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diff --git a/Fundamentals_of_Electrical_Machines/CH_3.ipynb b/Fundamentals_of_Electrical_Machines/CH_3.ipynb new file mode 100755 index 00000000..68c7ac6d --- /dev/null +++ b/Fundamentals_of_Electrical_Machines/CH_3.ipynb @@ -0,0 +1,883 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "CHAPTER 3: TRANSFORMER AND PER UNIT SYSTEM"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.1, Page number 90-91"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "V_1 = 2200.0 #Primary voltage of transformer(V)\n",
+ "V_2 = 220.0 #Secondary voltage of transformer(V)\n",
+ "N_2 = 56.0 #Number of turns in the secondary coil of transformer\n",
+ "kVA = 25.0 #Rating of transformer(kVA)\n",
+ "\n",
+ "#Calculation\n",
+ "a = V_1/V_2 #Turns ratio\n",
+ "#For case(i)\n",
+ "N_1 = a*N_2 #Number of primary turns\n",
+ "#For case(ii)\n",
+ "I_1 = kVA*10**3/V_1 #Primary full load current(A)\n",
+ "#For case(iii)\n",
+ "I_2 = kVA*10**3/V_2 #Secondary full load current(A)\n",
+ "\n",
+ "#Result\n",
+ "print('(i) Number of primary turns , N_1 = %.f ' %N_1)\n",
+ "print('(ii) Primary full load current , I_2 = %.2f A' %I_1)\n",
+ "print('(iii) Secondary full load current , I_2 = %.1f A' %I_2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(i) Number of primary turns , N_1 = 560 \n",
+ "(ii) Primary full load current , I_2 = 11.36 A\n",
+ "(iii) Secondary full load current , I_2 = 113.6 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.2, Page number 91"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "V_1 = 220.0 #Voltage(V)\n",
+ "N_1 = 150.0 #Number of turns in primary side\n",
+ "N_2 = 300.0 #Number of turns in secondary side\n",
+ "f = 50.0 #Frequency(Hz)\n",
+ "\n",
+ "#Calculation\n",
+ "#For case(i)\n",
+ "a = N_1/N_2 #Turns ratio\n",
+ "#For case(ii)\n",
+ "phi_m = V_1/(4.44*f*N_1)*10**3 #Mutual flux(mWb)\n",
+ "\n",
+ "#Result\n",
+ "print('(i) Turns ratio , a = %.1f ' %a)\n",
+ "print('(ii) Mutual flux in the core , \u03a6_m = %.2f mWb' %phi_m)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(i) Turns ratio , a = 0.5 \n",
+ "(ii) Mutual flux in the core , \u03a6_m = 6.61 mWb\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.3, Page number 92"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Variable declaration\n",
+ "V_1 = 2200.0 #Primary voltage(V)\n",
+ "V_2 = 220.0 #Secondary voltage(V)\n",
+ "I_0 = 0.5 #No-load current(A)\n",
+ "P_0 = 350.0 #Power absorbed(W)\n",
+ "\n",
+ "#Calculation\n",
+ "cos_phi_0 = P_0/(V_1*I_0) #No-load power factor\n",
+ "I_w = I_0*cos_phi_0 #Iron loss component of current(A)\n",
+ "phi_0 = math.acos(cos_phi_0) #Power factor angle\n",
+ "I_m = I_0*math.sin(phi_0) #Magnetizing component of current(A)\n",
+ "\n",
+ "#Result\n",
+ "print('Iron loss component of current , I_w = %.2f A' %I_w)\n",
+ "print('Magnetizing component of current , I_m = %.2f A' %I_m)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Iron loss component of current , I_w = 0.16 A\n",
+ "Magnetizing component of current , I_m = 0.47 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.4, Page number 94"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "N_1 = 450.0 #Number of turns in the primary side\n",
+ "N_2 = 45.0 #Number of turns in the secondary side\n",
+ "Z_L = 3.0 #Load impedance(ohm)\n",
+ "V_1 = 15.0 #Primary coil voltage of transformer(V)\n",
+ "\n",
+ "#Calculation\n",
+ "#For case(i)\n",
+ "a = N_1/N_2 #Turns ratio\n",
+ "#For case(ii)\n",
+ "Z_1 = a**2*Z_L #Load impedance referred to primary(ohm)\n",
+ "#For case(iii)\n",
+ "I_1 = V_1/Z_1 #Primary current(A)\n",
+ "\n",
+ "#Result\n",
+ "print('(i) Turns ratio , a = %.f ' %a)\n",
+ "print('(ii) Load impedance referred to primary , Z_1 = %.f ohm' %Z_1)\n",
+ "print('(iii) Primary current , I_1 = %.2f A' %I_1)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(i) Turns ratio , a = 10 \n",
+ "(ii) Load impedance referred to primary , Z_1 = 300 ohm\n",
+ "(iii) Primary current , I_1 = 0.05 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.5, Page number 96-97"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Variable declaration\n",
+ "V_1 = 400.0 #Primary voltage of transformer(V)\n",
+ "V_2 = 100.0 #Secondary voltage of transformer(V)\n",
+ "I_0 = 0.4 #No-load current(A)\n",
+ "I_2 = 100.0 #Current drawn by load(A)\n",
+ "cos_phi_0 = 0.3 #Power factor lagging from the supply\n",
+ "cos_phi_2 = 0.6 #Power factor lagging from the secondary\n",
+ "\n",
+ "#Calculation\n",
+ "phi_0 = math.acos(cos_phi_0) #Power factor angle(radians)\n",
+ "phi_0_deg = phi_0*180/math.pi #Power factor angle(degree)\n",
+ "phi_2 = math.acos(cos_phi_2) #Power factor angle(radians)\n",
+ "phi_2_deg = phi_2*180/math.pi #Power factor angle(degree)\n",
+ "phi_1 = phi_0-phi_2 #Angle(radians)\n",
+ "phi_1_deg = phi_1*180/math.pi #Angle(degree)\n",
+ "a = V_1/V_2 #Turns ratio\n",
+ "I_2_ = I_2/a #Secondary current equivalent to the primary(A) \n",
+ "I_1 = ((I_2_**2)+(I_0**2)+(2*I_2_*I_0*math.cos(phi_1)))**0.5 #Primary current(A)\n",
+ "\n",
+ "#Result\n",
+ "print('Primary current , I_1 = %.1f A' %I_1)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Primary current , I_1 = 25.4 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.6, Page number 101"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "V_1 = 2000.0 #Primary voltage of transformer(V)\n",
+ "V_2 = 400.0 #Secondary voltage of transformer(V)\n",
+ "kVA = 200.0 #Rating of transformer(kVA)\n",
+ "R_1 = 3.0 #Primary resistance(ohm)\n",
+ "X_1 = 12.0 #Primary reactance(ohm)\n",
+ "R_2 = 0.3 #Secondary resistance(ohm)\n",
+ "X_2 = 0.1 #Secondary reactance(ohm)\n",
+ "\n",
+ "#Calculation\n",
+ "a = V_1/V_2 #Turns ratio\n",
+ "R_01 = R_1+(a**2*R_2) #Total resistance referred to primary(ohm)\n",
+ "X_01 = X_1+(a**2*X_2) #Total reactance referred to primary(ohm)\n",
+ "Z_01 = ((R_01**2)+(X_01**2))**0.5 #Equivalent impedance referred to primary(ohm)\n",
+ "R_02 = R_2+(R_1/a**2) #Total resistance referred to secondary side(ohm)\n",
+ "X_02 = X_2+(X_1/a**2) #Total reactance referred to secondary side(ohm)\n",
+ "Z_02 = ((R_02**2)+(X_02**2))**0.5 #Equivalent impedance referred to secondary side(ohm)\n",
+ "\n",
+ "#Result\n",
+ "print('Equivalent impedance referred to primary , Z_01 = %.1f ohm' %Z_01)\n",
+ "print('Equivalent impedance referred to secondary , Z_02 = %.2f ohm' %Z_02)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Equivalent impedance referred to primary , Z_01 = 17.9 ohm\n",
+ "Equivalent impedance referred to secondary , Z_02 = 0.72 ohm\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.7, Page number 103-104"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Variable declaration\n",
+ "V_1 = 200.0 #Primary voltage(V)\n",
+ "V_2 = 400.0 #Secondary voltage(V)\n",
+ "R_1 = 0.3 #Primary resistance(ohm)\n",
+ "X_1 = 0.6 #Primary reactance(ohm)\n",
+ "R_2 = 0.8 #Secondary resistance(ohm)\n",
+ "X_2 = 1.6 #Secondary reactance(ohm)\n",
+ "I_2 = 10.0 #Secondary supply current(A)\n",
+ "cos_phi_2 = 0.8 #Power factor lagging\n",
+ "\n",
+ "#Calculation\n",
+ "a = V_1/V_2 #Turns ratio\n",
+ "R_02 = R_2+(R_1/a**2) #Total resistance referred to secondary(ohm)\n",
+ "X_02 = X_2+(X_1/a**2) #Total reactance referred to primary(ohm)\n",
+ "sin_phi_2 = math.sin(math.acos(cos_phi_2))\n",
+ "E_2 = complex((V_2*cos_phi_2+I_2*R_02),(V_2*sin_phi_2+I_2*X_02)) #No-load voltage(V)\n",
+ "V_reg = (abs(E_2)-V_2)/V_2*100 #Voltage regulation(percent)\n",
+ "\n",
+ "#Result\n",
+ "print('Voltage regulation = %.f percent' %V_reg)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Voltage regulation = 10 percent\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.8, Page number 105-106"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "P_i = 1.0 #Iron loss of transformer(kW)\n",
+ "P_cu = 2.0 #Full load copper loss of transformer(kW)\n",
+ "kVA = 200.0 #Rating of transformer(kVA)\n",
+ "pf_1 = 1.0 #Power factor\n",
+ "pf_2 = 0.95 #Power factor\n",
+ "\n",
+ "#Calculation\n",
+ "P_cu1 = (3.0/4)**2*P_cu #Copper loss at 3/4 full load(kW)\n",
+ "P_cu2 = (1.0/2)**2*P_cu #Copper loss at 1/2 full load(kW)\n",
+ "P_01 = (3.0/4)*kVA*pf_1 #Output power at 3/4 full load and unity pf(kW)\n",
+ "P_in1 = P_01+P_i+P_cu1 #Input power at 3/4 full load and unity pf(kW)\n",
+ "n_1 = (P_01/P_in1)*100 #Efficiency at 3/4 full load and unity pf(percent)\n",
+ "P_02 = (1.0/2)*kVA*pf_2 #Output power at 1/2 full load and 0.95 pf(kW)\n",
+ "P_in2 = P_02+P_i+P_cu2 #Input power at 1/2 full load and 0.95 pf(kW)\n",
+ "n_2 = (P_02/P_in2)*100 #Efficiency at 1/2 full load and 0.95 pf(percent)\n",
+ "\n",
+ "#Result\n",
+ "print('Efficiency at 3/4 full load and unity power factor , \u03b7_1 = %.2f percent' %n_1)\n",
+ "print('Efficiency at 1/2 full load and 0.95 power factor , \u03b7_2 = %.2f percent' %n_2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Efficiency at 3/4 full load and unity power factor , \u03b7_1 = 98.60 percent\n",
+ "Efficiency at 1/2 full load and 0.95 power factor , \u03b7_2 = 98.45 percent\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.9, Page number 108"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "P_i = 350.0 #Iron loss of transformer(W)\n",
+ "P_cu = 650.0 #Full load copper loss of transformer(W)\n",
+ "kVA = 30.0 #Rating of transformer(kVA)\n",
+ "pf = 0.6 #Power factor\n",
+ "\n",
+ "#Calculation\n",
+ "#For case(i)\n",
+ "P_tloss = (P_i+P_cu)*10**-3 #Total full load loss(kW)\n",
+ "P_out = kVA*pf #Output power at full load(kW)\n",
+ "P_in = P_out+P_tloss #Input power at full load(kW)\n",
+ "n_1 = (P_out/P_in)*100 #Efficiency at full load(percent)\n",
+ "#For case(ii)\n",
+ "kVA_out = kVA*(P_i/P_cu)**0.5 #Output kVA corresponding to maximum efficiency(kVA) \n",
+ "P_01 = kVA_out*pf #Output power(kW)\n",
+ "#For case(iii)\n",
+ "P_tloss1 = 2*P_i*10**-3 #Total loss(kW)\n",
+ "P_in1 = P_01+P_tloss1 #Input power(kW)\n",
+ "n_2 = (P_01/P_in1)*100 #Efficiency(percent)\n",
+ "\n",
+ "#Result\n",
+ "print('(i) Full load efficiency , \u03b7 = %.2f percent' %n_1)\n",
+ "print('(ii) Output kVA corresponding to maximum efficiency = %.1f kVA' %kVA_out)\n",
+ "print('(iii) Maximum efficiency , \u03b7 = %.2f percent' %n_2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(i) Full load efficiency , \u03b7 = 94.74 percent\n",
+ "(ii) Output kVA corresponding to maximum efficiency = 22.0 kVA\n",
+ "(iii) Maximum efficiency , \u03b7 = 94.97 percent\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.10, Page number 109-110"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "kVA = 12.0 #Rating of transformer(kVA)\n",
+ "n = 0.97 #Maximum efficiency at unity pf\n",
+ "pf = 1.0 #Power factor\n",
+ "t_1 = 8.0 #Time(hours)\n",
+ "P_1 = 10.0 #Load(kW)\n",
+ "pf_1 = 0.8 #Lagging power factor\n",
+ "t_2 = 10.0 #Time(hours)\n",
+ "P_2 = 15.0 #Load(kW)\n",
+ "pf_2 = 0.90 #Leading power factor\n",
+ "t_3 = 6.0 #Time at no-load(hours)\n",
+ "P_3 = 0 #Load(kW)\n",
+ "\n",
+ "#Calculation\n",
+ "P_01 = kVA*pf #Output power at full load and unity pf(kW)\n",
+ "P_in1 = P_01/n #Input power at full load(kW)\n",
+ "P_tloss = P_in1-P_01 #Total loss(kW)\n",
+ "P_cu = P_tloss/2 #Copper loss at 12 kVA(kW)\n",
+ "P_024 = P_1*t_1+P_2*t_2+P_3*t_3 #All-day output power(kWh)\n",
+ "P_i24 = 24*P_cu #Iron loss for 24 hours(kWh)\n",
+ "P_cu24 = P_cu*t_1*((P_1/pf_1)/kVA)**2+P_cu*t_2*((P_2/pf_2)/kVA)**2 #Copper loss for 24 hours(kW)\n",
+ "P_in24 = P_024+P_i24+P_cu24 #All day input power(kWh)\n",
+ "n_allday = (P_024/P_in24)*100 #All day efficiency(percent)\n",
+ "\n",
+ "#Result\n",
+ "print('All-day efficiency , \u03b7_allday = %.1f percent' %n_allday)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "All-day efficiency , \u03b7_allday = 96.0 percent\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.11, Page number 111"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Variable declaration\n",
+ "V_1 = 200.0 #Voltage(V)\n",
+ "f = 50.0 #Frequency(Hz)\n",
+ "I_0 = 0.6 #Current(A)\n",
+ "P_0 = 80.0 #Power(W)\n",
+ "\n",
+ "#Calculation\n",
+ "cos_phi_0 = P_0/(V_1*I_0) #Power factor\n",
+ "sin_phi_0 = math.sin(math.acos(cos_phi_0))\n",
+ "I_w = I_0*cos_phi_0 #Working component of no-load current(A)\n",
+ "I_m = I_0*sin_phi_0 #Magnetizing component of no-load current(A)\n",
+ "R_0 = V_1/I_w #No-load circuit resistance(ohm)\n",
+ "X_0 = V_1/I_m #No-load circuit reactance(ohm)\n",
+ "\n",
+ "#Result\n",
+ "print('No-load circuit resistance , R_0 = %.1f ohm' %R_0)\n",
+ "print('No-load circuit reactance , X_0 = %.1f ohm' %X_0)\n",
+ "print('\\nNOTE : Changes in obtained answer from that of textbook is due to more precision')"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "No-load circuit resistance , R_0 = 500.0 ohm\n",
+ "No-load circuit reactance , X_0 = 447.2 ohm\n",
+ "\n",
+ "NOTE : Changes in obtained answer from that of textbook is due to more precision\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.12, Page number 112-113"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Variable declaration\n",
+ "kVA = 25.0 #Rating of transformer(kVA)\n",
+ "V1 = 2200.0 #Voltage at low-voltage primary side(V)\n",
+ "V2 = 220.0 #Voltage at low-voltage secondary side(V)\n",
+ "V_1 = 40.0 #Voltage at h.v side(V)\n",
+ "I_1 = 5.0 #Current at high voltage side(A)\n",
+ "P = 150.0 #Power at high voltage side(W)\n",
+ "\n",
+ "#Calculation\n",
+ "#For case(i)\n",
+ "Z_01 = V_1/I_1 #Equivalent impedance referred to primary(ohm)\n",
+ "R_01 = P/I_1**2 #Equivalent resistance referred to primary(ohm)\n",
+ "phi = math.acos(R_01/Z_01) #Power factor angle(radians)\n",
+ "phi_deg = phi*180/math.pi #Power factor angle(degree)\n",
+ "X_01 = Z_01*math.sin(phi) #Equivalent reactance referred to primary(ohm)\n",
+ "#For case(ii)\n",
+ "a = V1/V2 #Turns ratio\n",
+ "Z_02 = Z_01/a**2 #Equivalent impedance referred to secondary(ohm)\n",
+ "R_02 = R_01/a**2 #Equivalent resistance referred to secondary(ohm)\n",
+ "X_02 = X_01/a**2 #Equivalent reactance referred to secondary(ohm)\n",
+ "#For case(iii)\n",
+ "I_2 = kVA*10**3/V2 #Secondary side current(A)\n",
+ "E_2 = V2+I_2*Z_02 #Secondary induced voltage(V)\n",
+ "VR = (E_2-V2)/V2*100 #Voltage regulation(percent)\n",
+ "\n",
+ "#Result\n",
+ "print('Case(i)')\n",
+ "print(' Equivalent resistance referred to primary , R_01 = %.1f ohm' %R_01)\n",
+ "print(' Equivalent reactance referred to primary , X_01 = %.1f ohm' %X_01)\n",
+ "print(' Equivalent impedance referred to primary , Z_01 = %.1f ohm' %Z_01)\n",
+ "print('\\nCase(ii)')\n",
+ "print(' Equivalent resistance referred to secondary , R_02 = %.2f ohm' %R_02)\n",
+ "print(' Equivalent reactance referred to secondary , X_02 = %.3f ohm' %X_02)\n",
+ "print(' Equivalent impedance referred to secondary , Z_02 = %.2f ohm' %Z_02)\n",
+ "print('\\nCase(iii)')\n",
+ "print(' Voltage regulation , VR = %.1f percent' %VR)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Case(i)\n",
+ " Equivalent resistance referred to primary , R_01 = 6.0 ohm\n",
+ " Equivalent reactance referred to primary , X_01 = 5.3 ohm\n",
+ " Equivalent impedance referred to primary , Z_01 = 8.0 ohm\n",
+ "\n",
+ "Case(ii)\n",
+ " Equivalent resistance referred to secondary , R_02 = 0.06 ohm\n",
+ " Equivalent reactance referred to secondary , X_02 = 0.053 ohm\n",
+ " Equivalent impedance referred to secondary , Z_02 = 0.08 ohm\n",
+ "\n",
+ "Case(iii)\n",
+ " Voltage regulation , VR = 4.1 percent\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.13, Page number 114-115"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "kVA = 120.0 #Rating of autotransformer(kVA)\n",
+ "V1 = 220.0 #Volteage at upper part of coil(V)\n",
+ "V2 = 2200.0 #Volteage at lower part of coil(V)\n",
+ "\n",
+ "#Calculation\n",
+ "I_pq = kVA*10**3/V1 #Current of upper winding(A)\n",
+ "I_qr = kVA*10**3/V2 #Current of lower winding(A)\n",
+ "I_1 = I_pq+I_qr #Current in primary side(A)\n",
+ "V_2 = V1+V2 #Voltage across the secondary side(V)\n",
+ "kVA_1 = I_1*V2/1000 #Rating of autotransformer(kVA)\n",
+ "kVA_2 = I_pq*V_2/1000 #Rating of autotransformer(kVA)\n",
+ " \n",
+ "\n",
+ "#Result\n",
+ "print('kVA ratings of the autotransformer')\n",
+ "print('\\t kVA_1 = %.f kVA' %kVA_1)\n",
+ "print('\\t kVA_2 = %.f kVA' %kVA_2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "kVA ratings of the autotransformer\n",
+ "\t kVA_1 = 1320 kVA\n",
+ "\t kVA_2 = 1320 kVA\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.14, Page number 119"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import cmath\n",
+ "\n",
+ "#Variable declaration\n",
+ "kVA_1 = 100.0 #Rating of transformer(kVA)\n",
+ "kVA_2 = 200.0 #Rating of transformer(kVA)\n",
+ "E_1 = 500.0 #Secondary induced voltage in 100 kVA transformer(V)\n",
+ "E_2 = 450.0 #Secondary induced voltage in 200 kVA transformer(V)\n",
+ "Z_1 = 0.05 #Impedance of 100 kVA transformer\n",
+ "Z_2 = 0.08 #Impedance of 200 kVA transformer\n",
+ "\n",
+ "#Calculation\n",
+ "Z1 = Z_1*E_1/(kVA_1*10**3/E_1) #Actual impedance of first transformer(ohm)\n",
+ "Z2 = Z_2*E_2/(kVA_1*10**3/E_2) #Actual impedance of second transformer(ohm)\n",
+ "I_c = (E_1-E_2)/complex(0,Z1+Z2) #Circulating current(A)\n",
+ "\n",
+ "#Result\n",
+ "print('Circulating current , I_c = %.2f\u2220%.f\u00b0 A' %(abs(I_c),cmath.phase(I_c)*180/math.pi))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Circulating current , I_c = 174.22\u2220-90\u00b0 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.15, Page number 125"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Variable declaration\n",
+ "V_L1 = 11.0 #Supply voltage(kV)\n",
+ "I_P1 = 6.0 #Current drawn by transformer(A)\n",
+ "a = 11.0 #Turns ratio\n",
+ "\n",
+ "#Calculation\n",
+ "#For delta-wye connections\n",
+ "V_dP1 = V_L1 #Phase voltage at primary side(kV)\n",
+ "V_dP2 = V_dP1*10**3/a #Phase voltage at secondary side(V)\n",
+ "V_dL2 = 3**0.5*V_dP2 #Line voltage at secondary side(V)\n",
+ "I_dP1 = a/3**0.5 #Phase current in the primary(A)\n",
+ "I_dL2 = a*I_dP1 #Line current in secondary(A)\n",
+ "#For Wye-delta connection \n",
+ "V_wP1 = V_L1*10**3/3**0.5 #Phase voltage at primary side(V)\n",
+ "V_wP2 = V_wP1/a #Phase voltage at secondary(V)\n",
+ "V_wL2 = V_wP2 #Line voltage at secondary(V)\n",
+ "I_wP2 = a*I_P1 #Phase current in secondary(A)\n",
+ "I_wL2 = 3**0.5*I_wP2 #Line current in secondary(A)\n",
+ "\n",
+ "#Result\n",
+ "print('For delta-wye connection')\n",
+ "print(' (i) Line voltage at secondary side , V_L2 = %.f V' %V_dL2)\n",
+ "print(' (ii) Line current in the secondary , I_L2 = %.2f A' %I_dL2)\n",
+ "print('\\nFor wye-delta connection')\n",
+ "print(' (i) Line voltage at secondary side , V_L2 = %.2f V' %V_wL2)\n",
+ "print(' (ii) Line current in the secondary , I_L2 = %.2f A' %I_wL2)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "For delta-wye connection\n",
+ " (i) Line voltage at secondary side , V_L2 = 1732 V\n",
+ " (ii) Line current in the secondary , I_L2 = 69.86 A\n",
+ "\n",
+ "For wye-delta connection\n",
+ " (i) Line voltage at secondary side , V_L2 = 577.35 V\n",
+ " (ii) Line current in the secondary , I_L2 = 114.32 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.16, Page number 132"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import cmath\n",
+ "\n",
+ "#Variable declaration\n",
+ "V_b = 220.0 #Voltage(V)\n",
+ "f = 50.0 #Frequency(Hz)\n",
+ "S_b = 600.0 #Base value of rating(VA)\n",
+ "R = 3.0 #Resistance(ohm)\n",
+ "X_L = 5.0 #Inductance(ohm)\n",
+ "Z = complex(R,X_L) #Impedance(ohm)\n",
+ "\n",
+ "#Calculation\n",
+ "I_b = S_b/V_b #Base value of current(A)\n",
+ "Z_b = V_b**2/S_b #Base impedance(ohm)\n",
+ "R_pu = R/Z_b #Per unit value of resistance\n",
+ "X_Lpu = X_L/Z_b #Per unit value of inductance\n",
+ "Z_pu = complex(R_pu,X_Lpu) #Per unit of value of impedance\n",
+ "Z_pu_alt = abs(Z)/Z_b #Per unit of value of impedance-alternative method\n",
+ "\n",
+ "#Result\n",
+ "print('Per unit value of resistance , R_pu = %.3f ' %R_pu)\n",
+ "print('Per unit value of inductance , X_Lpu = %.3f ' %X_Lpu)\n",
+ "print('Per unit of value of impedance , Z_pu = %.3f\u2220%.2f\u00b0 ' %(abs(Z_pu),cmath.phase(Z_pu)*180/math.pi))\n",
+ "print('Per unit of value of impedance by alternative method , Z_pu = %.3f ' %Z_pu_alt)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Per unit value of resistance , R_pu = 0.037 \n",
+ "Per unit value of inductance , X_Lpu = 0.062 \n",
+ "Per unit of value of impedance , Z_pu = 0.072\u222059.04\u00b0 \n",
+ "Per unit of value of impedance by alternative method , Z_pu = 0.072 \n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 3.17, Page number 132-134"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import cmath\n",
+ "\n",
+ "#Variable declaration\n",
+ "MVA_T1 = 100.0 #Rating of transformer T1(MVA)\n",
+ "V_T1_hv = 220.0 #Voltage of h.v side of T1(kV)\n",
+ "V_T1_lv = 132.0 #Voltage of l.v side of T1(kV)\n",
+ "X_T1 = 0.2 #Impedance of T1(pu)\n",
+ "MVA_T2 = 50.0 #Rating of transformer T2(MVA)\n",
+ "V_T2_hv = 132.0 #Voltage of h.v side of T2(kV)\n",
+ "V_T2_lv = 66.0 #Voltage of l.v side of T2(kV)\n",
+ "X_T2 = 0.05 #Impedance of T2(pu)\n",
+ "X_L = 4.0 #Line impedance(ohm)\n",
+ "P = 50.0 #Power absorbed(MW)\n",
+ "pf = 0.6 #Lagging power factor\n",
+ "\n",
+ "#Calculation\n",
+ "S_b = MVA_T1 #Base apparent power(MW)\n",
+ "V_b = V_T1_hv #Base voltage(kV)\n",
+ "a = V_T1_hv/V_T1_lv #Turns ratio for first transformer\n",
+ "V_bline = V_T1_hv/a #Base voltage of line(kV)\n",
+ "Z_bline = V_bline**2/S_b #Base impedance of line(ohm)\n",
+ "X_puline = X_L/Z_bline #Per unit reactance of line\n",
+ "X_pu_T1 = X_T1*(V_T1_hv/V_b)**2*(S_b/MVA_T1) #Per unit reactance of first transformer\n",
+ "V_bload = V_T2_hv/(V_T2_hv/V_T2_lv) #Load side base voltage(kV)\n",
+ "X_pu_load = X_T2*(V_T2_lv/V_bload)**2*(S_b/MVA_T2) #Per unit reactance of second transformer\n",
+ "I_b = S_b*1000/(3**0.5*V_bload) #Base current at the load(A)\n",
+ "I_L = MVA_T2*1000/(3**0.5*V_T2_lv*pf) #Actual current in load(A)\n",
+ "I_Lpu = I_L/I_b #Per unit value of load current(pu)\n",
+ "V_L = V_T2_lv/V_bload #Per unit value of voltage at the load terminal(pu)\n",
+ "V_gb = I_Lpu*cmath.exp(1j*math.acos(pf))*complex(0,X_T1+X_puline+X_pu_load)+V_L #Per unit value of grid to bus voltage(pu)\n",
+ "V_gba = V_gb*V_T1_hv #Actual value of grid to bus voltage(kV)\n",
+ "\n",
+ "#Result\n",
+ "print('Grid to bus voltage , V_gb = %.f\u2220%.2f\u00b0 kV' %(abs(V_gba),cmath.phase(V_gba)*180/math.pi))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Grid to bus voltage , V_gb = 176\u222011.63\u00b0 kV\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file |