How to calculate KW losses in a unbalanced motor

[COMAPRO]

I Know that if the current is unbalanced in a three phase motor , heat develops and the life of the winding coil is reduced. The formula to calculate the loss in KW is I x I x R but how do I calculate easy the R value in a motor , is it not a table available where one can read the % losses if one knows the HP of the motor and the % of current unbalanced ?
Appreciate your comments. thanks

 

[Baldor]

I know a voltage deviation of 5% gives you a .75 derating factor.
First, take an average of the 3 voltages (ex., 220, 208, 210 = 212.7 Vac). Find the largest deviation from the avg.(220-212.7 = 7.3). Divide the deviation by the avg.( 7.3/212.7 = .034) and multiply by 100 = 3.4%.

It's a fairly linear derate curve up to 5%.

4% = .85 derate factor
2.5% = .95
1% = .99

Don't run a motor with more than 5% voltage deviation

 

[COMAPRO]

Baldor, unfortunately your post did not answer my question . I talk about current unbalanced and not voltage unbalanced. Anyway thank you for the try

 

[GGOSS]

Hello COMAPRO,

Not sure if I can answer your question any more accurately, however I hope the information below, used together with that provided by Baldor will prove useful to you.

The standard specification for LV motors appears to be; for every 1% line voltage error you can expect between 6 & 10% line current error. As there is a relationship between current and voltage imbalance (albeit not fixed), I believe the formula given by Baldor is a good guide.

On looking at a derating curve provided to me by a motor manufacturer, derating is as follows:

1% voltage error, derate motor to approx 0.99
2% voltage error, derate motor to approx 0.95
3% voltage error, derate motor to approx 0.87
4% voltage error, derate motor to approx 0.80
5% voltage error, derate motor to approx 0.75

Regards,
GGOSS

 

[GGOSS]

Hello again,

Usefull link containing derating tables.

http://www.elongo.com/pdfs/voltages.PDF

regards,
GGOSS

 

[COMAPRO]

GGoss , thank you for your tips but let me try to explain myself better.first of all , for me "dearting" means reducing , in this case the load but I am after the KW savings if no losses are generated because of current balancing based that voltage is balanced. therefore I thought that I was going to find a table on the subject. for example : if 20 HP motor has a 15 % unbalanced current and one is able to reduce the unbalanced to lets say 5% the KW losses would be reduced to what ? What would be the R value of the 20 HP motor to calculate the standard formula P= I X I x R ? where can I find motor tables where one can read the R values of each motor ?
hope I have explained myself. thank you anyway.

 

[ScottyUK]

Comapro,

I'm curious how you propose to control individual phase currents. Are you suggesting balancing the currents by having some form of regulation on each phase and perhaps a controller to keep the imbalance to a minimum?

Sounds like a lot of work for limited gain, and almost certainly would reduce the reliability compared with living with the imbalance. Am I completely missing your point?

regards,

Scotty.

 

[jbartos]

Suggestion: R values for motors are usually not in tables since they are not much used. Usually, the motor manufacturer is contacted for specific motor parameters, such as the motor R. Also, the motor R is an ambiguous parameter since it may include the motor stator R; or motor stator R, and rotor Rr on stator side Rr’ combined.

 

[canhoto]

comapro: I also want to quantify the economic benefit of balancing phase currents. I work on air conditioning systems in office buildings and often measure imbalanced currents of 10 to 15 percent. These are usually accompanied by voltage imbalances of 1 to 2 percent. My buildings are dominated by single phase fluorescent lighting loads which can be redistributed among phases. I've always wondered if there is an economic incentive to do so. So far I have found only information on winding temperature, motor life, etc. Can somebody show us how to calculate excess power consumption caused by negative sequence currents?

 

[aolalde]

COMAPRO and canhoto:

Sorry is not that easy as “ I^2*R.”or a table of resistances.

Probably you will need a computer program to foresee the performance of a motor under unbalanced Voltage (the result of unbalanced voltage or winding or both is unbalanced current). Such a program probably has been developed at a University or by a Motor manufacturer.

I will try a brief explanation but I can’t attempt a calculation.

The worst resultant of unbalance is the creation of a negative sequence voltage system. The higher is the unbalance, the larger is the negative sequence. (If you are not familiar with electric circuits a negative sequence rotates in reverse direction as compared with the three phase main power phase sequence).

Then a rotating synchronous flux is created by the motor winding but rotating in reverse direction, the rotor bars cut this flux at a rate twice of the line frequency , resulting in high induced current in the rotor bars in spite of this negative sequence having low flux .

The I^2*R of the rotor increases generating heat and a negative torque which acts like a break. The stator winding reflects this rotor current with an increased current too and now the stator winding losses increase too.

The temperature rise increases and the conductors resistance increases too, then the losses increase.

Some times the rotor bars are melted.

My advice, “Try to keep as balanced phases as possible on lines feeding electric motors”

 

[canhoto]

I finally found one source at

http://www.oit.doe.gov.

Interestingly enough, it stresses the importance of eliminating voltage imbalance, but cites very low efficiency gains.

It referred to tests on a 100 hp motor at 75% load with a 1% voltage unbalance. It predicted current unbalance in the range of 6 to 10%. I observe conditions like that often. The efficiency loss was only 0.1%.

The same motor at 2.5% voltage unbalance had a 1.3% efficiency loss. In the absence of excessive failure rates, this is beginning to justify corrective action.

However, in my experience, voltage unbalance as large as 2.5% is uncommon. (It is typically accompanied by 25% current unbalance.)

The main thrust seems to remain motor life. Am I to conclude that unless we have a high failure rate there is no reason to worry about phase current unbalance?

 

[jbartos]

Comment: Generally, the imbalance current is mainly caused by imbalanced load in the power distribution, which in turn causes imbalanced voltages. Imbalanced voltages cause larger imbalance currents in the induction motors since the motor current rises fast with decrease in motor terminal voltage even for balanced voltage drops in excess of 5%, for example. The imbalanced current increase in the motor requires a modified electrical equivalent circuit for the motor since the often presented electrical equivalent motor circuit in textbooks for educational purposes does not include motor parameters required to justify the fast increase in the motor current by the motor imbalanced terminal voltage. Beside the nonlinear parameters in the motor parallel branch in the motor electrical equivalent circuit, e.g. magnetizing reactance, Eddy current resistance, remagnetization resistance, etc., there are no other motor parameters in the motor electrical equivalent circuit normally presented. If the symmetrical component analysis is considered, the motor symmetrical component impedance parameters are required and can be obtained from some motor manufacturers only. Presently, the simplest way to obtain the motor dependencies, e.g. current, power, etc. on the input motor imbalanced terminal voltage, is by empirical approach, i.e. by measurements.