{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"CHAPTER 9: SYNCHRONOUS GENERATOR"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.1, Page number 295"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"N = 300.0 #Speed of water turbine(rpm)\n",
"f = 50.0 #Frequency of induced voltage(Hz)\n",
"\n",
"#Calculation\n",
"P = 120*f/N #Number of poles\n",
"\n",
"#Result\n",
"print('Number of poles of the generator , P = %.f poles' %P)\n",
"print('Alternatively , %.f pairs of north(N) and south(S) poles' %(P/2))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Number of poles of the generator , P = 20 poles\n",
"Alternatively , 10 pairs of north(N) and south(S) poles\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.2, Page number 299-300"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"P = 8.0 #Number of poles\n",
"m = 3.0 #Number of phase \n",
"S = 144.0 #Number of slots\n",
"\n",
"#Calculation\n",
"T_p = S/P #Pole pitch(slots)\n",
"slots_1 = 180/T_p #Pole pitch per slot(degree)\n",
"gamma = 2*slots_1 #Short pitch angle(degree)\n",
"y = gamma*math.pi/180 #Short pitch angle(radian)\n",
"k_p = math.cos(y/2) #Pitch factor\n",
"\n",
"#Result\n",
"print('Pitch factor , k_p = %.2f ' %k_p)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Pitch factor , k_p = 0.98 \n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.3, Page number 300-301"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"P = 4.0 #Number of poles\n",
"m = 3.0 #Number of phase \n",
"S = 40.0 #Number of slots\n",
"s_1 = 1.0 #Coil span\n",
"s_2 = 9.0 #Coil span\n",
"\n",
"#Calculation\n",
"T_p = S/P #Pole pitch(slots)\n",
"T_c = s_2-s_1 #Coil pitch for coil spans 1 to 9(slots)\n",
"slots = 180/T_p #Pole pitch per slot(degree)\n",
"y = T_p-T_c #Short pitch angle(slots)\n",
"gamma = y*slots #Short pitch angle(degree)\n",
"y = gamma*math.pi/180 #Short pitch angle(radian)\n",
"k_p = math.cos(y/2) #Pitch factor\n",
"\n",
"#Result\n",
"print('Pitch factor , k_p = %.2f ' %k_p)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Pitch factor , k_p = 0.95 \n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.4, Page number 302"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"P = 4.0 #Number of poles\n",
"S = 48.0 #Number of slots\n",
"m = 3.0 #Number of phase \n",
"\n",
"#Calculation\n",
"T_p = S/P #Pole pitch(slots)\n",
"slot = 180/T_p #Pole pitch per slot(degree)\n",
"a = slot*math.pi/180 #Pole pitch per slot(radian)\n",
"n = S/(P*m) #Number of slots or coils per pole per phase\n",
"k_d = math.sin(n*a/2)/(n*math.sin(a/2)) #Distribution factor\n",
"\n",
"#Result\n",
"print('Distribution factor , k_d = %.2f ' %k_d)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Distribution factor , k_d = 0.96 \n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.5, Page number 304-305"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"P = 12.0 #Number of poles\n",
"S = 180.0 #Number of slots\n",
"phi_m = 0.05 #Flux per pole(Wb)\n",
"N = 600.0 #Speed of machine(rpm)\n",
"m = 3.0 #Number of phase\n",
"\n",
"#Calculation\n",
"T_p = S/P #Pole pitch(slots)\n",
"slot = 180/T_p #Slots per pole(degree)\n",
"n = S/(P*m) #Number of slots or coils per pole per phase\n",
"a = slot*math.pi/180 #Pole pitch per slot(radian)\n",
"k_d = math.sin(n*a/2)/(n*math.sin(a/2)) #Distribution factor\n",
"k_p = 1.0 #Pitch factor\n",
"Z = (180/m)*slot #Number of conductors per phase\n",
"T = Z/2 #Number of turns per phase\n",
"f = P*N/120 #Frequency(Hz)\n",
"E = 4.44*k_p*k_d*f*phi_m*T #Induced voltage(V)\n",
"E_L = 3**0.5*E #Line voltage(V)\n",
"\n",
"#Result\n",
"print('Line voltage , E_L = %.1f V' %E_L)\n",
"print('\\nNOTE : Changes in obtained answer from that of textbook answer is due to precision i.e more number of decimal places')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Line voltage , E_L = 7945.7 V\n",
"\n",
"NOTE : Changes in obtained answer from that of textbook answer is due to precision i.e more number of decimal places\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.6, Page number 305-307"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"P = 4.0 #Number of poles\n",
"m = 3.0 #Number of phase \n",
"f = 50.0 #Frequency(Hz)\n",
"phi_m = 0.05 #Flux per pole(Wb)\n",
"n = 6.0 #Number of slots per pole per phase\n",
"cond = 5.0 #Conductors per layer\n",
"no_layer = 2.0 #Number of layer winding\n",
"\n",
"#Calculation\n",
"T_p = n*m #Slots per pole\n",
"slot = 180/T_p #Slots per pole(degree)\n",
"a = slot*math.pi/180 #Pole pitch per slot(radian)\n",
"T_c = (5.0/6)*T_p #Coil pitch is 5/6 of full pitch\n",
"gamma = T_p-T_c #Short pitch angle(slots)\n",
"y_angle = gamma*slot #Short pitch(angle)\n",
"y = y_angle*math.pi/180 #Short pitch(radians)\n",
"k_p = math.cos(y/2) #Pitch factor\n",
"k_d = math.sin(n*a/2)/(n*math.sin(a/2)) #Distribution factor\n",
"T = 1.0/2*n*P*cond*no_layer #Number of turns in any phase\n",
"E = 4.44*k_p*k_d*f*phi_m*T #Voltage per phase(V)\n",
"\n",
"#Result\n",
"print('Voltage per phase , E = %.2f V' %E)\n",
"print('\\nNOTE : Changes in obtained answer from that of textbook answer is due to precision i.e more number of decimal places')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Voltage per phase , E = 1230.19 V\n",
"\n",
"NOTE : Changes in obtained answer from that of textbook answer is due to precision i.e more number of decimal places\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.7, Page number 307-308"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"P = 10.0 #Number of poles\n",
"m = 3.0 #Number of phase \n",
"f = 50.0 #Frequency(Hz)\n",
"n = 3.0 #Number of slots per pole per phase\n",
"phi_m1 = 0.05 #Fundamental component of flux(Wb)\n",
"phi_m3 = 0.006 #Third harmonic component of flux(Wb)\n",
"T_c = 150.0 #Coil span(degree)\n",
"cond = 5.0 #Conductors per layer\n",
"no_layer = 2.0 #Number of layer winding\n",
"\n",
"#Calculation\n",
"T_p = n*m #Slots per pole\n",
"slot = 180/T_p #Slots per pole(degree)\n",
"a = slot*math.pi/180 #Pole pitch per slot(radian)\n",
"gamma = 180-T_c #Short pitch angle(degree)\n",
"y = gamma*math.pi/180 #Short pitch angle(radian)\n",
"T = 1.0/2*P*n*cond*no_layer #Number of turns\n",
"k_p1 = math.cos(y/2) #Fundamental pitch factor\n",
"k_d1 = math.sin(n*a/2)/(n*math.sin(a/2)) #Fundamental distribution factor\n",
"E_1 = 4.44*k_p1*k_d1*f*phi_m1*T #Fundamental emf per phase(V)\n",
"k_p3 = math.cos(3*y/2) #Third harmonic pitch factor\n",
"k_d3 = math.sin(3*n*a/2)/(n*math.sin(3*a/2)) #Third harmonic distribution factor\n",
"E_3 = 4.44*k_p3*k_d3*f*phi_m3*T #Voltage(V)\n",
"E = (E_1**2+E_3**2)**0.5 #Induced voltage per phase(V)\n",
"\n",
"#Result\n",
"print('rms value of induced voltage per phase , E = %.1f V' %E)\n",
"print('\\nNOTE : Changes in obtained answer from that of textbook answer is due to precision i.e more number of decimal places')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"rms value of induced voltage per phase , E = 1546.5 V\n",
"\n",
"NOTE : Changes in obtained answer from that of textbook answer is due to precision i.e more number of decimal places\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.8, Page number 312"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"kVA = 50.0 #Ratings(kVA)\n",
"V_t = 220.0 #Voltage(V)\n",
"R_a = 0.011 #Effective resistance(ohm)\n",
"X_s = 0.09 #Synchronous reactance(ohm)\n",
"pf = 0.85 #Lagging power factor\n",
"\n",
"#Calculation\n",
"phi = math.acos(pf) #Power factor angle(radians)\n",
"I_a = kVA*10**3/V_t #Armature current(A)\n",
"E_f = ((V_t*pf+I_a*R_a)**2+(V_t*math.sin(phi)+I_a*X_s)**2)**0.5 #Induced voltage per phase(V)\n",
"VR = ((E_f-V_t)/V_t)*100 #Voltage regulation(percent)\n",
"\n",
"#Result\n",
"print('No-load induced voltage per phase , E_f = %.1f V' %E_f)\n",
"print('Voltage regulation , VR = %.1f percent' %VR)\n",
"print('\\nNOTE : Changes in obtained answer from that of textbook answer is due to precision i.e more number of decimal places')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"No-load induced voltage per phase , E_f = 233.5 V\n",
"Voltage regulation , VR = 6.1 percent\n",
"\n",
"NOTE : Changes in obtained answer from that of textbook answer is due to precision i.e more number of decimal places\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.9, Page number 314"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"kVA = 200.0 #Rating(kVA)\n",
"V_t = 33.0*10**3 #Voltage(V)\n",
"R_a = 0.54 #Armature resistance(ohm)\n",
"V_L = 415.0 #Voltage between lines for SC test(V)\n",
"I_sh = 25.0 #Short circuit current(A)\n",
"pf = 0.9 #Lagging power factor\n",
"\n",
"#Calculation\n",
"#For case(i)\n",
"V_P = V_L/3**0.5 #Phase voltage during short circuit test(V)\n",
"Z_s = V_P/I_sh #Synchronous impedance(ohm)\n",
"#For case(ii)\n",
"X_s = (Z_s**2-R_a**2)**0.5 #Synchronous reactance(ohm)\n",
"#For case(iii)\n",
"I_a = kVA*1000/(3**0.5*V_t) #Full load current(A)\n",
"V_ta = V_t/3**0.5 #Voltage per phase of alternator(V)\n",
"phi = math.acos(pf) #Power factor angle(radians)\n",
"E_f = ((V_ta*pf+I_a*R_a)**2+(V_ta*math.sin(phi)+I_a*X_s)**2)**0.5 #No-load voltage per phase(V) \n",
"VR = ((E_f-V_ta)/V_ta)*100 #Voltage regulation\n",
"\n",
"#Result\n",
"print('(i) Synchronous impedance , Z_s = %.1f ohm' %Z_s)\n",
"print('(ii) Synchronous reactance , X_s = %.2f ohm' %X_s)\n",
"print('(iii) Voltage regulation , VR = %.2f percent' %VR)\n",
"print('\\nNOTE : ERROR : In textbook calculation , R_a is taken instead of X_s in calculation of E_f')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(i) Synchronous impedance , Z_s = 9.6 ohm\n",
"(ii) Synchronous reactance , X_s = 9.57 ohm\n",
"(iii) Voltage regulation , VR = 0.09 percent\n",
"\n",
"NOTE : ERROR : In textbook calculation , R_a is taken instead of X_s in calculation of E_f\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.10, Page number 317"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"MVA = 30.0 #Rating(MVA)\n",
"V = 20.0 #Supply voltage(kV)\n",
"N = 1800.0 #Speed(rpm)\n",
"V_t = 15.0 #Voltage per phase(kV)\n",
"E_f = 10.0 #Per phase terminal voltage(kV)\n",
"delta = 40.0 #Power angle(degree)\n",
"X_s = 6.0 #Per phase synchronous reactance(ohm)\n",
"\n",
"#Calculation\n",
"#For case(i)\n",
"d = delta*math.pi/180 #Power angle(radians)\n",
"P = 3*V_t*E_f*math.sin(d)/X_s #3-phase power delivered to the load(MW)\n",
"#For case(ii)\n",
"P_max = 3*V_t*E_f/X_s #Three phase maximum power(MW)\n",
"\n",
"#Result\n",
"print('(i) Three-phase real power delivered to the load , P = %.2f MW' %P)\n",
"print('(ii) Three-phase maximum power , P_max = %.f MW' %P_max)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(i) Three-phase real power delivered to the load , P = 48.21 MW\n",
"(ii) Three-phase maximum power , P_max = 75 MW\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.11, Page number 321-322"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"kVA = 25.0 #Rating(kVA)\n",
"V = 440.0 #Suppy voltage(V)\n",
"f = 50.0 #Supply frequency(Hz)\n",
"pf = 0.8 #Lagging power factor\n",
"R_a = 0.3 #Resistance of machine per phase(ohm)\n",
"X_d = 5.0 #Reactance of machine per phase(ohm)\n",
"X_q = 3.0 #Reactance of machine per phase(ohm)\n",
"\n",
"#Calculation\n",
"#For case(i)\n",
"phi = math.acos(pf) #Power factor angle(radians)\n",
"phi_deg = phi*180/math.pi #Power factor angle(degree)\n",
"V_t = V/3**0.5 #Terminal voltage per phase(V)\n",
"I_a = kVA*10**3/(3**0.5*V) #Armature current(A)\n",
"tan_d = (I_a*X_q*pf/(V_t+I_a*X_q*math.sin(phi)))\n",
"d = math.atan(tan_d) #Torque angle(radians)\n",
"d_angle = d*180/math.pi #Torque angle(degree)\n",
"#For case(ii)\n",
"I_d = I_a*math.sin(d+phi) #Direct axis component of the current(A)\n",
"E_f = V_t*math.cos(d)+I_d*X_d #Induced voltage per phase(V)\n",
"#For case(iii)\n",
"VR = ((E_f-V_t)/V_t)*100 #Voltage regulation(percent)\n",
"\n",
"#Result\n",
"print('(i) Torque angle , \u03b4 = %.2f\u00b0 ' %d_angle)\n",
"print('(ii) Induced voltage per phase , E_f = %.2f V' %E_f)\n",
"print('(iii) Voltage regulation , VR = %.2f percent' %VR)\n",
"print('\\nNOTE : Changes in obtained answer from that of textbook answer is due to precision i.e more number of decimal places')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(i) Torque angle , \u03b4 = 14.12\u00b0 \n",
"(ii) Induced voltage per phase , E_f = 373.80 V\n",
"(iii) Voltage regulation , VR = 47.15 percent\n",
"\n",
"NOTE : Changes in obtained answer from that of textbook answer is due to precision i.e more number of decimal places\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.12, Page number 324-325"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"import cmath\n",
"\n",
"#Variable declaration\n",
"E_1 = 220.0 #Induced voltage per phase by alternator 1(V)\n",
"E_2 = 220*cmath.exp(1j*5*math.pi/180) #Induced voltage per phase by alternator 2(V)\n",
"Z_1 = complex(0,3) #Impedance of alternator 1(ohm)\n",
"Z_2 = complex(0,4) #Impedance of alternator 2(ohm)\n",
"Z = 5.0 #Load(ohm)\n",
"\n",
"#Calculation\n",
"#For case(i)\n",
"I = (E_1*Z_2+E_2*Z_1)/(Z_1*Z_2+Z*(Z_1+Z_2)) #Load current(A)\n",
"#For case(ii)\n",
"V_t = I*Z #Terminal voltage(V)\n",
"#For case(iii)\n",
"I_a1 = ((E_1-E_2)*Z+E_1*Z_2)/(Z_1*Z_2+Z*(Z_1+Z_2)) #Armature current(A)\n",
"P_1 = abs(V_t*I_a1)*math.cos(cmath.phase(V_t)-cmath.phase(I_a1))*10**-3 #Power per phase delivered by the first alternator(W)\n",
"\n",
"#Result\n",
"print('(i) Load current , I = %.1f\u2220%.f\u00b0 A' %(abs(I),cmath.phase(I)*180/math.pi))\n",
"print('(ii) Terminal voltage , V_t = %.f\u2220%.f\u00b0 V' %(abs(V_t),cmath.phase(V_t)*180/math.pi))\n",
"print('(iii) Power per phase delivered by the first alternator , P_1 = %.1f kW' %P_1)\n",
"print('\\nNOTE : ERROR : In textbook case(iii) power calculation current I is taken instead of I_a1')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(i) Load current , I = 41.6\u2220-17\u00b0 A\n",
"(ii) Terminal voltage , V_t = 208\u2220-17\u00b0 V\n",
"(iii) Power per phase delivered by the first alternator , P_1 = 4.4 kW\n",
"\n",
"NOTE : ERROR : In textbook case(iii) power calculation current I is taken instead of I_a1\n"
]
}
],
"prompt_number": 1
}
],
"metadata": {}
}
]
}