Calculate where pump is running on its curve in a modicon PLC

Hi,
I've been asked to display the pump efficiency on our HMI system (iFIX). They have requested a kind of bar graph to indicate if it's running near it's "Best efficiency point" or into cavitation zones. But they don't want the actual curve on the screen, just a moving bar as per ISA 101 HMI standards. The HMI part is easy, but I don't know how to calculate the actual value for efficiency.
I'd like to do it in our M340 PLC. We have the flow measurement of the pump and the VFD speed and the downstream pressure. I feel like it would be easy in Excel to do a VLOOKUP against a table of the curve values, but in a PLC? And it's a VFD so it's kind of a 3D lookup. I haven't been given the pump curve information yet so I'm not sure how many data points I'll actually have to work with.
I'm guessing I'll need some kind of arrays, but I've never worked with those much before. Any tips?
Thanks

First you need to find the operating point. That is the intersection of the system curve and the pump curve. The operating point indicated the pressure and flow. From this the output power can be computed. The current and voltage going to the more shows the input power to the pump. Efficiency in the output/input.

Yes, finding the operating point, that is what I am trying to do, but I don't know how to do that in the PLC.

They want to see basically an animated version of the pump curve showing where they are operating the pump at. We're not looking at power, it is being driven more by keeping the pump in a good range to avoid premature wear on the impellers and the power efficiency is just sort of a bonus on top of that.

BEP as a function of flow and pressure on a variable speed pump is a moving target, since the curve will shift down and to the left as the pump speed changes.

I am assuming you have three values to work with: pump motor kW from the VFD, discharge pressure, and flow rate. I am also assuming you are pumping water.

You will have to make some assumptions about motor efficiency and suction pressure. You will need to assume the value for these and assume they are constant.

Hydraulic power(hp) = gpm x head(ft) / 3960

Pump shaft power (hp) = VFD output(kW) x motor efficiency(decimal) / 0.746

Pump efficiency(%) = 100 x Hydraulic power(hp) / Pump shaft power(hp)

Another option is to determine the min and max flows from the pump curve at its base speed, and take the ratio of actual speed to base speed and multiply it by the min and max speed. That will give you the flow limits at your actual speed.

PLCengineer123, you need the formulas for the system curve and the pump curve as a function of power or flow. Now you have two equations and two unknowns and you solve for the the two unknowns. It is best to do this symbolically so the operating point can be computed as a function of the pump speed or power. Since the system curve and the pump curves are not linear functions the resulting function will not be a simple equation. I would compute the symbolic formula as a function of input power and flow too compute the operating point. I can do this easily but the math is beyond the grasp of most people. Finding the formulas for the operating point is the hard part and shouldn't be done in a PLC. I have tools like Mathcad and Mathematica for this.

Thanks. I'm clearly not familiar enough with these mechanical issues to be able to figure this out. I still don't understand what power has to do with it, but I understand the concept of getting the equations from the curves - I think excel can even do this. So if I have those then I shouldn't need to worry about trying to find where I am on the line with data in an array format and using some kind of Lookup function, I should be able to just solve the equation.
Since my main question was about figuring out if there is a way to do Lookups in the PLC, and I won't need to do that, I'll leave it there for now and ask the mechanical/hydraulic folks around here to help me wrap my head around what the equations really mean or how to figure them out.
Thanks again,
Treena

The attached example might help.