If you have power factor problems your current may be high in proportion to power and it's current that overheats the motors.

If there are transient voltage fluctuations in the power supply to a fixed speed drive, current draw will go up in order to compensate.
So it depends on why / what you want to monitor power (or current).

I'm definitely not an electrical guy but my understanding is that below 50% of nameplate power, there is very little difference in current. Even if reading properly, it's very hard to pick any setpoint that suitably protects without the risk of nuisance trips(which can lead to the operator bypassing protection entirely).

Because most pumps tend to operate at or to the left of BEP and most motors are sized to cover the entire flow range without going into safety factor, many motors routinely operate at well below the nameplate power in that relatively flat amperage range. In contrast, power tends to be much more linear over the entire range which allows for much better control. It also makes diagnosing pump issues much easier if you're looking directly at hp/kw as you can look at your performance curve to see where you are operating on the curve.

It depends on the purpose. Motor protection is primarily current. Process control could be current or power. Power can help you track the system operation.

TheHandModel is correct. I have tried both amp and power monitoring, and power monitoring is superior for mag drives where the objective of the monitor is to prevent dry-run. Amp monitoring is not sensitive when loads are not near the motor's nameplate load rating. For small pumps, this can actually be as high as 60-70% of nameplate where amperage is fairly flat with load.

See the reference below:

https://www.google.com/url?sa=t&rct=j&q=&a...

Current may tell you what you want to know about the motor, but power if far more informative about the performance of the pump.

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P.E. Metallurgy, consulting work welcomed