations and Results\n", "R = R2+(((V2/V1)**2)*R1)\n", "print \"Total resistance of the transformer in terms of the secondary winding = %fohms\"%(R)\n", "I2 = (kVA*1000)/V2;\n", "print \"Full load secondary current = %dA\"%(I2)\n", "print \"Total resistance load on full load = %fVolts\"%(I2*R)\n", "print \"Total copper loss on full load = %fWatts\"%((I2)**2*R)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Total resistance of the transformer in terms of the secondary winding = 0.033469ohms\n", "Full load secondary current = 160A\n", "Total resistance load on full load = 5.355000Volts\n", "Total copper loss on full load = 856.800000Watts\n" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.5 Page No : 206" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "# Given Data\n", "I2 = 300.; #Secondary current in amperes\n", "N1 = 1200.; #number of primary turns\n", "N2 = 300.; #number of secondary turns\n", "I0 = 2.5; #load current in amperes\n", "\n", "# Calculations\n", "I1 = (I2*N2)/N1;\n", "phi0 = math.degrees(math.acos(0.2));\n", "phi2 = math.degrees(math.acos(0.8));\n", "I1c = (I1*math.cos(math.radians(phi2)))+(I0*math.cos(math.radians(phi0)));\n", "I1s = (I1*math.sin(math.radians(phi2)))+(I0*math.sin(math.radians(phi0)));\n", "I = math.sqrt(I1c**2+I1s**2);\n", "phi = math.radians(math.atan(I1s/I1c))\n", "\n", "# Results\n", "print \"primary power factor = %fdegrees\"%(math.cos(math.radians(phi)));" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "primary power factor = 1.000000degrees\n" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.6 Page No : 207" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "# Given Data\n", "I0 = 1.5; #no-load current\n", "phi0 = math.degrees(math.acos(0.2))\n", "I2 = 40; #secondary current in amperes\n", "phi2 = math.degrees(math.acos(0.8))\n", "r = 3; #ratio of primary and secondary turns\n", "I1 = I2/r; \n", "\n", "# Calculations\n", "I1c = (I1*math.cos(math.radians(phi2)))+(I0*math.cos(math.radians(phi0)));\n", "I1s = (I1*math.sin(math.radians(phi2)))+(I0*math.sin(math.radians(phi0)));\n", "I = math.sqrt(I1c**2+I1s**2);\n", "\n", "# Results\n", "print \"I1 = %fA\"%(I)\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "I1 = 14.156879A\n" ] } ], "prompt_number": 7 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.7 Page No : 208" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "# Given Data\n", "V1 = 230.; #voltage in volts\n", "f = 50.; #frequency of supply in hertz\n", "N1 = 250.; #number of primary turns\n", "I0 = 4.5; #no-load current in amperes\n", "\n", "# Calculations and Results\n", "phi0 = math.degrees(math.acos(0.25));\n", "Im = I0*math.sin(math.radians(phi0))\n", "print \"magnetimath.sing current, Im = %fA\"%(Im);\n", "\n", "Pc = V1*I0*math.cos(math.radians(phi0));\n", "print \"Core loss = %dW\"%(Pc)\n", "print (\"neglecting I**2R loss in primary winding at no-load\")\n", "E1 = V1;\n", "phi = E1/(4.44*f*N1);\n", "print \"Maximium value of flux in the core = %fWb\"%(phi)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "magnetimath.sing current, Im = 4.357106A\n", "Core loss = 258W\n", "neglecting I**2R loss in primary winding at no-load\n", "Maximium value of flux in the core = 0.004144Wb\n" ] } ], "prompt_number": 8 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.8 Page No : 209" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "# Given Data\n", "I2 = 30.; #Secondary current in amperes\n", "I0 = 2.; #load current in amperes\n", "V1 = 660.; #primary voltage in volts\n", "V2 = 220.; #secondary voltage in volts\n", "\n", "# Calculations\n", "I1 = (I2*V2)/V1;\n", "phi0 = math.degrees(math.acos(0.225));\n", "phi2 = math.degrees(math.acos(0.9));\n", "I1c = (I1*math.cos(math.radians(phi2)))+(I0*math.cos(math.radians(phi0)));\n", "I1s = (I1*math.sin(math.radians(phi2)))+(I0*math.sin(math.radians(phi0)));\n", "I = math.sqrt(I1c**2+I1s**2);\n", "phi = math.degrees(math.atan(I1s/I1c))\n", "\n", "# Results\n", "print \"I1 = %fA\"%(I)\n", "print \"primary power factor = %fdegrees\"%(math.cos(math.radians(phi)));\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "I1 = 11.361713A\n", "primary power factor = 0.831741degrees\n" ] } ], "prompt_number": 9 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.9 Page No : 210" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "# Given Data\n", "phi_m = 7.5*10**(-3); #maximium flux\n", "f = 50.; #frequecy in hertz\n", "N1 = 144.; #number of primary turns\n", "N2 = 432.; #number of secondary turns\n", "kVA = 0.24; #rating of transformer\n", "\n", "# Calculations and Results\n", "E1 = (4.44*phi_m*f*N1)\n", "V1 = E1;\n", "print \"V1 = %dV\"%(V1)\n", "I0 = (kVA*1000)/V1;\n", "phi0 = math.degrees(math.acos(0.26));\n", "Im = I0*math.sin(math.radians(phi0));\n", "print \"Im = %fA\"%(Im);\n", "V2 = (E1*N2)/N1\n", "print \"V2 = %fV\"%(V2)\n", "print (\"At a load of 1.2kVA and power factor of 0.8 lagging\")\n", "kVA = 1.2;\n", "phi2 = math.degrees(math.acos(0.8));\n", "I2 = (kVA*1000)/V2;\n", "I = (I2*N2)/N1;\n", "I1c = (I*math.cos(math.radians(phi2)))+(I0*math.cos(math.radians(phi0)));\n", "I1s = (I*math.sin(math.radians(phi2)))+(I0*math.sin(math.radians(phi0)));\n", "I = math.sqrt(I1c**2+I1s**2);\n", "print \"I1 = %fA\"%(I);\n", "phi = math.degrees(math.acos(((I*math.cos(math.radians(phi2)))+(I0*math.cos(math.radians(phi0))))/I));\n", "print \"primary power factor = %flagging\"%(math.cos(math.radians(phi)))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "V1 = 239V\n", "Im = 0.966575A\n", "V2 = 719.280000V\n", "At a load of 1.2kVA and power factor of 0.8 lagging\n", "I1 = 5.825933A\n", "primary power factor = 0.844673lagging\n" ] } ], "prompt_number": 11 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.10 Page No : 211" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "# Given Data\n", "V1 = 6600.; #primary voltage in volts\n", "V2 = 240.; #secondary voltage in volts\n", "kW1 = 10.; #power\n", "phi1 = math.degrees(math.acos(0.8));\n", "I2 = 50.; #current in amperes\n", "kW3 = 5.; #power\n", "phi2 = math.degrees(math.acos(0.7))\n", "kVA = 8; #rating\n", "phi4 = math.degrees(math.acos(0.6)) \n", "\n", "# Calculations and Results\n", "I1 = (kW1*1000)/(math.cos(math.radians(phi1))*V2);\n", "I3 = (kW3*1000)/(1*V2);\n", "I4 = (kVA*1000)/V2;\n", "Ih = ((I1*math.cos(math.radians(phi1)))+(I2*math.cos(math.radians(phi2)))+I3+(I4*math.cos(math.radians(phi4))));\n", "Iv = ((I1*math.sin(math.radians(phi1)))+(I2*math.sin(math.radians(phi2)))-(I4*math.sin(math.radians(phi4))));\n", "I5 = math.sqrt((Ih**2)+(Iv**2))\n", "print \"I5 = %dA\"%(I5)\n", "Ip = (I5*V2)/V1;\n", "print \"The current drawn by the primary from 6600Vmains is equal to, Ip = %fA\"%(Ip);\n", "phi = math.degrees(math.atan(Iv/Ih));\n", "print \"power factor = %flagging\"%math.cos(math.radians(phi))\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "I5 = 124A\n", "The current drawn by the primary from 6600Vmains is equal to, Ip = 4.516939A\n", "power factor = 0.945934lagging\n" ] } ], "prompt_number": 12 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.11 Page No : 212" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Given Data\n", "kVA = 100.; #rating of the tronsfromer\n", "N1 = 400.; #number of primary turns\n", "N2 = 80.; #number of secondary turns\n", "R1 = 0.3; #primary resistance in ohms\n", "R2 = 0.01; #secondary resistance in ohms\n", "X1 = 1.1; #primary leakage reactance in ohs\n", "X2 = 0.035; #secondary leakage reactance in ohms\n", "\n", "# Calculations and Results\n", "Rr2 = (((N1/N2)**2)*R2)\n", "print \"R2 = %f ohms\"%(Rr2);\n", "Xx2 = (((N1/N2)**2)*X2);\n", "print \"X2 = %f ohms\"%(Xx2);\n", "Ze = math.sqrt((R1+Rr2)**2+(X1+Xx2)**2);\n", "print \"Equivqlent impedence = %f\"%(Ze);" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "R2 = 0.250000 ohms\n", "X2 = 0.875000 ohms\n", "Equivqlent impedence = 2.050152\n" ] } ], "prompt_number": 13 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.12 Page No : 216" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Given Data\n", "f = 50.; #frequency in hertz\n", "r = 6.; #turns ratio\n", "R1 = 0.90; #primary resistance in ohms\n", "R2 = 0.03; #secondary resistance in ohms\n", "X1 = 5.; #primary reactance in ohms\n", "X2 = 0.13; #secondary reactance in ohms\n", "I2 = 200.; #full-load current\n", "\n", "# Calculations and Results\n", "Re = (R1+(R2*r**2));\n", "print \"equivalent resistance reffered to primary, Re = %fohms\"%(Re);\n", "Xe = (X1+(X2*r**2));\n", "print \"equivalent reactance reffered to primary, Xe = %fohms\"%(Xe);\n", "Ze = math.sqrt(Re**2+Xe**2);\n", "print \"equivalent impedance reffered to primary, Ze = %fohms\"%(Ze);\n", "Ii2 = r*I2;\n", "print \"secondary current reffered to primary side = %fA\"%(Ii2);\n", "print \"a)Voltage to be applied to the high voltage side = %dvolts\"%(Ii2*Ze);\n", "print \"b)Power factor = %f\"%(Re/Ze);\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "equivalent resistance reffered to primary, Re = 1.980000ohms\n", "equivalent reactance reffered to primary, Xe = 9.680000ohms\n", "equivalent impedance reffered to primary, Ze = 9.880425ohms\n", "secondary current reffered to primary side = 1200.000000A\n", "a)Voltage to be applied to the high voltage side = 11856volts\n", "b)Power factor = 0.200396\n" ] } ], "prompt_number": 14 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.13 Page No : 216" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Given Data\n", "R1 = 0.21; #primary resistance in ohms\n", "X1 = 1.; #primary reactance in ohms\n", "R2 = 2.72*10**(-4); #secondary resistance in ohms\n", "X2 = 1.3*10**(-3); #secondary reactanced in ohms\n", "V1 = 6600.; #primary voltage in volts\n", "V2 = 250.; #secondary voltage in volts\n", "\n", "# Calculations and Results\n", "r = V1/V2; #turns ratio\n", "Re = R1+(r**2*R2);\n", "print \"Equivalent resistance referred to primary side = %fohms\"%(Re);\n", "Xe = X1+(r**2*X2);\n", "print \"Equivalent reactance referred to primary side = %fohms\"%(Xe);\n", "Ze = math.sqrt(Re**2+Xe**2);\n", "print \"equivalent impedance reffered to primary, Ze = %fohms\"%(Ze);\n", "V = 400.; #voltage in volts\n", "I1 = V/Ze;\n", "print \"I1 = %f\"%(I1);\n", "print \"Power input = %fW\"%(I1**2*Re);\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Equivalent resistance referred to primary side = 0.399573ohms\n", "Equivalent reactance referred to primary side = 1.906048ohms\n", "equivalent impedance reffered to primary, Ze = 1.947480ohms\n", "I1 = 205.393656\n", "Power input = 16856.612924W\n" ] } ], "prompt_number": 17 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.14 Page No : 217" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Given Data\n", "N1 = 90.; #number of primary turns\n", "N2 = 180.; #number of secondary turns\n", "R1 = 0.067; #primary resistance in ohms\n", "R2 = 0.233; #secondary resistance in ohms\n", "\n", "# Calculations and Results\n", "print \"Primary winding resistance referred to secondary side = %fohms\"%((R1*N2/N1)**2)\n", "print \"secondary winding resistance referred to primary side = %fohms\"%((R2*N1/N2)**2)\n", "print \"Total resistance of the transformer refferred to primary side = %fohms\"%((((R1*N2/N1)**2)+R2*N2/N1)**2)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Primary winding resistance referred to secondary side = 0.017956ohms\n", "secondary winding resistance referred to primary side = 0.013572ohms\n", "Total resistance of the transformer refferred to primary side = 0.234213ohms\n" ] } ], "prompt_number": 18 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.15 Page No : 217" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Given Data\n", "kVA = 30.; #rating of the transformer\n", "V1 = 6000.; #primary voltage in volts\n", "V2 = 230.; #secondary voltage in volts\n", "R1 = 10.; #primary resistance in ohms\n", "R2 = 0.016; #secondary resistance in ohms\n", "Xe = 23.; #total reactance reffered to the primary\n", "\n", "# Calculations and Results\n", "phi = math.degrees(math.acos(0.8)); #lagging\n", "Re = (R1+((V1/V2)**2*R2))\n", "print \"equivalent resistance, Re = %fohms\"%(Re)\n", "I2dash = (kVA*1000)/V1;\n", "V2dash = 5847;\n", "Reg = ((I2dash*((Re*math.cos(math.radians(phi)))+(Xe*math.sin(math.radians(phi)))))*100)/V2dash;\n", "print \"percentage regulation = %fpercent\"%(Reg)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "equivalent resistance, Re = 20.888469ohms\n", "percentage regulation = 2.609097percent\n" ] } ], "prompt_number": 19 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.16 Page No : 218" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Given Data\n", "kVA = 10.; #rating of the transformer\n", "V1 = 2000.; #primary voltage in volts\n", "V2 = 400.; #secondary voltage in volts\n", "R1 = 5.5; #primary voltage in ohms\n", "R2 = 0.2; #secondary voltage in ohms\n", "X1 = 12.; #primary reactance in ohms\n", "X2 = 0.45; #secondary reactance in ohms\n", "\n", "# Calculations and Results\n", "#assuming (V1/V2) = (N1/N2)\n", "Re = R2+(R1*(V2/V1)**2);\n", "print \"equivalent resistance referred to the secondary = %fohms\"%(Re);\n", "Xe = X2+(X1*(V2/V1)**2);\n", "print \"equivalent reactance referred to the secondary = %fohms\"%(Xe);\n", "Ze = math.sqrt(Re**2+Xe**2);\n", "print \"equivalent impedance referred to the secondary = %fohms\"%(Ze);\n", "phi = math.degrees(math.acos(0.8));\n", "Vl = 374.5;\n", "print \"Voltage across the full load and 0.8 p.f lagging = %fV\"%(Vl);\n", "reg = ((V2-Vl)*100)/Vl;\n", "print \"percentage voltage regulation = %f percent\"%(reg);\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "equivalent resistance referred to the secondary = 0.420000ohms\n", "equivalent reactance referred to the secondary = 0.930000ohms\n", "equivalent impedance referred to the secondary = 1.020441ohms\n", "Voltage across the full load and 0.8 p.f lagging = 374.500000V\n", "percentage voltage regulation = 6.809079 percent\n" ] } ], "prompt_number": 20 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.17 Page No : 219" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Given Data\n", "kVA = 80.; #rating of the transformer\n", "V1 = 2000.; #primary voltage in volts\n", "V2 = 200.; #secondary voltage in volts\n", "f = 50.; #frequency in hertz\n", "Id = 8.; #impedence drop\n", "Rd = 4.; #resistance drop\n", "\n", "# Calculations and Results\n", "phi = math.degrees(math.acos(0.8))\n", "I2Ze = (V2*Id)/100;\n", "I2Re = (V2*Rd)/100;\n", "I2Xe = math.sqrt(I2Ze**2-I2Re**2)\n", "reg = ((I2Re*math.cos(math.radians(phi)))+(I2Xe*math.sin(math.radians(phi))))*(100/V2)\n", "print \"percentage regulation = %fpercent\"%(reg)\n", "pf = I2Xe/math.sqrt(I2Re**2+I2Xe**2)\n", "print \"Power factor for zero regulation = %fleading)\"%(pf)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "percentage regulation = 7.356922percent\n", "Power factor for zero regulation = 0.866025leading)\n" ] } ], "prompt_number": 21 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.19 Page No : 225" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Given Data\n", "kVA = 50.; #rating of the transformer\n", "V1 = 3300.; #open circuit primary voltage\n", "Culoss = 540.; #copper loss from short circuit test\n", "coreloss = 460.; #core loss from open circuit test\n", "V1sc = 124.; #short circuit primary voltage in volts\n", "I1sc = 15.4; #short circuit primary current in amperes\n", "Psc = 540. #short circuit primary power in watts \n", "\n", "# Calculations and Results\n", "phi = math.degrees(math.acos(0.8))\n", "effi = (kVA*1000*math.cos(math.radians(phi))*100)/((kVA*1000*math.cos(math.radians(phi)))+Culoss+coreloss)\n", "print \"From the open-circuit test, core-loss = %dW\"%(coreloss);\n", "print \"From short circuit test, copper loss = %dW\"%(Culoss);\n", "print \"The efficiency at full-load and 0.8 lagging power factor = %f\"%(effi);\n", "Ze = V1sc/I1sc;\n", "Re = Psc/I1sc**2;\n", "Xe = math.sqrt(Ze**2-Re**2);\n", "V2 = 3203;\n", "phi2 = math.degrees(math.acos(0.8));\n", "phie = math.degrees(math.acos(Culoss/(V1sc*I1sc)));\n", "reg = (V1sc*math.cos(math.radians(phie-phi2))*100)/V1;\n", "print \"Voltage regulation = %dpercent\"%(reg)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "From the open-circuit test, core-loss = 460W\n", "From short circuit test, copper loss = 540W\n", "The efficiency at full-load and 0.8 lagging power factor = 97.560976\n", "Voltage regulation = 3percent\n" ] } ], "prompt_number": 22 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.20 Page No : 226" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "# Given Data\n", "kVA = 100.;\n", "V1 = 6600.; #primary voltage in volts\n", "V2 = 330.; #secondary voltage in volts\n", "f = 50.; #frequency in hertz\n", "V1sc = 100.; #short circuit primary voltage in volts\n", "I1sc = 10.; #short circuit primary current in amperes\n", "Psc = 436.; #short circuit primary power in watts \n", "\n", "# Calculations and Results\n", "Ze = V1sc/I1sc;\n", "Re = Psc/I1sc**2;\n", "phi = math.degrees(math.acos(0.8));\n", "Xe = math.sqrt(Ze**2-Re**2);\n", "print \"Total resistance = %fohms\"%(Re);\n", "print \"Total impedence = %fohms\"%(Ze)\n", "Il = (kVA*1000)/V1;\n", "V1dash = (math.sqrt(((V1*math.cos(math.radians(phi)))+(Il*Re))**2+((V1*math.sin(math.radians(phi)))+(Il*Xe))**2));\n", "print \"full voltage current, V1 = %dV\"%(V1dash)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Total resistance = 4.360000ohms\n", "Total impedence = 10.000000ohms\n", "full voltage current, V1 = 6735V\n" ] } ], "prompt_number": 23 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.21 Page No : 227" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "# Given Data\n", "V2 = 500.; #secondary voltage in volts\n", "V1 = 250.; #primary voltage in short circuit test in volts\n", "I0 = 1.; #current in short circuit test in amperes\n", "P = 80.; #core loss in watt\n", "Psc = 100.; #power in short circuit test in watts\n", "Vsc = 20.; #short circuit voltage in volts \n", "Isc = 12.; #short circuit current in amperes\n", "\n", "# Calculations and Results\n", "phi0 = math.degrees(math.acos(P/(V1*I0)));\n", "print \"From open circuit test , math.cos(phi0) = %f\"%(math.cos(phi0));\n", "Ic = I0*math.cos(math.radians(phi0));\n", "print \"Loss component of no-load current, Ic = %fA\"%(Ic)\n", "Im = math.sqrt(I0**2-Ic**2);\n", "print \"Magnetising current, Im = %fA\"%(Im);\n", "Rm = V1/Ic;\n", "Xm = V1/Im;\n", "Re = Psc/(Isc**2);\n", "Ze = Vsc/Isc;\n", "Xe = math.sqrt(Ze**2-Re**2);\n", "print \"Equvalent resistance referred to secondary = %fohms\"%(Re);\n", "print \"Equvalent reactance referred to secondary = %fohms\"%(Xe);\n", "print \"Equvalent impedance referred to secondary = %fohms\"%(Ze);\n", "K = V2/V1; #turns ratio\n", "print \"Equvalent resistance referred to primary = %fohms\"%(Re/K**2);\n", "print \"Equvalent reactance referred to primary = %fohms\"%(Xe/K**2);\n", "print \"Equvalent impedance referred to primary = %fohms\"%(Ze/K**2);\n", "V = 500; #output in volts\n", "I = 10; #output current in amperes\n", "phi = math.degrees(math.acos(0.80));\n", "effi = (V*I*math.cos(math.radians(phi))*100)/((V*I*math.cos(math.radians(phi)))+P+((I)**2*Re));\n", "print \"Effiency = %fpercent\"%(effi);" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "From open circuit test , math.cos(phi0) = -0.606173\n", "Loss component of no-load current, Ic = 0.320000A\n", "Magnetising current, Im = 0.947418A\n", "Equvalent resistance referred to secondary = 0.694444ohms\n", "Equvalent reactance referred to secondary = 1.515099ohms\n", "Equvalent impedance referred to secondary = 1.666667ohms\n", "Equvalent resistance referred to primary = 0.173611ohms\n", "Equvalent reactance referred to primary = 0.378775ohms\n", "Equvalent impedance referred to primary = 0.416667ohms\n", "Effiency = 96.398447percent\n" ] } ], "prompt_number": 26 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.22 Page No : 231" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "# Given Data\n", "kVA = 200.; #Rating of the transformer\n", "Pin = 3.4; #power input to two transformer in watt\n", "Pin2 = 5.2;\n", "coreloss = Pin; #core loss of two transformers\n", "\n", "# Calculations and Results\n", "phi = math.degrees(math.acos(0.8));\n", "print \"Core loss of two transformer = %fkW\"%(Pin)\n", "print \"Core loss of each transformer = %fkW\"%(Pin/2)\n", "print \"Full load copper loss of the two transformer = %fkW\"%(Pin2)\n", "print \"Therefore, full load copper loss of each transformer = %fkW\"%(Pin2/2);\n", "effi = (kVA*math.cos(math.radians(phi))*100)/((kVA*math.cos(math.radians(phi)))+(Pin/2)+(Pin2/2))\n", "print \"Full load efficiency at 0.8 p.f. lagging = %fpercent\"%(effi);" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Core loss of two transformer = 3.400000kW\n", "Core loss of each transformer = 1.700000kW\n", "Full load copper loss of the two transformer = 5.200000kW\n", "Therefore, full load copper loss of each transformer = 2.600000kW\n", "Full load efficiency at 0.8 p.f. lagging = 97.382836percent\n" ] } ], "prompt_number": 30 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.24 Page No : 233" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Given Data\n", "kVA = 50.; #rating of the transformer\n", "V1 = 6360.; #primary voltage rating\n", "V2 = 240.; #secondary voltage rating\n", "pf = 0.8\n", "coreloss = 2; #core loss in kilo watt from open circuit test\n", "Culoss = 2; #copper loss at secondary current of 175A\n", "I = 175.; #current in amperes\n", "\n", "# Calculations and Results\n", "I2 = (kVA*1000)/V2;\n", "print \"Full load secondary current, I2 = %fA\"%(I2);\n", "effi = (kVA*pf*100)/((kVA*pf)+coreloss+(Culoss*(I2/I)**2))\n", "print \"Efficiency = %fpercent\"%(effi)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Full load secondary current, I2 = 208.333333A\n", "Efficiency = 89.217075percent\n" ] } ], "prompt_number": 31 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.25 Page No : 234" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Given Data\n", "kVA = 500.; #rating of the transformer\n", "R1 = 0.4; #resistance in primary winding inohms\n", "R2 = 0.001; #resistance in secondary winding in ohms\n", "V1 = 6600.; #primary voltahe in volts\n", "V2 = 400.; #secondary voltage in volts\n", "ironloss = 3.; #iron loss in kilowatt\n", "pf = 0.8; #power factor lagging\n", "\n", "# Calculations and Results\n", "I1 = (kVA*1000)/V1; \n", "print \"Primary winding current = %fA\"%(I1);\n", "I2 = (I1*V1)/V2;\n", "print \"Secondary winding current = %fA\"%(I2);\n", "Culoss = ((I1**2*R1)+(I2**2*R2));\n", "print \"Copper losses in the two winding = %fWatts\"%(Culoss);\n", "effi = (kVA*pf*100)/((kVA*pf)+ironloss+(Culoss/1000));\n", "print \"Efficiency at 0.8 p.f = %fpercent\"%(effi);\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Primary winding current = 75.757576A\n", "Secondary winding current = 1250.000000A\n", "Copper losses in the two winding = 3858.184114Watts\n", "Efficiency at 0.8 p.f = 98.314355percent\n" ] } ], "prompt_number": 32 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.26 Page No : 234" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Given Data\n", "kVA = 400.; #rating of the transformer\n", "ironloss = 2.; #iron loss in kilowatt\n", "pf = 0.8; #power factor\n", "kW = 240.; #load in kilowatt\n", "\n", "# Calculations and Results\n", "kVA1 = kW/pf;\n", "print (\"Efficiency is maximium when,core-loss = copper-loss\")\n", "coreloss = ironloss;\n", "print (\"Maximium efficiency occurs at 240kw,0.8 power factor,i.e., at 300kVA load\")\n", "Cl300 = coreloss;\n", "Cl400 = (Cl300*(kVA/kVA1)**2);\n", "pf1 = 0.71; #power factor for full load\n", "effi = (kVA*pf1*100)/((kVA*pf1)+coreloss+Cl400);\n", "print \"Efficiency at full-load and 071 power factor = %dpercent\"%(effi);\n", "pf2 = 1 #maximium efficiency occurs at unity power factor\n", "MAXeffi = (kVA1*pf2*100)/((kVA1*pf2)+coreloss+Cl300)\n", "print \"Maximium efficiency at 300kVA and unity power factor = %fpercent\"%(MAXeffi);\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Efficiency is maximium when,core-loss = copper-loss\n", "Maximium efficiency occurs at 240kw,0.8 power factor,i.e., at 300kVA load\n", "Efficiency at full-load and 071 power factor = 98percent\n", "Maximium efficiency at 300kVA and unity power factor = 98.684211percent\n" ] } ], "prompt_number": 33 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.27 Page No : 235" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Given Data\n", "kVA = 40.; #rating of the transformer\n", "coreloss = 450.; #core-loss in watts\n", "Culoss = 800.; #copper loss in watt\n", "pf = 0.8; #power factor of the load\n", "\n", "# Calculations and Results\n", "FLeffi = (kVA*pf*100)/((kVA*pf)+((coreloss+Culoss)/1000));\n", "print \"Full-load efficiency = %fpercent\"%(FLeffi);\n", "print (\"For maximium efficiency, Core loss = copper loss\")\n", "Culoss2 = coreloss; #for maximium efficiency\n", "n = math.sqrt(Culoss2/Culoss);\n", "kVA2 = n*kVA; #load for maximium efficiency\n", "MAXeffi = (kVA2*pf*100)/((kVA2*pf)+((coreloss+Culoss2)/1000));\n", "print \"Value of maximium efficiency = %fpercent\"%(MAXeffi);\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Full-load efficiency = 96.240602percent\n", "For maximium efficiency, Core loss = copper loss\n", "Value of maximium efficiency = 96.385542percent\n" ] } ], "prompt_number": 34 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.28 Page No : 236" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Given Data\n", "kVA = 50.; #rating of the transformers\n", "I1 = 250.; #primary current in amperes\n", "Re = 0.006; #total resistance referred to the primary side\n", "ironloss = 200.; #iron loss in watt\n", "\n", "# Calculations and Results\n", "Culoss = (I1**2*Re); #copper loss in watt\n", "pf = 0.8; #power factor lagging\n", "print \"Full-load copper loss = %fW\"%(Culoss);\n", "TL1 = ((Culoss+ironloss)/1000); \n", "print \"Total loss on full load = %fkW\"%(TL1);\n", "TL2 = ((((Culoss*(1/2)**2))+ironloss)/1000)\n", "print \"Total loss on half load = %fkW\"%(TL2);\n", "effi1 = (kVA*pf*100)/((kVA*pf)+TL1);\n", "print \"Efficiency at full load, 0.8 power factor lagging = %f percent\"%(effi1)\n", "effi2 = ((kVA/2)*pf*100)/(((kVA/2)*pf)+TL2);\n", "print \"Efficiency at half load, 0.8 power factor lagging = %f percent\"%(effi2)\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Full-load copper loss = 375.000000W\n", "Total loss on full load = 0.575000kW\n", "Total loss on half load = 0.200000kW\n", "Efficiency at full load, 0.8 power factor lagging = 98.582871 percent\n", "Efficiency at half load, 0.8 power factor lagging = 99.009901 percent\n" ] } ], "prompt_number": 35 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.29 Page No : 237" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Given Data\n", "kVA = 10.; #rating of the transformers\n", "V1 = 400.; #primary voltage in volts\n", "V2 = 200.; #secondary voltage in volts\n", "f = 50.; #frequency in hertz\n", "\n", "# Calculations and Results\n", "MAXeffi = 0.96; #maximium efficiency\n", "output1 = (kVA*0.75); #output at 75% of full load\n", "input1 = (output1/MAXeffi);\n", "print \"Input at 75percent of full load = %fkW\"%(input1);\n", "TL = input1-output1;\n", "print \"Total losses = %fkW\"%(TL);\n", "Pi = TL/2;\n", "Pc = TL/2;\n", "print (\"Maximiunm efficiency occurs at 3/4th of full load\")\n", "Pc = Pi/(3./4)**2;\n", "print \"Thus, total losses on full load = %fW\"%((Pc+Pi)*1000);\n", "pf = 0.8; #power factor lagging\n", "effi = (kVA*pf*100)/((kVA*pf)+(Pc+Pi));\n", "print \"Efficiency on full load. 0.8 power factor lagging = %fpercent\"%(effi)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Input at 75percent of full load = 7.812500kW\n", "Total losses = 0.312500kW\n", "Maximiunm efficiency occurs at 3/4th of full load\n", "Thus, total losses on full load = 434.027778W\n", "Efficiency on full load. 0.8 power factor lagging = 94.853849percent\n" ] } ], "prompt_number": 38 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.30 Page No : 237" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Given Data\n", "kVA = 500.; #rating of the transformers\n", "V1 = 3300.; #primary voltage in volts\n", "V2 = 500.; #secondary voltage in volts\n", "f = 50.; #frequency in hertz\n", "MAXeffi = 0.97; \n", "x = 0.75; #fraction of full load for maximium efficiency\n", "pf1 = 1.;\n", "\n", "# Calculations and Results\n", "output1 = (kVA*x*pf1*1000);\n", "print \"Output at maximium efficiency = %dwatts\"%(output1);\n", "losses = ((1/MAXeffi)-1)*output1;\n", "print \"Thus, at maximium efficiency, lossses = %fW\"%(losses)\n", "Culoss = losses/2;\n", "print \"Copper losses at 75percent of full load = %dW\"%(Culoss);\n", "CulossFL = Culoss/x**2;\n", "print \"Copper losses at full load = %dW\"%(CulossFL);\n", "Re = CulossFL/(kVA*1000);\n", "Ze = 0.1; #equivalent impedence per unit\n", "Xe = math.sqrt(Ze**2-Re**2);\n", "phi = math.degrees(math.acos(0.8));\n", "reg = ((Re*math.cos(math.radians(phi)))+(Xe*math.sin(math.radians(phi))))*100;\n", "print \"percentage regulation = %f percent\"%(reg);\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Output at maximium efficiency = 375000watts\n", "Thus, at maximium efficiency, lossses = 11597.938144W\n", "Copper losses at 75percent of full load = 5798W\n", "Copper losses at full load = 10309W\n", "percentage regulation = 7.520562 percent\n" ] } ], "prompt_number": 39 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.32 Page No : 240" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Given Data\n", "V1 = 230.; #primary voltage of auto-transformer\n", "V2 = 75.; #secondary voltage of auto-transformer\n", "\n", "# Calculations\n", "r = (V1/V2); #ratio of primary to secondary turns\n", "I2 = 200.; #load current in amperes\n", "I1 = I2/r;\n", "\n", "# Results\n", "print \"Primary current, I1 = %fA\"%(I1);\n", "print \"Load current, I1 = %fA\"%(I2);\n", "print \"cirrent flowing through the common portion of winding = %fA\"%(I2-I1);\n", "print \"Economy in saving in copper in percentage = %fpercent\"%(100/r);" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Primary current, I1 = 65.217391A\n", "Load current, I1 = 200.000000A\n", "cirrent flowing through the common portion of winding = 134.782609A\n", "Economy in saving in copper in percentage = 32.608696percent\n" ] } ], "prompt_number": 40 } ], "metadata": {} } ] }