{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 08 : Synchronous Machines" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.2, Page No 148" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "#to determine voltage regulation by mmf method\n", "\n", " \n", "pf=0.85 \n", "P=150*10**6 \n", "V=13*1000.0\n", "\n", "#Calculations\n", "Iarated=P/(math.sqrt(3)*pf*V) \n", "If=750 \n", "Ifocc=810 \n", "B=math.degrees(math.acos(pf))\n", "Ff=math.sqrt((Ifocc+If*math.sin(math.radians(B)))**2+(If*math.cos(math.radians(B)))**2) \n", "Ef=16.3*1000 \n", "vr=Ef/V-1\n", "\n", "#Results\n", "print(vr*100,'voltage regulation(%)') " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(25.384615384615383, 'voltage regulation(%)')\n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.6, Page No 149" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "#to calculate the excitation emf\n", "\n", " \n", "Vt=3300.0 \n", "Xs=18/3.0 \n", "pf=.707 \n", "P=800*1000 \n", "\n", "#Calculations\n", "Ia=P/(math.sqrt(3)*Vt*pf) \n", "a=Ia*Xs/math.sqrt(2) \n", "b=Vt/math.sqrt(3.0) \n", "Ef=math.sqrt((a+b)**2+a**2)*math.sqrt(3.0)\n", "\n", "#Results\n", "print(Ef,'excitation emf(V)(line)') " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(4972.3367904266, 'excitation emf(V)(line)')\n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.7, Page No 149" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "\n", "#to compute the max power and torque,terminal voltage\n", "\n", " \n", "V=3300.0 \n", "Vt=V/math.sqrt(3) \n", "P=1000*10**3 \n", "pf=1 \n", "Ia=P/(V*math.sqrt(3)*pf) \n", "Xsm=3.24 \n", "j=math.sqrt(1.0) \n", "Efm=Vt-j*Ia*Xsm \n", "Efg=abs(Efm) \n", "P_emax=3*Vt*Efg/Xsm \n", "print(P_emax,'max power(W)') \n", "p=24 \n", "f=50 \n", "\n", "#Calculations\n", "w_sm=(120*f*2*math.pi)/(p*60) \n", "Tmax=P_emax/w_sm \n", "print(Tmax,'torque(Nm)') \n", "\n", "Xsg=4.55 \n", "Efm=Vt-j*Ia*Xsg \n", "Efmm=abs(Efm) \n", "X=Xsm+Xsg \n", "P_emax=3*Efg*Efmm/X \n", "print(P_emax,'max power(W)') \n", "Tmax=P_emax/w_sm \n", "print(Tmax,'torque(Nm)') \n", "\n", "d=90 \n", "Efm=Efg*complex(math.cos(math.radians(0)),math.sin(math.radians(0))) \n", "Efg=Efmm*complex(math.cos(math.radians(0)),math.sin(math.radians(0)))\n", "Ia=(Efg-Efm)/(j*X) \n", "v=j*Ia*Xsm \n", "Vt=Efm+j*Ia*Xsm \n", "\n", "#Results\n", "print(abs(Vt)*math.sqrt(3),'line voltage(V)') \n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(2361111.1111111115, 'max power(W)')\n", "(90187.80108540738, 'torque(Nm)')\n", "(571722.5941289428, 'max power(W)')\n", "(21838.194463906242, 'torque(Nm)')\n", "(2153.0750379274127, 'line voltage(V)')\n" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.8 Page No 150" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "#max power supplied, power angle d, corresponding field current\n", "\n", " \n", "j=math.sqrt(1) \n", "r=100*10**6.0 #va\n", "V=11000.0 \n", "P=100*10**6 \n", "Ef=1 #pu\n", "Vth=1 #pu\n", "Xs=1.3 #pu\n", "Xth=.24 #pu\n", "\n", "#Calculations\n", "P_emax=Ef*Vth/(Xs+Xth) \n", "print(P_emax,'max power delivered(pu)') \n", "\n", "Pe=1 \n", "Vt=1 \n", "d=math.degrees(math.asin(Pe*Xth/(Vt*Vth)))\n", "print(d,'power angle') \n", "Vt=math.exp(j*d) \n", "Ia=(Vt-Vth)/(j*Xth) \n", "Ef=Vth+j*(Xs+Xth)*Ia \n", "Voc=11000 \n", "If=256 \n", "Ff=19150 \n", "Iff=If*Ff/Voc\n", "\n", "#Results\n", "print(Iff,'If(A)') \n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(0.6493506493506493, 'max power delivered(pu)')\n", "(13.88654036262899, 'power angle')\n", "(445, 'If(A)')\n" ] } ], "prompt_number": 7 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.9, Page No 152" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "#to calculate the generator current and its pf\n", "\n", " \n", "j=math.sqrt(1) \n", "X=.24 \n", "r=400.0 #rating in MVA\n", "rr=600.0 #rating in MVA\n", "Pe=r/rr \n", "Vt=1 \n", "Vth=1 \n", "dl=math.degrees(math.asin(Pe*X/(Vt*Vth)))\n", "Ia=2*math.sin(math.radians(dl/2))/X \n", "V=24000 \n", "\n", "#Calculations\n", "IaB=(rr/3.0)*10**6/(V/math.sqrt(3.0)) \n", "Iaa=Ia*IaB \n", "print(Iaa,'generating current(A)') \n", "phi=dl/2.0 \n", "pf= math.cos(math.radians(phi))\n", "print(pf,'power factor') \n", "\n", "Pe=1 \n", "dl1=math.degrees(math.asin(Pe*X/(Vt*Vth)))\n", "Ia=2*math.sin(math.radians(dl1/2.0))/X \n", "Iaa=Ia*IaB \n", "print(Iaa,'generating current(A)') \n", "phi=dl1/2.0 \n", "pf= math.cos(math.radians(phi))\n", "print(pf,'power factor') \n", "Ef=Vt+j*Ia*(complex(math.cos(math.radians(-phi)),math.sin(math.radians(-phi))))*X \n", "Eff=abs(Ef)*V \n", "dl2=math.degrees(math.atan(Ef.imag/Ef.real))\n", "\n", "Xth=.24 \n", "Pe=abs(Ef)*Vth*math.sin(math.radians(dl1+dl2))/(X+Xth) \n", "\n", "#Results\n", "print(Pe,'Pe(pu)') " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(9653.646665937797, 'generating current(A)')\n", "(0.9967740502090344, 'power factor')\n", "(14540.391150848647, 'generating current(A)')\n", "(0.9926663306370695, 'power factor')\n", "(0.560889816748067, 'Pe(pu)')\n" ] } ], "prompt_number": 10 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.10 Page No 163" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "#to calculate armature resistance, sync reactance, full load stray load loss, Rac/Rdc,various categories of losses at full load,full load eff\n", "\n", " \n", "r=60*10**3.0 \n", "Psc=3950.0 \n", "Isc=108.0 \n", "\n", "#Calculations\n", "Raeff=Psc/(3*Isc**2) \n", "print(Raeff,'effective armature resistance(ohm)') \n", "V=400.0 \n", "Ifoc=2.85 \n", "Ifsc=1.21 \n", "I_SC=Isc*Ifoc/Ifsc \n", "Zs=(V/math.sqrt(3))/I_SC \n", "Xs=math.sqrt(Zs**2-Raeff**2) \n", "print(Xs,'sync reactance(ohm)') \n", "\n", "t1=25 \n", "t2=75 \n", "Rdc=0.075 \n", "Radc=Rdc*((273+t2)/(273+t1)) \n", "Iarated=r/(math.sqrt(3.0)*V) \n", "Pscc=Psc*(Iarated/Isc)**2 \n", "P=3*Iarated**2*Radc \n", "print(P,'armature loss(W)') \n", "loss=Pscc-P \n", "print(loss,'loss(W)') \n", "\n", "a=Raeff/Radc \n", "print(a,'Rac/Rdc') \n", "\n", "Pwf=900.0 \n", "print(Pwf,'windage and friction loss(W)') \n", "tloss=2440 \n", "closs=tloss-Pwf \n", "print(closs,'core loss(W)') \n", "If=3.1 \n", "Rf=110 \n", "Pcu=If**2*Rf \n", "print(Pcu,'field cu loss(W)') \n", "print(loss,'stray load loss(W)') \n", "b=loss+Pcu+closs+Pwf+P \n", "print(b,'total loss(W)') \n", "\n", "pf=0.8 \n", "op=r*pf \n", "ip=op+b \n", "eff=op/ip \n", "\n", "#Results\n", "print(eff,'efficiency') " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(0.11288294467306813, 'effective armature resistance(ohm)')\n", "(0.9008089329407498, 'sync reactance(ohm)')\n", "(1687.5, 'armature loss(W)')\n", "(852.3662551440325, 'loss(W)')\n", "(1.5051059289742417, 'Rac/Rdc')\n", "(900.0, 'windage and friction loss(W)')\n", "(1540.0, 'core loss(W)')\n", "(1057.1000000000001, 'field cu loss(W)')\n", "(852.3662551440325, 'stray load loss(W)')\n", "(6036.966255144032, 'total loss(W)')\n", "(0.8882808071304457, 'efficiency')\n" ] } ], "prompt_number": 11 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.11, Page No 164" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "#to calculate net power op,eff,line current and pf\n", "\n", " \n", "j=math.sqrt(1) \n", "Zs=(1.0/3)*(.3+j*6) \n", "phi=math.degrees(math.atan(Zs.imag/Zs.real))\n", "Vt=400.0/math.sqrt(3.0) \n", "Ef=600.0/math.sqrt(3.0) \n", "a=math.sqrt(Vt**2+Ef**2-2*Vt*Ef*math.cos(math.radians(phi))) \n", "Ia=a/abs(Zs) \n", "\n", "#Calculations\n", "print(Ia,'line current(A)') \n", "B=math.degrees(math.acos((Vt**2+a**2-Ef**2)/(2*Vt*a)))\n", "phi=90-(90-math.degrees(math.atan(Zs.imag/Zs.real)))-B \n", "print(math.cos(math.radians(phi)),'pf') \n", "Pein=Vt*Ia*math.cos(math.radians(phi)) \n", "Ra=.1 \n", "b=Ia**2*Ra \n", "loss=2400 \n", "Pmout=Pein-loss/3.0-b \n", "\n", "#Results\n", "print(Pmout,'net power op(W)') \n", "eff=Pmout/Pein \n", "print(eff*100,'efficiency(%)') " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(54.98573992282153, 'line current(A)')\n", "(-0.9999999999999998, 'pf')\n", "(-13800.755857898721, 'net power op(W)')\n", "(108.68095238095239, 'efficiency(%)')\n" ] } ], "prompt_number": 12 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.12 Page No 165" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "#to find pf\n", "\n", " \n", "j=math.sqrt(1) \n", "Zs=.8+j*5 \n", "Vt=3300.0/math.sqrt(3) \n", "Pein=800*10**3.0/3 #per ph\n", "pf=.8 \n", "Qe=-Pein*math.tan(math.radians(math.degrees(math.acos(pf))))\n", "#a=Ef*math.cos(math.radians(dl-a))\n", "#b=Ef=math.cos(math.radians(dl-a))\n", "\n", "#Calculations\n", "a=((abs(Zs)/Vt)*(Pein-Zs.real*(Vt/abs(Zs))**2)) \n", "b=((abs(Zs)/Vt)*(-Qe+(Zs.imag)*(Vt/abs(Zs))**2)) \n", "\n", "Ef=math.sqrt(a**2+b**2) \n", "\n", "Pein=(1200.0/3)*1000 \n", "a=math.degrees(math.asin((abs(Zs)/(Vt*Ef))*(Pein-pf*(Vt/abs(Zs))**2)))\n", "Qe=(Zs.imag)*(Vt/abs(Zs))**2-Ef*Vt*math.cos(math.radians(a))/abs(Zs) \n", "pf=math.cos(math.radians(math.degrees(math.atan(Qe/Pein))))\n", "\n", "#Results\n", "print(pf,'pf') d" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(0.8329179992811746, 'pf')\n" ] } ], "prompt_number": 15 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.13 Page No 165" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#to determine excitation emf, torque angle,stator current, pf, max power, kVAR delivered\n", "\n", " \n", "j=math.sqrt(1) \n", "P=10000.0 \n", "V=400.0 \n", "Ia=P/(math.sqrt(3)*V) \n", "pf=.8 \n", "phi=math.degrees(math.acos(pf))\n", "Iaa=Ia*complex(math.cos(math.radians(-phi)),math.sin(math.radians(-phi))) \n", "Vt=V/math.sqrt(3.0) \n", "X=16 \n", "Ef=Vt+j*X*Iaa \n", "print(abs(Ef),'excitation emf(V)') \n", "dl=math.degrees(math.atan(Ef.imag/Ef.real))\n", "print(dl,'torque angle') \n", "\n", "#Calculations\n", "Pe=P*pf \n", "Eff=abs(Ef)*1.2 \n", "dl=(Pe/3)*X/(Eff*Vt) \n", "ta=math.degrees(math.asin(dl))\n", "print(ta,'torque angle') \n", "Ia=(Eff*complex(math.cos(math.radians(ta)),math.sin(math.radians(ta)))-Vt)/(j*X) \n", "print(abs(Ia),'stator current(A)') \n", "print(math.cos(math.radians(-math.degrees(math.atan(Ia.imag/Ia.real)))),'pf') \n", "\n", "Ef=413 \n", "Pemax=Ef*Vt/X \n", "Ia=(Ef*complex(math.cos(math.radians(90)),math.sin(math.radians(90)))-Vt)/(j*X) \n", "print(abs(Ia),'stator current(A)') \n", "print(math.cos(math.radians(-math.degrees(math.atan(Ia.imag/Ia.real)))),'pf') \n", "\n", "Qe=((Ia.imag)/(Ia.real))*Pe \n", "\n", "#Results\n", "print(Qe,'kVar delivered') " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(438.17804600413285, 'excitation emf(V)')\n", "(-18.434948822922003, 'torque angle')\n", "(20.570777448577868, 'torque angle')\n", "(20.003478706674613, 'stator current(A)')\n", "(0.8165675681224028, 'pf')\n", "(29.57394950937959, 'stator current(A)')\n", "(0.48805644728523245, 'pf')\n", "(-14306.739670518926, 'kVar delivered')\n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.14 Page No 172" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "#to calculate armature current, pf ,power angle, power , shaft torques,kVar\n", "\n", "j=math.sqrt(1) \n", "P=8000.0 \n", "Prot=500.0 \n", "Pmg=P+Prot \n", "Pein=Pmg \n", "Ef=750.0/math.sqrt(3) \n", "Vt=231 \n", "Xs=16.0 \n", "dl=math.degrees(math.asin(Xs*(Pein/3)/(Ef*Vt)))\n", "Eff=Ef*complex(math.cos(math.radians(-dl)),math.sin(math.radians(-dl))) \n", "Ia=(Vt-Eff)/(j*Xs) \n", "\n", "#Calculations\n", "print(abs(Ia),'armature current(A)') \n", "print(math.cos(math.radians(-math.degrees(math.atan(Ia.imag/Ia.real)))),'pf') \n", "f=50 \n", "p=4 \n", "n_s=120*f/p \n", "w_s=2*math.pi*n_s/60 \n", "T=Pein/w_s \n", "print(T,'torque developed(Nm)') \n", "T_s=P/w_s \n", "print(T_s,'shaft torques(Nm)') \n", "\n", "Ef=600/math.sqrt(3) \n", "Ia=(Vt-Ef)/(j*Xs) \n", "rr=3*Vt*Ia/1000 \n", "print(rr,'kVar rating') \n", "c=(abs(Ia)/Vt)/(2*math.pi*f) \n", "print(-c,'capicator rating(F)') \n", "\n", "Ef=300/math.sqrt(3) \n", "Ia=(Vt-Ef)/(j*Xs) \n", "rr=3*Vt*Ia/1000 \n", "print(-rr,'kVar rating') \n", "L=(Vt/abs(rr))/(2*math.pi*f) \n", "print(L,'inductor rating(H)') \n", "\n", "Ia=j*2000/Vt \n", "Ef=Vt-j*Ia*Xs \n", "\n", "#Results\n", "print(abs(Ef)*math.sqrt(3),'excitation(V)') " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(15.629324184839682, 'armature current(A)')\n", "(0.6197800073964136, 'pf')\n", "(54.11268065124441, 'torque developed(Nm)')\n", "(50.929581789406505, 'shaft torques(Nm)')\n", "(-4.998702620565402, 'kVar rating')\n", "(-9.939446800839497e-05, 'capicator rating(F)')\n", "(-2.503242439717299, 'kVar rating')\n", "(0.2937373645549075, 'inductor rating(H)')\n", "(160.16596233973502, 'excitation(V)')\n" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.15, Page No 176" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "#find the excitation emf,mech power developed,pf\n", "\n", "j=math.sqrt(1) \n", "V=6600.0 \n", "Vt=V/math.sqrt(3) \n", "r=4*10.0**6 \n", "Ia=r/(math.sqrt(3)*V) \n", "Xs=4.8 \n", "#Vt**2+Ef**2-2*Vt*Efcosd(dl)=(Ia*Xs)**2\n", "#after solving\n", "#Ef**2-7.16*Ef+11.69=0 \n", "def quad(a,b,c):\n", " d=math.sqrt(b**2-4*a*c) \n", " x1=(-b+d)/(2*a) \n", " x2=(-b-d)/(2*a) \n", " return x1,x2\n", "\n", "Ef=[0,0]\n", "\n", "#Calculations\n", "Ef=quad(1,-7.16,11.69) \n", "dl=20.0\n", "print(Ef[0],'excitation(kV)') \n", "Pm=3*3.81*Ef[0]*math.sin(math.radians(dl))/Xs \n", "print(Pm,'power developed(MW)') \n", "pf1=Pm*10**6/(math.sqrt(3)*V*Ia) \n", "print(pf1,'pf1') \n", "\n", "print(Ef[1],'excitation(kV)') \n", "Pm=3*3.81*Ef[1]*math.sin(math.radians(dl))/Xs \n", "print(Pm,'power developed(MW)') \n", "pf2=Pm*10**6/(math.sqrt(3)*V*Ia) \n", "\n", "#Results\n", "print(pf2,'pf2') \n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(4.641319932913728, 'excitation(kV)')\n", "(3.780055563783382, 'power developed(MW)')\n", "(0.9450138909458456, 'pf1')\n", "(2.518680067086272, 'excitation(kV)')\n", "(2.0513023748834374, 'power developed(MW)')\n", "(0.5128255937208593, 'pf2')\n" ] } ], "prompt_number": 9 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.16, Page No 186" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "#to find power angle,field current\n", "j=math.sqrt(1.0) \n", "V=400 \n", "Vt=V/math.sqrt(3.0) \n", "pf=1.0 \n", "Ia=50.0 \n", "Xs=1.3 \n", "\n", "#Calculations\n", "Ef=Vt-j*Ia*Xs \n", "print(-math.degrees(math.atan(Ef.imag/Ef.real)),'power angle') \n", "\n", "Pm=Vt*Ia*pf \n", "pff=.8 \n", "Ia=Pm/(Vt*pff) \n", "ang=math.degrees(math.acos(pff))\n", "Eff=math.sqrt((Vt*math.cos(math.radians(ang)))**2+(Vt*math.cos(math.radians(ang))+Ia*Xs)**2) \n", "If=.9 \n", "Iff=If*Eff/abs(Ef)\n", "\n", "#Results\n", "print(Iff,'field current(A)') " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(-0.0, 'power angle')\n", "(1.7565442792743275, 'field current(A)')\n" ] } ], "prompt_number": 10 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.17, Page No 187" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "#to calculate motor eff,excitation emf and power angle, max power op,corresponding net op\n", "\n", " \n", "j=math.sqrt(1.0) \n", "Sop=40*1000.0 \n", "Vt=600.0 \n", "Ra=0.8 \n", "Xs=8 \n", "\n", "Pst=2000.0 \n", "Pmnet=30*1000.0 \n", "Pm_dev=Pst+Pmnet \n", "Ia=Sop/(math.sqrt(3)*Vt) \n", "Poh=3*Ia**2*Ra \n", "Pin=Pm_dev+Poh \n", "eff=(1-(Poh+Pst)/Pin)*100 \n", "print(eff,'motor eff(%)') \n", "\n", "#Calculations\n", "cos_phi=Pin/(math.sqrt(3.0)*Vt*Ia) \n", "phi=math.degrees(math.acos(cos_phi))\n", "Ia=Ia*(math.cos(math.radians(phi))+j*math.sin(math.radians(phi))) \n", "Vt=Vt/math.sqrt(3.0) \n", "Za=Ra+Xs*j \n", "Ef=Vt-Ia*Za \n", "Ef_line=Ef*math.sqrt(3.0) \n", "print(Ef_line,'excitation emf(V)') \n", "delta=math.degrees(math.atan((Ef.imag)/(Ef.real)))\n", "print(delta,'power angle(deg)') \n", "IaRa=abs(Ia)*Ra \n", "IaXs=abs(Ia)*Xs \n", "AD=Vt*math.cos(math.radians(phi))-IaRa\n", "CD=Vt*math.cos(math.radians(phi))+abs(Ia)*Xs \n", "Ef_mag=math.sqrt((abs(AD))**2+(abs(CD))**2) \n", "\n", "Pm_out_gross=-((abs(Ef_mag))**2*Ra/(abs(Za))**2)+(Vt*abs(Ef_mag)/abs(Za))\n", "\n", "#Results\n", "print(Pm_out_gross,'max power op(W)') \n", "power_angle=math.degrees(math.atan((Za.imag)/(Za.real))) \n", "print(power_angle,'power angle(deg)') " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(84.375, 'motor eff(%)')\n", "(-190.24688522544741, 'excitation emf(V)')" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n", "(-0.0, 'power angle(deg)')\n", "(24191.612053989564, 'max power op(W)')\n", "(0.0, 'power angle(deg)')\n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.18, Page No 197" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "#find the change in the poweer angle \n", "\n", "Pe=4000.0 \n", "V=400 \n", "pf=.8 \n", "\n", "#Calculations\n", "dl=math.degrees(math.acos(pf))\n", "Ia=Pe/(math.sqrt(3.0)*V*pf) \n", "Vt=V/math.sqrt(3.0) \n", "Xs=25 \n", "Ef=Vt+j*Ia*complex(math.cos(math.radians(-dl)),math.sin(math.radians(-dl)))*Xs \n", "a=math.degrees(math.atan((Ef.imag)/(Ef.real)))\n", "\n", "dl=math.degrees(math.asin((Pe/3)*Xs/(Vt*abs(Ef)))) \n", "ang=dl+a \n", "\n", "#Results\n", "print(ang,'change in power angle(deg)') " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(5.596898962201344, 'change in power angle(deg)')\n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.19, Page No 198" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "#to find no of poles,MVA rating, prime mover rating and op torque\n", " \n", "f=50.0 \n", "n_s=100.0 \n", "P=120*f/n_s \n", "print(P,'no of poles') \n", "r=110 #MVA rating\n", "pf=.8 \n", "\n", "#Calculations\n", "rr=r/pf \n", "print(rr,'MVA rating') \n", "eff=.971 \n", "rt=r/eff \n", "print(rt,'prime mover rating(MW)') \n", "T_PM=rt*1000*60/(2*math.pi*n_s) \n", "\n", "#Results\n", "print(T_PM,'op torque(Nm)') " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(60.0, 'no of poles')\n", "(137.5, 'MVA rating')\n", "(113.28527291452112, 'prime mover rating(MW)')\n", "(10817.946698316264, 'op torque(Nm)')\n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.20, Page No 198" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "# To calculate sec. line voltage, line current and output va\n", "\n", "print('(a)Y/D conn') \n", "V_LY=6600 \n", "V_PY=V_LY/math.sqrt(3) \n", "a=12 \n", "V_PD=V_PY/a \n", "V_LD=V_PD \n", "print(V_LD,'sec line voltage(V)') \n", "\n", "#Calculations\n", "I_PY=10 \n", "I_PD=I_PY*a \n", "I_LD=I_PD*math.sqrt(3) \n", "print(I_LD,'sec. line current(A)') \n", "r=math.sqrt(3)*V_LD*I_LD \n", "print(r,'output rating(va)') \n", "\n", "print('(b)D/Y conn') \n", "I_LD=10 \n", "I_PD=I_LD/math.sqrt(3) \n", "I_LY=I_PD*a \n", "print(I_LY,'sec. line current(A)') \n", "V_PD=6600 \n", "V_PY=V_PD/a \n", "V_LY=V_PY*math.sqrt(3) \n", "print(V_LY,'sec line voltage(V)') \n", "r=math.sqrt(3)*V_LY*I_LY \n", "\n", "#Results\n", "print(r,'output rating(va)') " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(a)Y/D conn\n", "(317.5426480542942, 'sec line voltage(V)')\n", "(207.84609690826525, 'sec. line current(A)')\n", "(114315.3532995459, 'output rating(va)')\n", "(b)D/Y conn\n", "(69.2820323027551, 'sec. line current(A)')\n", "(952.6279441628825, 'sec line voltage(V)')\n", "(114315.3532995459, 'output rating(va)')\n" ] } ], "prompt_number": 19 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.21, Page No 223" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "#to determine armature current,pf,power angle,mech power developed and eff\n", "\n", " \n", "j=math.sqrt(1.0) \n", "Vt=3300/math.sqrt(3.0) \n", "Ef=4270/math.sqrt(3.0) \n", "Pein=750000.0/3 \n", "Zs=.8+j*5.5 \n", "a=90-math.degrees(math.atan((Zs.imag)/(Zs.real)))\n", "dl=math.degrees(math.asin(Pein-(Zs.real)*(Vt/abs(Zs))**2)/((Vt*Ef/abs(Zs))))\n", "print(dl,'power angle(deg)') \n", "b=Vt-Ef*complex(math.cos(math.radians(-dl)),math.sin(math.radians(-dl))) \n", "Ia=b/Zs \n", "print(abs(Ia),'armature current(A)') \n", "phi=math.degrees(math.atan((Ia.imag)/(Ia.real)))\n", "print(math.cos(math.radians(phi)),'pf') \n", "Ef=math.sqrt(3)*Ef*complex(math.cos(math.radians(-dl)),math.sin(math.radians(-dl))) \n", "Pm=math.sqrt(3)*abs(Ef)*abs(Ia)*math.cos(math.radians(dl+phi))\n", "print(Pm,'mech power developed(W)') \n", "Pst=30000 \n", "Pmnet=Pm-Pst \n", "eff=Pmnet/(Pein*3)\n", "\n", "#Results\n", "print(eff*100,'efficiency(%)') " ], "language": "python", "metadata": {}, "outputs": [ { "ename": "ValueError", "evalue": "math domain error", "output_type": "pyerr", "traceback": [ "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mValueError\u001b[0m Traceback (most recent call last)", "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[0;32m 10\u001b[0m \u001b[0mZs\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m.8\u001b[0m\u001b[1;33m+\u001b[0m\u001b[0mj\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m5.5\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 11\u001b[0m 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\u001b[1;32mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdl\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;34m'power angle(deg)'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 14\u001b[0m \u001b[0mb\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mVt\u001b[0m\u001b[1;33m-\u001b[0m\u001b[0mEf\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mcomplex\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmath\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcos\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmath\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mradians\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m-\u001b[0m\u001b[0mdl\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mmath\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msin\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmath\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mradians\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m-\u001b[0m\u001b[0mdl\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", "\u001b[1;31mValueError\u001b[0m: math domain error" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.22, Page No 223" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "#to find armature current,power factor and power ip\n", "\n", " \n", "j=math.sqrt(1.0) \n", "Vt=3300/math.sqrt(3.0) \n", "Ef=4270/math.sqrt(3.0) \n", "Pein=600000/3 \n", "Zs=.8+j*5.5 \n", "\n", "#Calculations\n", "a=90-math.degrees(math.atan((Zs.imag)/(Zs.real)))\n", "dl=math.degrees(math.asin((Pein+(Zs.real)*(Ef/abs(Zs))**2)/((Vt*Ef/abs(Zs))))-a )\n", "print(dl,'power angle') \n", "b=Vt-Ef*complex(math.cos(math.radians(-dl)),math.sin(math.radians(-dl)))\n", "Ia=b/Zs \n", "print(abs(Ia),'armature current(A)') \n", "phi=math.degrees(math.atan((Ia.imag)/(Ia.real)))\n", "print(math.cos(math.radians(phi)),'pf') \n", "\n", "Peinn=math.sqrt(3.0)*3300*abs(Ia)*math.cos(math.radians(phi))\n", "print(Peinn,'power ip(W)') \n", "loss=Peinn-Pein*3 \n", "\n", "#Results\n", "print(loss,'ohmic loss(W)') \n" ], "language": "python", "metadata": {}, "outputs": [ { "ename": "ValueError", "evalue": "math domain error", "output_type": "pyerr", "traceback": [ "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mValueError\u001b[0m Traceback (most recent call last)", "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[0;32m 10\u001b[0m \u001b[0mZs\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m.8\u001b[0m\u001b[1;33m+\u001b[0m\u001b[0mj\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m5.5\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 11\u001b[0m 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\u001b[0mdl\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mmath\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdegrees\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmath\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0masin\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mPein\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mZs\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mreal\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mEf\u001b[0m\u001b[1;33m/\u001b[0m\u001b[0mabs\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mZs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m/\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mVt\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mEf\u001b[0m\u001b[1;33m/\u001b[0m\u001b[0mabs\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mZs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m-\u001b[0m\u001b[0ma\u001b[0m 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\u001b[0mb\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mVt\u001b[0m\u001b[1;33m-\u001b[0m\u001b[0mEf\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mcomplex\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmath\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcos\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmath\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mradians\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m-\u001b[0m\u001b[0mdl\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mmath\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msin\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmath\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mradians\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m-\u001b[0m\u001b[0mdl\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", "\u001b[1;31mValueError\u001b[0m: math domain error" ] } ], "prompt_number": 7 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.23, Page No 231" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "#to calculate pu adjusted sync reactance, feild reactance, reactive power op, rotor power angle\n", "\n", " \n", "j=math.sqrt(1.0) \n", "r=10*10**6 \n", "V_SC=13.8*10**3 \n", "Ia=r/(math.sqrt(3.0)*V_SC) \n", "If=226.0 \n", "\n", "\n", "#Calculations\n", "Iff=842.0 \n", "I_SC=Ia*Iff/If \n", "Xsadj=(V_SC/math.sqrt(3))/I_SC \n", "\n", "va_b=10*10**6 \n", "v_b=13800 \n", "Xspu=Xsadj*va_b/v_b**2 \n", "print(Xspu,'Xs(pu)') \n", "Ra=.75 \n", "Zs=Ra+j*Xsadj \n", "a=90-math.degrees(math.atan((Zs.imag)/(Zs.real))) \n", "\n", "pf=.9 \n", "phi=math.degrees(math.acos(pf)) \n", "Pe=8.75*10**6 \n", "Qe=Pe*math.tan(math.radians(phi)) \n", "Vt=V_SC/math.sqrt(3) \n", "Ia=(Pe/3.0)/(Vt*pf) \n", "Ef=Vt+abs(Ia)*abs(Zs)*complex(math.cos(math.radians(90-a-phi)),math.sin(math.radians(90-a-phi))) \n", "Ef=abs(Ef)*math.sqrt(3) \n", "If=Iff*Ef/V_SC \n", "print(If,'field current(A)') \n", "loss=3*abs(Ia)**2*Ra \n", "Pmin=Pe+loss \n", "print(Pmin,'reactive power op(W)') \n", "\n", "If=842 \n", "Voc=7968 \n", "Pmin=Pmin/3 \n", "dl=math.degrees(math.asin((Pmin-(Zs.real)*(Voc/abs(Zs))**2)/((Voc**2/abs(Zs)))))+a \n", "\n", "#Results\n", "print(dl,'power angle') \n", "Q=-(Voc/abs(Zs))**2*(Zs.imag)+Voc**2*math.cos(math.radians(dl+a))/abs(Zs) \n", "print(Q,'reactive power op(VAR)') " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(0.2684085510688836, 'Xs(pu)')\n", "(1074.3932057155528, 'field current(A)')\n", "(9122249.546858348, 'reactive power op(W)')\n", "(44.00614893481687, 'power angle')\n", "(-7524957.4047774, 'reactive power op(VAR)')\n" ] } ], "prompt_number": 11 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.25, Page No 231" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "#to calculate the excitation emf,power angle\n", "\n", " \n", "Vt=1.0\n", "Ia=1.0 \n", "pf=.8 \n", "phi=math.degrees(math.acos(pf)) \n", "Iaa=Ia*complex(math.cos(math.radians(-phi)),math.sin(math.radians(-phi))) \n", "Xq=.5 \n", "\n", "#Calculations\n", "j=math.sqrt(1) \n", "Ef=Vt+j*Iaa*Xq \n", "\n", "dl=17.1 \n", "w=phi+dl \n", "Id=Ia*math.sin(math.radians(w))\n", "Xd=.8 \n", "CD=Id*(Xd-Xq) \n", "Eff=abs(Ef)+CD \n", "Ef=Vt+j*Iaa*Xd \n", "\n", "#Results\n", "print(abs(Ef),'excitation emf(V)') \n", "print(math.degrees(math.atan((Ef.imag)/(Ef.real))),'power angle') " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(1.7088007490635064, 'excitation emf(V)')\n", "(-16.313852426260553, 'power angle')\n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.26, Page No 231" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "#calculate excitation emf\n", "\n", " \n", "V=3300.0 \n", "Vt=V/math.sqrt(3.0) \n", "pf=1 \n", "phi=math.degrees(math.acos(pf)) \n", "P=1500.0*1000 \n", "\n", "#Calculations\n", "Ia=P/(math.sqrt(3.0)*V*pf) \n", "Xq=2.88 \n", "Xd=4.01 \n", "w=math.degrees(math.atan((Vt*0-Ia*Xq)/Vt))\n", "dl=phi-w \n", "Id=Ia*math.sin(math.radians(w))\n", "Iq=Ia*math.cos(math.radians(w)) \n", "Ef=Vt*math.cos(math.radians(dl))-Id*Xd \n", "\n", "#Results\n", "print(Ef*math.sqrt(3.0),'excitation emf(line)(V)') " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(3739.5700468573696, 'excitation emf(line)(V)')\n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.27, Page No 231" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "#to calculate generator terminal voltage,excitation emf,power angle\n", " \n", "Xd=1.48 \n", "Xq=1.24 \n", "Xe=.1 \n", "Xdt=Xd+Xe \n", "Xqt=Xq+Xe \n", "\n", "MVA=1 \n", "Vb=1 \n", "pf=.9 \n", "\n", "#Calculations\n", "phi=math.degrees(math.acos(pf))\n", "#(Vt*math.cos(math.radians(phi)))**2+(Vt*math.sin(math.radians(phi))+Ia*Xe)**2=Vb**2 \n", "#after solving\n", "#Vt**2-.0870*Vt-.99=0 \n", "def\tquad(a,b,c):\n", " d=math.sqrt(b**2-4*a*c) \n", " x1=(-b+d)/(2*a) \n", " x2=(-b-d)/(2*a) \n", " if x1 < Vb :\n", " x=x2\n", " else :\n", " x=x1 \n", "\treturn x\n", "Vt=quad(1,-.0870,-.99) \n", "print(Vt,'terminal voltage(V)') \n", "#after solving\n", "phi=20 \n", "\n", "j=math.sqrt(1) \n", "Ia=1 \n", "Iaa=Ia*complex(math.cos(math.radians(-phi)),math.sin(math.radians(-phi))) \n", "Ef=Vb+j*Iaa*Xqt \n", "Eff=abs(Ef) \n", "dl=math.degrees(math.atan((Ef.imag)/(Ef.real)))\n", "print(dl,'power angle') \n", "w=dl+phi \n", "Id=Ia*math.sin(math.radians(w)) \n", "Ef=Ef+Id*(Xdt-Xqt) \n", "\n", "#Results\n", "print(abs(Ef),'excitation emf(V)') " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(1.0394378745684894, 'terminal voltage(V)')\n", "(-11.46760596259884, 'power angle')\n", "(2.34011465088481, 'excitation emf(V)')\n" ] } ], "prompt_number": 9 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.28, Page No 231" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "#to find max pu power, pu armature current, pu reactive power\n", "\n", " \n", "Vt=1 \n", "Xd=1.02 \n", "Xq=.68 \n", "Pmmax=Vt**2*(Xd-Xq)/(2*Xd*Xq) \n", "print(Pmmax,'max pu power') \n", "dl=.5*math.degrees(math.asin(Pmmax/(Vt**2*(Xd-Xq)/(2*Xd*Xq)))) \n", "\n", "#Calculations\n", "Id=Vt*math.cos(math.radians(dl))/Xd \n", "Iq=Vt*math.cos(math.radians(dl))/Xq \n", "Ia=math.sqrt(Id**2+Iq**2) \n", "print(Ia,'armature current(pu)') \n", "\n", "Qe=Id*Vt*math.cos(math.radians(dl))+Iq*Vt*math.sin(math.radians(dl)) \n", "print(Qe,'reactive power(pu)') \n", "\n", "pf=math.cos(math.radians(math.degrees(math.atan(Qe/Pmmax))))\n", "\n", "#Results\n", "print(pf,'pf') " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(0.2450980392156862, 'max pu power')\n", "(1.249759684704114, 'armature current(pu)')\n", "(1.2254901960784315, 'reactive power(pu)')\n", "(0.196116135138184, 'pf')\n" ] } ], "prompt_number": 11 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.29, Page No 231" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "#to calculate power angle,excitation emf,field current\n", "j=math.sqrt(1.0) \n", "MVA_b=300.0 \n", "kV_b=22.0 \n", "\n", "Pe=250.0/MVA_b \n", "pf=.85 \n", "Vt=1 \n", "\n", "#Calculations\n", "Ia=Pe/(pf*Vt) \n", "phi=math.degrees(math.acos(pf))\n", "Iaa=Ia*complex(math.cos(math.radians(-phi)),math.sin(math.radians(-phi))) \n", "Xq=1.16 \n", "Xd=1.93 \n", "Ef=Vt+j*Iaa*Xq \n", "dl=math.degrees(math.atan((Ef.imag)/(Ef.real)))\n", "print(dl,'power angle') \n", "w=phi+dl \n", "Id=abs(Iaa)*math.sin(math.radians(w)) \n", "Ef=abs(Ef)+Id*(Xd-Xq) \n", "print(Ef*kV_b,'excitation emf(V)') \n", "\n", "If=338.0 \n", "If=If*Ef/1 \n", "\n", "#Results\n", "print(If,'field current(A)') " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(-16.941789546757967, 'power angle')\n", "(49.48501576455793, 'excitation emf(V)')\n", "(760.2697876554809, 'field current(A)')\n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.30, Page No 231" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "#to find max andmin pu field excitation\n", "\n", " \n", "Xd=.71 \n", "Xq=.58 \n", "Xe=.08 \n", "Xdt=Xd+Xe \n", "Xqt=Xq+Xe \n", "\n", "#Calculations\n", "Pe=0 \n", "Vt=1 \n", "dl=0 \n", "phi=90 \n", "Ia=1 \n", "Iq=0 \n", "Id=Ia \n", "\n", "Ef=Vt+Id*Xdt \n", "Ifmax=Ef \n", "print(Ifmax,'max field excitation(A)') \n", "\n", "\n", "Ef=Vt-Id*Xdt \n", "Ifmin=Ef \n", "\n", "#Results\n", "print(Ifmin,'min field excitation(A)') " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(1.79, 'max field excitation(A)')\n", "(0.21000000000000008, 'min field excitation(A)')\n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.31, Page No 231" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "#to calculate synchronising power and torque coeff/deg mech shift\n", "\n", " \n", "V=11000.0\n", "Vt=V/math.sqrt(3) \n", "P=6*10**6.0 \n", "\n", "#Calculations\n", "Ia=P/(math.sqrt(3)*V) \n", "ohm_b=Vt/Ia \n", "Xs=.5 \n", "Xss=Xs*ohm_b \n", "\n", "f=50.0 \n", "P=8.0 \n", "n_s=(120*f/P)*(2*math.pi/60) \n", "\n", "Ef=Vt \n", "dl=0 \n", "Psyn=(math.pi/15)*(Ef*Vt/Xss)*math.cos(math.radians(dl))\n", "print(Psyn,'synchronising power(W)') \n", "Tsyn=Psyn/n_s \n", "print(Tsyn,'torque coeff(Nm)') \n", "\n", "pf=.8 \n", "phi=math.degrees(math.acos(pf)) \n", "Ef=Vt+j*Ia*Xss*complex(math.cos(math.radians(-phi)),math.sin(math.radians(-phi))) \n", "dl=math.degrees(math.atan((Ef.imag)/(Ef.real)))\n", "Psyn=(math.pi/15)*(abs(Ef)*Vt/Xss)*math.cos(math.radians(dl)) \n", "\n", "#Results\n", "print(Psyn,'synchronising power(W)') \n", "Tsyn=Psyn/n_s \n", "print(Tsyn,'torque coeff(Nm)') " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(837758.0409572781, 'synchronising power(W)')\n", "(10666.666666666666, 'torque coeff(Nm)')\n", "(1172861.257340189, 'synchronising power(W)')\n", "(14933.333333333328, 'torque coeff(Nm)')\n" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.32, Page No 231" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#to calculate syncronising power/elec deg,pu sync torque/mech deg\n", " \n", "j=math.sqrt(1.0) \n", "Xd=.8 \n", "Xq=.5 \n", "Vt=1 \n", "pf=.8 \n", "phi=math.degrees(math.acos(pf))\n", "Ia=1*complex(math.cos(math.radians(phi)),math.sin(math.radians(phi))) \n", "\n", "Ef=Vt-j*Ia*Xq \n", "Eff=abs(Ef) \n", "\n", "#Calculations\n", "dl=math.degrees(math.atan((Ef.imag)/(Ef.real))) \n", "w=-dl+phi \n", "Id=abs(Ia)*math.sin(math.radians(w))\n", "Ef=Eff+Id*(Xd-Xq) \n", "\n", "Psyn=abs(Ef)*Vt*math.cos(math.radians(dl))/Xd+Vt**2*((Xd-Xq)/(Xd*Xq))*math.cos(math.radians(2*dl))\n", "print(Psyn*(math.pi/180),'syncronising power(pu)/elec deg') \n", "f=50 \n", "P=12 \n", "n_s=(120*f/P)*(2*math.pi/60) \n", "Tsyn=Psyn/n_s \n", "\n", "#Results\n", "print(Tsyn,'pu sync torque/mech deg') \n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(0.02617993877991495, 'syncronising power(pu)/elec deg')\n", "(0.028647889756541166, 'pu sync torque/mech deg')\n" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.33, Page No 231" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#to calculate sync current, power and torque\n", "\n", " \n", "j=math.sqrt(1.0) \n", "P=12000.0 \n", "V=400.0 \n", "pf=.8 \n", "Ia=P/(math.sqrt(3)*V*pf) \n", "phi=math.degrees(math.acos(pf))\n", "Vt=V/math.sqrt(3) \n", "Xs=2.5 \n", "\n", "#Calculations\n", "Ef=Vt-j*Ia*complex(math.cos(math.radians(phi)),math.sin(math.radians(phi)))*Xs \n", "tandl=4 \n", "Es=2*abs(Ef)*math.cos(math.radians(tandl/2)) \n", "Is=Es/Xs \n", "print(Is,'sync current(A)') \n", "dl=math.degrees(math.atan((Ef.imag)/(Ef.real)))\n", "Ps=3*Vt*Is*math.cos(dl+tandl/2)\n", "print(Ps,'power(W)') \n", "n_s=25*math.pi \n", "T_s=Ps/n_s \n", "\n", "#Results\n", "print(T_s,'torque(Nm)') " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(152.2500120412367, 'sync current(A)')\n", "(3657.484067729796, 'power(W)')\n", "(46.568533492723965, 'torque(Nm)')\n" ] } ], "prompt_number": 7 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.34, Page No 231" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "#to calculate value of syncpower\n", "\n", " \n", "V=6600.0\n", "E=V/math.sqrt(3.0) \n", "\n", "P=12.0 \n", "dl=1.0*P/2 \n", "\n", "#Calculations\n", "r=20000.0*10**3 \n", "I=r/(math.sqrt(3.0)*V) \n", "Xs=1.65 \n", "\n", "Psy=dl*(math.pi/180.0)*E**2/Xs \n", "\n", "#Results\n", "print(Psy,'sync power(W)') \n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(921533.8450530063, 'sync power(W)')\n" ] } ], "prompt_number": 8 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.35, Page No 231" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "#to determine op current and pf\n", "\n", " \n", "P1=400.0*10**3 \n", "P2=400.0*10**3 \n", "P3=300.0*10**3 \n", "P4=800.0*10**3 \n", "pf1=1 \n", "pf2=.85 \n", "pf3=.8 \n", "pf4=.7 \n", "\n", "#Calculations\n", "phi1=math.degrees(math.acos(pf1))\n", "phi2=math.degrees(math.acos(pf2)) \n", "phi3=math.degrees(math.acos(pf3)) \n", "phi4=math.degrees(math.acos(pf4))\n", "P=P1+P2+P3+P4 \n", "Q1=P1*math.tan(math.radians(phi1))\n", "Q2=P2*math.tan(math.radians(phi2)) \n", "Q3=P3*math.tan(math.radians(phi3))\n", "Q4=P4*math.tan(math.radians(phi4)) \n", "Q=Q1+Q2+Q3+Q4 \n", "\n", "I=100 \n", "pf=.9 \n", "V=6600.0 \n", "P_A=math.sqrt(3)*V*I*pf \n", "P_B=P-P_A \n", "Q_A=P_A*math.tan(math.radians(math.degrees(math.acos(pf))) )\n", "Q_B=Q-Q_A \n", "phi=math.degrees(math.acos(Q_B/P_B))\n", "pf=math.cos(math.radians(phi))\n", "print(pf,'pf') \n", "I_B=P_B/(math.sqrt(3.0)*pf*V) \n", "\n", "#Results\n", "print(I_B,'op current(A)') " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(0.9077210377902825, 'pf')\n", "(83.9540921749662, 'op current(A)')\n" ] } ], "prompt_number": 9 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.36, Page No 231" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "#to find the pf and current supplied by the m/c\n", "\n", "P=50000.0\n", "pf=.8 \n", "phi=math.degrees(math.acos(pf))\n", "Q=P*math.cos(math.radians(phi)) \n", "P1=P/2 \n", "pf1=.9 \n", "\n", "#Calculations\n", "phi1=math.degrees(math.acos(pf1))\n", "Q1=P1*math.cos(math.radians(phi1)) \n", "P2=P/2 \n", "Q2=Q-Q1 \n", "phi2=math.degrees(math.atan(Q2/P2))\n", "pf=math.cos(math.radians(phi2)) \n", "print(pf,'pf') \n", "V_L=400.0\n", "I2=P2/(math.sqrt(3)*V_L*pf) \n", "\n", "#Results\n", "print(I2,'current supplied by m/c(A)') \n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(0.8192319205190405, 'pf')\n", "(44.04661356638744, 'current supplied by m/c(A)')\n" ] } ], "prompt_number": 10 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.37, Page No 231" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#to find initial current,current at the end of 2 cycles and at the end of 10s\n", "\n", " \n", "Ef=1.0 \n", "Xd2=.2 \n", "I2=Ef/Xd2 \n", "r=100*10**6 \n", "V=22000.0 \n", "\n", "#Calculations\n", "I_b=r/(math.sqrt(3)*V) \n", "I2=I2*I_b \n", "print(I2,'initial current(A)') \n", "\n", "Xd1=.3 \n", "I1=Ef/Xd1 \n", "Xd=1 \n", "I=Ef/Xd \n", "\n", "tau_dw=0.03 \n", "tau_f=1 \n", "\n", "def I_sc(t):\n", " a=(I2-I1)*math.exp(-t/tau_dw)+(I1-I)*math.exp(-t/tau_f)+1 \n", " return a\n", "#2 cycles=0.04s\n", "\n", "#Results\n", "print(I_sc(.2867)*I_b,'current at the end of 2 cycles(A)') \n", "print(I_sc(10)*I_b,'current at the end of 10s(A)') \n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(13121.597027036949, 'initial current(A)')\n", "(9656.315026038814, 'current at the end of 2 cycles(A)')\n", "(2624.5974078796426, 'current at the end of 10s(A)')\n" ] } ], "prompt_number": 12 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.39, Page No 231" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "#to calculate sync reactance,voltage regulation,torque angle, ele power developed, voltage and kva rating\n", "\n", " \n", "r=1000.0*10**3 \n", "V=6600.0 \n", "Ia=r/(math.sqrt(3.0)*V) \n", "pf=.75 \n", "\n", "#Calculations\n", "phi=-math.degrees(math.acos(pf))\n", "Vt=V/math.sqrt(3.0) \n", "Ef=11400.0/math.sqrt(3) \n", "#Ef*complex(cosd(dl),sind(dl))=Vt+j*Xs*Ia*complex(cosd(phi),sind(phi))\n", "#after solving\n", "#6.58*cosd(dl)=3.81+.058*Xs \n", "#6.58*sind(dl)=.0656*Xs \n", "#so after solving \n", "#cosd(dl-phi)=.434 \n", "dl=math.degrees(math.acos(0.434))+phi \n", "\n", "Xs=Ef*math.sin(math.radians(dl))/65.6 \n", "\n", "#Results\n", "print(Xs,'sync reactance(ohm)') \n", "vr=Ef*math.sqrt(3.0)/V-1 \n", "print(vr,'voltage regulation(%)') \n", "print(dl,'torque angle(deg)') \n", "P=3*Ef*Ia*math.cos(math.radians(dl-phi)) \n", "print(P,'ele power developed(W)') \n", "\n", "volr=V/math.sqrt(3) \n", "print(volr,'voltage rating(V)') \n", "ir=Ia*math.sqrt(3) \n", "print(ir,'current rating(A)') \n", "r=math.sqrt(3)*volr*ir \n", "print(r,'VA rating') \n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(38.99116776362744, 'sync reactance(ohm)')\n", "(0.7272727272727273, 'voltage regulation(%)')\n", "(22.86869850821798, 'torque angle(deg)')\n", "(749636.3636363635, 'ele power developed(W)')\n", "(3810.5117766515305, 'voltage rating(V)')\n", "(151.5151515151515, 'current rating(A)')\n", "(999999.9999999999, 'VA rating')\n" ] } ], "prompt_number": 13 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.40, Page No 231" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "#to determine m/c and pf\n", "\n", " \n", "j=math.sqrt(1.0) \n", "P=230.0*10**6 \n", "V=22000.0 \n", "pf=1.0 \n", "\n", "#Calculations\n", "Ia=P/(math.sqrt(3)*V*pf) \n", "Vt=V/math.sqrt(3) \n", "Xs=1.2 \n", "Ef=Vt+j*Xs*Ia \n", "#if Ef is inc by 30%\n", "Ef=1.3*abs(Ef) \n", "\n", "dl=math.degrees(math.asin((P/3.0)*Xs/(Ef*Vt)))\n", "Ia=((Ef*complex(math.cos(math.radians(dl)),math.sin(math.radians(dl))))-Vt)/(j*Xs) \n", "print(abs(Ia),'m/c current(A)') \n", "print(math.cos(math.radians(math.degrees(math.atan((Ia.imag)/(Ia.real))))),'pf') \n", "P=275*10**6 \n", "dl=math.degrees(math.asin((P/3.0)*Xs/(Ef*Vt)))\n", "Ia=((Ef*complex(math.cos(math.radians(dl)),math.sin(math.radians(dl))))-Vt)/(j*Xs) \n", "\n", "#Results\n", "print(abs(Ia),'m/c current(A)') \n", "print(math.cos(math.radians(math.degrees(math.atan((Ia.imag)/(Ia.real))))),'pf') \n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(11819.373430797657, 'm/c current(A)')\n", "(0.8597700086643913, 'pf')\n", "(12155.509739365927, 'm/c current(A)')\n", "(0.8046772266804496, 'pf')\n" ] } ], "prompt_number": 15 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.41, Page No 231" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#to calculate excitation emf,torque angle, eff, shaft op\n", "import math\n", "#initialisation of variables\n", " \n", "j=math.sqrt(1.0) \n", "Va=.8 \n", "Xa=5.5 \n", "Xs=Va+j*Xa \n", "V=3300.0 \n", "Ia=160.0 \n", "pf=.8 \n", "loss=30000.0\n", "\n", "#Calculations\n", "phi=math.degrees(math.acos(pf))\n", "Ef=V/math.sqrt(3.0)-Xs*Ia*complex(math.cos(math.radians(-phi)),math.sin(math.radians(-phi)))\n", "print(abs(Ef),'excitation emf(V)') \n", "dl=math.degrees(math.atan((Ef.imag)/(Ef.real)))\n", "print(dl,'torque angle(deg)') \n", "P_mech=3*abs(Ef)*Ia*math.cos(math.radians(-phi-dl)) \n", "op_sft=P_mech-loss \n", "print(op_sft,'shaft op(W)') \n", "Pip=math.sqrt(3.0)*V*Ia*pf \n", "eff=op_sft/Pip\n", "\n", "#Results\n", "print(eff*100,'efficiency(%)') \n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(1254.2995269504831, 'excitation emf(V)')\n", "(28.82797497778111, 'torque angle(deg)')\n", "(217778.26111709396, 'shaft op(W)')\n", "(29.76665191278476, 'efficiency(%)')\n" ] } ], "prompt_number": 18 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.42, Page No 231" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#to caculate generator current,pf, real power,ecitation emf\n", "import math\n", "#initialisation of variables\n", "\n", " \n", "r=500.0*10**6 \n", "V=22000 \n", "Ia=r/(math.sqrt(3.0)*V) \n", "print(Ia,'generator current(A)') \n", "Vt=V/math.sqrt(3.0) \n", "Zb=Vt/Ia \n", "MVA_b=500.0\n", "MW_b=500.0 \n", "Xsg=1.57 \n", "Xb=.4 \n", "Xb=Xb/Zb \n", "rr=250.0 \n", "rr=rr/MVA_b \n", "Vb=1 \n", "Vt=1 \n", "Ia=.5 \n", "\n", "#Calculations\n", "phi=math.degrees(math.asin(Xb*Ia/2))\n", "pf=math.cos(math.radians(phi))\n", "print(pf,'pf') \n", "Pe=rr*pf \n", "print(Pe,'real power(pu)') \n", "Eg=complex(Vt,Xsg*rr**complex(math.cos(math.radians(-phi)),math.sin(math.radians(-phi))))\n", "Egg=abs(Eg)*V \n", "print(Egg,'excitation emf(V)') \n", "\n", "\n", "rr=500.0 \n", "rr=rr/MVA_b \n", "Vb=1 \n", "Vt=1 \n", "Ia=1 \n", "phi=math.degrees(math.asin(Xb*Ia/2))\n", "pf=math.cos(math.radians(phi))\n", "print(pf,'pf') \n", "Pe=rr*pf \n", "print(Pe,'real power(pu)') \n", "Eg=complex(Vt,Xsg*rr**complex(math.cos(math.radians(-phi)),math.sin(math.radians(-phi))))\n", "Egg=abs(Eg)*V \n", "\n", "\n", "#Results\n", "print(Egg,'excitation emf(V)') " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(13121.597027036949, 'generator current(A)')\n", "(0.9946496442265089, 'pf')\n", "(0.49732482211325446, 'real power(pu)')\n", "(27016.768055398476, 'excitation emf(V)')\n", "(0.9784230470709913, 'pf')\n", "(0.9784230470709913, 'real power(pu)')\n", "(40951.33209066587, 'excitation emf(V)')\n" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.43, Page No 231" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#to ulate pf angle, torque angle,equivalent capicitor and inductor value\n", "import math\n", "#initialisation of variables\n", "\n", "of1=250.0 \n", "scr=0.52 #short ckt ratio\n", "of2=of1/scr \n", "r=25.0*10**6 \n", "V=13000.0 \n", "\n", "#Calculations\n", "Ia=r/(math.sqrt(3.0)*V) \n", "Isc=Ia*of1/of2 \n", "Xs=V/(math.sqrt(3.0)*Isc) \n", "Xb=V/(math.sqrt(3.0)*Ia) \n", "Xsadj=Xs/Xb \n", "\n", "f=50.0 \n", "If=200.0 \n", "Ef=V*If/of1 \n", "Vt=V/math.sqrt(3.0) \n", "Ia=(Vt-Ef/math.sqrt(3.0))/Xs \n", "dl=0 \n", "print(dl,'torque angle(deg)') \n", "pf=90.0 \n", "print(pf,'pf angle(deg)') \n", "L=(V/(math.sqrt(3.0)*Ia))/(2*math.pi*f) \n", "print(L,'inductor value(H)') \n", "\n", "If=300.0 \n", "Eff=V*If/of1 \n", "Vt=Ef/math.sqrt(3.0) \n", "Ia=(Eff/math.sqrt(3)-Vt)/Xs \n", "dl=0 \n", "print(dl,'torque angle(deg)') \n", "pf=90.0 \n", "print(pf,'pf angle(deg)') \n", "c=1.0/((V/(Ia))*(2.0*math.pi*f)) \n", "\n", "#Results\n", "print(c,'capacitor value(F)') \n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(0, 'torque angle(deg)')\n", "(90.0, 'pf angle(deg)')\n", "(0.2069014260194639, 'inductor value(H)')\n", "(0, 'torque angle(deg)')\n", "(90.0, 'pf angle(deg)')\n", "(5.654655337659404e-05, 'capacitor value(F)')\n" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.44, Page No 231" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#to determine Xs(saturated),scr,Xs(unsat)and If,generator current\n", "import math\n", "#initialisation of variables\n", "\n", " \n", "MVA_b=400.0 \n", "kV_b=22.0 \n", "\n", "#Calculations\n", "Ib=MVA_b/(math.sqrt(3.0)*kV_b) \n", "ohm_b=kV_b/(math.sqrt(3.0)*Ib) \n", "\n", "If=1120.0 \n", "Voc=kV_b/math.sqrt(3) \n", "Isc=13.2 \n", "Xssat=Voc/Isc \n", "print(Xssat,'Xs(saturated)(ohm)') \n", "Xss=Xssat/ohm_b \n", "print(Xss,'Xs(saturated)(pu)') \n", "scr=1/Xss \n", "print(scr,'SCR') \n", "Isc=Ib \n", "Voc=24.4/math.sqrt(3) \n", "Xsunsat=Voc/Isc \n", "\n", "#Results\n", "print(Xsunsat,'Xs(unsaturated)(ohm)') \n", "Xsuns=Xsunsat/ohm_b \n", "print(Xsuns,'Xs(unsaturated)(pu)') \n", "Iff=If*scr \n", "print(Iff,'generator current(A)') \n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(0.9622504486493764, 'Xs(saturated)(ohm)')\n", "(0.795248304668906, 'Xs(saturated)(pu)')\n", "(1.257468886295005, 'SCR')\n", "(1.342, 'Xs(unsaturated)(ohm)')\n", "(1.109090909090909, 'Xs(unsaturated)(pu)')\n", "(1408.3651526504057, 'generator current(A)')\n" ] } ], "prompt_number": 8 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.45, Page No 231" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "#find motor pf\n", "\n", " \n", "j=math.sqrt(1.0) \n", "V=6600.0 \n", "Vt=V/math.sqrt(3) \n", "pf=.8 \n", "\n", "#Calculations\n", "phi=math.degrees(math.acos(pf)) \n", "P=800000.0 \n", "Ia=P/(math.sqrt(3)*V*pf) \n", "Zs=2+20*j \n", "Ef=Vt-Zs*Ia*complex(math.cos(math.radians(phi))+math.sin(math.radians(phi))) \n", "Pip=1200*10**3.0 \n", "theta=math.degrees(math.atan((Zs.imag)/(Zs.real)))\n", "dl=math.degrees(math.acos(((Ef.real)**2*math.degrees(math.acos(theta))/abs(Zs)-P/3.0)/((Ef.real)*abs(Ef)/abs(Zs))))-theta \n", "\n", "Ia=((Ef.real)-abs(Ef)*complex(math.cos(math.radians(-dl)),math.sin(math.radians(-dl))))/Zs \n", "phi=math.degrees(math.atan((Ia.imag)/(Ia.real)))\n", "\n", "#Results\n", "print(math.cos(math.radians(phi)),'pf') " ], "language": "python", "metadata": {}, "outputs": [ { "ename": "ValueError", "evalue": "math domain error", "output_type": "pyerr", "traceback": [ "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mValueError\u001b[0m Traceback (most recent call last)", "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[0;32m 15\u001b[0m \u001b[0mPip\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m1200\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m10\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;36m3.0\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 16\u001b[0m \u001b[0mtheta\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mmath\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdegrees\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmath\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0matan\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mZs\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mimag\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m/\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mZs\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mreal\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 17\u001b[1;33m 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"\u001b[1;31mValueError\u001b[0m: math domain error" ] } ], "prompt_number": 10 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.46, Page No 231" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "#to find exciting emf neglecting saliency and accounting saliency\n", "\n", " \n", "j=math.sqrt(1.0) \n", "Xd=.12/3 \n", "Xq=.075/3.0 \n", "\n", "print('neglecting saliency') \n", "Xs=Xd \n", "V=440.0 \n", "pf=.8 \n", "\n", "#Calculations\n", "phi=math.degrees(math.acos(pf))\n", "Vt=V/math.sqrt(3.0) \n", "Ia=1000.0 \n", "Ef=Vt+j*Xs*Ia*complex(math.cos(math.radians(-phi)),math.sin(math.radians(-phi))) \n", "print(abs(Ef)*math.sqrt(3),'excitation emf(line)(V)') \n", "print('accounting saliency') \n", "w=math.degrees(math.atan((Vt*math.sin(math.radians(phi))+Ia*Xq)/(Vt*math.cos(math.radians(phi)))))\n", "dl=w-phi \n", "Ef=Vt*math.cos(math.radians(dl))+Ia*math.sin(math.radians(dl))*Xd\n", "\n", "#Results\n", "print(abs(Ef)*math.sqrt(3),'excitation emf(line)(V)') \n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "neglecting saliency\n", "(497.16652214438125, 'excitation emf(line)(V)')\n", "accounting saliency\n", "(443.9254541572264, 'excitation emf(line)(V)')\n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.47, Page No 231" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "#calculate excitation emf,max load motor supplies, torque angle\n", "\n", "Xd=23.2 \n", "Xq=14.5 \n", "V=6600.0 \n", "pf=.8 \n", "phi=math.degrees(math.acos(pf))\n", "Vt=V/math.sqrt(3.0) \n", "r=1500*1000.0\n", "\n", "#Calculations\n", "Ia=r/(math.sqrt(3.0)*V)\n", "w=math.degrees(math.atan((Vt*math.sin(math.radians(-phi))+Ia*Xq)/(Vt*math.cos(math.radians(phi)))))\n", "dl=-phi-w \n", "print(dl,'torque angle') \n", "Ef=Vt*math.cos(math.radians(dl))-Ia*math.sin(math.radians(w))*Xd \n", "print(Ef,'excitation emf(V)') \n", "\n", "Pe=V**2*((Xd-Xq)/(2*Xd*Xq)) \n", "\n", "#Results\n", "print(Pe,'load supplied(W)') \n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(-29.696320419057813, 'torque angle')\n", "(3690.199749168095, 'excitation emf(V)')\n", "(563275.8620689656, 'load supplied(W)')\n" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.49, Page No 231" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "#find no load freq setting,sys freq,at no load freq of swing generator, system trip freq\n", "\n", " \n", "loadtot=260.0\n", "r=125.0 \n", "pf=.84 \n", "\n", "#Calculations\n", "genfl=r*pf \n", "sld=75 #supply load\n", "n=3 #no of generators\n", "ls=loadtot-n*sld \n", "m=-5/genfl \n", "f=50 \n", "ff=f-m*sld \n", "print(ff,'set freq(Hz)') \n", "c=f-m*ls \n", "print(c,'set freq(Hz) supplied from swing generator') \n", "nld=sld+50/4 \n", "c=ff+m*nld \n", "print(c,'new system freq(Hz)') \n", "rld=310-n*sld \n", "c=f-m*rld \n", "print(c,'set freq(Hz) of swing generator') \n", "nld=310.0/n \n", "c=ff+m*nld \n", "\n", "#Results\n", "print(c,'system trip freq(Hz)') \n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(53.57142857142857, 'set freq(Hz)')\n", "(51.666666666666664, 'set freq(Hz) supplied from swing generator')\n", "(49.42857142857143, 'new system freq(Hz)')\n", "(54.04761904761905, 'set freq(Hz) of swing generator')\n", "(48.65079365079365, 'system trip freq(Hz)')\n" ] } ], "prompt_number": 1 } ], "metadata": {} } ] }