{
"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<ipython-input-6-af32ec64a4fb>\u001b[0m in \u001b[0;36m<module>\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 \u001b[0ma\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m90\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---> 12\u001b[1;33m \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[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[0mVt\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[0m\n\u001b[0m\u001b[0;32m 13\u001b[0m \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<ipython-input-7-f2810ca219fa>\u001b[0m in \u001b[0;36m<module>\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 \u001b[0ma\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m90\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---> 12\u001b[1;33m \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 \u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 13\u001b[0m \u001b[1;32mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdl\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;34m'power angle'\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": 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<ipython-input-10-84d5f78c41ee>\u001b[0m in \u001b[0;36m<module>\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 \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[0macos\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[0mreal\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;36m2\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[0macos\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mtheta\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\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[0mP\u001b[0m\u001b[1;33m/\u001b[0m\u001b[1;36m3.0\u001b[0m\u001b[1;33m)\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[0mreal\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mabs\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mEf\u001b[0m\u001b[1;33m)\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[0mtheta\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 18\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 19\u001b[0m \u001b[0mIa\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[0mreal\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m-\u001b[0m\u001b[0mabs\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mEf\u001b[0m\u001b[1;33m)\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[1;33m/\u001b[0m\u001b[0mZs\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
"\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": {}
}
]
}