Calculate the no-load current of three-phase LV motors 4

[zlatkodo]

It would be good to calculate the value of no-load currents before rewinding.
If all the winding-details and dimensions of the iron core and air gap are known, how to calculate the value of the no-load current?
Whether someone is involved with this?
Zlatkodo

 

[waross]

Would the air gap dimensions be a significant factor?

Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[zlatkodo]

Hi, Bill,
Yes, because any change in the size of the air gap affects the change in no-load currents.
Zlatkodo

 

[zlatkodo]

There is something about it but unfortunately images are not visible.

http://findarticles.com/p/articles/mi_qa3726/is_200509/ai_n15349943/?tag=mantle_skin;content

Zlatkodo

 

[electricpete]

It is probably obvious, but the no-load current is given by:
I_no-load = V / (X1 + Xm)

We have already neglected R1, which is much smaller and in quadrature, so has completely undetectable effect.

Since X1 < < Xm, you could get a close estimate simply using Xm.
I_no-load ~ V / Xm


Xm can be calculated from the dimensions and winding configuration. It is in any motors textbook. If you want me to go fish it out of a textbook, let me know.

Xm can also be estimated from the motor nameplate data (the more data available, the better the estimate). It has been mentioned in threads before.


=====================================
(2B)+(2B)' ?

 

[7anoter4]

By the way Air Gap dimension:
From "Design of Rotating Electrical Machines" By Juha Pyrhönen Professor and others

http://onlinelibrary.wiley.com/doi/10.1002/9780470740095.ch6/summary

Ch.6.4 Air Gap
The length of the air gap of a machine has a significant influence in the characteristics of an electric
machine. In machines, in which the magnetizing current is taken from the supply network, the
length of the air gap is dimensioned to produce a minimum magnetizing current, and on the other
hand, an optimal efficiency. A small air gap gives in principle a low magnetizing current, whilst the
eddy current losses of the rotor and stator surface increase due to permeance harmonics created by
the open or semi-closed slots. A small air gap also increases the surface losses in the rotor caused
by the mmf harmonics of the stator. Although the air gap is of great significance, no theoretical
optimum has been solved for its length, but usually empirical equations are employed instead in the
definition of the length of the air gap. An air gap ?of a 50 Hz asynchronous machine can be
calculated as a function of power P with equations
d[mm]=0.1+0.225*(P)^(1/3) P[kW] when p=1
d[mm]=0.1+0.145*(P)^(1/3) P[kW] when p>1
For network supplied slip-ring motors up to 250 kW and for induction motors up to 100 kW, VDE
2650/51 gives standard air gaps. The smallest technically possible air gap is approximately 0.2 mm,
and the largest air gap up to the pole pair number 5 is about 2.5 mm in practice. In drives for
extremely heavy duty, according to Richter (1954), the air gap is increased by 60 %. In machines
with an exceptionally large diameter, an air gap ratio of d/D =>0.001 has to be selected due to the
mechanical properties of the frame and the shaft of the machine.
If and asynchronous machine is designed for high speeds, to avoid excessive iron losses of the
stator and rotor teeth, the air gap has to be increased considerably form the value obtained from Eq.
(6.24) for a standard electric motor. If a high-speed machine is equipped with a solid rotor, the air
gap has to be designed with special care, since the losses at the surface of a solid rotor decrease
radically when the air gap is increased, whereas the increase in the magnetizing current in the stator
leads into a notably smaller increase in the losses. A suitable value for the length of the air gap has
thus to be determined individually in each case.

 

[electricpete]

http://books.google.com/books?id=4-...erromagnetic part of magnetic circuit&f=false

Handbook of Electric Motors, by Toliyat etc
Equation 4.138

Lm = 4.8E-5*D*L/ge * (Kw*Nph/p)^2
where
D = Diameter of stator bore (m)
L = active length of core (m)
ge = corrected airgap: ge = g*ke
g = airgap (m)
ke = Carter's coefficient Eq 4.13, or look up in a figure or use 1.2
kw = kp*kd = pitch factor * distribution factor
p = number of poles
Nph = number of series turns per phase. If you have 2 parallel paths, then use Nph corresponding to one parallel and then multiply Lm by 2 (don't use total turns as Nph or you'd be a factor of 2 high when you square it).


=====================================
(2B)+(2B)' ?

 

[electricpete]

Also of course
Ino-load ~ (VLL/sqrt3) / (2*pi*f*Lm)
when neglecting leakage reactance. Including leakage reactance, the current would be slightly lower.

=====================================
(2B)+(2B)' ?

 

[electricpete]

I would say including stator leakage reactance would on average reduce no-load current by 10%, because X1/Xm ~ 0.1 is a typical ratio. You can also calculate stator leakage reactance if you want...

=====================================
(2B)+(2B)' ?

 

[electricpete]

Actually I'm not positive what to do if there are 2 parallels. I'd have to think about that some more.

=====================================
(2B)+(2B)' ?

 

[zlatkodo]

Hi, Electricpete,
Thanks for useful information. I'll look in more detail in the aforementioned book.
I know that the value of air gap should be corrected with a air-gap coefficient (maybe this is Carter's coefficient).
In addition, there is a coefficient of magnetic saturation also, which should be taken into account.
Zlatkodo