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In the previous part, we solved a practical example where we sized a capacitor for power factor correction. In this part, we will verify if the size which we selected is optimal or not. Additionally, we will consider the consequences of over sizing the capacitor as well.

In the previous part 4a, we used our engineering judgment to decide on a capacitor of size 70 microfarads for our power factor correction requirements. We will now verify whether our selection has any positive effect on the system.

Let’s revisit the example used in part 4a.

We will now insert a 70 microfarads 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:

^{2}45.473

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. Therefore, it will directly oppose its effect.

Mathematically we can subtract both quantities to get the reactive power of the system.

Reactive power = 5.18 kVARs – 5.066 kVARs = 0.114 kVARs

Using this newly calculated value of reactive power, we can calculate the apparent power using the Pythagoras theorem, which comes out to be 5.0013 kVA.

Apparent power= √(real power)^{2} + (reactive power)^{2}

The effect of the capacitor can be visualized by adding an opposing vector to the reactive power in the power triangle.

The new power factor comes out to be 0.99 which is close to ideal.

This is one of the many ways we can use to bring our power factor close to unity. We can redraw the power triangle to visualize the effect.

The phase angle between the apparent and true power now comes out to be 8.1 degrees, which is massive reduction from the original phase angle of 46 degrees.

Cos^{-1}(0.99) = 8.1^{o}

But what if we used a capacitor of 72 microfarads instead of 70. If we redo the entire calculation for a 72 microfarads capacitor, then the resultant reactive power will come out to be more than what the inductive load requires. And the extra reactive power supplied by the capacitor will result in a leading power factor for the system, where the current will start leading the voltage by a phase angle.

A leading power factor can cause additional problems for the system such as an unnecessary rise in the system voltage. The negative phase angle would become dangerous for sensitive equipment and even possible damage to the generator, whose voltage regulator will not be able to handle the spontaneous changes in the system voltage and fail to adjust accordingly.

We will discuss generator protection in a future topic. With that given and said, we will now conclude the introduction to the power factor series.

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