Power Factor

Power Factor Correction

A capacitor is considered a generator of positive reactive power, and its function in the power system is to supply reactive power needed by inductive loads. It is desirable to operate with loads that are not highly inductive. By compensating such loads with a shunt capacitor, the source current and apparent power decrease, resulting in more efficient operation and better voltage regulation. Also, reduced current permits the use of smaller conductors, so a significant savings in equipment and wiring costs may be realized by keeping power factor close to unity. The practice of improving a lagging power factor by installing capacitors in parallel with an inductive load is called power factor correction.

Example Problem 1:
Draw the power triangle for a single-phase source which delivers 80 kW to a load at 0.7 pf lagging. If the source voltage is 480 V, calculate the current required by this load.


Solution:

1. Example Problem 
Size the shunt capacitor required to reduce the power factor in Example Problem 3 to 0.9 lagging.
Solution:
1. The original load impedance found in Example Problem 1 is

.

This impedance contains resistive and inductive elements:

After power factor correction, load impedance will be
.

Note that a change in load impedance from  to  is accomplished by adding a capacitive reactance of . The corresponding capacitance is
.
Now, examine the power triangle after power factor correction.

The result is significantly lower reactive power requirement, with a reduction in load current.

3-Phase Power

The 3-phase (3) power of a circuit is simply the sum of the power in the three individual phases. Thus for a Wye circuit, the equation is
 S₃ = S_a + S_b + S_c
 and for a Delta circuit, the equation is
S₃ = S_ab + S_bc + S_ca
Another adavantage of having a balanced circuit is that each phase has the same power. That is,
S = S_ab = S_bc = S_ca = S_a = S_b = S_c

so that,
S₃ = 3 S = 3 S_ab = 3 S_a
Just in case you didn't know, right now you should be thinking "This is very cool!" 

The single phase power can be found using either
S = V_a I_a* or S = V_ab I_ab*

We can do some interesting rearrangements to get the power in terms of the line voltage (V_ab) and line current (I_a) only.
S = V_a I_a* = |V_a| | I_a|  = {|V_ab| /  }| I_a|  = S
Thus, S₃ = 3 S = 3 {|V_ab| /  }| I_a|  =  |V_ab| | I_a| 

Note:

In balanced systems, all the S's and S₃ have the same power factor (pf) and thus the same power factor angle = impedance angle = .