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Introduction to power factor, Part 4b.
In the previous part, we solved a practical example where
we sized a capacitor for a power factor correction.
In this part, we will verify if that size which we selected is optimal or not.
Additionally, we will consider the consequences of oversizing the capacitor as well.
In the previous part 4a, we used our engineering judgment
to decide on a capacitor of size 70 microfarads for power factor correction requirements.
We will now verify whether or not the selection has any positive effect on the system.
Now let’s revisit this example that we used in part 4a.
Now let’s draw the diagram that we used in part 4a.
We will now insert a 70 microfarad capacitor into the system.
Since we sized a capacitor of 70 microfarads, we will need to calculate
the reactive power which it will supply to the system in order to improve the power factor.
A 70 microfarad capacitor gives us a capacitive reactance of 45.473 ohms
Using the derivative of Ohm’s law, we can find the reactive power as follows:
That the Reactive power is equal to 480 volt squared divided by the 45.473 ohms and that gives us 5.066kVAR
So, a 70 microfarad capacitor will supply a reactive power of 5.066 kilo VARs.
Recalling the operating mechanism of the capacitor,
we can see that the phase angle of the reactive power supplied by the capacitor
will be 180 degrees out of phase from the reactive power required by the inductive load.
And that’s the really important part.
Therefore, it will be directly opposing its effects.
Mathematically we can subtract both quantities to get the reactive power of the system.
So the reactive power is equal to 5.18 kVARs – 5.066 kVARs and that equals 0.114 kVARs.
Using this newly calculated value of reactive power, 0.114 kVARs,
we can finally calculate the apparent power using Pythagoras theorem,
which comes out to be about 5.0013 kVA.
Now the effect of the capacitor can be visualized by adding
an opposing vector to the reactive power in the power triangle.
So again the reactive power which is a purely inductive load
is directly negated by the capacitor which is a purely capacitive load at negative 90 degrees.
And the new power factor comes out to be 0.99 which is close to ideal.
Which is 5kW divided by 5.0013kVA.
This is one of many ways that we can use to bring our power factor close to unity, which is 1.
We can redraw the power factor triangle to visualize the effect.
And you can see that the true power and the apparent power are close to each other,
but not quite 100%, and there is still some reactive power that’s left over.
The phase angle between the apparent and the true power now comes out to be 8.1 degrees,
which is massive reduction from the original phase angle of 46 degrees.
Again we calculated that by inverse cosine of 0.99.
But what if we used a capacitor of 72 microfarads instead of 70 microfarads.
If we redo the entire calculation for a 72 microfarads capacitor,
then the resultant reactive power will come out to be more than the inductive load requires.
So the extra reactive power supplied by the capacitor will result in a leading power factor for the system,
where the current will start to lead the voltage by a known phase angle.
Something to keep in mind that a leading power factor can in fact cause additional problems in the power system.
Some are unnecessary rise in the system voltage.
The negative phase angle becomes dangerous for sensitive equipment
and even possibly damaging to generators, whose voltage regulators
will not be able to handle the spontaneous change in the system voltage and fail to adjust accordingly.
Now, we will discuss generator protection in future topics.
With that given and said, we will now conclude the introduction to power factor series.
And we hope, you have a continued interest in this topic and series as a student or professional.
And we also hope you find this content useful and enlightening.
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