INTRODUCTION
"Power Factor" is an electrical term used to rate the degree of the synchronization of power supply current with the power supply voltage. This term is often misunderstood by ourselves and our customers, or simply ignored.
It is important that we clearly understand the meaning of "Power Factor" and its effect on the electrical supply system for the following reasons:
- a low power factor can increase the cost of power to the user
- a low power factor can increase the cost of power transmission equipment to the user
- a customer may request assistance in selecting equipment to correct a low power factor
- over-correction of power factor by the addition of excessive capacitance is sometimes dangerous to a motor and the driven equipment. (above 95% power factor)
- a customer may, to some extent, use motor power factor rating as a power factor rating as a criterion in choosing among competing motors, especially when a large motor is involved.
The power factors in industrial plants are usually lagging due to the inductive nature of induction motors, transformers, lighting, induction heating furnaces, etc. This lagging power factor has two costly disadvantages for the power user. First, it increases the cost incurred by the power company because more current must be transmitted than is actually used to perform useful work. This increased cost is passed on to the industrial customer by means of power factor adjustments to the rate schedules. Second, it reduces the load handling capability of the industrial plants electrical transmission system which means that the industrial power user must spend more on transmission lines and transformers to get a given amount of useful power through his plant. This is shown in the figure below.
 |  | Figure 1 |
WHAT IS POWER FACTOR
Power factor is defined as the ratio of the actual power (Watts) to the apparent power (Volt-ampers). Power factor=Actual Power/Apparent Power
 | | Figure 2 |
From figure 2 above, it can be seen that the apparent power which is transmitted by the power plant is actually composed vectorially of the actual power and the reactive power. The active power is used by the motor and results in useful work. The reactive power is wasted and merely bounces energy back and forth between the motor and the generators at the power company's plant. If the power factor is corrected, figure (2) shows how the reaction power element decreases in size and the apparent power element approaches the size of the actual power used. This means that less power need be generated to obtain the same amount of useful energy for the motor. Power factor correction is discussed below. Power factor is also numerically equal to the cosine of the angle of the lag of the primary input current with respect to its voltage.
 | | Figure 3 |
From Figure (3) above, it can be seen that the current is lagging the voltage by an angle 0. An ideal power supply would have no lag on lead angle and the power transmitted to the motor would be an useful power. The equation for useful or actual power is:
P = El cos Ø Or
Power = Volts x Current x Cosine of the lag angle 0 Where:
| Cos Ø = Power Factor El = KVA El cos Ø = KW |
If the lag Ø is zero then the cos Ø is equal to one, and the useful or actual power equals El and no power is lost due to reactance in the system.
LOW P.F. DISADVANTAGES
The disadvantages of low power factors are three. The first is that transmission lines and other power circuit elements are usually more reactive than resistive. Reactive components of current produce larger voltage drops than resistive components, and add to the total IZ = (I(R + LX)) drop, therefore, the system-voltage regulation suffers more and additional voltage- regulating equipment may be required for satisfactory operation of the equipment using power. The second disadvantage is the inefficient utilization of the transmission equipment since more current flow per unit of real power transmitted is necessary due to the reactive power also carried in the power lines. If the current necessary to satisfy reactive power could be reduced, more useful power could be transmitted through the present system. The third disadvantage is the cost of the increased power loss in transmission lines. The increased power loss is due to the unnecessary reactive power which is in the system. The reactive power losses vary as the square of the reactive current or as the inverse of the power factor squared.
POWER FACTOR CORRECTION
There are two common P.F. correction techniques used by industry to correct an unacceptable lagging power factor. The expensive fix is to use an overexcited synchronous motor or generator in the power system. The cheaper and quicker fix is to connect properly sized capacitors to the motor supply line.
A synchronous machine furnishes the opposite (leading) reactive power to the system to which it is connected. It can provide very economical P.F. correction in low-speed drive applications (less than 51 4 RPM) such as a compressor because the cost of a synchronous motor is less than the cost of an AC induction motor in situations where the ratio of HP to speed is greater than 1 . There are two standard power factor ratings which are unity and .8 power factor. The .8 P.F. is larger and more expensive, but provides a good deal more reactive power to the system throughout its entire speed range. The use of a synchronous motor in hp-speed ratings that favor induction motors to correct P.F. requires careful economic study. In most cases the use of induction motors with capacitors can provide lower first cost and reduced maintenance expense in comparison.
The use of static capacitors connected in the motor power supply is a simple means of P.F. connection. The capacitor causes the current to lead the voltage which tends to offset the lagging current caused by the motor inductance. The effect on the power system is an improvement of the power factor and a reduction in the total power supply line current as shown below.
 | | Figure 4 |
Two common methods of connecting capacitors to the supply line are shown below.
 | | Figure 5 |
Note on three phase sources (A) and (B) above represent each leg of the supply connection. Capacitors are usually connected in such a way that they are removed from the system as the power is removed. In connection (A) above, the lower current through the motor overload relay requires the selection of lower rated overload relay to protect the motor. The overload relay should be selected in the normal fashion, however, an adjusted full load motor current should be used. This adjusted full load motor current can be obtained from the following formula:
Adjusted full load motor current = (Nameplate Motor / Full Load Current) x (Uncorrect P.F. / Corrected P.F.)
In connection (B) the adjusted current need not be used so the overload relay is selected in the conventional manner using the motor nameplate full load current.
CAPACITOR SELECTION*
(See note at bottom of page for above 95% P.F.)
For capacitor selection, the following steps must be observed:
| First: | | Use the formula below to determine the capacitor KVAR rating. KVAR=(K1-K2) x HP x 0.746 / Efficiency KVAR is reactive kilovolt amperes required to correct the P.F. HP is motor nameplate horsepower Efficiency is motor full load efficiency expressed or a percentage. K1 and K2 are constants from the following tables (Tables 1 and 2). |
| % PF (1) | Constant K1 | % PF (1) | Constant K1 | % PF (1) | Constant K1 | % PF (1) | Constant K1 |
|---|---|---|---|---|---|---|---|
| 60.0 60.5 61.0 61.5 62.0 62.5 63.0 63.5 64.0 64.5 65.0 65.5 66.0 66.5 67.0 67.5 68.0 68.5 | 1.333 1.316 1.299 1.282 1.266 1.249 1.233 1.217 1.201 1.185 1.169 1.154 1.138 1.123 1.108 1.093 1.078 1.064 | 69.0 69.5 70.0 70.5 71.0 71.5 72.0 72.5 73.0 73.5 74.0 74.5 75.0 75.5 76.0 76.5 77.0 77.5 | 1.049 1.035 1.020 1.006 0.992 0.978 0.964 0.950 0.936 0.923 0.909 0.896 0.882 0.868 0.855 0.842 0.829 0.815 | 78.0 78.5 79.0 79.5 80.0 80.5 81.0 81.5 82.0 82.5 83.0 83.5 84.0 84.5 85.0 85.5 86.0 86.5 | 0.802 0.789 0.776 0.763 0.750 0.737 0.724 0.711 0.698 0.685 0.672 0.659 0.646 0.633 0.620 0.607 0.593 0.580 | 87.0 87.5 88.0 88.5 89.0 89.5 90.0 90.5 91.0 91.5 92.0 92.5 93.0 93.5 94.0 94.5 95.5 | 0.567 0.553 0.540 0.526 0.512 0.498 0.484 0.470 0.456 0.441 0.426 0.411 0.395 0.379 0.363 0.346 0.329 |
Table 1
*Avoid over correction of the power factor above 95% since excessive capacitance is dangerous to the driven equipment and motor.
- Refer to motor department for P.F. correction over 95%.
- Refer to motor department for P.F. correction of multispeed motors.
| | Table 2 |
| Second: | | Make sure that the capacity voltage rating is equal to or greater than the rated motor voltage. |
| Third: | | Make sure the capacitor frequency and number of phases is the same as the motor. |
| Fourth: | | Note that the capacitor ambient temperature must not exceed 40°C. http://www.reliance.com/mtr/pwrfcr.htm |