I have an application where I have 4 variable speed pumps that can supply feedwater to a common header that in turn feeds up to 4 industrial boilers. It takes up to 3 of these pumps operating in parallel to handle the load of all 4 boilers. There is also a smaller, constant speed pump used for very low loads. The pumps are not identical, 2 are motor driven and 2 are turbine driven. Our goal is to maintain a constant header pressure. I would like suggestions on how to control the speed on the pumps over the load range, including cutting in and out pumps as required. Pump starting and stopping will be manual by operators based on some alert.

The previous comments should be most helpful, but I would want to also consider the type of turbines used and the reasons for using them.  Is there some process use for the exhaust steam from the turbines (presuming that these are steam turbines)?  It seems possible that the use of the steam pumps could alter the operation and economics of the connected system.  Do the boilers serve a common header, are they all the same size, capacity, etc.?

If these turbines are of the size range that I am assuming (relatively small compared to multi-thousand horsepower units), their heat rate probably implies substantial relative energy costs compared to the electrically powered pumps.

Another question that comes to mind is the load profile for these pumps.  If most of the time the load is great enough for the electrically powered pumps to operate at or near full speed, then the adjustable speed drives' losses simply represent a needless parasitic loss, and constant speed drive for these could make more sense for both initial and operating costs.

From the information provided, it seems likely that the turbine driven pumps would probably be best kept in reserve for emergencies and high load periods, and the electrically powered pumps probably do not need to have adjustable speed drives.  This would allow simplification (and substantial savings) in the control system both initially and long-term.  (Boiler feed pump duty is not usually one of the applications showing the greatest energy savings from the application of adjustable speed drives.  Some energy savings may be realized from adjustable speed drives, but they are usually quite modest and economic justification is frequently marginal at best.)

Granted that the temperature of cool water is lower as is the viscosity, so obviously longer running at reduced flow is possible, and lubricity must also be greater.

Temperature is not the only concern.  Low flowrates in most pumps do hurt, by causing increased bearing wear due to unbalanced hydraulic forces.  Flows less than 60% of BEP are not recommended by API, although with a VSD, the pump would not produce such proportionally high unbalanced forces, since discharge pressure is reduced.

Each pump having its own control valve does not ease the situation.  The pressure of the header (assumed to equal the highest discharge pressure of any connected pump) must be reached by any other pump in order for any other pump to discharge into that header.  A pump producing less pressure than the header pressure must have its own discharge check valve in order to avoid being spun backwards by fluid attempting to enter from the higher pressure header.  Placing a control valve betwen a pump discharging at a pressure lower than the header will still not improve that situation.  You could only close it in an attempt to avoid backspin.  Flow from the higher pressure header would enter the even lower pressure at the control valve's outlet and still attempt to backflow into the pump.  

Additionally, when a centrifugal pump is deadheaded its discharge pressure is deadheaded at shutoff pressure, which is the same pressure, if it has a discharge control valve or not.  Deadhead pressure with a control valve is not reduced and is in fact usually the maximum pressure that a centrifugal pump can produce.  And, power is not being expended on the fluid, except for minor internal recirculation flows and all the rest of the power used by the pump to overcome internal fluid, bearing and stuffing box friction is being converted to heat.  There is no possibility for improvement by deadheading a pump at a lower pressure or any other pressure other than its shutoff pressure,... without a VSD.

On the other hand, a VSD driven pump, especially with recirculation, could be used to lower the shutoff head corresponding to a lesser rpm, and reducing the heat load.  Even a VSD driven pump without recirculation would produce less pressure and less heat.  Total power consumption does drop off with lesser flow at reduced discharge head, and since head drops with the rpm^2, and flow drop is linear, a VSD w/ recirculation can improve the heat load.  

True there is less power consumption at lower flows, with or without a control valve on a non VSD equipped pump, but most all power delivered is converted to heat at the lesser efficiency, so a lesser power consumption is paid for with increased resulting temperature load to the pump.  

It also don't think that power consumption with a VSD drops, as you say, almost the same as if flow is restricted with a valve (on a pump without a VSD).  Power consumption drops with the cube root of the pump speed on a VSD equipped pump, but power consumption on a pump without a VSD looks like that on any typical centrifugal pump curve with reducing flows, which is an inverted curve that depends mostly on the pump's hydraulic efficiency at flows away from BEP Q.  Power consumption with a VSD dropping with the cube root of rpm and with only a very slight change in efficiency at different rpms and the same change in efficiency with flowrate as a non-VSD equipped pump, would appear as a cubic curve and power consumption drops very fast.  I think those curves are very different, however the power consumption of a VSD equipped pump with a control valve, or a VSD equipped pump without a control valve would indeed be equivalent.  The control valve has no effect on power consumption of the pump, as it mearly increases or decreases resisting head and consequently only changes the power required to flow into the system at any given control valve setting.

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