With a VFD you can do the same job with a smaller motor simply because it doesn't have to be sized for startup loads.
Motors can have a much lower efficiency outside their rated design point.
Precisely my point. The power factor losses for which a capacitor is meant to compensate are only an estimate of load. A VFD can adjust for same much more accurately in real time.
That didn't make any sense to me. And I've sized a lot of motors for process applications.
Pumps develop most of their load under mass flow. Fans develop most of their load as they come up to full speed. A VFD can adjust for same much more accurately in real time.
In a throttling type application, with a varying process, that is quite true. But in steady state applications, the pump/motor are select for 100% run speed and a VFD would only add losses at that point. That is why efficient applications that do vary, and come up to full speed for long times include VFD bypasses.