{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"CHAPTER 6: AC DYNAMO VOLTAGE RELATIONS-ALTERNATORS"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.1, Page number 160"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"kVA = 1000.0 #Rating of the 3-phase alternator(kVA) \n",
"V_L = 4600.0 #Rated line voltage(V)\n",
"R_a = 2.0 #Armature resistance per phase(ohm)\n",
"X_s = 20.0 #Synchronous armature reactance per phase(ohm)\n",
"pf_a = 1.0 #Unity power factor\n",
"pf_b = 0.75 #Lagging power factor\n",
"\n",
"#Calculation\n",
"V_P = V_L/3**0.5 #Phase voltage(V)\n",
"I_P = kVA*1000/(3*V_P) #Phase current(A)\n",
"I_a = I_P #Armature current(A)\n",
"#Case(a)\n",
"E_g_a = complex((V_P+I_a*R_a),(I_a*X_s)) #Full-load generated voltage per phase(V/phase)\n",
"#Case(b)\n",
"sin_theta_b = (1-pf_b**2)**0.5 #Sin of angle of theta_b\n",
"E_g_b = complex((V_P*pf_b+ I_a*R_a),(V_P*sin_theta_b+I_a*X_s)) #Full-load generated voltage per phase(V/phase)\n",
"\n",
"#Result\n",
"print('Case(a): Full-load generated voltage per phase at unity PF , E_g = %d V/phase' %(abs(E_g_a)))\n",
"print('Case(b): Full-load generated voltage per phase at 0.75 PF lagging , E_g = %d V/phase' %(abs(E_g_b)))\n",
"print('\\nNOTE: \u221a3 value is taken as %f instead of 1.73 as in textbook so slight variations in the obtained answer' %(3**0.5))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Case(a): Full-load generated voltage per phase at unity PF , E_g = 3840 V/phase\n",
"Case(b): Full-load generated voltage per phase at 0.75 PF lagging , E_g = 4820 V/phase\n",
"\n",
"NOTE: \u221a3 value is taken as 1.732051 instead of 1.73 as in textbook so slight variations in the obtained answer\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.2, Page number 161"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"kVA = 1000.0 #Rating of the 3-phase alternator(kVA) \n",
"V_L = 4600.0 #Rated line voltage(V)\n",
"R_a = 2.0 #Armature resistance per phase(ohm)\n",
"X_s = 20.0 #Synchronous armature reactance per phase(ohm)\n",
"pf_a = 0.75 #Leading power factor\n",
"pf_b = 0.40 #Leading power factor\n",
"\n",
"#Calculation\n",
"V_P = V_L/3**0.5 #Phase voltage(V)\n",
"I_P = kVA*1000/(3*V_P) #Phase current(A)\n",
"I_a = I_P #Armature current(A)\n",
"#Case(a)\n",
"sin_theta_a = (1-pf_a**2)**0.5 #Sin of angle of theta_a\n",
"E_g_a = complex((V_P*pf_a+I_a*R_a),(V_P*sin_theta_a-I_a*X_s)) #Full-load generated voltage per phase(V/phase)\n",
"#Case(b)\n",
"sin_theta_b = (1-pf_b**2)**0.5 #Sin of angle of theta_b\n",
"E_g_b = complex((V_P*pf_b+ I_a*R_a),(V_P*sin_theta_b+-I_a*X_s)) #Full-load generated voltage per phase(V/phase)\n",
"\n",
"#Result\n",
"print('Case(a): Full-load generated voltage per phase at 0.75 PF leading , E_g = %d V/phase' %(abs(E_g_a)))\n",
"print('Case(b): Full-load generated voltage per phase at 0.40 PF leading , E_g = %d V/phase' %(abs(E_g_b)))\n",
"print('\\nNOTE: \u221a3 value is taken as %f instead of 1.73 as in textbook so slight variations in the obtained answer' %(3**0.5))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Case(a): Full-load generated voltage per phase at 0.75 PF leading , E_g = 2366 V/phase\n",
"Case(b): Full-load generated voltage per phase at 0.40 PF leading , E_g = 1315 V/phase\n",
"\n",
"NOTE: \u221a3 value is taken as 1.732051 instead of 1.73 as in textbook so slight variations in the obtained answer\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.3, Page number 162"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"V_P = 2655.0 #Phase voltage(V) \n",
"E_g_a1 = 4820.0 #Full-load generated voltage per phase at 0.75 PF lagging(V/phase)\n",
"E_g_b1 = 3840.0 #Full-load generated voltage per phase at unity PF(V/phase)\n",
"E_g_a2 = 2366.0 #Full-load generated voltage per phase at 0.75 PF leading(V/phase)\n",
"E_g_b2 = 1315.0 #Full-load generated voltage per phase at 0.40 PF leading(V/phase)\n",
"\n",
"#Calculation\n",
"VR_a = (E_g_a1-V_P)/V_P*100 #Voltage regulation at 0.75 PF lagging(percent)\n",
"VR_b = (E_g_b1-V_P)/V_P*100 #Voltage regulation at unity PF(percent)\n",
"VR_c = (E_g_a2-V_P)/V_P*100 #Voltage regulation at 0.75 PF leading(percent)\n",
"VR_d = (E_g_b2-V_P)/V_P*100 #Voltage regulation at 0.75 PF leading(percent)\n",
"\n",
"#Result\n",
"print('Case(a): Voltage regulation at 0.75 PF lagging , VR = %.1f percent' %VR_a)\n",
"print('Case(b): Voltage regulation at unity PF , VR = %.1f percent' %VR_b)\n",
"print('Case(c): Voltage regulation at 0.75 PF leading , VR = %.2f percent' %VR_c)\n",
"print('Case(d): Voltage regulation at 0.40 PF leading , VR = %.1f percent' %VR_d)\n",
"print('\\nNOTE: \u221a3 value is taken as %f instead of 1.73 as in textbook so slight variations in the obtained answer' %(3**0.5))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Case(a): Voltage regulation at 0.75 PF lagging , VR = 81.5 percent\n",
"Case(b): Voltage regulation at unity PF , VR = 44.6 percent\n",
"Case(c): Voltage regulation at 0.75 PF leading , VR = -10.89 percent\n",
"Case(d): Voltage regulation at 0.40 PF leading , VR = -50.5 percent\n",
"\n",
"NOTE: \u221a3 value is taken as 1.732051 instead of 1.73 as in textbook so slight variations in the obtained answer\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.4, Page number 168"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"kVA = 100.0 #Rating of the 3-phase alternator(kVA)\n",
"V_L = 1100.0 #Line voltage of the 3-phase alternator(V)\n",
"E_gp1 = 6.0 #DC voltage between lines in dc resistance test(V)\n",
"I_a1 = 10.0 #DC current in lines dc resistance test(A)\n",
"pf_1 = 0.8 #Lagging power factor\n",
"pf_2 = 0.8 #Leading power factor\n",
"E_gp2 = 420.0 #Voltage between lines in open-circuit test(V)\n",
"I_f2 = 12.5 #DC Field current in open-circuit test(A)\n",
"I_f3 = 12.5 #DC Field current in short-circuit test(A)\n",
"\n",
"#Calculation\n",
"#Case(a)\n",
"I_a_rated = kVA*1000/(V_L*3**0.5) #Rated current per phase(A)\n",
"I_a = 3**0.5*I_a_rated #Rated Line current(A)\n",
"V_l = E_gp1\n",
"R_dc = V_l/(2*I_a1) #Effective dc armature resistance(ohm/winding)\n",
"R_ac = R_dc*1.5 #Effective ac armature resistance(ohm/phase)\n",
"R_a = R_ac #Effective ac armature resistance from dc resistance test(ohm/phase)\n",
"Z_p = E_gp2/I_a #Synchronous impedance per phase(ohm/phase)\n",
"X_s = (Z_p**2-R_a**2)**0.5 #Synchronous reactance per phase(ohm/phase)\n",
"#Case(b)\n",
"V_p = V_L/3**0.5 #Phase voltage(V/phase)\n",
"V_fl = V_p #Full-load voltage(V/phase)\n",
"sin_theta_1 = (1-pf_1**2)**0.5 #Sin value of theta 1\n",
"E_gp_lag = complex((V_p*pf_1+I_a_rated*R_a),(V_p*sin_theta_1+I_a_rated*X_s)) #Generated voltage per phase at 0.8 PF lagging(V/phase)\n",
"V_nl_lag = abs(E_gp_lag) #No-load voltage(V/phase)\n",
"VR1 = (V_nl_lag-V_fl)/V_fl*100 #Voltage regulation at 0.8 PF lagging(%)\n",
"sin_theta_2 = (1-pf_2**2)**0.5 #Sin value of theta 2\n",
"E_gp_lead = complex((V_p*pf_2+I_a_rated*R_a),(V_p*sin_theta_2-I_a_rated*X_s)) #Generated voltage per phase at 0.8 PF leading(V/phase)\n",
"V_nl_lead = abs(E_gp_lead) #No-load voltage(V/phase)\n",
"VR2 = (V_nl_lead-V_fl)/V_fl*100 #Voltage regulation at 0.8 PF leading(%)\n",
"\n",
"#Result\n",
"print('Case(a): Effective resistance per phase , R_ac = %.2f \u03a9/phase' %R_ac)\n",
"print(' Synchronous impedance per phase , Z_p = %.2f \u03a9/phase' %Z_p)\n",
"print(' Synchronous reactance per phase , X_s = %.1f \u03a9/phase' %X_s)\n",
"print('Case(b): Voltage regulation at 0.8 PF lagging = %.f percent' %VR1)\n",
"print(' Voltage regulation at 0.8 PF leading = %.1f percent' %VR2)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Case(a): Effective resistance per phase , R_ac = 0.45 \u03a9/phase\n",
" Synchronous impedance per phase , Z_p = 4.62 \u03a9/phase\n",
" Synchronous reactance per phase , X_s = 4.6 \u03a9/phase\n",
"Case(b): Voltage regulation at 0.8 PF lagging = 29 percent\n",
" Voltage regulation at 0.8 PF leading = -13.4 percent\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.5, Page number 169"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"kVA = 100.0 #Rating of the 3-phase alternator(kVA)\n",
"V_L = 1100.0 #Line voltage of the 3-phase alternator(V)\n",
"E_gp1 = 6.0 #DC voltage between lines in dc resistance test(V)\n",
"I_a1 = 10.0 #DC current in lines dc resistance test(A)\n",
"pf_1 = 0.8 #Lagging power factor\n",
"pf_2 = 0.8 #Leading power factor\n",
"E_gp2 = 420.0 #Voltage between lines in open-circuit test(V)\n",
"I_f2 = 12.5 #DC Field current in open-circuit test(A)\n",
"I_f3 = 12.5 #DC Field current in short-circuit test(A)\n",
"\n",
"#Calculation\n",
"#Case(a)\n",
"I_a_rated = kVA*1000/(V_L*3**0.5) #Rated current per phase(A)\n",
"I_L = I_a_rated #Rated Line current(A)\n",
"I_p = I_L/3**0.5 #Phase current(A)\n",
"I_a = I_p #Rated Line current(A)\n",
"Z_s = E_gp2/I_p #Synchronous impedance per phase(ohm/phase)\n",
"V_l = E_gp1\n",
"R_dc = V_l/(2*I_a1) #Effective dc armature resistance(ohm/winding)\n",
"R_ac = R_dc*1.5 #Effective ac armature resistance(ohm/phase)\n",
"R_eff = 3*R_ac #Effective resistance(ohm/phase)\n",
"R_a = R_eff\n",
"X_s = (Z_s**2-R_eff**2)**0.5 #Synchronous reactance per phase(ohm/phase)\n",
"#Case(b)\n",
"V_p = V_L #Phase voltage(V/phase)\n",
"V_fl = V_p #Full-load voltage(V/phase)\n",
"sin_theta_1 = (1-pf_1**2)**0.5 #Sin value of theta 1\n",
"E_gp_lag = complex((V_p*pf_1+I_a*R_a),(V_p*sin_theta_1+I_a*X_s)) #Generated voltage per phase at 0.8 PF lagging(V/phase)\n",
"V_nl_lag = abs(E_gp_lag) #No-load voltage(V/phase)\n",
"VR1 = (V_nl_lag-V_fl)/V_fl*100 #Voltage regulation at 0.8 PF lagging(%)\n",
"sin_theta_2 = (1-pf_2**2)**0.5 #Sin value of theta 2\n",
"E_gp_lead = complex((V_p*pf_2+I_a*R_a),(V_p*sin_theta_2-I_a*X_s)) #Generated voltage per phase at 0.8 PF leading(V/phase)\n",
"V_nl_lead = abs(E_gp_lead) #No-load voltage(V/phase)\n",
"VR2 = (V_nl_lead-V_fl)/V_fl*100 #Voltage regulation at 0.8 PF leading(%)\n",
"\n",
"print('Case(a): Effective resistance per phase , R_eff = %.2f \u03a9/phase' %R_eff)\n",
"print(' Synchronous impedance per phase , Z_s = %.2f \u03a9/phase' %Z_s)\n",
"print(' Synchronous reactance per phase , X_s = %.1f \u03a9/phase' %X_s)\n",
"print('Case(b): Voltage regulation at 0.8 PF lagging = %.f percent' %VR1)\n",
"print(' Voltage regulation at 0.8 PF leading = %.1f percent' %VR2)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Case(a): Effective resistance per phase , R_eff = 1.35 \u03a9/phase\n",
" Synchronous impedance per phase , Z_s = 13.86 \u03a9/phase\n",
" Synchronous reactance per phase , X_s = 13.8 \u03a9/phase\n",
"Case(b): Voltage regulation at 0.8 PF lagging = 29 percent\n",
" Voltage regulation at 0.8 PF leading = -13.4 percent\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.6, Page number 172"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"E_L = 11000.0 #Line voltage generated(V)\n",
"kVA = 165000.0 #Rating of the alternator(kVA)\n",
"Z_p = 1.0 #Synchronous reactance(ohm)\n",
"R_p = 0.1 #Armature resistance(ohm/phase)\n",
"Z_r = 0.8 #Reactor reactance(ohm/phase)\n",
"\n",
"#Calculation\n",
"E_p = E_L/3**0.5 #Rated phase voltage(V)\n",
"I_p = kVA*1000/(3*E_p) #Rated current per phase(A)\n",
"#Case(a)\n",
"I_max_a = E_p/R_p #Maximum short-circuit current(A)\n",
"overload_a = I_max_a/I_p #Overload\n",
"#Case(b)\n",
"I_steady = E_p/Z_p #Sustained short-circuit current(A)\n",
"overload_b = I_steady/I_p #Overload\n",
"#Case(c)\n",
"Z_t = complex(R_p,Z_r) #Total reactance per phase(ohm)\n",
"I_max_c = E_p/abs(Z_t) #Maximum short-circuit current(A)\n",
"overload_c = abs(I_max_c)/I_p #Overload\n",
"\n",
"#Result\n",
"print('Case(a): Maximum short-circuit current at instant of short-circuit , I_max = %.f A' %I_max_a)\n",
"print(' Overload = %.1f * rated current' %overload_a)\n",
"print('Case(b): Sustained short-circuit current , I_steady = %.f A' %I_steady)\n",
"print(' Overload = %.2f * rated current' %overload_b)\n",
"print('Case(c): Maximum short-circuit current with reactors , I_max = %.f A' %I_max_c)\n",
"print(' Overload = %.3f * rated current' %overload_c)\n",
"print('\\nNOTE: \u221a3 value is taken as %f instead of 1.73 as in textbook so slight variations in the obtained answer' %(3**0.5))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Case(a): Maximum short-circuit current at instant of short-circuit , I_max = 63509 A\n",
" Overload = 7.3 * rated current\n",
"Case(b): Sustained short-circuit current , I_steady = 6351 A\n",
" Overload = 0.73 * rated current\n",
"Case(c): Maximum short-circuit current with reactors , I_max = 7877 A\n",
" Overload = 0.910 * rated current\n",
"\n",
"NOTE: \u221a3 value is taken as 1.732051 instead of 1.73 as in textbook so slight variations in the obtained answer\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.7, Page number 174"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"import cmath\n",
"\n",
"#Variable declaration\n",
"kVA = 100.0 #Rating of the 3-phase alternator(kVA)\n",
"V_L = 1100.0 #Line voltage of the 3-phase alternator(V)\n",
"E_gp1 = 6.0 #DC voltage between lines in dc resistance test(V)\n",
"I_a1 = 10.0 #DC current in lines dc resistance test(A)\n",
"pf = 0.8 #Lagging power factor\n",
"E_gp2 = 420.0 #Voltage between lines in open-circuit test(V)\n",
"I_f2 = 12.5 #DC Field current in open-circuit test(A)\n",
"I_f3 = 12.5 #DC Field current in short-circuit test(A)\n",
"I_L = 52.5 #Rated line current(A)\n",
"I_a = I_L #Rated current per phase(A)\n",
"E_gp = complex(532,623) #Generated voltage at 0.8 PF lagging(V/phase)\n",
"X_s = 4.6 #Synchronous reactance per phase(ohm/phase)\n",
"V_p = 635.0 #Phase voltage(V)\n",
"\n",
"#Calculation\n",
"#Case(a)\n",
"P_T = 3**0.5*V_L*I_L*pf #Total output 3-phase power(W)\n",
"#Case(b)\n",
"P_p_b = P_T*10**-3/3.0 #Total output 3-phase power per phase(W)\n",
"#Case(d)\n",
"theta = math.acos(0.8)*180/math.pi #Phase angle of PF(degree)\n",
"theta_plus_deba = cmath.phase(E_gp)*180/math.pi #Phase angle of E_gp(degrees)\n",
"deba = theta_plus_deba-theta #Torque angle(degrees)\n",
"#Case(e)\n",
"P_p_e = abs(E_gp)*10**-3/X_s*V_p*math.sin(deba*math.pi/180) #Approximate output power per phase(W)\n",
"#Case(f)\n",
"P_p_f = abs(E_gp)*10**-3*I_a*math.cos(theta_plus_deba*math.pi/180) #Approximate output power per phase(W)\n",
"\n",
"#Result\n",
"print('Case(a): Total output 3-phase power , P_T = %.f W' %P_T)\n",
"print('Case(b): Output power per phase , P_p = %.2f kW' %P_p_b)\n",
"print('Case(c): Generated voltage , E_gp = %.1f\u2220%.1f\u00b0 V' %(abs(E_gp),cmath.phase(E_gp)*180/math.pi))\n",
"print('Case(d): Torque angle , \u03b4 = %.2f\u00b0 ' %deba)\n",
"print('Case(e): Approximate output power per phase , P_p = %.f W' %P_p_e)\n",
"print('Case(f): Approximate output power per phase , P_p = %.f W' %P_p_f)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Case(a): Total output 3-phase power , P_T = 80021 W\n",
"Case(b): Output power per phase , P_p = 26.67 kW\n",
"Case(c): Generated voltage , E_gp = 819.2\u222049.5\u00b0 V\n",
"Case(d): Torque angle , \u03b4 = 12.64\u00b0 \n",
"Case(e): Approximate output power per phase , P_p = 25 W\n",
"Case(f): Approximate output power per phase , P_p = 28 W\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.8, Page number 174"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"E_g = 819.0 #Magnitude of generated voltage(V)\n",
"V_p = 635.0 #Phase voltage(V)\n",
"X_s = 4.6 #Synchronous reactance per phase(ohm/phase)\n",
"S = 1200.0 #Synchronous speed(rpm)\n",
"delta = 12.64 #Angle(degree)\n",
"\n",
"#Calculation\n",
"#Case(a)\n",
"T_p_a = 7.04*E_g*V_p*math.sin(delta*math.pi/180)/(S*X_s) #Output torque per phase(lb-ft)\n",
"T_3ph_a = 3*T_p_a #Total output torque(lb-ft)\n",
"#Case(b)\n",
"omega = S*2*math.pi/60 #Speed(rad/s)\n",
"T_p_b = E_g*V_p*math.sin(delta*math.pi/180)/(omega*X_s) #Output torque per phase(N-m)\n",
"T_3ph_b = 3*T_p_b #Total output torque(N-m)\n",
"#Case(c)\n",
"T_p_c = T_p_a*1.356 #Output torque per phase(N-m)\n",
"T_3ph_c = 3.0*T_p_c #Total output torque(N-m)\n",
"\n",
"#Result\n",
"print('Case(a): Output torque per phase , T_p = %.f lb-ft' %T_p_a)\n",
"print(' Total output torque , T_3\u03c6 = %.f lb-ft' %T_3ph_a)\n",
"print('Case(b): Output torque per phase , T_p = %.f N-m' %T_p_b)\n",
"print(' Total output torque , T_3\u03c6 = %.f N-m' %T_3ph_b)\n",
"print('Case(c): Output torque per phase , T_p = %.f N-m' %T_p_c)\n",
"print(' Total output torque , T_3\u03c6 = %.f N-m' %T_3ph_c)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Case(a): Output torque per phase , T_p = 145 lb-ft\n",
" Total output torque , T_3\u03c6 = 435 lb-ft\n",
"Case(b): Output torque per phase , T_p = 197 N-m\n",
" Total output torque , T_3\u03c6 = 591 N-m\n",
"Case(c): Output torque per phase , T_p = 197 N-m\n",
" Total output torque , T_3\u03c6 = 590 N-m\n"
]
}
],
"prompt_number": 1
}
],
"metadata": {}
}
]
}