# Variable Speed Pumping Systems

Published On: April 17, 2024Categories: Engineering Your Business, Pumps and Water Systems

### Part 3. Commonalities for variable speed drive pumping systems.

By Ed Butts, PE, CPI

We continue our current series on variable flow and head pumping systems this month by continuing our discussion on variable speed drive (VSD) systems.

Whether at the motor or pump, all devices and systems that depend on varying the pump’s speed to affect changes in flow rate or head rely on a few common elements of pump performance. This is true for variable frequency drives (VFDs), eddy-current and hydraulic couplings, engine-driven units, and variable pitch sheaves and belts. This month’s column is intended to explain these commonalities and how they apply to all variable speed drive pumping systems.

### Minimum Flow and Head Limitations with Variable Speed Drives

Due to the inherent limitations associated with the affinity laws, the minimum output capacity and pump speed are limited by the ratio of the system’s static head to the total dynamic head.

For a water well, the minimum static head is the vertical lift from the static water level to the surface or water’s destination, while the total dynamic head is the sum of the vertical lift from the pumping water level to the surface or water’s destination plus all frictional losses from valves, pipelines, and fittings.

In actuality, the minimum flow rate estimated by this method will not be the true minimum flow rate but will be somewhat lower since the frictional head losses will vary as a component of the flow rate until the operating head intersects the pump curve at the appropriate speed. In these instances, the only accurate way to determine the true minimum flow rate will be through the plotting of a system head curve against a reduced speed pump curve.

Note that the information in Table 1 is based on use of the affinity laws with 60 hertz power for VFDs and applicable speed reduction values for other methods of variable speed drives. The values are to be used as generic approximations and provide a guide to estimating the ratio of adjusted capacity, head, and horsepower to the original parameters based on the ratio of speed reduction of the pump.

The typical range of speed is shown for values between 60 hertz down to 30 hertz, as this is the lowest practical speed for most efficient pumping applications and the lowest allowable speed for most submersible motors. Also, note that continuous operation below the pump’s applicable minimum continuous stable flow is never recommended. Therefore, consultation with the actual pump manufacturer or curve should be conducted before finalizing the minimum flow rates, head, or horsepower:

### Impact of MCSF with Variable Speeds

The minimum continuous stable flow (MCSF) is defined as the flow rate below which the pump should not be operated continuously. This value is typically shown on pump curves as a diagonal dashed or solid red line within the left region of the curve approaching shutoff head (Figure 1).

The allowable operating region to the right of the MCSF is often denoted by coloring of the curve. Note how the MCSF lowers with the impeller diameter. This is equivalent to reducing the rim speed and identical in function to lowering the pump speed.

Although this value varies between brands and models, basic rules apply. The main reasons to avoid operation below the MCSF are due to unstable operation, high radial or axial thrust, possible excessive fluid heat buildup, potential cavitation, and excessive vibration and noise—all of which ultimately can cause excessive shaft deflection; potential seal, bearing, and coupling damage; and significantly reduce reliability.

Reducing the speed of a pump will result in less energy being lost in the pump, but at the same time, a reduction of the flow rate. In addition, as the pump speed is lowered, efficiency will also generally drop.

The MCSF may vary at reduced speeds due to the relationship of the suction specific speed (NSS), which includes the elements of speed (in RPM), flow rate (in GPM), and NPSHR (in feet). Due to the affinity laws, a reduction in the shaft rotational speed will also result in a proportional reduction in the best efficiency flow rate.

The third element of NSS, NPSHR, will reduce by the square of the change in the speed. Therefore, the NSS will be proportionally lower with a reduction in the pump’s speed. It is therefore possible that for a small number of pumps, the MCSF will not markedly change by reducing the speed. However, this generally only occurs on low specific speed designs with low efficiencies. For the vast majority of centrifugal pumps, including most submersible and vertical turbine pumps, the MCSF will correspond with a reduction in the speed.

### Pump and Motor Efficiency Corrections with Variable Speed Devices

Figure 1. MCSF (minimum continuous stable flow) region on a pump curve.

To accurately calculate the energy savings gained from implementing variable speed drives (VSDs), the variation of pump and motor efficiency must be considered when operating conditions transition from the original design operating point (i.e., condition of service or COS) to the new operating points.

When the pump speed is reduced, the plotted efficiency curve versus the flow rate (Q) shifts to the left but is often assumed to maintain the same best efficiency point (BEP) at the adjusted flow rate. When the speed is decreased, the efficiency curve also narrows because the range of flows over which the pump can operate is reduced in proportion to the speed.

Many software programs and tools continue to use the efficiency curve at the nominal pump speed and therefore fail to correctly modify the curve to reflect the actual service conditions. This is particularly important for pumping systems in which the head consists of substantial amounts of static head, as these systems are more vulnerable to significant efficiency variations at lower flow rates as the system head is not as linear as a system with head primarily comprised mainly of frictional head. This is illustrated in Figure 2 and Figure 3 for a pump at 100%, 90%, 85%, 75%, 66.7% and 50% speed along with the efficiency ranges shown.

To accurately calculate the pump energy savings from implementing VSD devices, in addition to the measured flow rate and head at the new operating point, the pump’s efficiency at the new operating point must also be ascertained to determine the corrected power input. The pump’s efficiency at the new operating point can be dramatically different from the efficiency at the original design operating point. Unfortunately, many designers do not correctly estimate the pump efficiency at the new operating points.

Figure 2. Efficiency for a pumping system without static head.

For purposes of this discussion, pumping systems will be considered as those with either no static head or those with static head. For a pumping system with no static head, typically found in most closed-loop systems, the operating head starts at the origin intersection of the vertical axis (head) and the horizontal axis (capacity). It is comprised mainly of frictional losses; thus the pump operates at a fairly constant efficiency under variable speed control.

Changes to the resistance to flow in a system will change the relationship between the flow rate and operating head and will manifest as changes to the system curve. This change can result from changes in valve position, pipeline length, and the type and presence of inline equipment.

The operating point of the pump, relative to its best efficiency point, remains constant and the pump continues to operate in its ideal region. The affinity laws are obeyed, which means that there is a substantial reduction in power input accompanying the reduction in flow along with head, making variable speed the ideal control method.

For most centrifugal pumps—including standard horizontal and vertical end-suction, inline and split case centrifugal, vertical turbine, and submersible pumps—when the new operating speed is greater than 66.7% to 70% of rated full speed into a system without static head (i.e., closed-loop), it is typically acceptable to assume that the pump efficiency at the new operating point is the same as the efficiency at the design’s original operating point as shown in Equation 1:

Equation 1 (without static head): Pump efficiency for pump speed > 66.7%-70% of RPM= ƞ2 = ƞ1

When the new operating speed is less than 66.7% to 70% of its rated full speed condition in a system without static head, the pump efficiency degradation caused by the variation in pump speed can be expressed as shown in Equation 2 and Equation 3 (66.7% is generally used as the lowest threshold speed):

Equation 2: Pump efficiency for flow rate change < 66.7% of GPM: ƞ2 = 1 – (1-ƞ1) × (GPM1 ÷ GPM2)0.10

Equation 3: Pump efficiency for change in speed < 66.7% of RPM: ƞ2 = 1 – (1-ƞ1) × (RPM1 ÷ RPM2)0.10

For Equations 1, 2, and 3: where: ƞ2 = pump efficiency at the new operating point:

Ƞ1 = Pump efficiency at the original design point

RPM1 = Original design speed

RPM2 = Pump speed after change

GPM1 = Rated flow rate at original design condition

GPM2 = Revised flow rate after speed change.

Figure 3. Efficiency for a pumping system with static head.

According to Equations 1, 2, and 3, the efficiency decrease is greater for a large reduction of speed and further decreases the efficiency at already low efficiency points on the pump curve. If the original efficiency is already below 50%, the equation predicts a lower efficiency, even for a small reduction in speed.

The equations can also produce negative efficiencies, but these results are generally found in the lowest efficiency regions of a curve (η <30%) and for small relative speed reductions (RPM1/RPM2 < 0.40) that are usually avoided in practice.

For systems with static head (Figure 3), since the system curve does not start from the curve’s origin (0-0) but at some other value on the y-axis corresponding to the static head, the system curve does not precisely follow the affinity laws. Therefore, the pump does not maintain a constant pump efficiency relative to adjusted flow or speed when operated with a variable speed control.

In systems with a static head, this often results in a common design error from using the affinity laws to calculate the corrected pump efficiency and resultant energy savings. For this case, the calculation procedure requires use of a quadratic equation, described in the three steps presented as follows:

1. Determine the required pump operating speed for the new operating point.
2. Calculate the nominal flow rate with the same pump efficiency at the new operating point.
3. Find the nominal flow rate and nominal pump efficiency curve to determine the pump efficiency at the new operating point.

This algorithm requires the use of a quadratic curve that fits the pump head and efficiency. The curve fits can be directly provided by the designer or they can be derived from obtaining multiple performance data points.

Figure 4. VSD (variable speed drive) motor efficiency at various speeds and loads.

In order to avoid the need for using quadratic equations, the two curves shown in Figures 2 and 3 illustrate the typical differences in pump efficiency for systems without and with static head. This example pump displays a 100% to 50% speed efficiency range between a best efficiency window of 84% down to a low of 46%.

As seen in Figure 2, the efficiency remains fairly constant between full speed down to 50% speed for a system without static head. However, the same curve in Figure 3, now with a value of static head, experiences a significant drop in efficiency from 84% at full speed down to 67% at 50% speed. The curve also illustrates the importance of the 66.7% to 70% speed threshold.

This is strictly an illustrative example; the precise loss in efficiency will depend on the value of static head in relation to the total head, the system head and pump curve shapes and pump efficiency bands, and actual percentage of speed reduction. However, this estimation method will generally provide efficiency values to within +/– 3% of the actual adjusted efficiency. This example also underscores the importance of preparing an accurate system head curve to use with a variable speed pump curve for pumping systems with a static head.

An electric induction motor efficiency can also vary when operated with a variable speed drive. This is often the result of increased hysteresis losses. Most AC electric motors display the highest efficiency around 75% of full load, with 100% and 50% of full load generally displaying the same slightly lower efficiency.

The chart in Figure 4 illustrates the loss in efficiency for a typical induction motor under both reduced speed and load (T) conditions. The chart displays a motor with a full load efficiency of 95%, but this relationship can be used for any motor by proportionally adjusting the example motor’s efficiency to the actual value.

This calculation procedure is easy for designers to implement by using Excel spreadsheet calculators and in modern stand-alone software, or it can be used to enhance currently existing software tools such as EPANET to obtain more accurate pump energy savings results.

Until then, work safe and smart.

Engineering Your Business will include a column next year outlining the many methods used for riser (drop) pipe and pump column/lineshaft/oil tube lifting and suspension along with wellhead support that makes pump installation easier and safer.

It will also include some of the fishing tools that enable retrieving the seemingly lost string of drilling tools and pumping equipment possible.

The people in the water well industry are extremely innovative, so I know there are numerous tools that I don’t know about built for these purposes. Please email me information and photos of your home-made equipment for inclusion in this column. Send to epbpe58@outlook.com.

Ed Butts, PE, CPI, is the chief engineer at 4B Engineering & Consulting, Salem, Oregon. He has more than 40 years of experience in the water well business, specializing in engineering and business management. He can be reached at epbpe@juno.com.

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