1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
|
// Electric Machinery and Transformers
// Irving L kosow
// Prentice Hall of India
// 2nd editiom
// Chapter 12: POWER,ENERGY,AND EFFICIENCY RELATIONS OF DC AND AC DYNAMOS
// Example 12-19
clear; clc; close; // Clear the work space and console.
// Given data
V = 220 ; // Rated voltage of SCIM in volt
f = 60 ; // Frequency in Hz
P = 4 ; // Number of poles
PF = 0.85 ; // power factor of capacitor start IM
// nameplate details
hp_IM = 5 ; // power rating of IM in hp
I_L = 28 ; // Rated line current in A
S_r = 1620 ; // Rotor speed of IM in rpm
// No-load test data
I_nl = 6.4 ; // No-load line current in A
V_nl = 220 ; // No-load line voltage in volt
P_nl = 239 ; // No-load power reading in W
s_nl = 0.01 ; // No-load slip
// Blocked rotor test
I_br = 62 ; // Blocked rotor line current in A
V_br = 64 ; // Blocked rotor voltage in volt
P_br = 1922 ; // Blocked rotor power reading in W
s_br = 1 ; // blocked rotor slip(unity)
// Calculations
// case a
R_e1s = P_br / (I_br^2); // Equivalent total resistance of IM in ohm
// case b
P_in = P_nl ; // Input power to IM in W
I_1s = I_nl ; // Input current in A
P_ro = P_in - ((I_1s)^2 * R_e1s); // Rotational losses in W
// case c
S = (120*f/P); // Speed of synchronous magnetic field in rpm
S_fl = S_r ; // Full-load rotor speed of IM in rpm
s_fl = (S - S_fl)/S ; // Full-load Slip
LF1 = 1/4 ; // Load fraction
LF2 = 1/2 ; // Load fraction
LF3 = 3/4 ; // Load fraction
LF4 = 5/4 ; // Load fraction
s_LF1 = s_fl*LF1 ; // slip at 1/4 rated load
s_LF2 = s_fl*LF2 ; // slip at 1/2 rated load
s_LF3 = s_fl*LF3 ; // slip at 3/4 rated load
s_LF4 = s_fl*LF4 ; // slip at 5/4 rated load
// case d
s_o = s_nl ; // No-load slip
P_rs_LF1 = P_ro * (1 - s_LF1)/(1 - s_o); // Rotational losses in W at s_LF1
P_rs_LF2 = P_ro * (1 - s_LF2)/(1 - s_o); // Rotational losses in W at s_LF2
P_rs_LF3 = P_ro * (1 - s_LF3)/(1 - s_o); // Rotational losses in W at s_LF3
P_rs_fl = P_ro * (1 - s_fl)/(1 - s_o); // Rotational losses in W at full-load slip
P_rs_LF4 = P_ro * (1 - s_LF4)/(1 - s_o); // Rotational losses in W at s_LF4
// case e
I1s = I_L ; // Line current in A
P_cu_fl = (I1s)^2*R_e1s ; // Equivalent copper loss at full-load slip
P_cu_LF1 = (LF1)^2 * P_cu_fl ; // Equivalent copper loss at s_LF1
P_cu_LF2 = (LF2)^2 * P_cu_fl ; // Equivalent copper loss at s_LF2
P_cu_LF3 = (LF3)^2 * P_cu_fl ; // Equivalent copper loss at s_LF3
P_cu_LF4 = (LF4)^2 * P_cu_fl ; // Equivalent copper loss at s_LF4
// case f
Input = V*I_L*PF ; // Input to single phase capacitor start IM
// Efficiency at 1/4 rated load
eta_LF1 = ( Input*LF1 - (P_rs_LF1 + P_cu_LF1) ) / (Input*LF1) * 100 ;
// Efficiency at 1/2 rated load
eta_LF2 = ( Input*LF2 - (P_rs_LF2 + P_cu_LF2) ) / (Input*LF2) * 100 ;
// Efficiency at 3/4 rated load
eta_LF3 = ( Input*LF3 - (P_rs_LF3 + P_cu_LF3) ) / (Input*LF3) * 100 ;
// Efficiency at rated load
eta_fl = ( Input - (P_rs_fl + P_cu_fl) ) / (Input) * 100 ;
// Efficiency at 5/4 rated load
eta_LF4 = ( Input*LF4 - (P_rs_LF4 + P_cu_LF4) ) / (Input*LF4) * 100 ;
// case g
// since eta is calculated in percent divide it by 100 for hp calculations
P_o_LF1 = (Input*LF1*eta_LF1/100)/746 ; // Output hp at 1/4 rated load
P_o_LF2 = (Input*LF2*eta_LF2/100)/746 ; // Output hp at 1/2 rated load
P_o_LF3 = (Input*LF3*eta_LF3/100)/746 ; // Output hp at 3/4 rated load
P_o = (Input*eta_fl/100)/746 ; // Output hp at 1/4 rated load
P_o_LF4 = (Input*LF4*eta_LF4/100)/746 ; // Output hp at 5/4 rated load
// case h
hp = P_o ; // Rated output horsepower
S_fl = S_r ; // Full-load rotor speed in rpm
T_o = (P_o*5252)/S_fl ; // Outpue torque at full-load in lb-ft
T_o_Nm = T_o * 1.356 ; // Outpue torque at full-load in N-m
// Display the results
disp("Example 12-19 Solution : ");
printf(" \n a: Equivalent total resistance of IM :\n R_e1s = %.1f Ω \n",R_e1s);
printf(" \n b: Rotational losses :\n P_ro = %.1f W \n ",P_ro);
printf(" \n c: Slip at rated load : s = %.1f \n Slip,",s_fl);
printf(" \n s at %.2f rated load = %.3f",LF1,s_LF1);
printf(" \n s at %.2f rated load = %.3f",LF2,s_LF2);
printf(" \n s at %.2f rated load = %.3f",LF3,s_LF3);
printf(" \n s at %.2f rated load = %.3f \n ",LF4,s_LF4);
printf(" \n d: Rotational losses :\n ");
printf(" \n P_r at at %.2f rated load = %.1f W ",LF1,P_rs_LF1);
printf(" \n P_r at at %.2f rated load = %.1f W ",LF2,P_rs_LF2);
printf(" \n P_r at at %.2f rated load = %.1f W ",LF3,P_rs_LF3);
printf(" \n P_r at at full load = %.1f W ",P_rs_fl);
printf(" \n P_r at at %.2f rated load = %.1f W \n ",LF4,P_rs_LF4);
printf(" \n e: At full-load, P_cu = %d W \n",P_cu_fl);
printf(" \n P_cu at %.2f rated load = %.2f W",LF1,P_cu_LF1)
printf(" \n P_cu at %.2f rated load = %.2f W",LF2,P_cu_LF2)
printf(" \n P_cu at %.2f rated load = %.2f W",LF3,P_cu_LF3)
printf(" \n P_cu at %.2f rated load = %.2f W \n",LF4,P_cu_LF4)
printf(" \n f: Full-load input = %.f W \n",Input);
printf(" \n Efficiency :\n η at %.2f rated load = %.1f percent \n",LF1,eta_LF1);
printf(" \n η at %.2f rated load = %.1f percent \n",LF2,eta_LF2);
printf(" \n η at %.2f rated load = %.1f percent \n",LF3,eta_LF3);
printf(" \n η at rated load = η_fl = %.1f percent \n",eta_fl);
printf(" \n η at %.2f rated load = %.1f percent \n",LF4,eta_LF4);
printf(" \n Please note: Calculation error for η_fl in textbook.\n");
printf(" \n g: Output horsepower :\n P_o at %.2f rated load = %.3f hp \n",LF1,P_o_LF1);
printf(" \n P_o at %.2f rated load = %.3f hp \n",LF2,P_o_LF2);
printf(" \n P_o at %.2f rated load = %.3f hp \n",LF3,P_o_LF3);
printf(" \n P_o at rated load = %.3f hp \n",P_o);
printf(" \n P_o at %.2f rated load = %.3f hp \n",LF4,P_o_LF4);
printf(" \n h: Output torque at full-load :\n T_o = %.1f lb-ft",T_o);
printf(" \n T_o = %.2f N-m ≃ %.1f N-m",T_o_Nm,T_o_Nm);
|
