{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 05 : Basic concepts in rotating machines" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.1, Page No 148" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "# To calculate harmanic factor for stator\n", "\n", "S=36.0 #no of slots\n", "q=3.0 #no of phases\n", "p=4.0 #no of poles\n", "m=S/(q*p) #slots/pole/phase\n", "g=180*p/S #gamma elec\n", "\n", "#Calculations\n", "def bfctr(n):\n", " k=math.sin(math.radians(m*n*g/2))/(m*math.sin(math.radians(n*g/2))) \n", " return k\n", "\n", "K_b=bfctr(1) \n", "print(K_b,'K_b(fundamental)') \n", "\n", "K_b=bfctr(3.0) \n", "\n", "#Results\n", "print(K_b,'K_b(third harmonic)') \n", "\n", "K_b=bfctr(5.0) \n", "print(K_b,'K_b(fifth harmonic)') " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(0.9597950805239389, 'K_b(fundamental)')\n", "(0.6666666666666667, 'K_b(third harmonic)')\n", "(0.21756788155537973, 'K_b(fifth harmonic)')\n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.2, Page No 149" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "# to find the frequency and phase and line voltages\n", "\n", "n=375.0 #speed in rpm\n", "p=16.0 #no of poles\n", "f=n*p/120.0 \n", "print(f,'freq(Hz)') \n", "S=144.0 #no of slots\n", "c=10.0 #no of conductors/slot\n", "\n", "#Calculations\n", "t=S*c/2 #no of turns\n", "ph=3 \n", "N_ph=t/ph #no of turns/ph\n", "g=180*p/S #slots angle\n", "m=S/(p*ph) #slots/pole/phase\n", "K_b=math.sin(math.radians(m*g/2.0))/(m*math.sin(math.radians(g/2))) #breadth factor\n", "phi=0.04 #flux per pole\n", "E_p=4.44*K_b*f*N_ph*phi \n", "\n", "#Results\n", "print(E_p,'phase voltage(V)') \n", "E_l=math.sqrt(3)*E_p \n", "print(E_l,'line voltage(V)') \n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(50.0, 'freq(Hz)')\n", "(2045.5152756126188, 'phase voltage(V)')\n", "(3542.936385019311, 'line voltage(V)')\n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.3, Page No 149" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "# to find the phase and line voltages\n", "\n", "f=50 #freq\n", "n=600 #speed in rpm\n", "p=120*f/n \n", "ph=3 \n", "m=4 #slots/pole/ph\n", "S=p*ph*m #slots\n", "t=12 #turns per coil\n", "\n", "#Calculations\n", "N_ph=S*t/ph \n", "g=180*p/S \n", "K_b=math.sin(math.radians(m*g/2.0))/(m*math.sin(math.radians(g/2))) #breadth factor\n", "cp=10 #coil pitch\n", "pp=S/cp #pole pitch\n", "theta_sp=(pp-cp)*g #short pitch angle\n", "K_p=math.cos(math.radians(theta_sp/2))\n", "phi=.035 \n", "E_p=4.44*K_b*K_p*f*N_ph*phi\n", "\n", "#Results\n", "print(E_p,'phase voltage(V)') \n", "E_l=math.sqrt(3)*E_p \n", "print(E_l,'line voltage(V)')" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(3695.060690685099, 'phase voltage(V)')\n", "(6400.032853317139, 'line voltage(V)')\n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.4 Page No 150" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "# to calculate flux/pole\n", "\n", "S=42 \n", "p=2 \n", "ph=3 \n", "m=S/(p*ph) #slots/pole/phase\n", "g=180*p/S #slots angle\n", "\n", "#Calculations\n", "K_b=math.sin(math.radians(m*g/2.0))/(m*math.sin(math.radians(g/2))) #breadth factor\n", "cp=17 \n", "pp=S/p \n", "theta_sp=(pp-cp)*g #short pitch angle\n", "K_p=math.cos(math.radians(theta_sp/2)) \n", "N_ph=S*2/(ph*p*2) #2 parallel paths\n", "E_p=2300/math.sqrt(3) \n", "phi=E_p/(4.44*K_b*K_p*f*N_ph) \n", "\n", "#Results\n", "print(phi,'flux/pole(Wb)') \n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(0.9245870891715325, 'flux/pole(Wb)')\n" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.5, Page No 151" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "# to calculate useful flux/pole and ares of pole shoe\n", "\n", "p=1500*1000.0 #power\n", "v=600.0 \n", "I_a=p/v \n", "cu=25*1000 #copper losses\n", "\n", "#Calculations\n", "R_a=cu/I_a**2 \n", "E_a=v+I_a*R_a \n", "n=200 \n", "Z=2500 \n", "p=16 \n", "A=16 \n", "phi=E_a*60*A/(p*n*Z) \n", "print(phi,'flux/pole(Wb)') \n", "fd=0.85 #flux density\n", "a=phi/fd \n", "\n", "#Results\n", "print(a,'area of pole shoe(m*m)') " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(0.0732, 'flux/pole(Wb)')\n", "(0.08611764705882353, 'area of pole shoe(m*m)')\n" ] } ], "prompt_number": 5 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.6, Page No 152" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "# To calculate em power developed,mech power fed, torque provided by primemover\n", "\n", "phi=32*10**-3 #flux/pole\n", "n=1600 #speed in rpm\n", "Z=728 #no of conductors\n", "p=4 \n", "A=4 \n", "\n", "#Calculations\n", "E_a=phi*n*Z*(p/A)/60 \n", "I_a=100 \n", "P_e=E_a*I_a \n", "print(P_e,'electromagnetic power(W)') \n", "P_m=P_e \n", "print(P_m,'mechanical power(W) fed') \n", "w_m=2*math.pi*n/60 \n", "T=P_m/w_m \n", "\n", "#Results\n", "print(T,'primemover torque(Nm)') \n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(62122.66666666667, 'electromagnetic power(W)')\n", "(62122.66666666667, 'mechanical power(W) fed')\n", "(370.7673554268794, 'primemover torque(Nm)')\n" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.9 Page No 163" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "# To determine peak value of fundamental mmf\n", " \n", "f=50.0 \n", "n_s=300.0 \n", "p=120*f/n_s \n", "P=400*1000.0 #power\n", "V=3300.0 \n", "\n", "#Calculations\n", "I_L=P/(math.sqrt(3)*V) \n", "I_P=I_L \n", "I_m=math.sqrt(2)*I_P #max value of phase current\n", "S=180.0 \n", "g=180*p/S \n", "ph=3 \n", "m=S/(p*ph) #slots/pole/phase\n", "K_b=math.sin(math.radians(m*g/2.0))/(m*math.sin(math.radians(g/2))) #breadth factor\n", "c=8 #conductors/1 coil side\n", "N_ph=S*c/(ph*2) #turns/phase\n", "F_m=(4/math.pi)*K_b*(N_ph/p)*I_m \n", "F_peak=(3.0/2)*F_m \n", "\n", "#Results\n", "print(F_peak,'peak mmf(AT/pole)') \n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(2177.0157210889715, 'peak mmf(AT/pole)')\n" ] } ], "prompt_number": 7 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.10, Page No 164" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "# (a)to calculate field current and flux/pole(b)to calculate open ckt ph and line voltages\n", "# (c)to caculate field current\n", "\n", "B_peak=1.65 \n", "g=.008 \n", "u_o=4*math.pi*10**-7 \n", "P=4 \n", "K_b=.957 \n", "N_field=364.0/2 \n", "\n", "#Calculations\n", "I_f=B_peak*math.pi*g*P/((4*u_o)*(K_b*N_field)) \n", "print(I_f,'field current(A)') \n", "l=1.02 #rotor length\n", "r=.41/2 #rotor radius\n", "phi=(4/P)*B_peak*l*r \n", "print(phi,'flux/pole(Wb)') \n", "N_ph=3*11*P/2 \n", "ga=60/3 #slot angle\n", "m=3 \n", "f=50 \n", "K_b=math.sin(math.radians(m*g/2.0))/(m*math.sin(math.radians(g/2))) #breadth factor\n", "E_ph=math.sqrt(2)*math.pi*K_b*f*N_ph*phi \n", "print(E_ph,'E_ph(V)') \n", "E_line=math.sqrt(3)*E_ph\n", "\n", "#Results\n", "print(E_line,'E_line(V)') \n", "I_fnew=.75*I_f \n", "print(I_fnew,'I_f(new)(A)') " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(189.46570670708599, 'field current(A)')\n", "(0.34501499999999996, 'flux/pole(Wb)')\n", "(5058.442114926427, 'E_ph(V)')\n", "(8761.478750198738, 'E_line(V)')\n", "(142.0992800303145, 'I_f(new)(A)')\n" ] } ], "prompt_number": 8 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.11 Page No 165" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "# to find fundamental mmf wave,speed and its peak value\n", "\n", "p=4.0\n", "S=60.0 \n", "g=180*p/S \n", "ph=3 \n", "m=S/(p*ph) #slots/pole/phase\n", "\n", "#Calculations\n", "K_b=math.sin(math.radians(m*g/2.0))/(m*math.sin(math.radians(g/2))) #breadth factor\n", "I_L=48 \n", "I_P=I_L/math.sqrt(3) \n", "I_Pmax=I_P*math.sqrt(2) \n", "c=24 #conductors\n", "N_ph=S*c/(ph*2) #turns/phase\n", "F_m=(4/math.pi)*K_b*(N_ph/p)*I_Pmax \n", "print(F_m,'F_m(AT/pole)') \n", "F_peak=(3/2)*F_m \n", "\n", "#Results\n", "print(F_peak,'F_peak(AT/pole)') \n", "n=120*f/P \n", "print(n,'speed(rpm)') \n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(2864.325776100667, 'F_m(AT/pole)')\n", "(2864.325776100667, 'F_peak(AT/pole)')\n", "(1500, 'speed(rpm)')\n" ] } ], "prompt_number": 9 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.12 Page No 165" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "# to calculate resultant air gap flux/pole\n", "\n", "F1=400.0 \n", "F2=850.0 \n", "a=123.6 \n", "\n", "#Calculations\n", "Fr=math.sqrt(F1**2+F2**2+2*F1*F2*math.cos(math.radians(a))) \n", "P=1.408*10**-4 #permeance/pole\n", "phi_r=P*Fr \n", "\n", "#Results\n", "print(phi_r,'air gap flux/pole(Wb)') " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(0.10017539016595711, 'air gap flux/pole(Wb)')\n" ] } ], "prompt_number": 10 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.13 Page No 172" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "#To calculate resultant AT/pole and peak air gap flux density, rotor AT/pole, stator AT and its angle with the resultant AT, stator currrent\n", "\n", "ph=3.0 \n", "S=36.0 \n", "c=8.0*2 \n", "p=4.0 \n", "f=50.0 \n", "N_ph=S*c/(ph*2) #turns/phase\n", "ga=180.0*p/S \n", "m=S/(p*ph) #slots/pole/phase\n", "\n", "#Calculations\n", "K_b=math.sin(math.radians(m*g/2.0))/(m*math.sin(math.radians(g/2))) #breadth factor\n", "V_L=400 \n", "V_ph=V_L/math.sqrt(3) \n", "phi_r=V_ph/(4.44*K_b*f*N_ph) \n", "print(phi_r,'phi_r(Wb/pole)') \n", "D=.16 \n", "l=0.12 \n", "PA=math.pi*l*D/4 #pole area\n", "B_rav=phi_r/PA \n", "B_rpeak=(math.pi/2)*B_rav \n", "g=2*10**-3 \n", "u_o=4*math.pi*10**-7 \n", "F_r=g*B_rpeak/u_o \n", "print(F_r,'F_r(AT/pole)') \n", "T=60 #torque(Nm)\n", "d=26 \n", "F2=T/((math.pi/2)*(p/2)**2*phi_r*math.sin(math.radians(d))) \n", "print(F2,'F2(AT/pole)') \n", "F1=math.sqrt(F2**2+F_r**2-2*F2*F_r*math.sin(math.radians(d))) \n", "print(F1,'F1(AT/pole)') \n", "w=math.degrees(math.acos((F1**2+F_r**2-F2**2)/(2*F1*F_r)))\n", "print(w,'angle(deg)') \n", "K_w=K_b \n", "I_a=F1/((3/2)*(4*math.sqrt(2)/math.pi)*K_w*(N_ph/p))\n", "\n", "#Results\n", "print(I_a,'I_a(A)') " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(0.01099635147629408, 'phi_r(Wb/pole)')\n", "(1823.0455139875667, 'F_r(AT/pole)')\n", "(1980.9832697544216, 'F2(AT/pole)')\n", "(2020.2729202496512, 'F1(AT/pole)')\n", "(61.80134857667341, 'angle(deg)')\n", "(47.44026875335716, 'I_a(A)')\n" ] } ], "prompt_number": 11 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.14, Page No 176" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "#to determine in F2,peak rotor AT, max torque, ele i/p at max torque(motoring mode),open ckt voltage(generating mode)\n", "\n", "print('motoring mode') \n", "K_w=.976 \n", "N_pole=746 \n", "p=4 \n", "I_f=20 \n", "\n", "#Calculations\n", "F2=(4/math.pi)*K_w*(N_pole/p)*I_f \n", "print(F2,'F2(AT)') \n", "B_r=1.6 \n", "D=.29 \n", "l=.35 \n", "T_max=(p/2)*(math.pi*D*l/2)*F2*B_r \n", "print(T_max,'T_max') \n", "f=50 \n", "w_m=4*math.pi*f/p \n", "P_in=T_max*w_m \n", "print(P_in,'P_in(W)') \n", "\n", "print('generating mode') \n", "m=S/(3*p) \n", "ga=180*p/S \n", "K_b=math.sin(math.radians(30))/(3*math.sin(math.radians(15.0/2))) \n", "K_w=K_b \n", "u_o=4*math.pi*10**-7 \n", "phi_r=((2*D*l/p)*(u_o/g))*F2 \n", "N_ph=20*p*4/2 \n", "E_ph=4.44*K_b*f*N_ph*phi_r \n", "E_l=math.sqrt(3)*E_ph \n", "\n", "#Results\n", "print(E_l,'E_l(V)') " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "motoring mode\n", "(4622.77627986085, 'F2(AT)')\n", "(2358.515712, 'T_max')\n", "(370474.781709765, 'P_in(W)')\n", "generating mode\n", "(11579.863937164595, 'E_l(V)')\n" ] } ], "prompt_number": 12 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.15, Page No 186" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "# to find motor speed\n", "\n", "n=1500.0 #speed of sync generator\n", "p=4 \n", "f=n*p/120 \n", "\n", "#Calculations\n", "p_im=6.0 \n", "n_s=120*f/p_im \n", "s=0.05 #slip\n", "n_im=(1-s)*n_s \n", "\n", "#Results\n", "print(n_im,'speed of induction motor(rpm)') " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(950.0, 'speed of induction motor(rpm)')\n" ] } ], "prompt_number": 13 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.16, Page No 187" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "#to find voltage available b/w slip rings and its freq\n", "\n", "print('(a)') \n", "f=50.0 \n", "p=6.0 \n", "n_s=120*f/p \n", "n=-1000 \n", "\n", "#Calculations\n", "s=(n_s-n)/n_s \n", "f_s=f*s \n", "print(f_s,'slip freq(Hz)') \n", "v2=100 \n", "V2=s*v2 \n", "print(V2,'slip ring voltage(V)') \n", "\n", "print('(b)') \n", "n=1500 \n", "s=(n_s-n)/n_s \n", "f_s=abs(f*s) \n", "print(f_s,'slip freq(Hz)') \n", "v2=100 \n", "V2=s*v2 \n", "\n", "#Results\n", "print(V2,'slip ring voltage(V)') " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(a)\n", "(100.0, 'slip freq(Hz)')\n", "(200.0, 'slip ring voltage(V)')\n", "(b)\n", "(25.0, 'slip freq(Hz)')\n", "(-50.0, 'slip ring voltage(V)')\n" ] } ], "prompt_number": 14 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.18, Page No 197" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "#to find no of poles, slip and freq of rotor currents at full load, motor speed at twice of full load\n", "\n", "n_s=600.0\n", "f=50.0 \n", "P=120*f/n_s \n", "print(p,'no of poles') \n", "n=576.0 \n", "\n", "#Calculations\n", "s=(n_s-n)/n_s \n", "print(s,'slip') \n", "f2=s*f \n", "n_r=s*n_s \n", "print(n_r,'rotor speed wrt rotating field(rpm)') \n", "ss=f2*s \n", "n=(1-ss)*n_s \n", "print(n,'motor speed(rpm)') \n", "nn=528 \n", "s_old=s \n", "s_new=(n_s-nn)/n_s \n", "fac=s_new/s_old \n", "\n", "#Results\n", "print(fac,'factor is') " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(6.0, 'no of poles')\n", "(0.04, 'slip')\n", "(24.0, 'rotor speed wrt rotating field(rpm)')\n", "(552.0, 'motor speed(rpm)')\n", "(3.0, 'factor is')\n" ] } ], "prompt_number": 15 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.19, Page No 198" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "# to calculate amplitude of travelling wave mmf,peak value of air flux density, velocity of wave, current freq at some desired velocity\n", " \n", "K_w=.925 \n", "N_ph=48 \n", "I=750.0/math.sqrt(2) \n", "wndnglgth=2 \n", "wavelgth=wndnglgth/0.5 \n", "p=2*wavelgth \n", "\n", "#Calculations\n", "F_peak=(3.0/2)*(4*math.sqrt(2)/math.pi)*K_w*(N_ph/p)*I \n", "print(F_peak,'F_peak(A/m)') \n", "g=.01 \n", "u_o=4*math.pi*10**-7 \n", "B_peak=u_o*F_peak/g \n", "print(B_peak,'B_peak(T)') \n", "f=25 \n", "B=.5 \n", "v=f*B \n", "print(v,'velocity(m/s)') \n", "vv=72*10**3/3600 #given velocity\n", "f=vv/0.5 \n", "\n", "#Results\n", "print(f,'freq(Hz)') " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(7949.789407440174, 'F_peak(A/m)')\n", "(0.9990000000000002, 'B_peak(T)')\n", "(12.5, 'velocity(m/s)')\n", "(40.0, 'freq(Hz)')\n" ] } ], "prompt_number": 16 } ], "metadata": {} } ] }