{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Chapter 6: Phase Controlled Rectifiers" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 6.10: to_find_avg_value_of_load_current_and_new_value_under_given_changed_conditions.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clear;\n", "clc;\n", "V_s=230;\n", "f=50;\n", "a=50;\n", "R=6;\n", "E=60;\n", "V_o=((sqrt(2)*2*V_s)/(%pi))*(cosd(a));\n", "I_o=(V_o-E)/R; printf('avg o/p current=%.3f A',I_o);\n", "\n", "//ATQ after applying the conditions\n", "V_o=((sqrt(2)*V_s)/(%pi))*(cosd(a));\n", "I_o=(V_o-E)/R; printf('\navg o/p current after change=%.4f A',I_o);" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 6.11: to_calculate_the_input_and_output_performance_parameters_for_full_conductor.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clear;\n", "clc;\n", "V_s=230;\n", "V_m=sqrt(2)*V_s;\n", "a=45;\n", "R=10;\n", "V_o=(2*V_m/%pi)*cosd(a);\n", "I_o=V_o/R;\n", "V_or=V_m/sqrt(2);\n", "I_or=I_o;\n", "P_dc=V_o*I_o;\n", "P_ac=V_or*I_or;\n", "RE=P_dc/P_ac; printf('rectification efficiency=%.4f',RE);\n", "FF=V_or/V_o; printf('\nform factor=%.4f',FF);\n", "VRF=sqrt(FF^2-1); printf('\nvoltage ripple factor=%.4f',VRF);\n", "I_s1=2*sqrt(2)*I_o/%pi;\n", "DF=cosd(a);\n", "CDF=.90032;\n", "pf=CDF*DF; printf('\npf=%.5f',pf);\n", "HF=sqrt((1/CDF^2)-1); printf('\nHF=%.5f',HF);\n", "printf('\nactive power=%.2f W',P_dc);\n", "Q=2*V_m*I_o*sind(a)/%pi; printf('\nreactive power=%.3f Var',Q);" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 6.12: EX6_12.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clear;\n", "clc;\n", "V_s=230;\n", "V_m=sqrt(2)*V_s;\n", "a=45;\n", "R=10;\n", "V_o=(V_m/%pi)*(1+cosd(a));\n", "I_o=V_o/R;\n", "V_or=V_s*sqrt((1/%pi)*((%pi-a*%pi/180)+sind(2*a)/2));\n", "I_or=I_o;\n", "P_dc=V_o*I_o;\n", "P_ac=V_or*I_or;\n", "RE=P_dc/P_ac; printf('rectification efficiency=%.4f',RE);\n", "FF=V_or/V_o; printf('\nform factor=%.3f',FF);\n", "VRF=sqrt(FF^2-1); printf('\nvoltage ripple factor=%.3f',VRF);\n", "I_s1=2*sqrt(2)*I_o*cosd(a/2)/%pi;\n", "DF=cosd(a/2); printf('\nDF=%.4f',DF);\n", "CDF=2*sqrt(2)*cosd(a/2)/sqrt(%pi*(%pi-a*%pi/180)); printf('\nCDF=%.4f',CDF);\n", "pf=CDF*DF; printf('\npf=%.4f',pf);\n", "HF=sqrt((1/CDF^2)-1); printf('\nHF=%.4f',HF);\n", "printf('\nactive power=%.3f W',P_dc);\n", "Q=V_m*I_o*sind(a)/%pi; printf('\nreactive power=%.2f Var',Q);\n", "//Answers have small variations from that in the book due to difference in the rounding off of digits." ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 6.13: EX6_13.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clear;\n", "clc;\n", "V_s=230;\n", "R=10;\n", "V_ml=sqrt(2)*V_s;\n", "V_om=3*V_ml/(2*%pi);\n", "V_o=V_om/2;\n", "th=30;\n", "a=acosd((2*%pi*sqrt(3)*V_o/(3*V_ml)-1))-th; printf('delay angle=%.1f deg',a);\n", "I_o=V_o/R; printf('\navg load current=%.3f A',I_o);\n", "V_or=V_ml/(2*sqrt(%pi))*sqrt((5*%pi/6-a*%pi/180)+.5*sind(2*a+2*th));\n", "I_or=V_or/R; printf('\nrms load current=%.3f A',I_or);\n", "RE=V_o*I_o/(V_or*I_or); printf('\nrectification efficiency=%.4f',RE);" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 6.15: EX6_15.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clear;\n", "clc;\n", "V=400;\n", "V_ml=sqrt(2)*V;\n", "v_T=1.4;\n", "disp('for firing angle = 30deg');\n", "a=30;\n", "V_o=3*V_ml/(2*%pi)*cosd(a)-v_T; printf('avg output voltage=%.3f V',V_o);\n", "disp('for firing angle = 60deg');\n", "a=60;\n", "V_o=3*V_ml/(2*%pi)*cosd(a)-v_T; printf('avg output voltage=%.2f V',V_o);\n", "\n", "I_o=36;\n", "I_TA=I_o/3; printf('\navg current rating=%.0f A',I_TA);\n", "I_Tr=I_o/sqrt(3); printf('\nrms current rating=%.3f A',I_Tr);\n", "printf('\nPIV of SCR=%.1f V',V_ml);\n", "\n", "P=I_TA*v_T; printf('\npower dissipated=%.1f W',P);" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 6.17: to_compute_firing_angle_delay_and_supply_pf.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clear;\n", "clc;\n", "E=200;\n", "I_o=20;\n", "R=.5;\n", "V_o=E+I_o*R;\n", "V_s=230;\n", "V_ml=sqrt(2)*V_s;\n", "a=acosd(V_o*%pi/(3*V_ml)); printf('firing angle delay=%.3f deg',a);\n", "th=120;\n", "I_s=sqrt((1/%pi)*I_o^2*th*%pi/180);\n", "P=E*I_o+I_o^2*R;\n", "pf=P/(sqrt(3)*V_s*I_s); printf('\npf=%.3f',pf);\n", "\n", "V_o=E-I_o*R;\n", "a=acosd(-V_o*%pi/(3*V_ml)); printf('\nfiring angle delay=%.2f deg',a);" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 6.18: to_find_commutation_time_and_reverse_voltage_across_SCR.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clear;\n", "clc;\n", "V=230;\n", "f=50;\n", "w=2*%pi*f;\n", "disp('for firing angle delay=0deg');\n", "a=0;\n", "t_c=(4*%pi/3-a*%pi/180)/w; printf('commutation time=%.2f ms',t_c*1000);\n", "printf('\npeak reverse voltage=%.2f V',sqrt(2)*V);\n", "\n", "disp('for firing angle delay=30deg');\n", "a=30;\n", "t_c=(4*%pi/3-a*%pi/180)/w; printf('commutation time=%.2f ms',t_c*1000);\n", "printf('\npeak reverse voltage=%.2f V',sqrt(2)*V);" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 6.19: to_find_the_magnitude_of_per_phase_input_supply_voltage.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clear;\n", "clc;\n", "a=30;\n", "R=10;\n", "P=5000;\n", "V_s=sqrt(P*R*2*%pi/(2*3)/(%pi/3+sqrt(3)*cosd(2*a)/2));\n", "V_ph=V_s/sqrt(3); printf('per phase voltage, V_ph=%.3f V',V_ph);\n", "I_or=sqrt(P*R);\n", "V_s=I_or*%pi/(sqrt(2)*3*cosd(a));\n", "V_ph=V_s/sqrt(3); \n", "printf('\nfor constant load current');\n", "printf('\nV_ph=%.2f V',V_ph);" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 6.1: to_calculate_the_power_absorbed_in_the_heater_element.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clear;\n", "clc;\n", "V=230;\n", "P=1000;\n", "R=V^2/P;\n", "disp('when firing angle delay is of 45deg');\n", "a=%pi/4;\n", "V_or=(sqrt(2)*V/(2*sqrt(%pi)))*sqrt((%pi-a)+.5*sin(2*a));\n", "P=V_or^2/R; printf('power absorbed=%.2f W',P);\n", "\n", "disp('when firing angle delay is of 90deg');\n", "a=%pi/2;\n", "V_or=(sqrt(2)*V/(2*sqrt(%pi)))*sqrt((%pi-a)+.5*sin(2*a));\n", "P=V_or^2/R; printf('power absorbed=%.2f W',P);" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 6.20: to_find_magnitude_of_input_per_phase_supply_voltage.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clear;\n", "clc;\n", "a=30;\n", "R=10;\n", "P=5000;\n", "V_s=sqrt(P*R*4*%pi/(2*3)/(2*%pi/3+sqrt(3)*(1+cosd(2*a))/2));\n", "V_ph=V_s/sqrt(3); printf('per phase voltage, V_ph=%.3f V',V_ph);\n", "I_or=sqrt(P*R);\n", "V_s=I_or*2*%pi/(sqrt(2)*3*(1+cosd(a)));\n", "V_ph=V_s/sqrt(3); \n", "printf('\nfor constant load current');\n", "printf('\nV_ph=%.2f V',V_ph);" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 6.21: to_find_magnitude_of_input_per_phase_supply_voltage.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clear;\n", "clc;\n", "a=90;\n", "R=10;\n", "P=5000;\n", "V_s=sqrt(P*R*4*%pi/(2*3)/((%pi-%pi/2)+(sind(2*a))/2));\n", "V_ph=V_s/sqrt(3); printf('per phase voltage, V_ph=%.2f V',V_ph);\n", "I_or=sqrt(P*R);\n", "V_s=I_or*2*%pi/(sqrt(2)*3*(1+cosd(a)));\n", "V_ph=V_s/sqrt(3); \n", "printf('\nfor constant load current');\n", "printf('\nV_ph=%.1f V',V_ph);" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 6.22: to_compute_firing_angle_delay_and_supply_pf.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clear;\n", "clc;\n", "E=200;\n", "I_o=20;\n", "R=.5;\n", "V_o=E+I_o*R;\n", "V_s=230;\n", "V_ml=sqrt(2)*V_s;\n", "a=acosd(V_o*2*%pi/(3*V_ml)-1); printf('firing angle delay=%.2f deg',a);\n", "a1=180-a;\n", "I_sr=sqrt((1/%pi)*I_o^2*(a1*%pi/180));\n", "P=V_o*I_o;\n", "pf=P/(sqrt(3)*V_s*I_sr); printf('\npf=%.4f',pf);" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 6.23: to_calculate_rectification_efficiency_TUF_and_input_power_factor.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clear;\n", "clc;\n", "V_s=400;\n", "f=50;\n", "I_o=15;\n", "a=45;\n", "I_TA=I_o*120/360;\n", "I_Tr=sqrt(I_o^2*120/360);\n", "I_sr=sqrt(I_o^2*120/180);\n", "V_ml=sqrt(2)*V_s;\n", "V_o=3*V_ml*cosd(a)/%pi;\n", "V_or=V_ml*sqrt((3/(2*%pi))*(%pi/3+sqrt(3/2)*cosd(2*a)));\n", "I_or=I_o;\n", "P_dc=V_o*I_o;\n", "P_ac=V_or*I_or;\n", "RE=P_dc/P_ac; printf('rectification efficiency=%.5f',RE);\n", "VA=3*V_s/sqrt(3)*I_sr;\n", "TUF=P_dc/VA; printf('\nTUF=%.4f',TUF);\n", "pf=P_ac/VA; printf('\ninput pf=%.3f',pf);" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 6.24: to_find_DF_CDF_THD_and_pf_and_to_calculate_the_active_and_reative_input_powers.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clear;\n", "clc;\n", "I=10;\n", "a=45;\n", "V=400;\n", "f=50;\n", "DF=cosd(a);\n", "printf('DF=%.3f',DF);\n", "I_o=10;\n", "I_s1=4*I_o/(sqrt(2)*%pi)*sin(%pi/3);\n", "I_sr=I_o*sqrt(2/3);\n", "I_o=1; //suppose\n", "CDF=I_s1/I_sr; printf('\nCDF=%.3f',CDF);\n", "THD=sqrt(1/CDF^2-1); printf('\nTHD=%.5f',THD);\n", "pf=CDF*DF; printf('\nPF=%.4f',pf);\n", "P=(3*sqrt(2)*V*cosd(a)/%pi)*I; printf('\nactive power=%.2f W',P);\n", "Q=(3*sqrt(2)*V*sind(a)/%pi)*I; printf('\nreactive power=%.2f Var',Q);" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 6.25: calculate_the_power_delivered_to_load_and_input_pf.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "//calculate the power delivered to load and i/p pf\n", "\n", "clc;\n", "disp('for firing angle=30deg');\n", "a=30;\n", "V=400;\n", "V_ml=sqrt(2)*V;\n", "V_o=3*V_ml*cosd(a)/%pi;\n", "E=350;\n", "R=10;\n", "I_o=(V_o-E)/R;\n", "I_or=I_o;\n", "P=V_o*I_o; printf('power delivered to load=%.2f W',P);\n", "I_sr=I_o*sqrt(2/3);\n", "VA=3*V/sqrt(3)*I_sr;\n", "pf=P/VA; printf('\npf=%.4f',pf);\n", "\n", "disp('for firing advance angle=60deg');\n", "a=180-60;\n", "V=400;\n", "V_ml=sqrt(2)*V;\n", "V_o=3*V_ml*cosd(a)/%pi;\n", "E=-350;\n", "R=10;\n", "I_o=(V_o-E)/R;\n", "I_or=I_o;\n", "P=-V_o*I_o; printf('power delivered to load=%.2f W',P);\n", "I_sr=I_o*sqrt(2/3);\n", "VA=3*V/sqrt(3)*I_sr;\n", "pf=P/VA; printf('\npf=%.4f',pf);\n", "//Answers have small variations from that in the book due to difference in the rounding off of digits." ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 6.26: calculate_overlap_angle_for_different_firing_angles.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clear;\n", "clc;\n", "a=0;\n", "u=15;\n", "i=cosd(a)-cosd(a+u);\n", "disp('for firing angle=30deg');\n", "a=30;\n", "u=acosd(cosd(a)-i)-a; printf('overlap angle=%.1f deg',u);\n", "disp('for firing angle=45deg');\n", "a=45;\n", "u=acosd(cosd(a)-i)-a; printf('overlap angle=%.1f deg',u);\n", "disp('for firing angle=60deg');\n", "a=60;\n", "u=acosd(cosd(a)-i)-a; printf('overlap angle=%.2f deg',u);" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 6.28: to_calculate_firing_angle_delay_and_overlap_angle.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clear;\n", "clc;\n", "E=400;\n", "I_o=20;\n", "R=1;\n", "V_o=E+I_o*R;\n", "f=50;\n", "w=2*%pi*f\n", "L=.004;\n", "V=230;//per phase voltage\n", "V_ml=sqrt(6)*V;\n", "a=acosd(%pi/(3*V_ml)*(V_o+3*w*L*I_o/%pi)); printf('firing angle delay=%.3f deg',a);\n", "u=acosd(%pi/(3*V_ml)*(V_o-3*w*L*I_o/%pi))-a; printf('\noverlap angle=%.2f deg',u);\n", "//Answers have small variations from that in the book due to difference in the rounding off of digits." ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 6.29: to_calculate_firing_angle_firing_angle_delay_and_overlap_angle.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clear;\n", "clc;\n", "V=400;\n", "f=50;\n", "w=2*%pi*f;\n", "R=1;\n", "E=230;\n", "I=15;\n", "V_o=-E+I*R;\n", "V_ml=sqrt(2)*V;\n", "a=acosd(V_o*2*%pi/(3*V_ml)); printf('firing angle=%.3f deg',a);\n", "L=0.004;\n", "a=acosd((2*%pi)/(3*V_ml)*(V_o+3*w*L*I/(2*%pi))); printf('\nfiring angle delay=%.3f deg',a);\n", "u=acosd(cosd(a)-3*f*L*I/V_ml)-a; printf('\noverlap angle=%.3f deg',u);\n", "//Answers have small variations from that in the book due to difference in the rounding off of digits." ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 6.2: EX6_2.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clear;\n", "clc;\n", "V=230;\n", "E=150;\n", "R=8;\n", "th1=asind(E/(sqrt(2)*V));\n", "I_o=(1/(2*%pi*R))*(2*sqrt(2)*230*cosd(th1)-E*(%pi-2*th1*%pi/180)); \n", "printf('avg charging curent=%.4f A',I_o);\n", "\n", "P=E*I_o; printf('\npower supplied to the battery=%.2f W',P);\n", "I_or=sqrt((1/(2*%pi*R^2))*((V^2+E^2)*(%pi-2*th1*%pi/180)+V^2*sind(2*th1)-4*sqrt(2)*V*E*cosd(th1)));\n", "P_r=I_or^2*R; printf('\npower dissipated by the resistor=%.3f W',P_r);\n", "\n", "pf=(P+P_r)/(V*I_or); printf('\nsupply pf=%.3f',pf);" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 6.31: calculate_the_peak_value_of_circulating_current.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clear;\n", "clc;\n", "V=230;//per phase\n", "V_ml=sqrt(3)*sqrt(2)*V;\n", "f=50;\n", "w=2*%pi*f;\n", "a1=60;\n", "L=0.015;\n", "i_cp=(sqrt(3)*V_ml/(w*L))*(1-sind(a1)); printf('circulating current=%.4f A',i_cp);" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 6.32: EX6_32.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clear;\n", "clc;\n", "V=230;\n", "V_m=sqrt(2)*V;\n", "a=30;\n", "V_o=2*V_m*cosd(a)/%pi; printf('avg o/p voltage=%.3f V',V_o);\n", "R=10;\n", "I_o=V_o/R; printf('\navg o/p current=%.2f A',I_o);\n", "I_TA=I_o*%pi/(2*%pi); printf('\navg value of thyristor current=%.3f A',I_TA);\n", "I_Tr=sqrt(I_o^2*%pi/(2*%pi)); printf('\nrms value of thyristor current=%.2f A',I_Tr);\n", "I_s=sqrt(I_o^2*%pi/(%pi)); \n", "I_o=I_s;\n", "pf=(V_o*I_o/(V*I_s)); printf('\npf=%.4f',pf);\n", "//Answers have small variations from that in the book due to difference in the rounding off of digits." ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 6.33: to_determine_1_avg_output_voltage_2_angle_of_overlap_3_pf.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clear;\n", "clc;\n", "V=230;\n", "V_m=sqrt(2)*V;\n", "a=30;\n", "L=.0015;\n", "V_o=2*V_m*cosd(a)/%pi; \n", "R=10;\n", "I_o=V_o/R; \n", "f=50;\n", "w=2*%pi*f;\n", "V_ox=2*V_m*cosd(a)/%pi-w*L*I_o/%pi; printf('avg o/p voltage=%.3f V',V_ox);\n", "u=acosd(cosd(a)-I_o*w*L/V_m)-a; printf('\nangle of overlap=%.3f deg',u);\n", "I=I_o;\n", "pf=V_o*I_o/(V*I); printf('\npf=%.4f',pf);\n", "//Answers have small variations from that in the book due to difference in the rounding off of digits." ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 6.34: calculate_the_generator_mean_voltage.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clear;\n", "clc;\n", "V=415;\n", "V_ml=sqrt(2)*V;\n", "a1=35;//firing angle advance\n", "a=180-a1;\n", "I_o=80;\n", "r_s=0.04;\n", "v_T=1.5;\n", "X_l=.25;//reactance=w*L\n", "E=-3*V_ml*cosd(a)/%pi+2*I_o*r_s+2*v_T+3*X_l*I_o/%pi; printf('mean generator voltage=%.3f V',E);" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 6.35: find_the_mean_value_of_E.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clear;\n", "clc;\n", "V=415;\n", "V_ml=sqrt(2)*V;\n", "R=.2;\n", "I_o=80;\n", "r_s=0.04;\n", "v_T=1.5;\n", "X_l=.25;//reactance=w*L\n", "\n", "disp('when firing angle=35deg');\n", "a=35;\n", "E=-(-3*V_ml*cosd(a)/%pi+I_o*R+2*I_o*r_s+2*v_T+3*X_l*I_o/%pi); printf('mean generator voltage=%.3f V',E);\n", "disp('when firing angle advance=35deg');\n", "a1=35;\n", "a=180-a1;\n", "E=(-3*V_ml*cosd(a)/%pi+I_o*R+2*I_o*r_s+2*v_T+3*X_l*I_o/%pi); printf('mean generator voltage=%.3f V',E);" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 6.36: to_find_avg_current_through_battery.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clear;\n", "clc;\n", "R=5;\n", "V=230;\n", "V_mp=sqrt(2)*V;\n", "a=30;\n", "E=150;\n", "B=180-asind(E/V_mp);\n", "I_o=(3/(2*%pi*R))*(V_mp*(cosd(a+30)-cosd(B))-E*((B-a-30)*%pi/180));\n", "printf('avg current flowing=%.2f A',I_o);" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 6.37: EX6_37.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clear;\n", "clc;\n", "a=30;\n", "V=230;\n", "V_m=sqrt(2)*V;\n", "V_o=V_m*(1+cosd(a))/%pi; printf('avg o/p voltage=%.3f V',V_o);\n", "E=100;\n", "R=10;\n", "I_o=(V_o-E)/R; printf('\navg o/p current=%.2f A',I_o);\n", "I_TA=I_o*%pi/(2*%pi); printf('\navg value of thyristor current=%.2f A',I_TA);\n", "I_Tr=sqrt(I_o^2*%pi/(2*%pi)); printf('\nrms value of thyristor current=%.3f A',I_Tr);\n", "printf('\navg value of diode current=%.2f A',I_TA);\n", "printf('\nrms value of diode current=%.3f A',I_Tr);\n", "I_s=sqrt(I_o^2*(1-a/180)*%pi/(%pi));\n", "I_or=I_o;\n", "P=E*I_o+I_or^2*R;\n", "pf=(P/(V*I_s)); printf('\npf=%.4f',pf);\n", "f=50;\n", "w=2*%pi*f;\n", "t_c=(1-a/180)*%pi/w; printf('\ncircuit turn off time=%.2f ms',t_c*1000);" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 6.38: to_calculate_peak_value_of_circulating_currents_and_of_both_convertors.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clear;\n", "clc;\n", "V=230;\n", "V_m=sqrt(2)*V;\n", "L=0.05;\n", "f=50;\n", "w=2*%pi*f;\n", "a=30;\n", "i_cp=2*V_m*(1-cosd(a))/(w*L); printf('peak value of circulating current=%.3f A',i_cp);\n", "R=30;\n", "i_l=V_m/R;\n", "i1=i_cp+i_l; printf('\npeak value of current in convertor 1=%.3f A',i1);\n", "i2=i_cp; printf('\npeak value of current in convertor 2=%.3f A',i2);" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 6.39: to_estimate_triggering_angle_for_no_current_transients_and_for_worst_transients.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clear;\n", "clc;\n", "f=50;\n", "w=2*%pi*f;\n", "R=5;\n", "L=0.05;\n", "disp('for no current transients');\n", "phi=atand(w*L/R); printf('triggering angle=%.2f deg',phi);\n", "disp('for worst transients');\n", "phi=90+atand(w*L/R); printf('triggering angle=%.2f deg',phi);" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 6.3: EX6_3.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clear;\n", "clc;\n", "V=230;\n", "E=150;\n", "R=8;\n", "a=35;\n", "th1=asind(E/(sqrt(2)*V));\n", "th2=180-th1;\n", "I_o=(1/(2*%pi*R))*(sqrt(2)*230*(cosd(a)-cosd(th2))-E*((th2-a)*%pi/180)); \n", "printf('avg charging curent=%.4f A',I_o);\n", "\n", "P=E*I_o; printf('\npower supplied to the battery=%.2f W',P);\n", "I_or=sqrt((1/(2*%pi*R^2))*((V^2+E^2)*((th2-a)*%pi/180)-(V^2/2)*(sind(2*th2)-sind(2*a))-2*sqrt(2)*V*E*(cosd(a)-cosd(th2))));\n", "P_r=I_or^2*R; printf('\npower dissipated by the resistor=%.2f W',P_r);\n", "\n", "pf=(P+P_r)/(V*I_or); printf('\nsupply pf=%.4f',pf);\n", "//Answers have small variations from that in the book due to difference in the rounding off of digits." ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 6.4: to_find_ckt_turn_off_time_avg_output_voltage_and_avg_load_current.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clear;\n", "clc;\n", "B=210;\n", "f=50; //Hz\n", "w=2*%pi*f;\n", "a=40; //firing angle\n", "V=230;\n", "disp('for R=5ohm and L=2mH');\n", "R=5;\n", "L=2*10^-3;\n", "t_c=(360-B)*%pi/(180*w); printf('ckt turn off time=%.3f msec',t_c*1000);\n", "V_o=(sqrt(2)*230/(2*%pi))*(cosd(a)-cosd(B)); printf('\navg output voltage=%.3f V',V_o);\n", "I_o=V_o/R; printf('\navg output current=%.4f A',I_o);\n", "\n", "disp('for R=5ohm, L=2mH and E=110V');\n", "E=110;\n", "R=5;\n", "L=2*10^-3;\n", "th1=asind(E/(sqrt(2)*V));\n", "t_c=(360-B+th1)*%pi/(180*w); printf('ckt turn off time=%.3f msec',t_c*1000);\n", "V_o=(sqrt(2)*230/(2*%pi))*(cosd(a)-cosd(B)); printf('\navg output voltage=%.3f V',V_o); \n", "I_o=(1/(2*%pi*R))*(sqrt(2)*230*(cosd(a)-cosd(B))-E*((B-a)*%pi/180)); printf('\navg output current=%.4f A',I_o);\n", "V_o=R*I_o+E; printf('\navg output voltage=%.3f V',V_o);\n", "\n", " " ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 6.5: EX6_5.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clear;\n", "clc;\n", "V_s=230;\n", "f=50;\n", "R=10;\n", "a=60;\n", "V_m=(sqrt(2)*V_s);\n", "V_o=V_m/(2*%pi)*(1+cosd(a));\n", "I_o=V_o/R;\n", "V_or=(V_m/(2*sqrt(%pi)))*sqrt((%pi-a*%pi/180)+.5*sind(2*a));\n", "I_or=V_or/R;\n", "P_dc=V_o*I_o;\n", "P_ac=V_or*I_or;\n", "RE=P_dc/P_ac; printf('rectification efficiency=%.4f',RE);\n", "FF=V_or/V_o; printf('\nform factor=%.3f',FF);\n", "VRF=sqrt(FF^2-1); printf('\nvoltage ripple factor=%.4f',VRF);\n", "TUF=P_dc/(V_s*I_or); printf('\nt/f utilisation factor=%.4f',TUF);\n", "PIV=V_m; printf('\nPIV of thyristor=%.2f V',PIV);" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 6.6: to_find_power_handled_by_mid_pt_convertor_and_single_phase_bridge_convertor.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clear;\n", "clc;\n", "V=1000;\n", "fos=2.5; //factor of safety\n", "I_TAV=40;\n", "disp('for mid pt convertor');\n", "V_m=V/(2*fos);\n", "P=(2*V_m/%pi)*I_TAV; printf('power handled=%.3f kW',P/1000);\n", "disp('for bridge convertor');\n", "V_m=V/(fos);\n", "P=(2*V_m/%pi)*I_TAV; printf('power handled=%.3f kW',P/1000);" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 6.7: compute_firing_angle_delay_and_pf.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clear;\n", "clc;\n", "V_s=230;\n", "V_m=sqrt(2)*V_s;\n", "R=.4;\n", "I_o=10;\n", "I_or=I_o;\n", "E=120;\n", "a=acosd((E+I_o*R)*%pi/(2*V_m)); printf('firing angle delay=%.2f deg',a);\n", "pf=(E*I_o+I_or^2*R)/(V_s*I_or); printf('\npf=%.4f',pf);\n", "\n", "E=-120;\n", "a=acosd((E+I_o*R)*%pi/(2*V_m)); printf('\nfiring angle delay=%.2f deg',a);\n", "pf=(-E*I_o-I_or^2*R)/(V_s*I_or); printf('\npf=%.4f',pf);" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 6.9: to_find_avg_output_current_and_power_delivered.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clear;\n", "clc;\n", "V_s=230;\n", "f=50;\n", "a=45;\n", "R=5;\n", "E=100;\n", "V_o=((sqrt(2)*V_s)/(2*%pi))*(3+cosd(a));\n", "I_o=(V_o-E)/R; printf('avg o/p current=%.3f A',I_o);\n", "P=E*I_o; printf('\npower delivered to battery=%.4f kW',P/1000);" ] } ], "metadata": { "kernelspec": { "display_name": "Scilab", "language": "scilab", "name": "scilab" }, "language_info": { "file_extension": ".sce", "help_links": [ { "text": "MetaKernel Magics", "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" } ], "mimetype": "text/x-octave", "name": "scilab", "version": "0.7.1" } }, "nbformat": 4, "nbformat_minor": 0 }