Well, giving you the benefit of the doubt that you are not a very clever student, here is my take.
dpc beat me to it a bit. VFDs definately save energy WHEN there s a variable flow rate involved. So using your wetwell application, the prime use of the VFDs there is to match inflow rates by lowering the pump speed, but have higher pumping capacity available for the occasional higher inflow. That way you are not having to stage multiple pumps on and off and using the wetwell as a surge tank all of the time.
How much energy do they save? It is totally dependant on the average running speed. At full speed, VFDs actually WASTE a little more energy, but the energy savings vary by the cube of the speed. So at 70% speed, they are only consuming 34% of the energy compared to full speed, a dramatic diference. I picked 70% for a reason however, because many VFD salesmen will tell you that at 50% speed it uses only 25% of the energy, but fail to mention that at 50% speed you may not be pumping anything! In a wetwell application, it is a little different because when the well is filling up and the first pump has not yet been called for, the pumps consume NO energy, then turn on at full speed and consume a lot for a brief time, then shut off again. So you must consider avarage energy savings over time based on inflow rates, and that is tricky. In spite of that, VFDs generally come out as saving more energy.
But energy cost is only part of the problem. Reliability is another concern, and lets face it, as good as VFDs have become, they contain a lot more critical parts than full speed controls, therefore their MTBF is always lower. So if a remote lift station might take someone 2 hours to get to in an emergncy shutdown situation, it can be a major liability if the VFD dies. If you get fined for spillage, all your energy savings went for naught. A VFD in the headworks of a manned WWTP however is a different story, because someone is there and can deal with any issues immediately.
The comparisons can go on and on, that's why it is better to consider each specific application on it's own merits rather that rely on generalizations.
One generalization I will make however is that it is NEVER beter to consider Y-Delta starters. They save absolutely nothing except some up front costs, and risk the equipment they are connected to as well as the power system. If you are considering full speed operation but want reduced voltage starting to protect the equipment mechanically, consider soft starters. They are less expensive than autotransformers and will not expose the mechanical equipment to risks of damage from switching transients.
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