Variable Frequency Drive System Efficiency – Part 2

In my last post, I took a look at the results of some research I did regarding variable speed drive efficiency and motor efficiency.  In this post, I’ll take a look at why designers, in particular, building system designers, are driven to apply variable speed technology in their systems.  This, combined with the previous post, will lay the foundation for the next post, where I will look at what happens when you apply a VFD to motor serving a centrifugal machine in an HVAC system.  Its mostly good news, but there are a few surprises.

Variable Speed and Building System Loads

For folks like me in the building industry, VSDs in general and VFDs in particular are just about always applied to a centrifugal machine like a fan or a pump or a centrifugal chiller.  To some extent, the ability to vary the speed of a centrifugal machine as the demand on it changes is “God’s gift” to the industry because for HVAC and other building systems, just about everything varies all of the time.  Here is an example.

What you are looking at is the daily and seasonal load profile for a facility in Southern California that we developed using the building trend data.  We were going to add chiller capacity and instead of doing a model, we let the building tell us what the best chiller size would be and what “sweet spot” we should target on its performance curve by picking hourly flow and temperature data (which we knew was reliable) and doing the math.

Those results, along with the Excel “CountIf” function let us make the following load profile graph, which caused us to target a life cycle cost RFP at a chiller with a capacity of 550 tons and a “sweet spot” in the 250 to 350 ton range.

But that’s really a different story, maybe a post some time. If you are interested in the technique and details behind it, I actually wrote an article about it that you can read in the August 2008 issue of Consulting Specifying Engineer.  Its called Decrypting Building Data and starts on page 36.  (The link should take you to the digital edition.)

My point in bringing it up here is that it illustrates the highly variable nature of building loads, which is why VSDs are so attractive to the building design community.  Varying speed allows us to follow the constantly changing load profiles and save a lot of energy compared to the other options.

Variable Speed and Flow in Conduits

Energy is saved because for centrifugal machines, there is a cubic relationship between speed and horsepower, assuming you are operating against a fixed system.  That relationship has its roots in the Darcy-Weisbach equation, which basically says that for fully developed turbulent flow in a pipe or duct, the pressure required to produce a given flow rate in a given system will vary with the square of the change in flow rate.   Here is a slide I use when I talk about this with the key information.

ASHRAE research has shown that for HVAC systems, the exponent is more like 1.85 vs. 2 because there are places in our systems where the flow is not fully developed turbulent flow (filters, tubes in coils at low load, etc.).  But as you can see from the graph in the slide, for practical purposes, which for me, means in the context of what I can measure out in the field, assuming an exponent of “2” is reasonable.

Varying Capacity of Centrifugal Machines

For a real system, the line in the graph above is called the system curve;  its a statement of the systems performance in terms of flow rate and pressure or head for a given configuration.  The “given configuration” part of that sentence is important.  If you move a valve or damper in the system after assessing the system curve, you have in effect, changed the configuration.  That means you are now operating on a different system curve.

The reality is that most HVAC systems operate on a family of system curves since we typically tailor flows to load conditions by modulating valves and dampers.  In the real world, even constant volume systems probably are not perfectly constant volume.

Constant Volume Pumping (Not)

In the pumping system version of a constant volume system, the three way valves we use to modulate flow to the load probably have different pressure drops in the path through the load vs. the path around the load. Here are slides from an example I used in class based on the cooling coil in the main AHU at the Pacific Energy Center.

This first slide just orients you to the various points in the physical world vs. the system diagram.

These next two slides illustrate the physical path through the coil, which includes multiple passes through small tubes.

These next two slides contrast the path for flow through the coil with full bypass;   if you think about it in the context of the previous slides, you will probably conclude that the bypass path has less resistance, a hypothesis we demonstrate with a functional test in one of the PEC classes Ryan and I do.

When the valve is in an intermediate position (flow through both paths), then even if each flow path had been set up with an identical resistance to the other, you would see a flow variation.  This is because with both paths open, you have two resistances in parallel vs. a single resistance.  For some folks (myself included), when trying to understand this phenomenon, it helps to think about what happens in an electrical circuit when you put two identical  resistances in parallel vs. only one of them with the same voltage applied across the network.

Systems with multiple pumped loads in parallel, like condenser water systems also can exhibit significant flow variations from the design targets, especially if the portion of the piping network that is shared by all of the pumps and loads is extensive and/or if there is a significant difference between the flow rate with smallest pump operating and the flow rate with all of the pumps operating.

Here is an example of such a system from a recent project.

Incidentally, if you want a higher resolution version of this diagram and/or a discussion about some of the other issues that showed up in this particular system you will find that information in a post I did back in February of 2009, including a link to a .jpg on my Google Photo page.

Getting back to our discussion, the system consists of three chiller condensers with their pumps (the pumps are in the magenta, blue, and red dotted squares), all piped in parallel to allow a common set of cooling tower cells (inside the cyan dotted square) to serve all of them. The piping mains are 14″ diameter mains and run about 500 feet round trip from the plant in the basement of the building to the cooling towers on the roof.

At low load conditions, only the small pumps serving the multi-stack chiller (inside the red square) operate, moving about 200 gallons per minute.  At that flow rate, there is virtually no pressure drop associated with moving the water through the mains to the roof and back because the lines are so large relative to the flow that is moving through them.

But, if everything is running, the mains are carrying about 3,400 gpm of flow and it takes 15 ft of head to move the water through them to the roof and back.  Thus, there can be a 15 ft. difference in pump head seen by the various pumps in the system, depending on load.   And, even though the temptation is to think that the pumps are always producing their design flow, if you go out and test flow rates in different operating conditions (Ron and Gary, a couple of guys I work with did), you find that the flow actually varies from a low of about 87% of the design target to 123% of the design target.  Not exactly constant volume.

A similar thing happens when you modulate the valves that provide the cooling tower bypass function.  As soon as the bypass valve opens, flow wants to divert through it rather than make the trip all the way to the roof and back, even though the automatic valve in the line to the cooling towers works in conjunction with it.  That’s because the bypass valve is in the same room as the chillers and also because both valves are line size and don’t have very good control characteristics in the first place.

Constant Volume Air Handling (also Not)

In constant volume air handling systems, it’s very easy for most people to recognize that there is a change in pressure drop associated with the filters loading up.  The added filter resistance shifts the system curve and the flow will tend to drop off if nothing is done to correct for it.  The difference in a wet vs. dry cooling coil can cause a similar shift, as can the difference in mixed air plenum pressure that is caused by the modulation of the economizer dampers, especially if the dampers are not particularly well sized.

The Bottom Line on Variable Flow and Not So Constant Flow Systems

The bottom line is that most HVAC systems see variable operating points.  Sometimes that is the intent of the design as is the case for a variable flow, primary secondary pumping system or a VAV air handling system.  But other times, like in the examples in the preceding section of the post, it is the unintended consequence of the physics of the system and its components.

In either situation, VSDs, in general, and VFDs in particular can provide a means to optimize performance and save energy in systems were the goal is to vary the flow.  And, they can provide the same benefit and/or address the potential operating problems that can come up if flows vary when the intent was for them to remain constant.

The Operating Point;  Where the System Curve and the Pump or Fan Performance Curve Meet

As I mentioned above, the system curve is a statement of the flow versus pressure required to produce the flow for a system.  Frequently, pump and fan performance is stated in a similar fashion using a pump or fan curve.  Here are examples of each.

For both the pump and the fan in the examples above, the operating point is where the system curve (the parabola starting at 0 flow, 0 static/head) intersects the fan performance curve or impeller line.  Incidentally, these curves are generated using some handy free resources from Twin City Blower and Bell and Gossett.

Let’s focus on the pump curve to illustrate a few things.  If you wanted to reduce the flow in the system associated with the system curve  that has been projected onto the 5BC pump curve from 800 gpm to 750 gpm, one way to do it would be to trim the impeller to the size associated with the point where the system curve crosses the 750 gpm line.  That would be about a 7-3/8″ impeller and the pump would generate about 38 ft.w.c. of head at the new operating point.

Notice that as you move down the system curve, you move away from the peak efficiency point.  And, if in this system, you wanted to increase flow and moved up a projection of the system curve towards higher flow rates, you would move towards the peak efficiency point.

The bottom line is that changing impeller sizes can optimize pump performance, but at the cost of pump efficiency.  This is because trimming the impeller with out making other modifications to the pump to maintain geometric similarity (for instance, making a proportional size reduction in the volute and the impeller eye diameter) impacts the efficiency in an adverse manner.

Here is the pump curve for the same pump but with performance curves for different speeds instead of different impeller diameters.

Notice how the speed curves are very similar to the smaller impeller size curves, but with one important difference.  That difference is that the performance modification associated with moving around on the system curve is accomplished with out much impact on the pump efficiency.  In fact, reducing speeds can improve efficiency slightly because some of the factors that impact pump efficiency (like the bearing loads and leakage losses; i.e. recirculation from the discharge side of the impeller to the eye through the clearance between the impeller and volute) are somewhat independent of pump speed.

You probably have realized where I am heading at this point, which is to say that the beauty of using a variable speed drive to make a performance change to a centrifugal machine is that it allows the change to be made with out a major impact on the efficiency of the machine.  This can be a big advantage compared to some other approaches for achieving the same result.

Having said that, its also important to realize there are some down sides.  For instance, if you save 3% in pump efficiency by using a VFD to shift a pumps operating point, but the drive losses associated with doing it are 4%, then you actually lost ground.  So, there are a few surprises like that which need to be considered when applying VFDs.  Discussing them was my original goal when I set out to write what has turned into a string of blog posts.

At this point, I think I have the foundation laid for that discussion and will proceed with it in my next post.


David Sellers
Senior Engineer – Facility Dynamics Engineering

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