The “two-thirds” Rule for Locating Sensors to Control Variable Flow Systems – Part 3

In the past two posts, we have been using this simple variable flow system …

… to look at why the 2/3 rule optimizes a pumps performance as the load on the system drops.

In the first post, we looked at how the pressure requirements at different points in the system varied as the flow varied. In the 2nd post, we looked at how allowing the load’s control valve to push the pump up its curve saved some energy, but not nearly as much as is possible in theory. In this post, we will look at how the application of a VFD to the pump and the application of the “2/3 rule” to the VFD control algorithm can allow us to approach the theoretical energy savings possible as the system unloads.

As a starting point, I made a pump selection for the part load requirement of 400 gpm and 26 ft.w.c. to serve as a baseline. (See table 1 in the 1st post to refresh your memory on where the 26 ft.w.c comes from.)

The selection is a slightly different pump from the best efficiency selection we made for our design load of 800 gpm at 44 ft.w.c. The size of the pump is a bit smaller and its provided with an 1,150 rpm motor instead of a 1,750 rpm motor. Obviously, changing the pump every time the load on the system changes is not a practical approach. But, this selection gives us a target to shoot for in our effort to optimize the system in a practical manner.

Here is our original pump selection, but instead of showing the performance with different size impellers, this curve shows the performance at different speeds.

Here is the more common version of the curve with different size impellers as a frame of reference.

If you contrast the two curves, you will notice that you can change the pumps performance by changing the impeller or by changing the speed. But, if you change the impeller size, the efficiency of the pump tends to be reduced as you reduce flow and/or head from the peak efficiency point or “sweet spot”.

If you change speeds, you can get the same effect in terms of a reduction in head and/or flow, but you tend to preserve the efficiency. This is one of the advantages offered by a speed change vs. an impeller change.

Bear in mind though that if you make the speed change with a variable speed drive, the drive itself has losses. Thus, using the drive purely as a balancing device may not be the best option when compared to an impeller trim if only a modest change in speed is required.

Here is the variable speed curve with the system curves for a number of optimization options superimposed on it.

Lets see what this tells us about VFDs and the “2/3 rule”. (Note that the white line with red dots highlights our part load design flow rate target.)

The red curve is the system curve associated with allowing the control valves at the loads to push the pump up its impeller curve with out changing speed.

Note that the flow is reduced, which saved some energy as discussed in the previous post, but the efficiency is also reduced and the head is significantly above what is required.  As a result, the control valve(s) must throttle significantly to drive the system to the desired flow rate.

The pressure drop across the throttled control valve(s) represents an energy loss in the system (remember, flow and head both appear in the numerator of the pump power equation). It is this loss, coupled with the reduction in pump efficiency that causes this approach to use more energy than a pump specifically selected to deliver design flow to one load with the load’s control valve wide open.

The orange curve shows what happens if we add a VFD to the pump and then control the VFD to maintain the design head at the pump discharge.

As the control valve starts to throttle and push the pump up its curve, the control system senses the rise in pressure and slows the pump down to about 1,605 rpm. As a result the control valve does not have to throttle as hard as it would have had to if the pump did not have a VFD.  This, combined with the improved pump efficiency associated with the operating point at reduced speed makes the VFD more attractive than pushing the pump up its curve on a pure energy savings basis.

But the head produced at the load by controlling in this manner will still be significantly above what is required because the control point is based on the head required at the pump to deliver the design flow to the loads and we are only delivering half of the design flow in the scenerio under discussion.

The blue curve shows what happens if we move the sensor controlling the VFD from the pump discharge to the magical “2/3 of the way down the system” point.

The magic is that moving the sensor away from the pump allows the sensor to “see” the pressure drop in the piping circuit between it and the pump location. If we adjust the system to control the pressure at the 2/3 point to the value associated with design flow at that location then, when the flow is reduced (and the head required to move water to that location drops as the square of the reduction in flow) the system responds accordingly and slows the pump down even further than a system with a sensor located at the pump discharge would.

The purple curveshows what would happen if we located a sensor right at the point where our load connected to the mains and controlled to maintain the differential pressure to the load at the value required for design flow.

This location allows our optimization strategy to approach the savings that would be achieved by a pump selected specifically for the requirements at the reduced load condition.

The table below summarizes our discussion.

Watch for the next post where I’ll summarize our discussion with a few bottom lines before moving on to a new topic.


David Sellers
Senior Engineer – Facility Dynamics Engineering

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