{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 10 : Fractional Kilowatt Motors" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 10.1, Page No 148" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "# to compute the ratio of E_mf/E_mb,V_f/V_b,T_f/T_b,gross total torque,T_f/total torque, T_b/total torque\n", "\n", " \n", "R_lm=3.0 \n", "X_lm=5.0 \n", "R_2=1.5 \n", "X_2=2.0 \n", "s=1-.97 #slip\n", "\n", "#Calculations\n", "a=complex(R_2/s,X_2) \n", "b=complex(R_2/(2-s),X_2) \n", "c=abs(a)/abs(b) \n", "print(c,'E_mf/E_mb') \n", "a=(1.0/2)*complex((R_lm+R_2/s),(X_lm+X_2)) \n", "b=(1.0/2)*complex((R_lm+R_2/(2-s)),(X_lm+X_2)) \n", "c=abs(a)/abs(b) \n", "print(c,'V_f/V_b') \n", "d=(2.0-s)/s \n", "print(d,'T_f/T_b') \n", "Z_tot=a+b \n", "V=220.0 \n", "I_m=V/abs(Z_tot) \n", "P=6.0 \n", "f=50.0 \n", "n_s=120.0*f/P \n", "w_s=2*math.pi*n_s/60 \n", "T_f=(I_m**2*R_2/(2*w_s))*(1/s) \n", "T_b=(I_m**2*R_2/(2*w_s))*(1/(2-s)) \n", "T_tot=T_f-T_b \n", "print(T_tot,'gross total torque(Nm)') \n", "a=T_f/T_tot \n", "b=T_b/T_tot \n", "\n", "#Results\n", "print(a,'T_f/T_total') \n", "print(b,'T_b/T_total') \n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(23.38275544101299, 'E_mf/E_mb')\n", "(6.727447444111447, 'V_f/V_b')\n", "(65.66666666666661, 'T_f/T_b')\n", "(13.316745850891841, 'gross total torque(Nm)')\n", "(1.0154639175257731, 'T_f/T_total')\n", "(0.015463917525773207, 'T_b/T_total')\n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 10.2, Page No 149" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "# to calculate parameters of the ckt model, line current, power factor, shaft torque and efficiency\n", "\n", " \n", "V_0=215.0 \n", "I_0=3.9 \n", "P_0=185.0 \n", "R_1=1.6 \n", "V_sc=85 \n", "I_sc=9.8 \n", "P_sc=390.0 \n", "X=(V_0/I_0)*2.0 #magnetisation reactance\n", "phi_sc=math.degrees(math.acos(P_sc/(V_sc*I_sc)))\n", "I_e=V_sc/complex(0,X) \n", "I_SC=I_sc*complex(math.cos(math.radians(phi_sc*(-1))),math.sin(math.radians(phi_sc*(-1)))) \n", "I_m=I_SC-I_e \n", "Z=V_sc/I_m \n", "R_2=(Z.real)-R_1 #real(Z)=R=R1+R2\n", "print(R_2,'R_2(ohm)') \n", "print((Z.imag),'X_1+X_2(ohm)') \n", "\n", "#Calculations\n", "n=1500.0 \n", "nn=1440 \n", "s=(n-nn)/n \n", "a=1.55/s \n", "b=1.55/(2-s) \n", "Z_ftot=(complex(0,X/2))*(complex(a+.8,(Z.imag)/2))/((complex(0,X/2))+(complex(a+.8,(Z.imag)/2))) \n", "Z_btot=(complex(0,X/2))*(complex(b+.8,(Z.imag)/2))/((complex(0,X/2))+(complex(b+.8,(Z.imag)/2))) \n", "Z_tot=Z_ftot+Z_btot \n", "I_m=V_0/Z_tot \n", "I_L=abs(I_m) \n", "print(I_L,'line current(A)') \n", "pf=math.cos(math.radians(math.degrees(math.atan((I_m.real)/(I_m.imag)))))\n", "print(pf,'pf') \n", "P_in=V_0*I_L*pf \n", "I_mf=I_m*complex(0,X/2)/complex(39.55,59.12) \n", "I_mb=I_m*complex(0,X/2)/complex(1.59,59.12) \n", "T=(1/157.1)*(abs(I_mf)**2*38.75-abs(I_mb)**2*.79) \n", "P_m=157.1*(1-s)*T \n", "P_L=185 \n", "P_out=P_m-P_L \n", "eff=P_out/P_in \n", "\n", "#Results\n", "print(eff*100,'efficiency(%)') \n", "T_shaft=P_out/157.1 \n", "print(T_shaft,'shaft torque(Nm)') \n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(3.0828571185946845, 'R_2(ohm)')\n", "(8.051321578491317, 'X_1+X_2(ohm)')\n", "(6.261296470855541, 'line current(A)')\n", "(0.6818110490832134, 'pf')\n", "(72.4748020932455, 'efficiency(%)')\n", "(4.234260916702234, 'shaft torque(Nm)')\n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 10.3, Page No 149" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "#to compute ampitudes of forward and backward stator mmf waves,magnitude of auxillary currrent and its ph angle diff\n", "\n", " \n", "N_m=80.0\n", "N_a=100.0 \n", "I_m=15*complex(math.cos(math.radians(0)),math.sin(math.radians(0))) \n", "I_aa=7.5*complex(math.cos(math.radians(45)),math.sin(math.radians(45))) \n", "I_a=7.5*complex(math.cos(math.radians(60)),math.sin(math.radians(60))) \n", "F_m=N_m*I_m \n", "F_a=N_a*I_a \n", "F_aa=N_a*I_aa #mmf at 45 angle\n", "\n", "#Calculations\n", "F_f=(1.0/2)*(F_m+1j*F_aa) \n", "a=abs(F_f) \n", "print(a,'forward field(AT)') \n", "F_b=(1.0/2)*(F_m-1j*(F_aa)) \n", "b=abs(F_b) \n", "print(b,'backward field(AT)') \n", "#1200+100*I_a*complex(sind(a),cosd(a))=0\n", "#equating real and imaginery parts\n", "#100*I_a*cosd(a)=0 \n", "a=90 \n", "print(a,'phase angle diff') \n", "I_a=-1200.0/(100*math.sin(math.radians(a))) \n", "\n", "#Results\n", "print(I_a,'auxillery current(A)') \n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(427.1146783547173, 'forward field(AT)')\n", "(904.8884193832665, 'backward field(AT)')\n", "(90, 'phase angle diff')\n", "(-12.0, 'auxillery current(A)')\n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 10.4 Page No 150" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "#to determine value of capacitor\n", "\n", " \n", "f=50.0 \n", "w=2*math.pi*f \n", "Z_lm=complex(3,2.7) \n", "Z_la=complex(7,3) \n", "\n", "#Calculations\n", "I_m=(-1)*math.degrees(math.atan((Z_lm.imag)/(Z_la.imag))) \n", "a=90.0 \n", "I_a=a+I_m \n", "c=1/(w*((Z_lm.real)-(Z_la.real)*math.cos(math.radians((-1)*I_a)))) \n", "\n", "#Results\n", "print(c,'value of capacitor(F)') " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(-0.0018916018169502632, 'value of capacitor(F)')\n" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 10.6, Page No 151" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "#to calculate starting torque and atarting current,motor performance\n", "\n", " \n", "V_a=110*complex(math.cos(math.radians(90)),math.sin(math.radians(90))) \n", "V_m=220*complex(math.cos(math.radians(0)),math.sin(math.radians(0))) \n", "R_1=3 \n", "R_2=2.6 \n", "X_1=2.7 \n", "X_2=2.7 \n", "X=110 \n", "V_f=(1.0/2)*(V_m-1j*V_a)\n", "V_b=(1.0/2)*(V_m+1j*V_a) \n", "\n", "#Calculations\n", "Z_f=(complex(0,X)*complex(R_2,X_2))/(complex(0,X)+complex(R_2,X_2)) \n", "Z_b=Z_f \n", "Z_ftot=complex(R_1,X_1)+Z_f \n", "Z_btot=complex(R_1,X_1)+Z_b \n", "I_f=V_f/Z_ftot \n", "I_b=V_b/Z_btot \n", "T_s=(2/157)*(Z_f.real)*(abs(I_f)**2-abs(I_b)**2) \n", "print(T_s,'starting torque(Nm)') \n", "I_m=I_f+I_b \n", "I_a=1j*(I_f-I_b) \n", "print(abs(I_a),'starting current(A)') \n", "s=0.04 \n", "\n", "Z_f=(complex(0,X)*complex(R_2/s,X_2))/(complex(0,X)+complex(R_2/s,X_2)) \n", "Z_b=(complex(0,X)*complex(R_2/(2-s),X_2))/(complex(0,X)+complex(R_2/(2-s),X_2)) \n", "Z_ftot=complex(R_1,X_1)+Z_f \n", "Z_btot=complex(R_1,X_1)+Z_b \n", "I_f=V_f/Z_ftot \n", "I_b=V_b/Z_btot \n", "w_s=157.1 \n", "T_s=(2/157.1)*(abs(I_f)**2*(Z_f.real)-abs(I_b)**2*(Z_b.real)) \n", "print(T_s,'starting torque(Nm)') \n", "I_m=I_f+I_b \n", "m=math.degrees(math.atan((I_m.imag)/(I_m.real)))\n", "I_a=1j*(I_f-I_b) \n", "a=math.degrees(math.atan((I_a.imag)/(I_a.real)))\n", "P_m=w_s*(1.0-s)*T_s \n", "P_L=200.0 \n", "P_out=P_m-P_L \n", "P_min=V*abs(I_m)*math.cos(math.radians(m)) \n", "P_ain=V*abs(I_a)*math.cos(math.radians(a))\n", "P_in=P_min+P_ain \n", "n=P_out/P_in \n", "print(n,'efficiency') \n", "\n", "r=Z_ftot/Z_btot #r=V_mf/V_bf\n", "#V_mf+V_bf=220\n", "V_mf=220/(1+r) \n", "V_mb=220-V_mf \n", "V_a=1j*(V_mf-V_mb) \n", "\n", "#Results\n", "print(abs(V_a),'V_a(V)')" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(0.0, 'starting torque(Nm)')\n", "(14.313452498677325, 'starting current(A)')\n", "(3.5887587638431966, 'starting torque(Nm)')\n", "(0.12798421082025385, 'efficiency')\n", "(176.4417668704772, 'V_a(V)')\n" ] } ], "prompt_number": 5 } ], "metadata": {} } ] }