VFD controlled Pump relationship clarification

[DM7.ENG]

We Know that when configured for scaler control, a VFD willadapt its switching modulation to ensure that when frequency is changed, motorterminal voltage will change hence the term Voltage frequency ratio.
Similarly, if we look at the affinity laws for a centrifugalpump we see that a 10 % increase in speed will result in approximately a 33% increasein power.
The correlation I am looking to clarify is if the voltageand frequency are altered more or less proportionally to ensure constantmagnetisation flux and thus, current. What is the variable in the below formulathat causes such drastic increase in power consumption?

Motor Active power [kW] =

Of course

is a constant, and thecurrent is supposed to exhibit minimal fluctuation as per voltage frequencylaws above therefore, the only variables left to consider are V and PF.
Voltage
We Know that if the frequency is halved,so will the voltage in this equation.
PowerFactor
In addition, as the frequency isincreased the inductive reactance and hence reactive power will increasemeaning a reduced power factor.
Therefore, as the 2 remaining variablesare decreasing with respect to increase in motor speed, Surely this contradictsthe affinity laws whereby a 10 % increase in speed will result in a 33% powerincrement?
For this to be the case I would expectthe Motor active power equations numerator to increase not decrease as shown.
Perhaps I am looking at this the wrong way………..?

 

[Marvo]

With a centrifugal pump your impellor presents a highly variable mechanical load to the shaft of the motor that increases drastically with respect to it's rotation speed. This increasing mechanical load on the output of the motor causes a mirrored increase in the electrical load. This is a highly variable torque application, V/f control of the supply means the motor doesn't become over saturated at lower speeds due to lowering the DS bus voltage and it's usually done on a preset curve that's pre-programmed in the drive.

 

[DM7.ENG]

With a centrifugal pump your impellor presents a highly variable mechanical load to the shaft of the motor that increases drastically with respect to it's rotation speed. This increasing mechanical load on the output of the motor causes a mirrored increase in the electrical load. This is a highly variable torque application, V/f control of the supply means the motor doesn't become over saturated at lower speeds due to lowering the DS bus voltage and it's usually done on a preset curve that's pre-programmed in the drive.

Hey,

Thanks for the reply. To clarify the application, a client has asked us to alter the drives parameters so that the current drawn by the motor is below a certain value [Seems strange but I'll omit the specifics]
I thought that by lowering the speed we could in turn reduce the current as a function of speed however, I remember from previous studies that the drive will maintain magnetisation flux within a frequency spectrum of say 5Hz to 50Hz like you said so that when frequency is decreased to a minimum and thus so is the inductive reactive portion of the impedance, the current will not increase to levels that will saturate and burn out the stator. So I guess in layman terms my question would be, If the V to Hz ratio maintains the current at an almost constant, How does the current fluctuate with speed? I'm guessing this may have something to do with the difference between stator/ rotor current and the reactive current needed for magnitisation?

 

[Lucien Nunes]

Someone with experience of this application might have a rule of thumb for VFD pump performance limits. To work it out from the raw data, one really needs the torque curve for the specific pump and the hydraulic load it is driving. The ratio you mention will relate to one particular loading of a typical pump (e.g. open flow) and the behaviour when throttled or presented with a fixed head near its maximum static head could be significantly different. A small deviation in the curve can mean a large difference in power requirement because as a guide, power absorbed incresases approximately as the cube of speed, and torque approximately as the square. Obviously whatever the exponents are for power and torque as functions of speed, they will always differ by unity, so the power curve can be got from the torque curve and vice versa.

Assuming that with your decreased speed the motor is still delivering a large fraction of its nameplate power, so that the power current dominates over the magnetising current, then the line current will reduce approximately in proportion with torque. Find the available torque at your maximum permissible line current and use the pump curve or equation to determine the speed at which the pump absorbs that torque. In most pumping applications, this will always remain within the capability of the drive because of the high exponential factor of load torque with speed.

 

[marconi]

I have spent a little while researching and pondering on your problem - is it possible to use a VFD(PWM) to control a 3 phase asynchronous induction motor in such a way as to limit the maximum current it draws. I believe the answer to be no.

A VFD(PWM) acts as a constant current variable frequency and variable voltage supply to the motor. To preserve voltage stability in the motor the ratio of voltage applied to frequency is kept constant; this maintains a constant air gap flux density B, because the stator excitation is constant through constant stator current. Through transformer effect, the rotor current at synchronous frequency is also kept constant. How so if as the frequency of motor supply and thus applied voltage both increase in equal proportion? The reason is as the synchronous speed increased the rotor spins at a higher angular speed in the constant air gap flux which generates a proportionate increase in back emf (Lenz's Law) to counteract the induced emf.

Since the stator and rotor currents are both constant the torque is constant (Lorentz's Law). The mechanical power output is purely determined by the product of the constant torque and the rotor's spin speed which in turn is controlled by the supply frequency.

The electrical power input is the real part of supply voltage times motor current. Motor current, though constant is a function of applied voltage and frequency since the current is voltage divided by frequency dependent impedance. Thus the motor electrical power is proportional to voltage squared divided by frequency or through the voltage stability criterion v=kf to f - doubling the supply frequency doubles motor power output.

All this applied when the rotor spins at less than the rated synchronous frequency. For spinning greater than the rated sync frequency the voltage output is kept constant. Now the rotor currents decrease with increasing spin speed thus the torque declines with speed, albeit power output remains constant. there is a nice graph of this at Variable Frequency Drive or VFD | Electrical4u


For the VFD-Motor-Pump combo the open loop stable operating point is when the motor torque v speed curve is intersected by the pump's torque v impeller speed plot (where torque is derivative of pump power wrt to impeller speed).

PM me if you want more.

 

[Lucien Nunes]

Since the stator and rotor currents are both constant the torque is constant (Lorentz's Law). The mechanical power output is purely determined by the product of the constant torque and the rotor's spin speed which in turn is controlled by the supply frequency.

By inspection, this cannot be correct - the stator current of a fully loaded motor cannot be equal to that of an unloaded motor running at the same frequency. The current depends on the torque, which in turn depends, as you state later, on the intersection of the motor curve and the load curve. Along the shallow gradient of an induction motor curve where for a given frequency the speed is sensibly constant over a large fraction of the useful torque range, the torque, and hence the in-phase component of stator current depends mainly on the load.

The magnetising component might remain unchanged with load and frequency but not the total line current which is what the OP seeks to reduce. I referred to this point when stating that my approximate method assumed that the stator current at the operating point would still be much greater than the magnetising current.

I don't understand your point about the rotor current at synchronous frequency. The rotor current of interest is that at the slip frequency, a rotor currrent at synchronous frequency implies a locked rotor. For any induction motor, the rotor current (and torque) are zero at synchronous speed.

Anyway, to return to the original point, with a generalised centrifugal pump load the torque falls off at a greater than unity exponential power of speed. Obviously the pumping capacity is reduced drastically compared to the line current in the process, so without figures from the OP there's no way of knowing whether it will still serve its purpose with an acceptable current. Some pumps are so vastly over-specced that it might, if the necessary current reduction is small. The problem can be likened to an impedance-matching scenario, except that the (non-linear) load is a hydraulic one not an electrical one. Probably what is required is a pump with a lower Qmax at Imax.

 

[LeeH]

 

[marconi]

I have been pondering a VFD(PWM) with the appropriate voltage frequency law for the 3 phase induction motor it drives, and how this electro-mecha-tronic combo performs in the steady state - the dynamic is too difficult. At first glance, and forgive me for that, you seem - I may be wrong - only to be talking about the induction motor and not what I am considering an IM fed by a constant current variable frequency and voltage source where there is a law for Voltage change against frequency.

Thank you for pointing about my error in terminology - yes I agree the slip frequency for the applied supply frequency and loading.

In mitigation I had to write my attempt at explanation out three times because for some reason I kept loosing later paragraphs.

Hey, this more for my amusement and education than anyone else. So please help me understand more because this is not my specialist topic.

I will send you my source papers next for you to look at if you wish.

 

[marconi]

Consider VFDs for Centrifugal Pumps | Chemical Processing

Variable Frequency Drive or VFD | Electrical4u

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.192.8207&rep=rep1&type=pdf

http://www.ijsei.com/papers/ijsei-10512-09.pdf

https://www.google.co.uk/webhp?rct=...kp-YCA#q=mathematical+modeling+of+pump+system

 

[marconi]

I realise now I have only considered the constant torque load case - such as a building lift - for which current remains constant because load torque remains constant. Of course as you say for the variable torque load, such as a centrifuge pump, the torque changes with speed and thus the current drawn by the motor will too. The relationship depends on the load's torque v speed curve and that of the motor. It should then be able to limit the current drawn by the motor driving the centrifugal pump using a VFD.

As ever, thank you very much for your scrutiny and comments which have indeed helped me understand better - albeit not yet perfectly!

 

[marconi]

For DM7.ENG: I have turned up a paper which might be useful to you. It recommends using using a V(f) law V(f) =k x f x f for pump applications to maintain motor efficiency and correct magnetisation levels instead of V(f) = k x f.

I think there is a rule on the electricians' forum about not advertising in a thread so I will send in a PM a link to the paper.

 

[Lucien Nunes]

You can make it follow the generalised square law for the pump torque, but we don't know the pumping conditions so it's all speculation as to what law applies. OP needs more info and preferably a good pump expert. I'm assuming here it's a reasonable size plant, we might be overthinking it if it turns out to be something small and simple.

 

[DM7.ENG]

For DM7.ENG: I have turned up a paper which might be useful to you. It recommends using using a V(f) law V(f) =k x f x f for pump applications to maintain motor efficiency and correct magnetisation levels instead of V(f) = k x f.

I think there is a rule on the electricians' forum about not advertising in a thread so I will send in a PM a link to the paper.

Hi Marconi

Thanks for the additional literature. I commission quite a number of those pumps [without naming the brand]. It's clear that different laws apply for constant torque and variable torque loads. To add to the confusion I recently read that ABB drives employ DTC technology as a pose to conventional PWM