Nick, good question. IMO many dual installations are an attempt to fix, I use that term loosely, a bad pump selection. Having both is usually not a sign of an efficient system design. In 95% of all cases there will be a more efficient solution than using both vfd and control valve, Personally I struggle to fabricate any specific example of the 5%, but I don't know everything yet, so I leave that allowance. It could easily be 2%, or 0%. There are also practical control problems. It is very difficult to control both flow and pressure. In fact, you can not. You set one, you get whatever the other must be. A certain flow into a fixed system will require and result in a certain pressure. Any pressure applied to a fixed system results in a certain flow. Its not a mix and match thing. As you know, a voltage applied to a resistor, results in a given current and a given current applied to that resistor requires a certain voltage. Can you seperate the effect of V, same as pressure, and I, same as flow? If you control V across a fixed resistance you get X amps. If you then tweek the amps, then the Voltage starts moving, but a voltage controller wouldn't let it go where it wants to and holding it fixed, results in no change in amps. So, then you start playing with R, a control valve actually changes system resistance to get the flow (if its FCV) you want, or the pressure you want (if PCV), the voltage controller hangs on and keeps V constant, but now current starts going off.
Any change in pump speed has a corresponding change in pump flow rate. Speeding up a pump increases both pump flow and pump discharge pressure. If you do that with the idea to control flow, you (your piping system) must accept the resulting pressure. If you do that to control pressure, you must accept the resulting flow. That reality creates a control problem.
Trying to control both creates a short circuit in the control logic.
Vfd pressure control, with flow control valve.
Say your system pressure is running high and you want to reduce it by using vfd. Your pressure transmitter signal is high, so it must slow the pump speed to reduce pressure. Well, that reduces pressure, but also reduces flow. Now your flow rate transmitter is telling the flow control valve to open, which it does, and that causes the system pressure to rise. But how can it rise? Your pump is slowing down. Opening the flow valve also wants to increases flow. But your vfd is slowing down the pump while the flow control valve is opening even more. So, where does that lead? A pump running at 0 rpm with the flow control valve at full open, or anywhere inbetween?
Say your system pressure is running low and you want to increase it by using vfd. Your pressure transmitter signal is low, so it must increase the pump speed to increase pressure. Well, that increases pressure, but also increases flow. Now your flow rate transmitter is telling the flow control valve to close, which it does, and that also causes the system pressure to drop. But how can it drop? Your pump is running faster. Closing the flow valve also wants to decrease pressure. But your vfd is speeding up, pressure is increasing, while the flow control valve is closing even more. So, where does that lead? A pump running full speed with a closed flow control valve, or anywhere inbetween.
Vfd flow control, with pressure control valve.
Say your system flow is running high and you want to reduce it by using vfd. Your flow transmitter signal is high, so it must slow the pump speed to reduce it. Well, that reduces flow, but also reduces pressure. Now your pressure transmitter is telling the pressure control valve to open, which it does, and that causes the system pressure to rise. But how can pressure rise while the vfd slows the pump down with the pressure valve opening even more. So, where does that lead? A pump running at 0 rpm, producing no pressure, or flow with the pressure control valve at full open, but with no flow, or anywhere inbetween?
I'll let you think about the remaining cases. They all produce unstable results. Then they start adding limit switches, trying to keep the instabilities from running away too far off the map.
--Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."