Reveal the true identity of reactive power

 

 

 

 

 

Mr. Penguin, what is actually reactive power? I heard that reactive power does not work but it exists in an AC circuit. I’m confused.

 

You can easily understand it by only using trigonometric functions.

 

Hmm.. Do I have to use math?

 

You don’t have to but that’s the easiest way to comprehend what reactive power is like.

 

Are you going to use difficult trigonometric functions?

 

Nope. I’m going to use only trigonometric functions in high school.

 

If so, I’m ready to listen to your lecture.

 

 

Express electric power in trigonometric functions

 

I applied voltage to a certain circuit and electric current is flowing in the circuit. Please take a look below. I drew the graphs of the voltage and the current.

 

 

The current is out of phase with the voltage by theta . What will the active and the reactive power be like in this case?

 

No rush. First off, I introduce an expression below that gives electric power.

 

 

Right. We can get electric power by multiplying current by voltage.

 

The result of the calculation is the red graph in the figure below. We are going to analyze the graph.

 

 

Firstly, can you express the graph of the voltage and the graph of the current?

 

Yes, I think that’s easy. Is this correct?

 

 

Yes, it’s correct. Secondly, can you express the graph of the electric power?

 

I just multiply the voltage by the current, right? It’s easy. I did it in the figure below.

 

 

 

Take electric power apart in 2 terms

 

It’s okay but let me expand the expression of the electric power. Here is the expression.

 

 

How did you get it?

 

Please take a look below. You don’t have to understand how you can rearrange the expressions but if you are interested in it, this website may help you.

 

 

Thanks. But how is the expression you’ve got related to reactive power?

 

Actually, it’s strongly related to reactive power. Please take a look below.

 

 

Eh, why can you say that the left term is active power and the right term is reactive power?

 

Before moving on to the topic, can you rewrite the expression of the electric power using effective values so that the expression looks simpler.

 

Sure. I’ll substitute effective values as below.

 

 

Yeah, you should.

 

The expression of the electric power looks a little simpler.

 

 

Thank you. We are going to analyze the expression of electric power carefully.

 

 

What is actually active power

 

We have the expression of active power and the expression of reactive power. Why don’t we draw the graphs of them? I’d like you to start with active power first.

 

Sure. The yellow graph below is active power.

 

 

Good, but will you tell me the way how you drew the graph?

 

As shown below, VIcosθ is constant and 1-con2ωt is a function that oscillates between 0 to 2. That’s why the average of the graph of active power is VIcosθ and the amplitude is VIcosθ as well.

 

What is the graph implying?

 

It has become obvious that the formula of active power is VIcosθ because the average of the graph of active power is VIcosθ.

 

Right. The amount of work done by active power is VIcosθ in average.

 

 

What is actually reactive power?

 

Can you draw the graph of reactive power next?

 

The shape of the expression of reactive power is “ Constant × sin2ωt ”. It’s easy to draw the graph. Here it is.

 

 

Perfect. Then, can you say that reactive power is doing work?

 

No, I can’t say so because the average of the graph of reactive power is 0.

 

Has everything been clear about reactive power?

 

I mostly understood but I have a question. What does the lower half of the graph of reactive power mean? Reactive power is doing negative work but what does it mean by “negative work”??

 

Is it understandable if I say that reactive power is returning electric power to the power source because of electric discharge?

 

Well… I can’t say I totally understand it…

 

Let me explain it in ” What is actually reactive power -explanation without math- (in production…) “.

 

Thank you. I’ll attend the lecture.