{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"CHAPTER 7: PARALLEL OPERATION"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.1, Page number 182"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"R_sh = 120.0 #Shunt field resistance(ohm)\n",
"R_a = 0.1 #Armature resistance(ohm)\n",
"V_L = 120.0 #Line voltage(V)\n",
"E_g1 = 125.0 #Generated voltage by dynamo A(V)\n",
"E_g2 = 120.0 #Generated voltage by dynamo B(V)\n",
"E_g3 = 114.0 #Generated voltage by dynamo C(V)\n",
"\n",
"#Calculation\n",
"#Case(a) #1\n",
"I_gA = (E_g1-V_L)/R_a #Current in the generating dynamo A(A)\n",
"I_f = V_L/R_sh #Shunt field current(A)\n",
"I_a1 = I_gA+I_f #Armature current for dynamo A(A)\n",
"I_L1 = I_gA #Current delivered by dynamo A to the bus(A)\n",
"#2\n",
"I_gB = (E_g2-V_L)/R_a #Current in the generating dynamo B(A)\n",
"I_a2 = I_gB+I_f #Armature current for dynamo B(A)\n",
"I_L2 = I_gB #Current delivered by dynamo B to the bus(A)\n",
"#3\n",
"I_gC = (V_L-E_g3)/R_a #Current in the generating dynamo C(A)\n",
"I_a3 = I_gC #Armature current for dynamo C(A)\n",
"I_L3 = I_gC+I_f #Current received by dynamo C from the bus(A)\n",
"#Case(b) #1\n",
"P_LA = V_L*I_L1 #Power delivered to the bus by dynamo A(W)\n",
"P_gA = E_g1*I_a1 #Power generated by dynamo A(W)\n",
"#2\n",
"P_LB = V_L*I_L2 #Power delivered to the bus by dynamo B(W)\n",
"P_gB = E_g2*I_a2 #Power generated by dynamo B(W)\n",
"#3\n",
"P_LC = V_L*I_L3 #Power delivered by the bus to dynamo C(W)\n",
"P_gC = E_g3*I_a3 #Power generated by dynamo C(W)\n",
"\n",
"#Result\n",
"print('Case(a) 1: Line current delivered by dynamo A to the bus , I_LA = %.f A' %I_L1)\n",
"print(' Armature current , I_a = %.f A' %I_a1)\n",
"print(' 2: Line current delivered by dynamo B to the bus , I_LB = %.f A. Thus dynamo B is floating' %I_L2)\n",
"print(' Armature current , I_a = %.f A' %I_a2)\n",
"print(' 3: Line current received by dynamo C from the bus , I_LC = %.f A' %I_L3)\n",
"print(' Armature current , I_a = %.f A' %I_a3)\n",
"print('\\nCase(b) 1: Power delivered to the bus by dynamo A , P_LA = %.f W' %P_LA)\n",
"print(' Power generated by dynamo A , P_gA = %.f W' %P_gA)\n",
"print(' 2: Dynamo B neither receives or delivers power , P_LB = %.f W' %P_LB)\n",
"print(' Power generated by dynamo B to excite its field , P_gB = %.f W' %P_gB)\n",
"print(' 3: Power delivered by the bus to dynamo C , P_LC = %.f W' %P_LC)\n",
"print(' Internal power delivered in the direction of rotation of its prime mover , P_gC = %.f W' %P_gC)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Case(a) 1: Line current delivered by dynamo A to the bus , I_LA = 50 A\n",
" Armature current , I_a = 51 A\n",
" 2: Line current delivered by dynamo B to the bus , I_LB = 0 A. Thus dynamo B is floating\n",
" Armature current , I_a = 1 A\n",
" 3: Line current received by dynamo C from the bus , I_LC = 61 A\n",
" Armature current , I_a = 60 A\n",
"\n",
"Case(b) 1: Power delivered to the bus by dynamo A , P_LA = 6000 W\n",
" Power generated by dynamo A , P_gA = 6375 W\n",
" 2: Dynamo B neither receives or delivers power , P_LB = 0 W\n",
" Power generated by dynamo B to excite its field , P_gB = 120 W\n",
" 3: Power delivered by the bus to dynamo C , P_LC = 7320 W\n",
" Internal power delivered in the direction of rotation of its prime mover , P_gC = 6840 W\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.2, Page number 182"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"R_a = 0.1 #Armature resistance(ohm)\n",
"R_f = 100.0 #Field circuit resistance(ohm)\n",
"V_L_b = 120.0 #Bus voltage(V)\n",
"V_L_a = 140.0 #Generated voltage of the generator(V)\n",
"\n",
"#Calculation\n",
"#Case(a)\n",
"V_f = V_L_a #Voltage across the field(V)\n",
"I_f_a = V_f/R_f #Field current(A)\n",
"I_a_a = I_f_a #Armature current(A)\n",
"E_g_a = V_L_a+I_a_a*R_a #Generated EMF(V)\n",
"P_g_a = E_g_a*I_a_a #Generated power(W)\n",
"#Case(b)\n",
"I_a_b = (E_g_a-V_L_b)/R_a #Armature current(A)\n",
"I_f_b = V_L_b/R_f #Field current(A)\n",
"I_Lg = I_a_b-I_f_b #Generated line current(A)\n",
"P_L = V_L_b*I_Lg #Power generated across the lines(W)\n",
"E_g_b = V_L_a\n",
"P_g_b = E_g_b*I_a_b #Generated power(W)\n",
"\n",
"#Result\n",
"print('Case(a): Generated current before it is connected to the bus , I_a = %.1f A' %I_a_a)\n",
"print(' Generated power before it is connected to the bus , P_g = %.1f W' %P_g_a)\n",
"print('Case(b): Generated armature current after it is connected to the bus , I_a = %.1f A' %I_a_b)\n",
"print(' Generated line current after it is connected to the bus , I_Lg = %.1f A' %I_Lg)\n",
"print(' Generated power across the line after it is connected to the bus , P_g = %.f W' %P_L)\n",
"print(' Generated power after it is connected to the bus , P_g = %.f W' %P_g_b)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Case(a): Generated current before it is connected to the bus , I_a = 1.4 A\n",
" Generated power before it is connected to the bus , P_g = 196.2 W\n",
"Case(b): Generated armature current after it is connected to the bus , I_a = 201.4 A\n",
" Generated line current after it is connected to the bus , I_Lg = 200.2 A\n",
" Generated power across the line after it is connected to the bus , P_g = 24024 W\n",
" Generated power after it is connected to the bus , P_g = 28196 W\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.3, Page number 183"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"R_a1 = 0.1 #Armature resistance of shunt generator 1(ohm)\n",
"R_a2 = 0.1 #Armature resistance of shunt generator 2(ohm)\n",
"R_a3 = 0.1 #Armature resistance of shunt generator 3(ohm)\n",
"R_L = 2.0 #Load resistance(ohm)\n",
"E_g1 = 127.0 #Voltage generated by shunt generator 1(V)\n",
"E_g2 = 120.0 #Voltage generated by shunt generator 2(V)\n",
"E_g3 = 119.0 #Voltage generated by shunt generator 3(V)\n",
"\n",
"#Calculation\n",
"#Case(a)\n",
"V_L = ((E_g1/R_a1)+(E_g2/R_a2)+(E_g3/R_a3))/((1/R_a1)+(1/R_a2)+(1/R_a3)+(1/R_L))\n",
"#Case(b)\n",
"I_L1 = (E_g1-V_L)/R_a1 #Current delivered/received by generator 1(A)\n",
"I_L2 = (E_g2-V_L)/R_a2 #Current delivered/received by generator 2(A)\n",
"I_L3 = (E_g3-V_L)/R_a3 #Current delivered/received by generator 3(A)\n",
"I_L = -V_L/R_L #Current received by 2 ohm load(A)\n",
"#Case(c)\n",
"I_a1 = I_L1 #Armature current for generator 1(A)\n",
"I_a2 = I_L2 #Armature current for generator 2(A)\n",
"I_a3 = I_L3 #Armature current for generator 3(A)\n",
"P_g1 = E_g1*I_a1 #Power generated by generator 1(W)\n",
"P_g2 = E_g2*I_a2 #Power generated by generator 2(W)\n",
"P_g3 = E_g3*I_a3 #Power generated by generator 3(W)\n",
"#Case(d)\n",
"P_L1 = V_L*I_L1 #Power delivered/received from generator 1(W)\n",
"P_L2 = V_L*I_L2 #Power delivered/received from generator 2(W)\n",
"P_L3 = V_L*I_L3 #Power delivered/received from generator 3(W)\n",
"P_L = V_L*I_L #Power delivered/received from 2 ohm load(W)\n",
"\n",
"#Result\n",
"print('Case(a): Terminal bus voltage , V_L = %.f V' %V_L)\n",
"print('Case(b): Current delivered to the bus by generator 1 , I_L1 = %.f A (to bus)' %I_L1)\n",
"print(' Current delivered to the bus by generator 2 , I_L2 = %.f A' %I_L2)\n",
"print(' Current received by the generator 3 from the bus , I_L3 = %.f A (from bus)' %I_L3)\n",
"print(' Current received from the bus by load , I_L3 = %.f A (from bus)' %I_L)\n",
"print('Case(c): Power generated by generator 1 , P_g1 = %.f W' %P_g1)\n",
"print(' Power generated by generator 2 , P_g2 = %.f W (floating)' %P_g2)\n",
"print(' Power generated by generator 3 , P_g3 = %.f W' %P_g3)\n",
"print('Case(d): Power delivered to the bus from generator 1 , P_L1 = %.f W' %P_L1)\n",
"print(' Power delivered to the bus from generator 2 , P_L2 = %.f W' %P_L2)\n",
"print(' Power received from the bus by generator 3 , P_L2 = %.f W' %P_L3)\n",
"print(' Power received from the bus by load , P_L = %.f W' %P_L)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Case(a): Terminal bus voltage , V_L = 120 V\n",
"Case(b): Current delivered to the bus by generator 1 , I_L1 = 70 A (to bus)\n",
" Current delivered to the bus by generator 2 , I_L2 = 0 A\n",
" Current received by the generator 3 from the bus , I_L3 = -10 A (from bus)\n",
" Current received from the bus by load , I_L3 = -60 A (from bus)\n",
"Case(c): Power generated by generator 1 , P_g1 = 8890 W\n",
" Power generated by generator 2 , P_g2 = 0 W (floating)\n",
" Power generated by generator 3 , P_g3 = -1190 W\n",
"Case(d): Power delivered to the bus from generator 1 , P_L1 = 8400 W\n",
" Power delivered to the bus from generator 2 , P_L2 = 0 W\n",
" Power received from the bus by generator 3 , P_L2 = -1200 W\n",
" Power received from the bus by load , P_L = -7200 W\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.4, Page number 184"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"P1 = 300.0 #Power rating of generator 1(kW)\n",
"P2 = 600.0 #Power rating of generator 2(kW)\n",
"V = 220.0 #Voltage rating of generator 1 and 2(V)\n",
"V_o = 250.0 #No-load voltage applied to both the generators(V)\n",
"V_1 = 230.0 #Terminal voltage(V)\n",
"V_2 = 240.0 #Terminal voltage(V)\n",
"\n",
"#Calculation\n",
"#Case(a)\n",
"kW1_a = (V_o-V_1)/(V_o-V)*P1 #Load carried by generator 1(kW)\n",
"kW2_a = (V_o-V_1)/(V_o-V)*P2 #Load carried by generator 2(kW)\n",
"#Case(b)\n",
"kW1_b = (V_o-V_2)/(V_o-V)*P1 #Load carried by generator 1(kW)\n",
"kW2_b = (V_o-V_2)/(V_o-V)*P2 #Load carried by generator 2(kW)\n",
"#Case(c)\n",
"frac_a = (V_o-V_1)/(V_o-V) #Fraction of rated kW carried by each generator\n",
"frac_b = (V_o-V_2)/(V_o-V) #Fraction of rated kW carried by each generator\n",
"\n",
"#Result\n",
"print('Case(a): When the terminal voltage is 230 V Generator 1 carries = %.f kW' %kW1_a)\n",
"print(' When the terminal voltage is 230 V Generator 2 carries = %.f kW' %kW2_a)\n",
"print('Case(b): When the terminal voltage is 240 V Generator 1 carries = %.f kW' %kW1_b)\n",
"print(' When the terminal voltage is 240 V Generator 2 carries = %.f kW' %kW2_b)\n",
"print('Case(c): Both generators carry no-load at 250 V ; %.3f rated load at %d V ; %.3f rated load at %d V ; and rated load at %d V ;' %(frac_b,V_2,frac_a,V_1,V))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Case(a): When the terminal voltage is 230 V Generator 1 carries = 200 kW\n",
" When the terminal voltage is 230 V Generator 2 carries = 400 kW\n",
"Case(b): When the terminal voltage is 240 V Generator 1 carries = 100 kW\n",
" When the terminal voltage is 240 V Generator 2 carries = 200 kW\n",
"Case(c): Both generators carry no-load at 250 V ; 0.333 rated load at 240 V ; 0.667 rated load at 230 V ; and rated load at 220 V ;\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.5, Page number 191"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"E_1 = 220.0 #Terminal voltage of alternator 1(V)\n",
"E_2 = 222.0 #Terminal voltage of alternator 2(V)\n",
"f_1 = 60.0 #Frequency of alternator 1(Hz)\n",
"f_2 = 59.5 #Frequency of alternator 2(Hz)\n",
"\n",
"#Calculation\n",
"E_max = (E_1+E_2)/2 #Maximum effective voltage across each lamp(V) \n",
"E_min = (E_2-E_1)/2 #Minimum effective voltage across each lamp(V) \n",
"f = f_1-f_2 #Frequency of the voltage across the lamps(Hz)\n",
"E_peak = E_max/0.7071 #Peak value of the voltage across each lamp(V)\n",
"n = (1.0/2)*f_1 #Number of maximum light pulsations per minute\n",
"\n",
"#Result\n",
"print('Case(a): Maximum effective voltage across each lamp , E_max/lamp = %.f V (rms)' %E_max)\n",
"print(' Minimum effective voltage across each lamp , E_min/lamp = %.f V' %E_min)\n",
"print('Case(b): Frequency of the voltage across the lamps , f = %.1f Hz' %f)\n",
"print('Case(c): Peak value of the voltage across each lamp , E_peak = %.f V' %E_peak)\n",
"print('Case(d): Number of maximum light pulsations per minute , n = %.f pulsations/min' %n)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Case(a): Maximum effective voltage across each lamp , E_max/lamp = 221 V (rms)\n",
" Minimum effective voltage across each lamp , E_min/lamp = 1 V\n",
"Case(b): Frequency of the voltage across the lamps , f = 0.5 Hz\n",
"Case(c): Peak value of the voltage across each lamp , E_peak = 313 V\n",
"Case(d): Number of maximum light pulsations per minute , n = 30 pulsations/min\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.6, Page number 191"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"E_1 = 220.0 #Voltage generated by alternator 1(V)\n",
"E_2 = 220.0 #Voltage generated by alternator 2(V)\n",
"f_1 = 60.0 #Frequency of alternator 1(Hz)\n",
"f_2 = 58.0 #Frequency of alternator 2(Hz)\n",
"\n",
"#Calculation\n",
"E_max = (E_1+E_2)/2 #Maximum effective voltage across each lamp(V)\n",
"f = f_1-f_2 #Frequency of the voltage across the lamp(Hz)\n",
"E_min = (E_2-E_1)/2 #Minimum effective voltage across each lamp(V) \n",
"\n",
"#Result\n",
"print('Case(a): Maximum effective voltage across each lamp , E_max/lamp = %.f V' %E_max)\n",
"print(' Frequency of the voltage across each lamp , f = %.f Hz' %f)\n",
"print('Case(b): The voltages are equal and opposite in the local circuit')\n",
"print('Case(c): Minimum effective voltage across each lamp , E_min/lamp = %.f V' %E_min)\n",
"print(' Frequency of the voltage across each lamp , f = 0 Hz')\n",
"print('Case(d): The voltages are in phase in the local circuit')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Case(a): Maximum effective voltage across each lamp , E_max/lamp = 220 V\n",
" Frequency of the voltage across each lamp , f = 2 Hz\n",
"Case(b): The voltages are equal and opposite in the local circuit\n",
"Case(c): Minimum effective voltage across each lamp , E_min/lamp = 0 V\n",
" Frequency of the voltage across each lamp , f = 0 Hz\n",
"Case(d): The voltages are in phase in the local circuit\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.7, Page number 193"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"import cmath\n",
"\n",
"#Variable declaration\n",
"E_1 = 220.0 #Terminal voltage of alternator 1(V) From Ex. 7-5\n",
"E_2 = 222.0 #Terminal voltage of alternator 2(V)\n",
"f_1 = 60.0 #Frequency of alternator 1(Hz)\n",
"f_2 = 59.5 #Frequency of alternator 2(Hz)\n",
"E1 = 220.0 #Voltage generated by alternator 1(V) From Ex. 7-6\n",
"E2 = 220.0 #Voltage generated by alternator 2(V)\n",
"f1 = 60.0 #Frequency of alternator 1(Hz)\n",
"f2 = 58.0 #Frequency of alternator 2(Hz)\n",
"R_a1 = 0.1 #Armature resistance of alternator 1(ohm)\n",
"R_a2 = 0.1 #Armature resistance of alternator 2(ohm)\n",
"X_a1 = 0.9 #Armature reactance of alternator 1(ohm)\n",
"X_a2 = 0.9 #Armature reactance of alternator 2(ohm)\n",
"\n",
"#Calculation\n",
"Z_1 = complex(R_a1,X_a1) #Effective impedance of alternator 1(ohm)\n",
"Z_2 = complex(R_a2,X_a2) #Effective impedance of alternator 2(ohm)\n",
"#In Ex.7-5\n",
"E_r = E_2-E_1 #Effective voltage generated(V) \n",
"I_s = E_r/(Z_1+Z_2) #Synchronizing current in the armature(A)\n",
"#In Ex.7-6\n",
"Er = E2 -E1 #Effective voltage generated(V)\n",
"Is = Er/(Z_1+Z_2) #Synchronizing current in the armature(A)\n",
"\n",
"#Result\n",
"print('In Ex.7-5 the synchronizing current in the armatures of both alternators , I_s = %.3f\u2220%.2f\u00b0 A' %(abs(I_s),cmath.phase(I_s)*180/math.pi))\n",
"print('In Ex.7-6 the synchronizing current in the armatures of both alternators , I_s = %.f\u2220%.f\u00b0 A' %(abs(Is),cmath.phase(Is)*180/math.pi))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"In Ex.7-5 the synchronizing current in the armatures of both alternators , I_s = 1.104\u2220-83.66\u00b0 A\n",
"In Ex.7-6 the synchronizing current in the armatures of both alternators , I_s = 0\u22200\u00b0 A\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.8, Page number 195"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"import cmath\n",
"\n",
"#Variable declaration\n",
"E_gp1 = 200.0 #Terminal voltage of alternator 1(V)\n",
"E_gp2 = 220.0 #Terminal voltage of alternator 2(V)\n",
"R_a1 = 0.2 #Armature resistance of alternator 1(ohm)\n",
"R_a2 = 0.2 #Armature resistance of alternator 2(ohm)\n",
"X_a1 = 2.0 #Armature reactance of alternator 1(ohm)\n",
"X_a2 = 2.0 #Armature reactance of alternator 1(ohm)\n",
"\n",
"#Calculation\n",
"#Case(a)\n",
"Z_p1 = complex(R_a1,X_a1) #Effective impedance of alternator 1(ohm)\n",
"Z_p2 = complex(R_a2,X_a2) #Effective impedance of alternator 2(ohm)\n",
"E_r = (E_gp2-E_gp1) #Effective voltage generated(V)\n",
"I_s = E_r/(Z_p1+Z_p2) #Synchronizing current in the armature(A)\n",
"Is = abs(I_s) #Magnitude of Synchronizing current(A)\n",
"theta = cmath.phase(I_s)*180/math.pi #Angle of Synchronizing current(degree)\n",
"P_2 = E_gp2*Is*math.cos(theta*math.pi/180) #Generator action developed by alternator 2(W)\n",
"#Case(b)\n",
"P_1 = -E_gp1*Is*math.cos(theta*math.pi/180) #Synchronizing power received by alternator 1(W) \n",
"#Case(c)\n",
"P1 = abs(P_1) #Magnitude of P1(W)\n",
"losses = P_2-P1 #Power loss in both armatures(W)\n",
"check = E_r*Is*math.cos(theta*math.pi/180) #Verifying losses(W) by Eq.7-7\n",
"double_check = Is**2*(R_a1+R_a2) #Verifying losses(W) by Eq.7-7\n",
"#Case(d)\n",
"V_p2 = E_gp2-Is*abs(Z_p2) #Generator action(V)\n",
"V_p1 = E_gp1+Is*abs(Z_p1) #Motor action(V)\n",
"\n",
"#Result\n",
"print('Case(a): Generator action developed by alternator 2 , P_2 = %.1f W' %P_2)\n",
"print('Case(b): Synchronizing power received by alternator 1 , P_1 = %.1f W' %P_1)\n",
"print('Case(c): Power loss in both armature , Losses = %.f W' %losses)\n",
"print('Case(d): Terminal voltage of alternator 2 , V_p2 = %.f V (generator action)' %V_p2)\n",
"print(' Terminal voltage of alternator 1 , V_p2 = %.f V (motor action)' %V_p1)\n",
"print('Case(e): Phasor diagram is shown in Fig 7-14 in textbook page no 195')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Case(a): Generator action developed by alternator 2 , P_2 = 108.9 W\n",
"Case(b): Synchronizing power received by alternator 1 , P_1 = -99.0 W\n",
"Case(c): Power loss in both armature , Losses = 10 W\n",
"Case(d): Terminal voltage of alternator 2 , V_p2 = 210 V (generator action)\n",
" Terminal voltage of alternator 1 , V_p2 = 210 V (motor action)\n",
"Case(e): Phasor diagram is shown in Fig 7-14 in textbook page no 195\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.9, Page number 199"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"import cmath\n",
"\n",
"#Variable declaration\n",
"E_2 = 230.0*cmath.exp(1j*180.0*math.pi/180) #Voltage generated by alternator 2(V)\n",
"E_1 = 230.0*cmath.exp(1j*20.0*math.pi/180) #Voltage generated by alternator 1(V)\n",
"Z = 2.01*cmath.exp(1j*84.3*math.pi/180) #Impedance(ohm)\n",
"\n",
"#Calculation\n",
"E_r = E_2+E_1 #Total voltage generated by Alternator 1 and 2(V)\n",
"Z_1 = Z\n",
"Z_2 = Z\n",
"#Case(a)\n",
"I_s = E_r/(Z_1+Z_2) #Synchronizing current(A)\n",
"Is = abs(I_s) #Magnitude of Synchronizing current(A)\n",
"I_s_a = cmath.phase(I_s)*180/math.pi #Phase angle of Synchronizing current(degrees)\n",
"#Case(b)\n",
"E_gp1 = abs(E_1)\n",
"E_gp1_Is = (cmath.phase(E_1)*180/math.pi)-I_s_a #Angle(degree)\n",
"P_1 = E_gp1*Is*math.cos(E_gp1_Is*math.pi/180) #Synchronizing power developed by alternator 1(W)\n",
"#Case(c)\n",
"E_gp2 = abs(E_2)\n",
"E_gp2_Is = (cmath.phase(E_2)*180/math.pi)-I_s_a #Angle(degree)\n",
"P_2 = E_gp2*Is*math.cos(E_gp2_Is*math.pi/180) #Synchronizing power developed by alternator 2(W)\n",
"#Case(d)\n",
"P2 = abs(P_2);\n",
"losses = P_1-P2 #Losses in the armature(W)\n",
"theta = cmath.phase(Z)*180/math.pi #Angle(degree)\n",
"check = abs(E_r)*Is*math.cos(theta*math.pi/180) #Verifying losses(W) by Eq.7-7\n",
"R_aT = 2*Z.real #Total armature resistance of alternator 1 and 2(ohm)\n",
"double_check = Is**2*R_aT #Verifying losses(W) by Eq.7-7\n",
"\n",
"#Result\n",
"print('Case(a): Synchronizing current , I_s = %.2f\u2220%.1f\u00b0 A' %(Is,I_s_a))\n",
"print('Case(b): Synchronizing power developed by alternator 1 , P_1 = %.f W (power delivered to bus)' %P_1)\n",
"print('Case(c): Synchronizing power developed by alternator 2 , P_2 = %.f W (power received from bus)' %P_2)\n",
"print('Case(d): Losses in the armature , Losses = %.f W' %losses)\n",
"print('\\nNOTE: Changes in obtained answer from that of textbook is due to more precision i.e more number of decimal places')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Case(a): Synchronizing current , I_s = 19.87\u222015.7\u00b0 A\n",
"Case(b): Synchronizing power developed by alternator 1 , P_1 = 4557 W (power delivered to bus)\n",
"Case(c): Synchronizing power developed by alternator 2 , P_2 = -4400 W (power received from bus)\n",
"Case(d): Losses in the armature , Losses = 158 W\n",
"\n",
"NOTE: Changes in obtained answer from that of textbook is due to more precision i.e more number of decimal places\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.10, Page number 200"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"import cmath\n",
"\n",
"#Variable declaration\n",
"E_2 = 230.0*cmath.exp(1j*180.0*math.pi/180) #Voltage generated by alternator 2(V)\n",
"E_1 = 230.0*cmath.exp(1j*20.0*math.pi/180) #Voltage generated by alternator 1(V)\n",
"Z = 6.0*cmath.exp(1j*50.0*math.pi/180) #Impedance(ohm)\n",
"\n",
"#Calculation\n",
"E_r = E_2+E_1 #Total voltage generated by Alternator 1 and 2(V)\n",
"Z_1 = Z\n",
"Z_2 = Z\n",
"#Case(a)\n",
"I_s = E_r/(Z_1+Z_2) #Synchronizing current(A)\n",
"Is = abs(I_s) #Magnitude of Synchronizing current(A)\n",
"I_s_a = cmath.phase(I_s)*180/math.pi #Phase angle of Synchronizing current(degrees)\n",
"#Case(b)\n",
"E_gp1 = abs(E_1)\n",
"E_gp1_Is = (cmath.phase(E_1)*180/math.pi)-I_s_a #Angle(degree)\n",
"P_1 = E_gp1*Is*math.cos(E_gp1_Is*math.pi/180) #Synchronizing power developed by alternator 1(W)\n",
"#Case(c)\n",
"E_gp2 = abs(E_2)\n",
"E_gp2_Is = (cmath.phase(E_2)*180/math.pi)-I_s_a #Angle(degree)\n",
"P_2 = E_gp2*Is*math.cos(E_gp2_Is*math.pi/180) #Synchronizing power developed by alternator 2(W)\n",
"#Case(d)\n",
"P2 = abs(P_2);\n",
"losses = P_1-P2 #Losses in the armature(W)\n",
"theta = cmath.phase(Z)*180/math.pi #Angle(degree)\n",
"check = abs(E_r)*Is*math.cos(theta*math.pi/180) #Verifying losses(W) by Eq.7-7\n",
"R_aT = 2*Z.real #Total armature resistance of alternator 1 and 2(ohm)\n",
"double_check = Is**2*R_aT #Verifying losses(W) by Eq.7-7\n",
"\n",
"#Result\n",
"print('Case(a): Synchronizing current , I_s = %.2f\u2220%.1f\u00b0 A' %(Is,I_s_a))\n",
"print('Case(b): Synchronizing power developed by alternator 1 , P_1 = %.f W (power delivered to bus)' %P_1)\n",
"print('Case(c): Synchronizing power developed by alternator 2 , P_2 = %.f W (power received from bus)' %P_2)\n",
"print('Case(d): Losses in the armature , Losses = %.f W' %losses)\n",
"print('\\nNOTE: Changes in obtained answer from that of textbook is due to more precision i.e more number of decimal places')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Case(a): Synchronizing current , I_s = 6.66\u222050.0\u00b0 A\n",
"Case(b): Synchronizing power developed by alternator 1 , P_1 = 1326 W (power delivered to bus)\n",
"Case(c): Synchronizing power developed by alternator 2 , P_2 = -984 W (power received from bus)\n",
"Case(d): Losses in the armature , Losses = 342 W\n",
"\n",
"NOTE: Changes in obtained answer from that of textbook is due to more precision i.e more number of decimal places\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.11, Page number 207"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"import cmath\n",
"import numpy\n",
"\n",
"#Variable declaration\n",
"V_AB = 100.0*cmath.exp(1j*0.0*math.pi/180) #Voltage supplied across A & B(V)\n",
"V_BC = 100.0*cmath.exp(1j*-120.0*math.pi/180) #Voltage supplied across B & C(V)\n",
"V_CA = 100.0*cmath.exp(1j*120.0*math.pi/180) #Voltage supplied across C & A(V)\n",
"I1_1 = complex(6,0)\n",
"I1_2 = complex(-3,0)\n",
"I2_1 = complex(-3,0)\n",
"I2_2 = complex(3,-4)\n",
"V_1 = complex(100,0)\n",
"V_2 = complex(-50,-86.6)\n",
"\n",
"#Calculation\n",
"A = [[I1_1,I2_1],[I1_2,I2_2]] #Matrix containing mesh equations array\n",
"delta = numpy.linalg.det(A) #Determinant of A\n",
"#Case(a)\n",
"I_1 = numpy.linalg.det([[V_1,I2_1],[V_2,I2_2]])/delta #Mesh current I_1(A) \n",
"I_2 = numpy.linalg.det([[I1_1,V_1],[I1_2,V_2]])/delta #Mesh current I_2(A) \n",
"#Case(b)\n",
"I_A = I_1 #Line current(A)\n",
"I_B = I_2-I_1 #Line current(A)\n",
"I_C = -I_2 #Line current(A)\n",
"#Case(c)\n",
"Z_A = complex(3,0) #Impedance(ohm)\n",
"Z_B = complex(3,0) #Impedance(ohm)\n",
"Z_C = complex(0,-4) #Impedance(ohm)\n",
"V_AO = I_A*Z_A #Phase voltage(V)\n",
"V_BO = I_B*Z_B #Phase voltage(V)\n",
"V_CO = I_C*Z_C #Phase voltage(V)\n",
"\n",
"#Result\n",
"print('Case(a): Mesh current , I_1 = (%.3f%.4fj) A = %.1f\u2220%.2f\u00b0 A' %(I_1.real,I_1.imag,abs(I_1),cmath.phase(I_1)*180/math.pi))\n",
"print(' Mesh current , I_2 = (%.2f%.3fj) A = %.2f\u2220%.2f\u00b0 A' %(I_2.real,I_2.imag,abs(I_2),cmath.phase(I_2)*180/math.pi))\n",
"print('Case(a): Line current , I_A = (%.2f%.3fj) A = %.1f\u2220%.2f\u00b0 A' %(I_A.real,I_A.imag,abs(I_A),cmath.phase(I_A)*180/math.pi))\n",
"print(' Line current , I_B = (%.3f%.3fj) A = %.3f\u2220%.2f\u00b0 A' %(I_B.real,I_B.imag,abs(I_B),cmath.phase(I_B)*180/math.pi))\n",
"print(' Line current , I_C = (%.2f+%.3fj) A = %.2f\u2220%.2f\u00b0 A' %(I_C.real,I_C.imag,abs(I_C),cmath.phase(I_C)*180/math.pi))\n",
"print('Case(c): Phase voltage , V_AO = %.1f\u2220%.2f\u00b0 V' %(abs(V_AO),cmath.phase(V_AO)*180/math.pi))\n",
"print(' Phase voltage , V_BO = %.2f\u2220%.1f\u00b0 V' %(abs(V_BO),cmath.phase(V_BO)*180/math.pi))\n",
"print(' Phase voltage , V_CO = %.2f\u2220%.2f\u00b0 V' %(abs(V_CO),cmath.phase(V_CO)*180/math.pi))\n",
"print('Case(d): The phasor diagram is shown in fig 7-23b in textbook page no.208')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Case(a): Mesh current , I_1 = (26.157-3.5589j) A = 26.4\u2220-7.75\u00b0 A\n",
" Mesh current , I_2 = (18.98-7.118j) A = 20.27\u2220-20.56\u00b0 A\n",
"Case(a): Line current , I_A = (26.16-3.559j) A = 26.4\u2220-7.75\u00b0 A\n",
" Line current , I_B = (-7.176-3.559j) A = 8.010\u2220-153.62\u00b0 A\n",
" Line current , I_C = (-18.98+7.118j) A = 20.27\u2220159.44\u00b0 A\n",
"Case(c): Phase voltage , V_AO = 79.2\u2220-7.75\u00b0 V\n",
" Phase voltage , V_BO = 24.03\u2220-153.6\u00b0 V\n",
" Phase voltage , V_CO = 81.09\u222069.44\u00b0 V\n",
"Case(d): The phasor diagram is shown in fig 7-23b in textbook page no.208\n"
]
}
],
"prompt_number": 1
}
],
"metadata": {}
}
]
}