Effects of 50/60Hz freq on 3phase motor CURRENT 3

[skrab]

Hi
Most posts regarding the performance of 50hz motors running on 60hz power and vice/versa have been concerned with the most important motor characteristics such as motor speed, torque output and efficiency.

I would like to know the effect on no-load CURRENT when the voltage is the same but the frequency is different than nameplate. Specifically, what would be the change in the no-load running current of small (1-5hp range) motors designed for 380V 50Hz if run on 380V 60Hz. Any and all information/explanations would be greatly appreciated.

Thanks in advance

 

[electricpete]

If you increase frequency and keep voltage magnitude the same, then the no-load current will decrease, and any harmonic content of the no-load current present at 50hz may also decrease.

1 - Why does current decrease:
In the linear model the impedance limiting the no-load current is

I = V/Z = V / [X1+Xm] = V /[j*2*Pi*f(L1+Lm)]

where X1 & L1 are associated with stator leakage reactance/inductance and Lm and Xm are magnetizing reactance/inductance.

2 - Why does harmonic content decrease:
Because your taking the core further away from saturation.

 

[skrab]

Thanks Electricpete!

With only the standard motor manufactures data (nameplate, PF, Eff etc.) is there any method to estimate the value of the increased current?

joe

 

[jbartos]

Suggestion: The no-load motor run also includes losses by Eddy Currents and Magnetization Losses (Steinmetz Law). Both losses will be higher for higher frequency, i.e. 60Hz.

 

[cbarn24050]

Hi, not to mention that the fan on the motor will increase the load on the motor and hence the current.

 

[electricpete]

The current will very nearly go to 5/6 as predicted by the above formula.

Yes, there will also be change in the losses, which affects the resistive component of the current. But since the current is primarily inductive (vs resistive), the small change in resistive component associated with the losses will have even smaller effect on total current.

 

[jbartos]

Question to electricpete (Electrical)Nov 10, 2002 marked ///\\2 - Why does harmonic content decrease:
Because your taking the core further away from saturation.
///Please, could you clarify this in terms of voltage V increase across the jXm parallel branch on no-load conditions?\\\

 

[electricpete]

For no-load conditions, I would choose an approximate equiavelent circuit for fundamental power frequency which has only two impedances: j*2*Pi*L1 and j*2*Pi*Lm.

Fundamental voltage accross magnetizing branch is
Vm = (j*2*Pi*Lm) / (j*2*Pi*L1 + j*2*Pi*Lm) = Lm/(L1+Lm).

That fundamental voltage magnitude does not change as we increase frequency. But the fundamental flux does change (decrease) since
Phi ~ Integral(Vm)dt ~ Vm/(2*Pi*f)
f increase => Phi decrease

 

[jbartos]

Suggestion: Please, would you clarify:
Fundamental voltage across magnetizing branch is
Vm = (j*2*Pi*Lm) / (j*2*Pi*L1 + j*2*Pi*Lm) = Lm/(L1+Lm).
in terms of voltage on the right hand side. I do not see voltage there and dimensions on the equation sides do not match, namely:
the left side of equation has Voltage dimension [Volts] and the right hand side has dimensions [per unit]. This is not acceptable in engineering and design (i.e. it is a nonsense).

Also, if the no load voltage increases across the parallel Xm branch, then the increased voltage on no load is bringing the operating point further into nonlinear B-H curve causing the current Im in Xm to be nonlinear with spikes. An oscilloscope may help to evidence it.

 

[electricpete]

jbartos - I have assumed the applied voltage is 1 (per unit representation).

Fundamental no-load voltage across the magnetizing branch does not increase with increasing frequency. That is what I showed with the equivalent circuit:
Vm p.u.= Lm/(L1+Lm) has no dependence on f.

Increasing frequency with constant voltage under no-load conditions moves the core further away from saturation and current harmonic content will decrease or remain the same.

Decreasing frequency with constant voltage under no-load conditions moves the core further into saturation and current harmonic content will decrease.

 

[jbartos]

Suggestion to electricpete (Electrical) Nov 12, 2002 marked ///\\jbartos - I have assumed the applied voltage is 1 (per unit representation).
Fundamental no-load voltage across the magnetizing branch does not increase with increasing frequency.
///Never disputed.\\ That is what I showed with the equivalent circuit:
Vm p.u.= Lm/(L1+Lm) has no dependence on f.
///Agreed. Never disputed. However, this equation presentation is mathematically objectionable since the voltage variable is missing on the right hand side. It is supposed to be shown there as a variable, e.g. Vt or 1.0. My claim is that Vm on no load increased and it may have increased into saturation region of the nonlinear Lm causing current spikes.\\
Increasing frequency with constant voltage under no-load conditions moves the core further away from saturation and current harmonic content will decrease or remain the same.
///Please, could you prove it or provide some references.
Notice, that Vm=constant=jXm x Im for fundamental wave in Xm linear region. For harmonics: Vm= Xm(Im), i.e. Vm is a nonlinear function of Im over nonlinear characteristic called Xm.\\Decreasing frequency with constant voltage under no-load conditions moves the core further into saturation and current harmonic content will decrease.

 

[Marke]

I aggree with electricpete on this one. Increasing the frequency for a fixed voltage will reduce the no load current and the harmonic content. Reducing the frequency with a constant voltage, increases the current and the harmonic content. A relatively small reduction in frequency at fixed voltage will result in iron saturation and a rapid increase in current.

As the frequency increases at a constant voltage, the motor operates at a higher speed, but with reducing torque.
Best regards, Mark Empson

http://www.lmphotonics.com

 

[jbartos]

Suggestion: I disagree with Marke's and ElectriPete's postings. There is also the Steinmetz Equation that pertains to remagnetization. So far, it has been downplayed in the above postings.
The Pr power loss due to the remagnetization is proportional to the frequency raised to power exponent 1.6 (actually range 1.4 to 1.8, 1.6 is the average). This Pr increases with frequency faster than Xm=j x 2 x pi x f since here the exponent at frequency f is equal to 1.0. That is why some manufacturers impose a limit on the inverter motor RPM to prevent the motor from overheating and damage.

 

[electricpete]

jbartos - As I have addressed on 11/10, core losses do increase with increasing frequency. But that will produce a very small increase in resistive current which will be overcome by the decrease in inductive current, remembering that the total current is primarily inductive.

Regarding harmonic current, the non-linearity of magnetizing current results from saturation. As you increase frequency you move further away from saturation and reduce harmonic content.

 

[Marke]

jbartos
You are correct, the core losses for a constant flux density, will increase with increasing frequency.

Additionally, core losses with fixed frequency will reduce with reducing flux density.
In the case of an unloaded induction motor driven from a constant voltage but increased frequency, we will have an increase in "remagnetisation losses" per unit of flux, but the flux will reduce due to the increased frequency into an inductive load.

If we look at the total current vector at no load, it is made up of reactive current (primarily magnetising current) and resistive current (loss current).

The power factor of an unloaded motor is typically 0.1 to 0.2 depending on losses, design etc. This shows that the reactive component of the current is significantly higher than the resistive component and therefore the variation in the resistive current component has a small influence in the total current measured relative to the effect of the change in the reactive current component.
Best regards, Mark Empson

http://www.lmphotonics.com

 

[jbartos]

Comment to electricpete (Electrical) Nov 10, 2002
If you increase frequency and keep voltage magnitude the same, then the no-load current will decrease, and any harmonic content of the no-load current present at 50hz may also decrease.
///I am essentially questioning the how well this idea is posed. If the B-H curve (or V-I) curve of magnetic material is considered and relationships stated below:\\
1 - Why does current decrease:
In the linear model the impedance limiting the no-load current is

I = V/Z = V / [X1+Xm] = V /[j*2*Pi*f(L1+Lm)]

where X1 & L1 are associated with stator leakage reactance/inductance and Lm and Xm are magnetizing reactance/inductance.
///with V=constant, L1=constant and assuming L1 negligible for this topic, B-H curve holds, and Lm=constant. These constants constrain the I current to constant by means of B-H curve (or V-I curve) relationship. Supposing that this is so, then varying frequency is causing this topic being mathematically ill-posed. This is why I inquired about any references or laboratory test that would confirm this.
Of course, the f frequency can be varied; however, something must be unconstrained in the above relationships. Assuming that B-H curve relationship stays, then the Voltage V cannot be constant to produce well-posed physical relationship and physical realizebility. Please, have you had it reviewed by any Professional Mathematician?\\

 

[electricpete]

jbartos -
I = V/Z = V / [X1+Xm] = V /[j*2*Pi*f(L1+Lm)]
is the linear model to demonstrate that the no-load current magnitude decreases when frequency increases. It comes directly from the basic induction motor equivalent circuit with s=1 => R2/s >> (Xm) and => load branch current is neglected. This linear model is valid for the linear range of the b-h curve.

You wrote: "These constants constrain the I current to constant by means of B-H curve (or V-I curve) relationship. Supposing that this is so, then varying frequency is causing this topic being mathematically ill-posed" Apparently you believe that a fixed B-H curve implies a fixed frequency-indepdent relationship between voltage and current magnitude. You are wrong in this belief. The relationship between voltage and B is frequency-dependent. In the linear range for sinusoidal v and B that relationship is |v|~dB/dt~2*pi*f*|B|. This gives rise to the frequency-dependent inductive reactance terms in the equivalent circuit and the frequency-dependent relationship between voltage and current.

You wrote:
This is why I inquired about any references or laboratory test that would confirm this.
I don't need a lab tests to prove my statement that induction motor no-load current magnitude and harmonic content will decrease when we increase frequency. It is self-evident from basic principles. You are welcome to run a lab test if you'd like.

you wrote:
Please, have you had it reviewed by any Professional Mathematician
I don't find that to be necessary. This is basic knowledge for any electrical engineer familiar with motors.

 

[jbartos]

Comment to the previous posting: Thank you for adding the
|v|~dB/dt~2*pi*f*|B|
to your earlier posting:
"2 - Why does harmonic content decrease:
Because your taking the core further away from saturation."
However, your clarification just confirms that the voltage across the parallel magnetizing branch must vary with varying frequency. It cannot be constant as stipulated in above postings. The constant voltage |v| actually makes the topic or problem ill-posed as I mentioned when it comes to frequency variations. Please, would you prove or evidence where I was "wrong" as you indicated in the previous posting.

 

[electricpete]

Comment to the previous posting: Thank you for adding the
|v|~dB/dt~2*pi*f*|B|
to your earlier posting:
"2 - Why does harmonic content decrease:
Because your taking the core further away from saturation."
However, your clarification just confirms that the voltage across the parallel magnetizing branch must vary with varying frequency.

No. I have assumed constant applied voltage and neglected leakage reactance. This results in constant magnetizing branch voltage. Therefore from the above relationship |B| changes with f, not |V|.

The constant voltage |v| actually makes the topic or problem ill-posed as I mentioned when it comes to frequency variations. Please, would you prove or evidence where I was "wrong" as you indicated in the previous posting.

Well, I think I have already answered that. I believe you were mistaken when you wrote:

with V=constant, L1=constant and assuming L1 negligible for this topic, B-H curve holds, and Lm=constant. These constants constrain the I current to constant by means of B-H curve (or V-I curve) relationship. Supposing that this is so, then varying frequency is causing this topic being mathematically ill-posed. ....
Of course, the f frequency can be varied; however, something must be unconstrained in the above relationships. Assuming that B-H curve relationship stays, then the Voltage V cannot be constant to produce well-posed physical relationship and physical realizebility
The logic you are using is that |V| is constant and |V|-|I| curve arising from the B-H curve is unchanged with changing frequency, therefore I must be constant with changing frequency. More specifically |V| establishes |B| establishes |H| establishes |Imagnetizing|, with each of these relationships independent of frequency by your logic.

As I have discussed above the relationship between |V| and |B| is not frequency independent. |B| ~ |V|/f as shown above. The statement which I believe I have shown to be wrong was ...These constants constrain the I current to constant

So in summary .... increasing frequency with applied voltage magnitude constant causes no-load current magnitude to decrease and any harmonic content in that current to decrease. I don't believe I'm going out on a limb with that statement.

 

[jbartos]

Suggestion: Reference:
1. L.J. Giacoletto "Electronics Designers' Handbook," Second Edition, McGraw-Hill Book Company, 1977,
1a. Page 2-87 Section 2.4b Hysteresis Effects,
1b. Page 2-90 Section 2.4c Soft Magnetic Materials,
Reference 1 indicates in 1b that the flux density B decreases by a factor 1/e in a skin depth, Xdelta (refers to Table 2.18). Thus for utilization of magnetic material Xthickness < Xdelta.
Else, if H(t)=Hp x sinwt, then
B(t)=Bw x sin(wt-d) + B3w x sin(3wt) + ...
This means that B has higher harmonic components.
The hysteresis losses (the area of Rayleigh loop) increases as the cube of the peak magnetic field excitation.
C.P. Steinmetz hysteresis loop energy Wh=eta x f x Bp**1.6
Eddy Currents Losses We=[(pi x r x f x Bmax)**2]/(4 x ro)
(Notice that if frequency increases from 60Hz to 600Hz, the Eddy Current Losses increase 100 times, e.g. from 1kW to 100kW).
With increasing frequency the Eddy current and magnetization losses will increase more rapidly, Ir through the branch of this losses will increase more rapidly than the decrease of the current due to any reduction of B due to skin depth, Im', since the B is reduced by a coefficient 1/e only, e=2.71.. . The parallel branch current Im = Ir + jIm'. However, the form of B-H curve (or V-I) curve of the magnetic material stays since it is characteristic to the magnetic material, e.g. soft iron.
Please, notice that if the frequency does not increase sufficiently enough, i.e. Xthickness < Xdelta, the Bmax=Bpeak=Bp stays approximately constant. So that the current Im' does not decrease much, if at all.