# Power factor correction of induction motors

## Connection of a capacitor bank and protection settings

 Individual motor compensation is recommended where the motor power (kVA) is large with respect to the declared power of the installation

General precautions
Because of the small kW consumption, the power factor of a motor is very low at no-load or on light load. The reactive current of the motor remains practically constant at all loads, so that a number of unloaded motors constitute a consumption of reactive power which is generally detrimental to an installation, for reasons explained in preceding sections.
Two good general rules therefore are that unloaded motors should be switched off, and motors should not be oversized (since they will then be lightly loaded).

Connection
The bank of capacitors should be connected directly to the terminals of the motor.

Special motors
It is recommended that special motors (stepping, plugging, inching, reversing motors, etc.) should not be compensated.

Effect on protection settings
After applying compensation to a motor, the current to the motor-capacitor combination will be lower than before, assuming the same motor-driven load conditions. This is because a significant part of the reactive component of the motor current is being supplied from the capacitor, as shown in Figure L23.
Where the overcurrent protection devices of the motor are located upstream of the motor capacitor connection (and this will always be the case for terminal-connected capacitors), the overcurrent relay settings must be reduced in the ratio:
cos ϕ before compensation / cos ϕ after compensation
For motors compensated in accordance with the kvar values indicated in Figure L24 (maximum values recommended for avoidance of self-excitation of standard induction motors), the above-mentioned ratio will have a value similar to that indicated for the corresponding motor speed in Figure L25.

Fig. L23: Before compensation, the transformer supplies all the reactive power; after compensation, the capacitor supplies a large part of the reactive power

3-phase motors 230/400 V
Nominal power kvar to be installed
Speed of rotation (rpm)
kW hp 3000 1500 1000 750
22 30 6 8 9 10
30 40 7.5 10 11 12.5
37 50 9 11 12.5 16
45 60 11 13 14 17
55 75 13 17 18 21
75 100 17 22 25 28
90 125 20 25 27 30
110 150 24 29 33 37
132 180 31 36 38 43
160 218 35 41 44 52
200 274 43 47 53 61
250 340 52 57 63 71
280 380 57 63 70 79
355 482 67 76 86 98
400 544 78 82 97 106
450 610 87 93 107 117

Fig L24: Maximum kvar of power factor correction applicable to motor terminals without risk of self excitation

Speed in rpm Reduction factor
750 0.88
1000 0.90
1500 0.91
3000 0.93

Fig. L25: Reduction factor for overcurrent protection after compensation

## How self-excitation of an induction motor can be avoided

 When a capacitor bank is connected to the terminals of an induction motor, it is important to check that the size of the bank is less than that at which self-excitation can occur

When a motor is driving a high-inertia load, the motor will continue to rotate (unless deliberately braked) after the motor supply has been switched off.
The “magnetic inertia” of the rotor circuit means that an emf will be generated in the stator windings for a short period after switching off, and would normally reduce to zero after 1 or 2 cycles, in the case of an uncompensated motor.
Compensation capacitors however, constitute a 3-phase reactive load for this decaying emf, which causes capacitive currents to flow through the stator windings. These stator currents will produce a rotating magnetic field in the rotor which acts exactly along the same axis and in the same direction as that of the decaying magnetic field.
The rotor flux consequently increases; the stator currents increase; and the voltage at the terminals of the motor increases; sometimes to dangerously-high levels. This phenomenon is known as self-excitation and is one reason why AC generators are not normally operated at leading power factors, i.e. there is a tendency to spontaneously (and uncontrollably) self excite.

Notes:
1. The characteristics of a motor being driven by the inertia of the load are not rigorously identical to its no-load characteristics. This assumption, however, is sufficiently accurate for practical purposes.

2. With the motor acting as a generator, the currents circulating are largely reactive, so that the braking (retarding) effect on the motor is mainly due only to the load represented by the cooling fan in the motor.

3. The (almost 90° lagging) current taken from the supply in normal circumstances by the unloaded motor, and the (almost 90° leading) current supplied to the capacitors by the motor acting as a generator, both have the same phase relationship to the terminal voltage. It is for this reason that the two characteristics may be superimposed on the graph.

In order to avoid self-excitation as described above, the kvar rating of the capacitor bank must be limited to the following maximum value:
$Qc \le 0.9 \times lo \times Un \times \sqrt3$
where Io = the no-load current of the motor and Un = phase-to-phase nominal voltage of the motor in kV. Figure L24 previous page gives appropriate values of Qc corresponding to this criterion.

Example
A 75 kW, 3,000 rpm, 400 V, 3-phase motor may have a capacitor bank no larger than 17 kvar according to Figure L24. The table values are, in general, too small to adequately compensate the motor to the level of cos ϕ normally required. Additional compensation can, however, be applied to the system, for example an overall bank, installed for global compensation of a number of smaller appliances.

High-inertia motors and/or loads
In any installation where high-inertia motor driven loads exist, the circuit-breakers or contactors controlling such motors should, in the event of total loss of power supply, be rapidly tripped.
If this precaution is not taken, then self excitation to very high voltages is likely to occur, since all other banks of capacitors in the installation will effectively be in parallel with those of the high-inertia motors.
The protection scheme for these motors should therefore include an overvoltage tripping relay, together with reverse-power checking contacts (the motor will feed power to the rest of the installation, until the stored inertial energy is dissipated).
If the capacitor bank associated with a high inertia motor is larger than that recommended in Figure L24, then it should be separately controlled by a circuit-breaker or contactor, which trips simultaneously with the main motor-controlling circuit-breaker or contactor, as shown in Figure L26.
Closing of the main contactor is commonly subject to the capacitor contactor being previously closed.

Fig. L26: Connection of the capacitor bank to the motor