Estimating Motor I & V under VFD operation 1

[bill318]

What is the best way to estimate 3-phase motor current and voltage when driven by a modern VFD at different RPM and torque loads?

Example Motor:

HP - 25
Poles - 4
Volts - 230V
RPM - 1748 rated (1800 SYN)
FLA - 59A
FL Eff - 92%
Torque ~ 75 ft/lbs

VFD input V - 460V (allows full torque above rated speed)

The formulas that I have run across require knowing intimate details about the motor and are usually applied using a sine wave and known line voltage, not a VFD. Is there any way to at least get close when required shaft torque and RPM is known?

Thank-you, Bill

 

[jraef]

I'm assuming hat you can't just read the information from the VFD's display, because that would be the best way. If a "reasonable estimate" is sufficient, then basic formulae will always apply, they just will not reflect losses in the drive and motor. Seeing that you are using North American voltages and HP:

HP = Tq (in ft-lbs) x RPM / 5250, so since you say you know the shaft Tq ad RPMs, you can get HP.

I (current) = 746 x HP / 1.732 x E (Voltage) x Eff. x Pf.

The output voltage of the VFD it will be basically linear to speed percentage (assuming it is a constant torque application), i.e. at 50% speed you should be at 230V output, at 75% speed you should be at 345V etc. etc. You can estimate the Eff. of a standard or Inverter Duty motor at 80%, 90% if it's an energy efficient one, and you can estimate pf at the motor as .7 if you like.

 

[bill318]

Thank-you jraef,

The application, sadly, does not have constant torque over the RPM range. From what I understand, the VFD is able to keep the motor in a fairly linear torque vs current mode, except perhaps down at the very low torque levels and RPMs.

If I can solve for voltage or current reasonably under different RPM and Torque levels, then the formula you posted above should get me close. The system has not been built yet, so the estimates are needed for equipment selection / performance purposes.

Bill

 

[jraef]

By "constant torque" I meant as opposed to "variable torque", in which the VFD output V/Hz ratio is optimized for energy savings. On variable torque loads such as centrifugal pumps, the load HP requirement drops off more rapidly with speed. I mentioned that because the voltage at low speeds may end up LOWER than the speed would indicate in a VT application. It sounds as though you are going to use the VFD in a CT mode.

But now you have me curious as to why you needed this information "for equipment selection / performance purposes." You must always select equipment for the worst case scenario anyway, which would be full speed at full load, not the reduced case.

 

[bill318]

The load is a variable torque type (low torque at low RPM, high torque at high RPM).

I'm trying to graph what the motor and drive are seeing under various loading conditions and adjusting equipment selection and performance expectations until I reach a happy compromise. While I can do this by treating the drive and motor as a pair sized for worse case, I wanted to estimate what the VFD output voltage and current levels would be under different loading conditions below maximum.

Thank-you, Bill

 

[jraef]

Well, it's going to be relatively impossible to calculate it with any accuracy, but if you ignore the variable torque aspect and think of it as a constant torque application, your estimates will err slightly on the high side, which would lead to relative safety if thinking about equipment selection and performance expectations.

 

[bill318]

Thank-you jraef,

I'll give it a go and see what it looks like.

Bill

 

[geo168]

You can estimete HP of the load, providing its a fan or pump, by using the speed ^3 law.

Equation used for speeds below 100%
Hp = k * speed^3 (centrifugal pump)
Hp = 100% = 1
Speed = 100% = 1
1 = k * 1^3
K = 1/1^3 = 1

50hz/60hz=.833, hp = .833^3=57.8%, 57.8%hp at 50hz.
40hz/60hz=.666, hp = .666^3=29.5%, 29.5%hp at 40hz.
30hz/60hz=.500, hp = .500^3=12.5%, 12.5%hp at 30hz.
20hz/60hz=.333, hp = .333^3=3.64%, 3.64%hp at 20hz.
10hz/60hz=.166, hp = .166^3=.457%, .457%hp at 10hz.

You can estimate the motor current based on the calculated HP by using the methods described above by Jaref.
Please note the power factor will decrease as you reduce the HP of the motor via the VFD. You should be able to estimate the PF from the motor data. The data should give PF for 1/4, 2/4, 3/4, 4/4 load. The efficiency should be close throught the speed range.

Also remember the power factor on the input to the VFD will be constant throught the speed range ~0.95