Saving energy with a VSD requires that you must operate a lot of the time within 50% and 85% of the pump's BEP flowrate and that the head delivered when at reduced speed is sufficient to circulate the reduced flow.
Below 50% speed, motor and VFD efficiencies at reduced load starts to hurt the economics considerably (I have the typical tables), which is why I don't recommend that, not to mention that you are only producing a head of 0.5^2 * BEP_H = 0.25 At 33% speed, that's 10% of BEP_H. Those two factors combined will kill VSD applications right there.
Its true that control valves waste energy, but at reduced flows, they don't waste a lot of energy and what they waste is usually less than the energy used with a VFD, due to the above inefficiencies,
unless you are in a range of 50% to 85% of BEP_Q.
Above the range of 85%, the energy saved by a VFD
OVER that of a properly sized pump and control valve is simply not worth (IMO) the extra maintenance headaches and sometimes the power quality problems that VFDs often bring along with them.
Once the energy use at various flowrates is established, to know if you will save energy or not requires that you know what flowrates you will have to run in the system over a given time period. Then you can determine the energy you will save over that time period. As I say, typically between 50% and 85% BEP_Q is where there is a potential to save energy, so you have to be operating inside that range to do it. Look at your system history and see if and how much time you operate there. Calculate the energy savings over those times.
Since variations in flowrate are needed in order for a VFD to produce savings over a properly sized pump, there are a few other possibilities you can consider. Look at how you can eliminate flowrate variations. Can you provide a tank and let the level in the tank fluctuate to smooth down those peaks and valleys in the flowrate? Can you adjust your process so that there is less variations in the batch sizes? Can you operate the system for longer time periods and pump at a constant average flowrate over, say 24 hours rather than just pumping at a big flowrate for only 8 hours per day and a small flowrate during the night? Fill a tank at the average flowrate then have the process draw from the tank at high demand periods. There may be many possibilities you could draw upon to eliminate any need for a VSD at all. I simply recommend that you consider those too.
VSDs do serve very well in certain situations. I find them most useful for,
Adjusting flowrates in a process where the output required today is typically less than the original design parameters of the system.
Adjusting the head in a system that has an unusual fluid, such as a heavy nonNewtonian hot crude oil that requires very high pressures to get it moving, but as the pipeline fills with hot oil and forces out the cold heavy oil, less and less pressure is needed to hold the design flowrate. Having said that, it is often just as economical to use two pumps arranged in series, operating 2, then 1. Which one is better? That depends on the specific fluid properties, the pipeline thermodynamics and the flowrates you need to run during startup and shutdown.
VSDs may also serve a purpose where you have many pipeline branches that are operated individually and each branch has a widely varying head requirement, such as in an irrigation distribution system, but then you must be very carefull to get the head you need at each flowrate. Too much head needed and a VSD won't deliver it at reduced flow. For that reason, in irrigation systems I usually prefer to open each branch with a valve, flow a certain time to deliver the needed water and close, then move to another branch. That way a pump can be sized for a constant flowrate. If head varies considerably a VSD may help, but again subject to its ability to deliver that head at a different flowrate. Because when a VSD changes speed to adjust head, it also changes flowrate, so be carefull if it can deliver the water needed during the operating time available for any given branch.
In general, I think I can agree with jonr, that VSDs are not the energy savings panicea that many manufacturers claim, but its not only their fault. Some guy (hopefully not an engineer) still has to install them in a system where they do not belong. If flow varies between 50-85% of BEP_Q, and you have to operate there, and at the same time head varies from 0.25-0.72 of BEP_H, you stand a chance to save some bucks.
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"Pumping accounts for 20% of the world’s energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that
99% for pipeline companies)