# Induction motors

The nominal power in kW (Pn) of a motor indicates its rated equivalent mechanical power output.

The apparent power in kVA (Pa) supplied to the motor is a function of the output, the motor efficiency and the power factor: $\displaystyle{ Pa=\frac{Pn}{\eta\cos\varphi} }$

## Current demand

The rated current In supplied to the motor is given by the following formulae:

### 3-phase motor

$\displaystyle{ I_n=\frac{P_n \times 10^3}{\sqrt 3 \times U \times \eta \times cos\varphi} }$

### 1-phase motor

$\displaystyle{ I_n=\frac{P_n \times 10^3}{U \times \eta \times cos\varphi} }$

where

In = rated demand (in amps)
Pn = nominal power (in kW)
U = voltage between phases for 3-phase motors and voltage between the terminals for single-phase motors (in volts). A single-phase motor may be connected phase-to-neutral or phase-to-phase.
η = per-unit efficiency, i.e. output kW / input kW
cos φ = power factor, i.e. kW input / kVA input

## Subtransient current and protection setting

• Subtransient current peak value can be very high; typical value is about 12 to 15 times the rms rated value In. Sometimes this value can reach 25 times In.
• Schneider Electric circuit-breakers, contactors and thermal relays are designed to withstand motor starts with very high subtransient current (subtransient peak value can be up to 19 times the rms rated value In).
• If unexpected tripping of the overcurrent protection occurs during starting, this means the starting current exceeds the normal limits. As a result, some maximum switchgear withstands can be reached, life time can be reduced and even some devices can be destroyed. In order to avoid such a situation, oversizing of the switchgear must be considered.
• Schneider Electric switchgears are designed to ensure the protection of motor starters against short-circuits. According to the risk, tables show the combination of circuit-breaker, contactor and thermal relay to obtain type 1 or type 2 coordination (see chapter Characteristics of particular sources and loads).

## Motor starting current

Although high efficiency motors can be found on the market, in practice their starting currents are roughly the same as some of standard motors. The use of start-delta starter, static soft start unit or variable speed drive allows to reduce the value of the starting current (Example: 4 In instead of 7.5 In).

## Compensation of reactive-power (kvar) supplied to induction motors

It is generally advantageous for technical and financial reasons to reduce the current supplied to induction motors. This can be achieved by using capacitors without affecting the power output of the motors.

The application of this principle to the operation of induction motors is generally referred to as “power-factor improvement” or “power-factor correction”. As discussed in chapter Power Factor Correction, the apparent power (kVA) supplied to an induction motor can be significantly reduced by the use of shunt-connected capacitors. Reduction of input kVA means a corresponding reduction of input current (since the voltage remains constant).

Compensation of reactive-power is particularly advised for motors that operate for long periods at reduced power.

As noted above $\displaystyle{ \mbox{cos}\,\varphi= \frac{\mbox{kW input} }{\mbox{kVA input} } }$ so that a kVA input reduction in kVA input will increase (i.e. improve) the value of cosφ

The current supplied to the motor, after power-factor correction, is given by:

$\displaystyle{ \mbox{I} = \mbox{Ia}\frac{\mbox{cos}\,\varphi}{\mbox{cos}\,\varphi^{'}} }$

where cos φ is the power factor before compensation and cos φ' is the power factor after compensation, In being the original current.

Figure A4 below shows, in function of motor rated power, standard motor current values for several voltage supplies (IEC 60947-4-1 Annex G).

Fig. A4 – Rated operational power and currents
kW hp 230V 380 - 415V 400V 440- 480 V 500V 690V
A A A A A A
0.18
0.25
0.37
-
-
-
1.0
1.5
1.9
-
-
-
0.6
0.85
1.1
-
-
-
0.48
0.68
0.88
0.35
0.49
0.64
-
0.55
-
1/2
-
3/4
-
2.6
-
1.3
-
1.8
-
1.5
-
1.1
-
1.6
-
1.2
-
-
0.87
-
-
0.75
1.1
1
-
-
-
3.3
4.7
2.3
-
-
-
1.9
2.7
2.1
-
-
-
1.5
2.2
-
1.1
1.6
-
-
1.5
1-1/2
2
-
-
-
6.3
3.3
4.3
-
-
-
3.6
3.0
3.4
-
-
-
2.9
-
-
2.1
2.2
-
3.0
-
3
-
8.5
-
11.3
-
6.1
-
4.9
-
6.5
-
4.8
-
3.9
-
5.2
2.8
-
3.8
4
-
5.5
-
5
-
15
-
20
9.7
9.7
-
8.5
-
11.5
7.6
7.6
-
6.8
-
9.2
4.9
-
6.7
-
-
7.5
7-1/2
10
-
-
-
27
14.0
18.0
-
-
-
15.5
11.0
14.0
-
-
-
12.4
-
-
8.9
11
-
-
-
15
20
38.0
-
-
-
27.0
34.0
22.0
-
-
-
21.0
27.0
17.6
-
-
12.8
-
-
15
18.5
-
-
-
25
51
61
-
-
-
44
39
35
-
-
-
34
23
28
-
17
21
-
22
-
-
-
30
40
72
-
-
-
51
66
41
-
-
-
40
52
33
-
-
24
-
-
30
37
-
-
-
50
96
115
-
-
-
83
55
66
-
-
-
65
44
53
-
32
39
-
-
45
55
60
-
-
-
140
169
103
-
-
-
80
97
77
-
-
-
64
78
-
47
57
-
-
75
75
100
-
-
-
230
128
165
-
-
-
132
96
124
-
-
-
106
-
-
77
90
-
110
-
125
-
278
-
340
-
208
-
160
-
195
-
156
128
-
156
93
-
113
-
132
-
150
-
200
-
400
-
240
-
320
-
230
-
180
-
240
-
184
-
-
134
-
150
160
185
-
-
-
-
487
-
-
-
-
-
280
-
-
-
-
-
224
-
-
162
-
-
200
220
250
-
-
-
609
-
403
-
-
-
350
-
302
-
-
-
280
-
-
203
-
-
250
280
300
-
-
-
748
-
482
-
-
-
430
-
361
-
-
-
344
-
-
250
-
-
-
300
350
400
-
-
-
-
560
636
-
-
-
-
414
474
-
-
-
-
-
-
-
315
-
335
-
450
-
940
-
-
-
-
-
540
-
-
-
515
-
432
-
-
313
-
-
355
-
375
-
500
-
1061
-
-
-
786
-
610
-
-
-
590
-
488
-
-
354
-
-
400
425
450
-
-
-
1200
-
-
-
-
-
690
-
-
-
-
-
552
-
-
400
-
-
475
500
530
-
-
-
-
1478
-
-
-
-
-
850
-
-
-
-
-
680
-
-
493
-
560
600
630
-
-
-
1652
-
1844
-
-
-
950
-
1060
-
-
-
760
-
848
551
-
615
670
710
750
-
-
-
-
2070
-
-
-
-
-
1190
-
-
-
-
-
952
-
-
690
-
800
850
900
-
-
-
2340
-
2640
-
-
-
1346
-
1518
-
-
-
1076
-
1214
780
-
880
950
1000
-
-
-
2910
-
-
-
1673
-
-
-
1339
-
970