The chart about is from a DENT ELOG and shows the difference in KW and PF for a 5 HP, 230 volt, three phase centrifugal pump, controlled by a CSV and a VFD. As you can see at 100 GPM there is no difference in KW or PF. At 75 GPM there is very little difference. At 50 GPM the VFD shows to use 12.5% less KW than when using a CSV. At 25 GPM the VFD shows to use 20% less KW than when controlled by a CSV. Over the entire range of flow the VFD shows to use an average of only 9.53% less KW than when using a CSV.
At low flow, VFD controlled pumps use slightly less energy than a pump controlled by a CSV. However, neither is saving energy. At low flow the VFD is using 200% more energy per gallon compared to maximum flow. The CSV is using 240% more energy per gallon than when running at maximum flow.
The difference in energy consumption of a VFD compared to a CSV is minimal. With power factor correction the PF of a pump controlled by a CSV can be equal that of a pump controlled by a VFD. The difference in energy consumption between CSV and VFD can be so slight that harmonics, voltage spikes, resonance vibration, bearing currents and many other side effects of VFD control can more than outweigh any possible benefits.
When varying the flow of a pump is required, a CSV can have many benefits over VFD control. If someone tells you that a Valve burns energy and varying the speed saves energy, they should get a pump curve and learn how pumps really work. VFD manufacturers push so hard because they make a lot of money with VFD's. They are all too often able to wrongly convince the end user a VFD saves energy. This locks you into a product that costs a lot and doesn't last very long, which is why VFD's are a Cash Cow for the manufacturer.