# A View from Australia: Efficiency Curves, System Volumes and the Compressor System Factor

This article introduces a new and useful compressed air system parameter called the “Compressor System Factor,” or CSF. The CSF of a given system defines the relationship between an air compressor, its system, and how the compressor is being operated. Knowing the CSF of a system allows comparisons to be made between existing operating characteristics and the characteristics of a proposed system. Changing a system by applying energy efficiency measures like adding storage receiver capacity, changing pressure bandwidth, or switching to different compressor control modes also changes the CSF. The results of the change can be easily predicted using the CSF number.

The unit used for CSF is the percentage of a minute, making the result useful and compatible with any unit of measurement, whether it is an SI base unit or a standard unit used by North American manufacturers.

The calculation of the CSF is a simple yet powerful tool that can:

- Provide insight into the state of a compressed air system
- Help identify low capital cost projects to improve the efficiency of compressed air systems
- Help assess the merits of supply side and demand side compressed air efficiency projects

The CSF of a given system:

- Largely governs the curve shape, and therefore the efficiency, of a compressor’s power versus flow characteristics for those compressors running in load/unload (online/offline, OLOL) mode
- Can be calculated during the design of a system to help predict system efficiency for different equipment choices
- Can be easily determined for an installed compressor using a stopwatch and a simple calculation

### Compressor System Factor Basics

What CSF measures is not profound, and it is not a hard concept to understand.

CSF is simply the percentage of a compressor’s capacity per minute stored and released by the system volume during each load/unload cycle. |

For example, if a 1000 cfm compressor has a CSF of 10, its compressed air system will store and then release 10 percent of 1000 cfm, or 100 cubic feet of air in each load/unload cycle. A 25-cfm compressor could also have a CSF of 10, but its system would only be storing and releasing 2.5 cubic feet of air during each cycle. Compressors that have the same CSF have the same cycle characteristics, regardless of the size of the compressor. It is important to note that the amount of air stored and released in each cycle depends on the effective volume of the storage receivers and the width of the load/unload pressure band.

Many readers will recognize the percent power versus percent capacity curves found in the U.S. Department of Energy’s guidebook “Improving Compressed Air System Performance: A Sourcebook for Industry.” These curves show how changing the system volume affects the efficiency of a typical lubricated screw compressor running in load/unload mode. The curves shown in Figure 1 are generated with a fixed load/unload pressure bandwidth of 10 psi. For the graph to be correct for compressors not operating with a 10-psi pressure band, a new set of curves would have to be generated. But, if each line on the graph represented a given CSF, the curves could become valid for any combination of system storage and pressure bandwidth with about the same middle pressure.

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**Figure 1: Typical Power vs. Flow Graph for Load/Unload Compressors**

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**Source: Compressed Air Challenge**

Knowing the pressure change used to construct the original graph was 10 psi, the legend could be changed from 1, 3, 5 and 10 gal/cfm to the corresponding CSF values of 5.3, 15.9, 26.5 and 53.

### How and Why Does the Volume Stored and Released for Each Cycle Affect Part Load Power?

The units of CSF are percentage of a minute (i.e. time). This provides a clue as to how it affects compressor efficiency. A large CSF means the compressor cycles are longer than those if the compressor had a small CSF. If system storage is large, or the pressure band is wide, it takes a longer time for the compressor to increase the system pressure from the load setting to the unload setting. It also takes a longer time for the demand to use up the stored air, causing the pressure to drop to the load setting. If the compressor CSF is very small, these same times would be short, and the compressor would cycle quickly. This may cause short cycling, which is known to waste power.

The next plot will help you understand why long cycle times result in lower power consumption.

**Figure 2: Example Compressor Cycles Showing Power and Pressure**

Figure 2 shows the power and pressure changes during four load and unload cycles of an example 37-kW compressor. Note that during the cycles, the flow is changing, which changes the characteristics of each load/unload cycle. Observe the following from the chart:

- For some of the cycles, the compressor is unloaded for a longer time and the compressor power drops to low values, resulting in a lower average unloaded power.
- Some of the cycles are short. When this happens, the power doesn’t drop as far, and the average unloaded power is higher.
- The compressor is only “online” and producing air for the peaks of the power curve (i.e. between the “delivery starts” and “unload” points). These are highlighted for one of the four cycles shown. At this time, the power and pressure both increase together.
- The power used by the compressor at any other time is wasted.
- From the unload point, the power can be seen to drop quickly (to around 24 kW) as the inlet valve closes. The compressor is now in full modulation.
- The power then drops with time as the separator tank is vented through the blow down valve. It stabilizes after 30 to 80 seconds, which varies with compressor design. Only then is the compressor fully unloaded. The compressor is never fully unloaded in this plot.
- When the compressor reloads, a delay of 2 to 5 seconds occurs as the compressor pumps up its internal volumes so air can be delivered into the system. This pump up power is wasted.

Compressors with high load/unload cycle frequencies due to a low CSF system value (small system storage, narrow pressure band) have the following characteristics compared to machines with larger CSF values:

- The unloaded power is higher.
- The power wasted doing “internal pump up” occurs more often.
- The overall power use is higher.

For example, the same compressor at 50 percent load will use less power if it’s load/unload cycle times are, say, 30 seconds / 30 seconds (CSF 25) compared to times of 10 seconds /10 seconds for lower system values (CSF 8).

At the same average load, longer cycle times due to a bigger CSF value means the compressor is unloaded for longer, the average unloaded power will be less, and the compressor more efficient than if it had a smaller CSF value.

Figure 3 below shows typical percent power/flow curves for the following:

- Fixed-speed load/unload compressors for different CSF values, including a curve for the same system but with two half-sized compressors (2 x 50 percent x CSF 7)
- Variable geometry-controlled compressors with different CSF values (Note that for capacities below the turn valve minimum output, the compressors operate load/unload like a fixed-capacity machine. Hence CSF affects these machines.)
- Different variable speed compressors scaled to fixed-speed compressors (where possible with the same air end) from the same OEM

**Click here to enlarge**

**Figure 3: Comparison of Compressor Operating Modes**

Many people believe that the way to make a compressor system more efficient is to make the trim compressor load/unload pressure band as narrow as possible. This is not the case, as a small pressure band will store little air per cycle, resulting in a CSF value that is very small.

This is not to say that the pressure band should be as big as possible. A bigger pressure band results in increased power use by all compressors on the system and increased artificial demand. When these factors are considered with CSF, it is no surprise that there is an Optimal Pressure Band (OPB) for each system and its operating conditions at any time.

### How Can You Use CSF To Improve Your Compressed Air System Efficiency?

CSF values can be used in many ways to improve the efficiency of a compressed air system:

- The concept of CSF provides insight on how the trimming compressor size, the operating mode, the system volume, and the wet-to-dry side pressure drop affect its part load efficiency.
- The equations used to calculate CSF from known and measured parameters can be used to find any of the parameters used in the equations. For example, CSF could be found from measured values. If the compressor load and unload settings are also noted, the (effective) system volume (Insert Image020.png in parentheses) can be calculated. If the wet side volume and the dry side pressure changes are also known, the dry side volume can be estimated as well.
- The CSF value for a compressor can be used directly with efficiency curve data to estimate the power consumption of the compressor at a specific percentage load. This assists in the modelling of new or changed compressed system power consumption based on a known (measured or assumed) load profile.
- It allows the development of the Per Unit Power and savings Yield (PUP-Y) chart (Figure 4 shown below).

The PUP-Y chart displays average Per Unit Power and savings Yield for different CSF values. The PUP trends are based on averaging power values at specific loads (20, 40, 60 and 80 percent) for a CSF value. These power values are compared to the power value at 100 percent load. Hence, the PUP curve provides a means of estimating the average power consumption of a trimming compressor.

The Yield trend of the chart is based on the average slope between points on the percent power/flow curve (80 to 60 percent, 80 to 40 percent, 80 to 20 percent) for different CSF values. It is a ratio between the change in percentage load of a compressor to the change in average power use.

For example, based on the PUP-Y chart, a compressor with CSF 10 will:

- Have an average specific power consumption 1.59 x that of its full-load specific power.
- Have a Yield of 30 percent: For example, an average compressor load reduction (e.g. from leak repairs) from 60 to 40 percent will result in a 6 percent reduction in average power use (i.e. 30 percent of 60 – 40 = 6).

If the effective system volume is increased so that the resulting CSF is now 20:

- The trimming compressor average specific power becomes 1.5 x the full-load value, resulting in a 5.6 percent saving.
- The Yield becomes 38 percent, making the same load reduction from the previous example larger (60 to 40 percent now saves 7.6 percent in power).

Together the PUP-Y trends allow a quick estimate of power consumption and savings.

Some other comments:

- The PUP-Y chart is based on the compressor spending equal time at all loads between 20 and 80 percent. This will not be the case for all trimming compressors. Hence, the PUP-Y chart is only a guide to allow a quick estimate in a few minutes instead of hours of detailed modelling. If highly accurate values are required, then detailed modelling should be done.
- The PUP-Y chart shows that there are diminishing returns from increasing the CSF value.
- The PUP-Y chart allows modelling work to find the Optimal Pressure Band (i.e. the best choice of pressure bandwidth) when relative compressor sizes, leak and artificial demand loads, and the system volume are considered.

**Figure 4: Compressor PUP-Y Chart**

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This article has introduced the compressor system parameter CSF. It has shown how to find the CSF value for a compressor in its system. It has also shown how CSF can be a powerful tool in improving the efficiency of compressor systems and in evaluating compressed air efficiency-related projects.

Future articles will further explore the application of CSF. For example, by affecting CSF value, one can find the Optimal Pressure Band for a compressor and evaluate how air treatment pressure drop affects power use.

**Author Bio**

Murray Nottle is a university-qualified mechanical engineer based in Melbourne, Australia. He has worked in the compressed air industry for well over 15 years. Some of this time has been with pneumatics companies, however, most was with compressor companies. This included establishing the energy auditing abilities of one organization. Murray consults on compressed air productivity and efficiency with The Carnot Group. He can be contacted via email at mnottle@carnot.com.au or visit www.carnot.com.au

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