'Load Angle'- What it means for a Reluctance motor

Load Angle is a term we often face while reading a electrical machine paper, but I have often noticed that there is a big confusion over its definition from people to people. So I will show you in this article with all the nice video simulation that what it exactly means inside the machines. But before that, please bare with me for a couple of minutes, I want to set the perfect prelude in understanding the Load angle.

Boring Definition: By definition of a synchronous machines, the golden equation of load angle is presented here. The delta in the below equation is load angle.

In other way the angle between the electromotive force(Ef) and terminal voltage is the load angle. The q axis current Iq is always parallel to Ef, so in some other books, the definition can be also the q axis current and voltage vector. These are all good definition when you have a field winding or a permanent magnet inside your rotor. But now the confusion arise when you have a reluctance rotor , where there is no field coming from the rotor.

Reluctance rotor - Why the confusion?

In a reluctance machine, you can set your voltage vector and rotor angle in a way that all the current goes to the d axis. In this case, you dont have any q axis current, so according to the golden equation the angle between q axis current and terminal voltage should be zero. And it should go hand in hand if you slighly change the rotor angle. But in practice you always get some angle difference like 2 to 3 degree between them. This primarily comes for saturation. If you are working with finite element with non-linear iron, you have probably noticed that the golden equation is not always respected.

So, the best way to define a load angle in a reluctance motor is to define it as the angle between the d axis current and the q axis current. It will atleast ensure from a physical point of view that the more you are increasing the Iq with respect to Id, the load angle also change hand in hand. Ofcourse in this case, the maximum torque for 45 degree of load angle is not respected either because of saturation.

Voltage vector adjusted for only d-axis current:

Have you noticed how beautifully the flux lines are passing through the rotor, as if there is no flux barrier in rotor.

On the other way, you think that the flux has the best free path to travel in rotor without any kind of obstruction. And if you carefully noticed, you will see that in the d axis of the rotor, the flux lines are entering almost perpendicularly.

Id and some Iq:

If you have noticed the flux lines you can clearly see that the rotor the flux lines are lagging behind the stator flux lines, and the rotor flux lines of course doesnot like that.

When the flux lines face the flux barrier, it is pushing the fluxbarrier hard to catch up. This is what we call TORQUE in layman terms.

WE ARE ALL HAPPY NOW UPTO THIS!!!!

So what happen when your rotor fluxbarrier perpendicularly face all the flux lines coming from the stator. This is situation that arrives when you give only q axis current and no d axis current. This again a no-load situation, but this time only Iq. Check the video and picture below.

Now you see my point of expressing load angle with Iq and Id instead the traditional definition. Isnt it easy to perceive?

A famous person in my last conference agreed with my idea, and then I got the courage to put it down here. I put this question infront of you, feel free to disagree, thats the beauty of our field, and another good reason to hang out over cofee or beer.