Power and Power factor

Getting the basics right

As an electrical engineer, power is central to what I learned. Every good interviewer asks to explain the power and power factor. It may seem childish, but it is extremely important to be able to explain both.

It takes a lot of imagination to be an electrical engineer, as you see we cannot really see the current or how electrons are flowing. We pretty much have to visualize electrons flowing from one end of the wire to another. Think how much brain power it needs. Just as one would be beginning to get hang of it and someone else comes and says, well what about a current than can go in both ways. And now you have discovered the alternating AC current, which is a waveform and changes direction. AC brings out its own set of problems- phase, phase difference, phase sequence and frequency.

Understanding electrical circuits is at times, pretty much a leap of faith. We rely a lot of complex numbers and trigonometry to help us out. One of the places where complex numbers are very handy is to explain the complex phenomenon of Reactive Power. This is very different from the Real or active power, and the difference gives rise to the confusion regarding the power factor.

Beer and power 

Lets start with the real power, as you would expect this is the power which can give you the useful work- be it light, or rotation for your fan. This is much easier to comprehend, than the part which is reactive. However, the thing is electricity and magnetism are kind of coupled, where one goes the other follows. And the magnetic action, definitely needs some electric power. Hence the reactive power, which is not totally useless as you see, because your fan cannot rotate without the magnet.

So we have the Active and Reactive power, and as mathematics would have it the first one is considered as real and the second as its imaginary counterpart. We electrical engineers call it P + j Q, P being the real active power, and Q the imaginary reactive power. As we, electrical engineers consider ourselves very fancy we use 'j' in place of 'i', which is often used to represent the square root of negative 1.

You need not bother too much about the math, just realise that the reactive power is imaginary. One interesting analogy for the same comes in the form of a beer mug. The real power is the liquid, and the reactive power is the froth, and everyone knows there is no fun without the froth.

Power factor confusion

If you are still with me, I will walk you through basic trigonometry explanation. See we have Voltage, the force and Current, the flow. Technically if you were to multiply the force and flow, i.e. the Voltage and Current you should get power. But now you have to ask again, what power, real or reactive?

Since the power has real and reactive parts, we bring in the triangle to help us. Mathematically, the imaginary axis is perpendicular to the real axis, and hence it's a right angle triangle. If you remember good old Pythagoras from School, you know that we get the sum total of the active and reactive power by drawing the yellow line called hypotenuse.

Jogging your brain a bit more you will remember Sin (Sine) and Cos (Cosine) functions. I need you to only focus on Cos for this, because mostly we are interested to see the real power, or the actual work we got. The ratio of the real power, to the resultant power is represented by the Cos function. The resultant power is called Apparent power and represented by S.

So the Cos function or the ratio of Real power to Apparent power (P/S) is called Power factor. This ratio helps one understand how much power is actually turned to useful work. This also helps to comprehend how much was spend in reactive part- say magnetising.

Cos is a beautiful mathematical function, because its limits are between zero and one. The zero and one helps us explain the foundations of why power factor is important.

1. Power Factor:Zero is the case when, there is no Real power and all power is Reactive. This implies you are not doing any useful work.
2. Power Factor:One is the case when all power is Real and there is no reactive power. This is a case where all the power is transferred to useful energy

The truth is both the above cases are theoretical limits, in real life we encounter power factors in terms of 0.9-0.99, almost close to one. And in cases, where it is not close to one we recommend power factor correction to bring it close to one, as that is the best efficiency case.

Can power factor be ever greater than one?

The easier answer is no, because, its impossible. Its not possible to create more useful Real Power. Your best case is when both real and apparent power are equal. Mathematically the upper limit of Cos function, the ratio between the Real and Apparent power is one. If you don't believe me, I will try to dig a bit deeper and explain. Lets focus on the angle associated with the Cos function. Since we, electrical engineers love Greek's, we call this angle lovingly "Theta".

This angle "Theta" between the P and S, the Real and Apparent power, by divinity in design is also the angle between Voltage and Current. Remember we are talking of quantities which change direction. This implies wave forms, because we are dealing with Alternating Current (AC). Voltage (the force), and Current (the flow) could have three possible relations between them- they could be in sync or one could be leading the other. That is your three cases are : Current and Voltage in sync, Current lagging behind the Voltage, and Current leading the Voltage. This corresponds, to resistive, inductive and capacitve loads.

Lets not complicate it here, discussing if the load is reactive, inductive or capacitive. Only thing to remember is that ,

1. if Voltage and Current are in sync, then the angle between them "Theta" is zero, and the power factor the cosine function is 1. This means all power is real power
2. if Voltage and Current are not in sync, the angle " Theta" could be positive or negative. But this does not mean that power factor is more than one in one case. Honestly, it does not matter because, Cos is such a function that even for a negative angle its value is always positive.
3. The maximum difference in "Theta" the voltage and current can achieve looking at the wave form is 90 degrees, and at both of these cases the power factor, that is Cos 90 is zero.

One of the common mistakes people make is to assume that the angle "Theta" is the power factor. Remember that its always the cos function of the angle and not the angle.

Suppose, if there were no change in direction at all, then we need not worry about how much Current is behind or in front of Voltage. This also implies there is no power factor when we talk about DC .

End note

Let me end this with another favourite question of interviewers, the difference between power and energy. In simple mathematics, power multiplied by time is energy. If you were to examine it philosophically, it gets more complex. Power is the rate of energy transfer, very instantaneous phenomena. While energy is something which determines how much capacity is there to perform work.

A useful analogy for the same would be to see how loud I can sing and how long I can sing. The loudness will represent the power, and the duration will depend on the energy I have. As some of you might have understood, both are related yet different. It quite possible that someone can sing for a loudly for a long time or vice versa. Well, in my case you better wish both are on the lower end, as I am in fact a terrible singer. I just wish my writing is not as bad.