What a Variable Speed Drive Changes About a Pumped System

Why this matters

A drive moves the pump curve. It does not move the system curve. Everything that surprises people about variable speed pumping follows from that one asymmetry, and the surprise is always in the same direction: the savings promised by the cube law arrive in full on a closed loop and arrive badly, or not at all, on any system that has to lift liquid. On a high-static system there is also a speed below which the pump delivers nothing whatsoever, and it is much higher than anyone expects. This card runs one speed command against two systems and shows them resolving oppositely, using the same pump both times.

A sibling card covers what a drive changes about the machinery itself, including bearing currents, motor cooling at low speed and the isolation hazard the DC bus creates. This one is about the hydraulics of the circuit the pump sits in.

Writing a lower speed is a process command, and it has its own hazards

A speed command is an instruction to the machine, and the extreme end of the range is where it does damage, so establish what stops first before you type a number. On a system with static lift, a low enough speed stops flow completely while the pump keeps turning and keeps putting shaft energy into a trapped volume, which heats it; on a hot system, that water can flash when a valve is later opened. Confirm the pump's minimum continuous flow from the manufacturer's curve sheet and confirm that a flow proving device or a low-flow interlock is in service before you take the speed below the commissioned minimum.

Do not test a reduced speed on a loop serving a fired appliance or a chiller evaporator without the flow interlock proved first. Losing flow across a heat exchanger that is still firing or still making ice is the process hazard your command creates, one step upstream of touching the equipment, and it deserves the same treatment as opening the machine: name the interlock, prove it, then move the setpoint.

Reading a drive's kW display needs no cover removed. If the work requires opening the enclosure, that is 29 CFR 1910.333(b)(2) in general industry, with 29 CFR 1926.417 as the construction counterpart, and the DC bus holds charge after the disconnect opens; the sibling mechanical card covers that sequence in full.

What the drive moves and what stays exactly where it was

The system curve is a property of the piping, the valves, the fittings and the elevation the liquid has to be raised through. Nothing in that list knows what the motor is doing. So when the speed falls:

• The pump curve slides down and to the left. Every point on it moves.
• The friction part of the system curve is unchanged. It is still the same parabola through the origin, because it is a function of flow, not of speed.
• The static part of the system curve does not move at all and does not scale. A 60 ft lift is 60 ft at every speed including zero. This is the term that breaks every simple prediction.

The operating point is still where the two curves cross. All the drive did was hand you a family of pump curves instead of one.

The three affinity relationships, and the conditions they were derived under

For one pump, at a fixed impeller diameter, over a speed range where the efficiency at the corresponding point is roughly unchanged, and comparing points that correspond to each other on the curve rather than any two points you like:

• Flow varies with speed, directly.
• Head varies with the square of speed.
• Shaft power varies with the cube of speed.

Three conditions are doing real work in that sentence. Fixed diameter, because trimming an impeller follows a different and less reliable set of relationships. Corresponding points, which means the relationships describe how the curve transforms, not how a system responds. And roughly constant efficiency, which fails as soon as reduced speed pushes the operating point away from best efficiency, and it fails hardest on exactly the systems where the drive helps least. Because efficiency falls rather than rises when you move off best efficiency, the cube law is an upper bound on savings: actual shaft power >= the cube-law figure, always, never below it.

One gate, two systems: cut the command to 80 percent

The same pump both times. Published curve at full speed, full diameter: 104 ft at shutoff, 100 ft at 100 gpm, 96 ft at 150 gpm, 90 ft at 200 gpm, 82 ft at 250 gpm. Best efficiency is near 200 gpm and the curve sheet shows about 78 percent there, falling to roughly 45 percent down at 75 to 80 gpm. Both systems are designed at 200 gpm and 90 ft. Both get the identical command: speed to 80 percent.

System A is a closed hydronic loop. All 90 ft is friction, no static lift, because what goes up comes back down inside a closed circuit.

System B lifts to an elevated tank. Of the 90 ft, 60 ft is static lift and 30 ft is friction at 200 gpm.

Outcome A: the friction-only loop tracks the affinity laws

At 80 percent speed the pump makes 80 percent of the flow at 64 percent of the head: 160 gpm at 57.6 ft. Check it against the system: friction head at 160 gpm is 90 x (160/200)^2 = 57.6 ft. The two agree, and they agree for a structural reason rather than a coincidence. A friction-only system curve is a parabola through the origin, and the affinity laws move the pump's operating point along a parabola through the origin. On this system alone, the pump follows the system curve as speed changes.

• Cube-law shaft power: 0.80^3 = 0.512 of design power
• Efficiency correction: 160 gpm is still close enough to best efficiency that the correction is small, so actual power >= 0.512 of design, call it 0.53 to 0.55 with a modest efficiency drop
• Power per unit of delivered flow: 0.512 / 0.80 = 0.64, so every gallon costs about 36 percent less to move

Outcome B: the same command, on a system with 60 ft of lift

The static head does not scale, so it is printed as a constant on every line below.

• Pump at 80 percent speed: shutoff head becomes 104 x 0.64 = 66.6 ft
• System at any flow: 60 ft static (unchanged) + 30 ft x (Q/200)^2 friction
• Crossing: solve those two against each other and the operating point lands at roughly 77 gpm at 64.5 ft

That is 38.6 percent of design flow, not 80 percent. The command was a 20 percent speed cut and the system gave back a 61 percent flow cut, because the pump had to spend nearly all of its reduced head just standing still against the lift, leaving almost nothing to push friction with.

• Hydraulic power ratio: (77 x 64.5) / (200 x 90) = 0.277 of design
• Efficiency correction, and this is where the cube law's third condition fails: 78 percent at design against roughly 45 percent at 77 gpm, so shaft power = 0.277 x (0.78 / 0.45) = 0.48 of design
• Written as the bound it is: actual shaft power >= 0.48 of design, before drive and motor losses
• Power per unit of delivered flow: 0.48 / 0.386 = 1.24

Every gallon delivered on System B now costs 24 percent more energy than it did at full speed. The drive did not save anything on this system; it made the pumping less efficient and delivered a great deal less water. That is not a defect in the drive, it is what the static term does to the arithmetic, and it is why "put a drive on it" is a recommendation that has to be qualified by the system's static fraction in the same breath.

Two things are declared uncorrected here. All the figures above are pump shaft power, so drive and motor losses sit outside them, and both fall in efficiency at reduced load, which makes the wire-side picture slightly worse on both systems rather than better. And the efficiency figures are read off a published curve, which is a test-stand number for a new pump.

The speed at which System B delivers nothing at all

Flow stops when the pump's shutoff head falls to the static head, because at that point the pump cannot open the check valve. Shutoff head scales with the square of speed, so:

104 x n^{2 = 60, which gives n}2 = 0.577 and n = 0.76

Below about 76 percent speed this pump delivers zero gpm into this system, no matter how long it runs. At 78 percent it delivers about 55 gpm. At 80 percent, 77 gpm. The whole useful range of the drive on System B is compressed into the top quarter of the speed band, and the bottom three quarters is a pump churning against a closed check valve, heating the casing, with the flow transmitter reading zero and nobody able to explain it.

This is the single most useful number to compute before you promise a customer anything: the square root of the ratio of static head to shutoff head is the speed floor, and on high-lift systems it is often 70 to 80 percent.

What changes the answer

A pressure-controlled system with a remote sensor. Holding a differential pressure at the far end of a distribution loop rather than at the pump makes the control curve steeper than pure friction but far shallower than a static-head system, and the savings land in between. Which sensor location the control loop uses is worth reading off the drive's own configuration rather than assuming.

A system whose static term is a control setpoint rather than an elevation. Boosting into a pressurized main behaves exactly like static lift for this arithmetic even though nothing is being raised. Treat the maintained pressure as static head and the same speed floor applies.

Minimum continuous flow. A pump held at very low flow overheats and recirculates internally regardless of what the energy arithmetic says. The manufacturer's curve sheet owns that number, not this article, and it is a hard floor that sits on top of everything above.

How to verify you got this right

Do not verify a drive by watching the speed feedback. Verify it at the delivered end, with three readings taken together at two different speeds: the speed, the pump differential head, and either a true kW reading or a flow reading. Then check that the head you measured at the reduced speed sits above the system's static head by a plausible friction amount. If reduced-speed head has landed within a few feet of the static head, you are near the speed floor and flow is collapsing regardless of what the setpoint says.

The tell that someone got this wrong on a live site is a drive that spends its life pinned at 100 percent with an operator complaint that "the automatic control does not work." On a high-static system it never did; it just took a year for someone to lock it out at full speed and stop looking.

References

• Hydraulic Institute guidance on variable speed pumping and system head curves, in the edition your specification or service contract references
• Pump manufacturer curve sheet for the specific unit, which owns the efficiency values, the minimum continuous flow and the permissible speed range
• 29 CFR 1910.333(b)(2), with 29 CFR 1926.417 as the construction counterpart, for work inside an energized drive enclosure
• See related: How a Variable Speed Drive Changes the Mechanical Picture; What a Pump Curve and a System Curve Do Together; Why a Throttling Valve Is the Most Expensive Flow Control There Is