Introduction for the theory of star connection and delta connection for motors

 

 

 

 

 

 

 

 

 

Which current values are we comparing with each other?

 

In the previous lecture, I learned the difference between star connection and delta connection for motors. A star connection can keep the current value lower than a delta connection.

 

 

Right.

 

But I still don’t know what makes the difference. Why is the current value in a star connection lower than that in a delta connection?

 

First of all, do you know the reason why complex numbers can…

 

I don’t wanna listen to difficult math!

 

I see… I’ll do my best without using math.

 

Thanks.

 

By the way, which amount of electric current are you comparing in a star connection with in a delta connection?

 

What?

 

You learned that the current value in a star connection is lower than the current value in a delta connection, right?

 

Yes?

 

Which current values are you comparing with each other? The current values in the figure below?

 

 

Well… I have no idea..

 

Actually, we compare the current values in the figure below.

 

 

Are the current values more important than the other current values?

 

Not really but comparing the current values is the same as comparing current values that flow through a motor.

 

 

It may be useful to know how many amperes are flowing through a motor.

 

Yes. If a lot of electric current is flowing through a motor, which means that the motor is working so hard and you should know the situation.

 

By the way, how can I measure the current value that flows through a motor?

 

Have you heard of a clamp meter?

 

Yes, but I’ve not actually used it.

 

The figure below enables you to imagine how you can use a clamp meter.

 

 

Yeah. I can easily imagine the situation where I’m actually using it.

 

 

Find the current value in a star connection

 

Okay so now, let’s move on to our main topic today.

 

What was our main topic?

 

Seriously? You wanna know the reason why a star connection can keep the current value lower, don’t you?

 

You know well.

 

Okay… First of all, let’s find the current values in the figure below. After that, we are going to compare the current values with each other. The current value in a star connection must be lower.

 

 

Sounds interesting.

 

Firstly, let me give you a question. How many volts do you think are applied to V in the future below?

 

 

In some countries, it’s around 400 volts. In other countries, it’s around 200 volts. But actually it depends on a factory.

 

You know well. Then let me give you another question. What information do you need if you’d like to find the value of the electric current Iy in the figure below? You can use Z as the *resistance value.

*To be precise, it’s an impedance.

 

 

In order to find Iy, I need to know the value of Vy in the figure below.

 

 

Why do you think so?

 

If I know the value of Vy, I can apply Ohm’s law to the red area in the figure below.

 

 

Can you show me the Ohm’s law?

 

Here it is.

 

 

Wow.. You suddenly became a genius. So now, the only value we need to find is

 

Vy!

 

Rright. How are you going to find the value of Vy?

 

It’s easy to find it. Would you pay attention to the yellow circuit in the figure below? The circuit has two resistances and they have the same resistance value Z, right?

 

 

So, the voltage V can be equally divided in each of the resistances. Vy equals V/2.

 

 

Really??

 

Am I wrong?

 

Actually, it’s not that simple. If it were a DC circuit, your idea would work but, as you know, we are analyzing a 3-phase AC circuit. We need to use a different way to find Vy.

To tell you the truth, Vy is not half of V but the value divided by square root 3 as seen in the figure below.

 

 

Why!?

 

If you’d like to know the reason, this lecture may help you.

Relation between trigonometric functions and complex numbers

 

Okay, I’ll check it out later.

 

Thanks. Let’s go back to this lecture.

You almost get the current value Iy because you’ve already found the value of Vy. You just substitute it into the equation you derived by using Ohm’s law.

 

 

Yeah. I’ve got the value of Iy.

 

 

 

 

Find the current value in a delta connection

 

We’d like to know the current value in a delta connection next, right? I define the current value in a delta connection as Iδ as seen in the figure below. According to the theory of star and delta, Iy must be lower than Iδ, isn’t it?

 

 

Yes. Let’s try to confirm it. How are you going to find Iδ?

 

Well… Firstly, since Iδ should be equally divided in the two electric currents like the figure below, each of the current values flowing through a *resistance will be Iδ/2.

*To be precise, it’s an impedance.

 

 

And then, I tried applying Ohm’s law to the red area in the figure below. I can say I’ve got the value of Iδ.

 

 

Hmm.. The idea works only in a DC circuit…

 

Again!?

 

You said that Iδ should be equally divided in the two electric currents like the figure below. However, that doesn’t happen to an AC circuit.

 

 

If Iδ can’t be divided equally, how is Iδ divided in the two resistances?

 

Iδ is not equally divided in half.  The current value we’d like to know now is Iδ divided by square root 3 as seen in the figure below.

 

 

I see.. The way of how Iδ is divided is similar to the way of how V is divided in a star connection.

 

 

Yup. If I have a chance, I’ll explain the reason. It’s not difficult to understand it if you understand
the relation between trigonometric functions and complex numbers.

Let’s go back to our topic. Can you find Iδ? Actually, you are perfectly ready to find it.

 

Yes, I can. I just apply Ohm’s law to the red area in the figure below and then I’ve just got the equation below.

 

 

Good. Will you solve the equation for Iδ.

 

Sure. I just multiply both sides by square root 3. Here it is.

 

 

 

 

Compare the current value in a star connection with the current value in a delta connection

 

Thank you. We have succeeded in finding the current value in a star connection and the current value in a delta connection as well. We are in the last part in this lecture.

 

We are going to compare Iy with Iδ, right?

 

Yes. Please take a look at the figure below. The current value in the star connection is 1/3 of the current value in the delta connection.

 

 

Right.

 

Now, it has been proved that a star connection can keep the current value lower, right?

 

Thank you so much.