The Power Chronicles – Power Factor

Even after getting acquainted to the various concepts related to electrical engineering, there is always one important concept which most electrical engineers, including me, tend to forget. What exactly is reactive power? What is power factor? Why is it so damn important? What do you actually mean by lag and lead? So this discussion would be an informative recap into the basics.

Disclaimer: You could find this highly descriptive, but a short circuit is the only thing ‘short’ in Electrical Engineering. :P

It all begins like this…

To understand power factor, first consider the following circuits and the corresponding waveform for sinusoidal voltage and current at steady state.

1. Purely resistive load

In case of a purely resistice load, when V= Vo sin(wt+ф) , the corresponding current, I = Io sin(wt+ф) , where  Io = Vo/R. This indicates that there is no phase difference between voltage and current in case of a purely resistive circuit.

2. Purely inductive Load

In case of a purely inductive load, we observe that the current lags voltage by 90⁰. This is due to the fact that an inductor does not allow a sudden change in current.  Mathematically, for input V = Vo sin(wt+ф), the corresponding current I = Io sin(wt+ф-90⁰), according to the equation 

V=L dI/dt

3. Purely capacitive Load

In case of a purely capacitive load, we observe that the current leads voltage by 90⁰. This is due to the fact that a capacitor does not allow a sudden change in voltage.  Mathematically, for input V = Vo sin(wt+ф), the corresponding current I = Io sin(wt+ф+90⁰), according to the equation 

I=C dV/dt

Beat The Heat:
Confused which leads what?? Here is a simple way to remember, which is applicable to all types of voltage and current equations.

1. Write down the voltage and current equation as per the circuit.
2. The quantity which appears first when seen read normally leads the others.

For eg: In the purely capacitor ckt
I=C dV/dt
Current I, appears first and then the voltage.  So current leads voltage in case of a capacitor. This can also be confirmed with purely inductive, R-L-C and even motor/generator equations.
So, finally we are at:

For a resistive load, the power waveform (which is the product of the current and voltage waveforms) is given as shown below:

Similarly, for a purely capacitive and inductive load the power waveforms are given as:

Thus, it can be observed that the average power is:

1. (Vo*Io)/2 in case of a purely resistive circuit
2. 0 in case of a purely inductive and capacitive circuit.

Patience guys, patience.

Now, let’s consider an R-L series (common load) circuit. It has the following waveform. 

Initially, let R=0, this implies the circuit is purely inductive and its average power is zero. As the value of R increases, the value of value of average also increases. When L=0 or R>>L, the average power reaches (Vo*Io)/2 i.e. a purely resistive circuit.

Similarly, for an R-C circuit,

"Note: it seems that the Pav line in the above graphs are constant and the graph is shifting down. But its actually the value of Pav which is increading"

Beat The Heat:

• Average Power is maximum for purely resistive load.
• R-L and R-C circuits have some portion of the power curve going negative. Hence their average values are less than (Vo*Io)/2.
• This negative power is nothing but reactive power and the positive power is active power. Thus, reactive power can be viewed as the power supplied back by the load to the source.

Power Factor:

Thus, power factor is defined as a measure of the degree to which a given load matches that of a pure resistance.

• PF = 1;         if load appears as R
• PF = 0;         if load appears as L or C;
• For R-L, PF is between 0 and 1, and is lagging in nature.
• For R-C, PF is between 0 and 1 but leading in nature.

Importance of Power Factor:

Power factor is an important parameter in power system. It defines the health of a power system. A system with pf much lesser than unity is termed as an ill-maintained system. PF also is an important factor considered while designing electrical machines like synchronous machines, induction machines et al.

How is power factor calculated?

Power factor is calculated as the ratio of average power of the load (PLoad) to the average power of a purely resistive power (PR). I.e.,

 PF=PLoad/PR

This definition of power factor is true for all types of waveforms.

For a sinusoidal waveform (don’t ever, ever forget this criterion), the power factor is given as:

PF = cosф.

So, power fact….. 

Summary:

• Power factor is defined as a measure of the degree to which a given load matches that of a pure resistance.
• PF=PLoad/PR
• Reactive power can be viewed as the power supplied back by the load to the source.
• For a sinusoidal voltage and current,

PF = cosф.

Queries?? Feel free to comment below.. ;)

Source:
1. https://www.youtube.com/watch?v=7S22cJ_aF9M (do have a look at this, preferably at 2x speed :P )
2. Google (obviously)
3. A-Textbook-of-Electrical-Technology (Vol1) – B.L.Theraja

Credits: 

Kishore Seshadri