Why Part Load Behaviour Decides the Energy Bill

Why this matters

Compressor specifications compare machines at full load, and full load is the condition a compressor spends the least of its life in. A plant whose demand swings all shift is buying a machine on a number that describes maybe a tenth of its operating hours. The consequence is concrete: two machines with identical full-load specific power, on the same plant, delivering exactly the same air, can differ in annual energy by a large fraction, and the entire difference lives in the shape of the power-versus-capacity curve between zero and full output. That shape is published, it is machine-specific, and almost nobody asks for it.

The number that gets quoted and the number that governs

Full-load specific power is the power the machine draws divided by the air it delivers at its rated point. It is a fair comparison of how efficiently a machine compresses when it is working flat out, and it is the number on every specification sheet.

What governs the bill is the integral of power over the year, and that is the operating-hour distribution multiplied point by point against the part-load curve. Two machines that agree at the rated point can disagree everywhere else, because the part-load curve is set by the control scheme, not by the airend.

This card is about building that integral from data you can actually collect. What the control schemes are and how they trade against each other is covered separately in this library, and the shapes used below come from those published curves rather than being derived here.

The artifact: an hours-at-load histogram

The deliverable is one small table. Bin the year's operating hours by how much air the machine was delivering as a percent of its capacity, then apply the machine's published power fraction at each bin's midpoint.

Both data sources mean touching live equipment, and they are two different hazards. Fitting a flow meter opens a pressurised line: close the upstream isolation, open the vent, confirm zero on a gauge open to the section with the vent still flowing, and lock and tag the compressor's disconnect under 29 CFR 1910.147, because a packaged compressor restarts on its own pressure switch and a machine that looks off is not off. Fitting a power meter is electrical and separate: de-energise and lock the feeder under 29 CFR 1910.333(b)(2), with 29 CFR 1926.417 as the construction counterpart, and prove dead live-dead-live per NFPA 70E-2021, 120.5, in the edition your employer's electrical safety programme has adopted. Where both meters are already fitted, this whole card is a desk exercise and nothing gets opened.

You need two data sources. Delivered flow, from a flow meter in the discharge or from a load/no-load machine's own loaded-time record over short intervals. And the machine's published power-versus-capacity curve, from the manufacturer, for the specific control scheme fitted.

Here is a filled-in one for a single-shift plant running about 5,800 hours a year:

Hours total 5,800. The air-share column is hours times midpoint, divided by the total of hours times midpoint, which is 274,000 in midpoint-hours. So 900 times 10 is 9,000, which is 3.3 percent of the air; 1,900 times 50 is 95,000, which is 34.7 percent.

Weighted average output is 274,000 divided by 5,800, which is 47 percent of capacity. That single figure is worth saying to a customer before anything else: their machine is on average delivering less than half its capacity, and the specification they bought it on describes a condition it reaches for 600 hours out of 5,800.

Running the histogram against two curves

Take the published curves for two control schemes on the same machine. Use the machine's own numbers; the two shapes below are stated here so that every figure in the arithmetic that follows comes from the general case rather than appearing for the first time inside it.

For load and no-load with storage adequate to complete blowdown, power runs roughly linearly from the machine's unloaded fraction at zero output up to 1.0 at full output. Take the unloaded fraction as 0.25. Published values for oil-injected screws run from about a quarter to a third depending on how blowdown is arranged, so substitute your machine's, and note that a machine whose unloaded window is shorter than its blowdown time never reaches the published figure at all. The 0.25 here is illustrative: substitute the published value for your machine, because it depends on how blowdown is arranged. That gives power equal to 0.25 plus 0.75 times output.

For inlet modulation without blowdown, published curves are much flatter, starting well above half of full-load power at zero output. Take 0.70 at zero output rising to 1.0 at full, so power equals 0.70 plus 0.30 times output. Again, read your machine's curve; the shape is the point, not these two constants.

Load and no-load. Power fractions at the bin midpoints are 0.325, 0.475, 0.625, 0.775 and 0.925. Multiply by hours and sum: 292.5 plus 617.5 plus 1,187.5 plus 852.5 plus 555 gives 3,505 power-fraction-hours. Divide by 5,800 and the machine averages 0.604 of its full-load power.

Inlet modulation. Power fractions are 0.73, 0.79, 0.85, 0.91 and 0.97. Multiply and sum: 657 plus 1,027 plus 1,615 plus 1,001 plus 582 gives 4,882. Divide by 5,800 and the machine averages 0.842 of its full-load power.

The ratio is 0.842 divided by 0.604, which is 1.39. The modulating machine uses about 39 percent more energy over the year to deliver identical air, with identical full-load specific power on the specification sheet.

Notice which bins did the damage. The bottom two bins hold 2,200 of 5,800 hours, which is 38 percent of the time, and carry only 17 percent of the air. Under modulation those same bins carry 1,684 of 4,882 power-fraction-hours, which is 34 percent of the energy. The plant is spending a third of its compressed air energy in the region where it is getting a sixth of its air.

The meter's error basis decides where it matters, and it is not where you expect

Before any of that arithmetic is trustworthy, the flow measurement needs its error labelled with two things: what the percentage is a percentage of, and what kind of error it is.

Basis. A meter specified as a percent of full scale carries a fixed absolute error across its whole range, so at the 10 percent bin the relative error is ten times what it is at the top bin. A meter specified as a percent of reading holds its relative error down the range. This is the single most important line on a flow meter's datasheet for this job, and a specification quoting a plus or minus figure with no denominator is not a specification.

Now work out where a full-scale-basis error actually hurts, because the intuitive answer is wrong. The low bins carry only 3 and 14 percent of the air, so a large relative error there barely moves the air total. But those same bins carry 8 and 18 percent of the power-fraction-hours under load and no-load, and 13 and 21 percent under modulation, because power at low output is not small. So a full-scale-basis meter is nearly harmless for the delivered-air total and matters considerably more for the energy total, which is the opposite of how most people size the concern.

Character. If the flow meter's error and the power meter's error are independent random spreads, they combine in quadrature, so two independent 2 percent terms give about 2.8 percent on the product rather than 4 percent. If either is stated as a worst-case bound rather than a spread, the two bounds add linearly and the result is reported as a bound, never as a plus-or-minus interval. And if a single meter's error is a fixed systematic offset applied to both the before and the after of a control-scheme comparison, it largely cancels in the difference, leaving that percentage of the difference rather than of either reading. Which of those three you are in changes the answer by up to a factor of two on the comparison the histogram exists to support.

What changes the conclusion

The 39 percent gap above is specific to a histogram centred at 47 percent output. Two named conditions move it, and one of them reverses the recommendation.

If the plant's demand is flat and high, sitting near capacity for most of its hours, the two curves converge and the control scheme stops mattering. A plant at 90 percent output all shift would see the two schemes differ by a few percent, and the money is then in pressure and in losses rather than in control.

If the storage is too small for the unloaded period to exceed the machine's blowdown time, the load/no-load curve is not the one printed in the manual. The machine never reaches its low unloaded power, and its real curve moves up toward the modulation curve. In that case converting the control scheme without adding storage delivers a fraction of the calculated saving, and the calculation above becomes a promise the plant cannot keep. Check the unloaded window against the published blowdown time before quoting any figure from this method.

Verifying the histogram rather than trusting it

Two cross-checks, both cheap, and both catch the error that a recomputation will not.

First, the histogram's weighted average output multiplied by the machine's capacity and by the operating hours must reproduce the plant's total delivered air from an independent source, most usefully the loaded-hour counter on a load/no-load machine. If those two disagree by more than the meter's stated uncertainty on the correct basis, one of them is wrong before any energy conclusion is drawn.

Second, sanity-check the bin that holds the most hours against what the plant does. A histogram peaking at 40 to 60 percent on a plant that runs one heavy process most of the shift is telling you something the operators would recognise or dispute, and asking them is faster than re-reading the data.

References

• Manufacturer documentation for the machine's power-versus-capacity curve at the fitted control scheme, its unloaded power fraction, and its blowdown time
• Flow meter and power meter datasheets, specifically the accuracy basis (percent of reading against percent of full scale) and whether the figure is a spread or a bound
• See related: What a Compressor Control Strategy Is Choosing Between; What a Variable Speed Compressor Changes and What It Does Not; What Storage Buys You That Horsepower Cannot