Variable Speed Pumping Systems

Published On: March 20, 2024By Categories: Engineering Your Business, Pumps and Water Systems

Part 2. Variable speed drives and their application.

By Ed Butts, PE, CPI

Figure 1. Types of variable speed pumping.

We began an eight-part series on variable flow and head pumping applications and equipment in the last column by doing an overview of the various methods of variable flow and head systems for pump applications using a pressure regulating valve. We continue the topic this month with an enhanced discussion on variable speed drives and their application.

History and Types of Variable Speed Devices

Variable speed pumping devices encompass both mechanical and electrical methods illustrated in Figure 1. Where control valves have the ability to restrict the flow rate and head, variable speed devices or adjustable speed devices have the added advantage and benefit of being able to reduce input power by using the well-known characteristics of the affinity laws.

This results in a much more rapid drop in horsepower per lowered flow rate than using flow or pressure regulating or sustaining control valves. Although variable frequency drives are currently the most popular form of variable speed pump control, they are by no means the only method available.

The use of variable speed drives to control and regulate the speed of pumps is not exactly a new technology. Mechanical speed devices have been in existence for as long as electric motors and include several methods, some of which remain in common use today.

Figure 2. Efficiency comparison of variable speed device methods.

The efficiency of a variable speed device often varies with the transformation of rotative speed. The efficiency of four of the most common methods of variable speed devices are shown in Figure 2.

The most recognized and common method of mechanical speed control still in use includes pulleys and drive belts and is often referred to as the reeve system. The reeve system incorporates a variable pitch V-belt drive with movable flanges. The flanges can be adjusted to different widths, allowing the belts to run on different diameter pulleys. This system allows the motor to operate at a constant speed while the driven load operates at varying speeds, depending on the selected pulley.

The method is effective at accommodating needed changes of speed but is generally limited to manual adjustment and only one ratio of speed difference (or step) can occur at one time. The system also has several maintenance concerns, including the constant need to maintain proper belt tension as well as lubricate the belts and bearings and the inevitable grooving of the pulleys due to wear. However, it is effective for
light to medium duty applications and where speed changes are not frequent or need to be automatic.

When the three-phase alternating current (AC) induction motor was introduced in 1888 by Nikolai Tesla, he knew the invention was more efficient and reliable than the popular motor of the time: Edison’s direct current (DC) motor. However, providing AC motor speed control requires either varying the magnetic flux (frequency) through the windings or changing the number of poles on the motor.

Even after the induction motor gained greater popularity and widespread use, changing the frequency for speed control remained an extremely difficult task and the physical construction of the motor prevented manufacturers from effectively creating motors with more than two set speeds. As a result, continued use of DC motors remained necessary where accurate speed control and reduction, along with significant power output reductions, were required.

In contrast to AC motor speed control requirements, DC motor speed control was achieved by inserting an adjustable rheostat into the low-power DC field circuit, which was feasible with available technology of the time.

These simple motor controls varied the motor’s speed and torque and were the most economical method of variable speed output used for many decades. Beginning in the mid-1930s, systems using hydraulic fluid couplings (Figure 3) became available from various manufacturers for water pump speed control for various commercial, municipal, and irrigation applications.

Figure 3. Variable speed device vs. control valve.

These devices, still available and often referred to as hydroconstant couplings, feature a hydraulically fluid-filled chamber that is generally situated between the electric motor and pump. The chamber varies the speed between the motor and pump by allowing a slipping arrangement where the hydraulic fluid is forced to operate between two fluid drive devices. Individually, these devices are referred to as an impeller and a runner, and both are enclosed by an outer cover called a casing. An inner tube called a scoop tube regulates the fluid flow between the running components.

Figure 4. Electrical schematic of a wound rotor motor.

The pressure setting on the control pilot would control the amount of fluid allowed to remain between the impeller and runner, thus providing partial slippage between the two components, resulting in variable speed operation. This technology is similar to the technology seen in many current applications of automatic transmissions found in most modern automobiles.

This method of speed control offers several advantages over DC motor control; chief among them is good torque transference, excellent speed response, the ability to use fixed-speed AC motors, and no effect on the local power systems.

However, these systems also had several drawbacks, including the need to maintain adequate and clean hydraulic fluid levels, possible contamination issues due to hydraulic fluid leakage, high heat buildup, more complex control systems, and continual maintenance of the required close tolerances of the inner workings of the drive. This method of hydraulic speed control should not be confused with the hydraulic control systems that allow bypass of the pumped fluid back to the pump suction or one that uses hydraulic in-line control valves
to regulate outlet pressure.

An additional method of speed control for pumps was developed in the mid-1950s but used an electrical method of speed control using DC motor controls and a special type of electric motor referred to as a wound rotor motor. A typical schematic for a wound rotor motor is shown in Figure 4.

Figure 5a. Eddy current coupling.

One common method of DC speed control used with a wound rotor motor is referred to as the wound rotor-liquid rheostat method, which operates with electrical current flowing through an electrolyte (often saline) solution between copper electrodes (i.e., rheostat) contained within a tank situated in the bottom of the motor. As the electrolyte solution rises over the electrodes, the electrical resistance of the circuit decreases, causing the speed of the motor to increase. Conversely, as the solution lowers, the electrical resistance increases, resulting in a decrease in the speed of the motor. Thus, the rheostat load varies depending on the height displacement of the electrodes with respect to the electrolytic solution.

In automated systems, the position of the electrodes can be regulated by a PLC-controlled (programmable logic controller) DC motor, pneumatic cylinders, or automated winch. In manual systems, the height of the electrodes can usually be adjusted by a wrench.

In some systems, the electrolyte level may be regulated while the electrodes remain stationary. This method of speed control is informally referred to as an electrical DC drive and is still available from various manufacturers, such as Flomatcher and TECO-Westinghouse.

Figure 5b. Eddy current principle.

However, this method also has an inherent possible contamination risk due to the saline solution that may affect control accuracy and limited speed rangeability. It also requires constant maintenance, a special type of motor and service training, and is therefore more limited in its application to water well work.

An additional method of DC-electrical speed control uses a device called an eddy current coupling (Figure 5a) in which an adjustable slip of speed between the motor and pump is provided through a specialized electrical intermediate coupling. Eddy currents are loops of electric current that are induced within conductors by a changing magnetic field in the conductor or by the relative motion of a conductor in a magnetic field (Figure 5b).

This method uses an electrified DC control field mounted in a coupling placed between an AC motor and the driven load. An exciter is used to vary the DC output voltage, and thus the changing of speed within the coupling. The higher the current within the coupling, the higher the resulting output speed is, while conversely, a low current will result in increased slip and lowered speed.

The efficiency of this method is relatively low, while maintenance and heat buildup are often high. In addition, specialized cooling systems are usually needed to cool the electrical components of this system.

No method of motor speed control is currently more popular than the many systems now in production using electrical AC power drive technology. By the 1980s, AC motor drive technology had become more reliable and inexpensive enough to compete with traditional DC motor control used for motor speed regulation. Variable frequency drives (VFDs) can accurately control the speed of standard AC induction or synchronous motors and are now widely used. With VFDs, speed control with full torque is achieved from 0 RPM through the maximum rated speed, and if required, above the rated speed at a reduced torque.

VFDs manipulate the motor’s frequency by rectifying an incoming AC voltage and current and converting it into a DC voltage and current, which then, using pulse-width modulation (PWM) technology, recreates a modified AC current and voltage output waveform to the motor.

However, this back-and-forth frequency conversion process causes up to 2% to 4% of loss as heat in the gross VFD energy consumption must be dissipated or otherwise removed using heat sinks or forced ventilation with exhaust fan-driven cooling methods. The process also often yields overvoltage spikes and harmonic currents that can damage a motor and other electrical equipment.

The VFD method has gained widespread popularity and use since the early to mid-1980s due to significant improvements in electronic technology and improved design of standard AC electrical motors. A VFD, when combined with a fairly new technology, a permanent magnet motor (PMM), is rapidly becoming an efficient, cost-effective, and reliable method of variable speed operation.

Figure 6. Affinity laws for flow, head (pressure), and horsepower.

Energy Conservation Devices

Variable speed drives (VSDs) are excellent energy conservation devices when properly applied to variable torque systems that adhere to the affinity laws such as fans for air and pumps for water. However, contrary to popular belief, they do not inherently improve motor or pump efficiency.

VSDs help improve the overall system operating efficiency over the functional speed range because most systems do not continuously operate at full speed. Using a VSD helps increase the system efficiency because it has the capability to slow down the motor and pump to use the benefits attached to the affinity laws as opposed to the less efficient process of throttling the pump or bypassing flow.

They are also limited in their effectiveness, and in the case of VFDs, subject to extreme variations in output voltage and frequency when misapplied and used in systems with a flat type of operating curve or a limited or narrow best efficiency window (BEW) or single best efficiency point (BEP).

For optimum effectiveness, each individual application should be fully analyzed throughout the projected flow and associated speed range to ensure an adequate percentage of speed reduction between maximum and minimum flows will occur to provide the desired level of energy conservation while maintaining adequate pump performance.

The addition of a new analysis tool in 2022, NEMA MG 10011-2022 Power Index Calculation Procedure—Standard Rating Methodology for Power Drive Systems and Complete Drive Modules, known as the Power Index (PI), introduces a PI metric that allows power drive systems and drives to be compared for optimal energy savings for end-users.

Principles of Variable Speed Performance with Pumps

Pumps are unique but fairly predictable devices in which a fundamental series of physical laws apply. These laws, known as the affinity laws, state the capacity of a pump will vary directly with the ratio of speed; the head will vary with the square of the speed ratio; and the horsepower demand will vary with the cube of the speed ratio.

These three relationships, although not precisely valid for all applications and shown in Figure 6, are what we depend upon to make the predicted use of a VFD or other variable speed device work so well with most water and wastewater pumps.

Law 1. Flow varies directly with a change in speed (N) or impeller diameter (D)

Law 1a: Impeller diameter (D) constant: Flow (Q) is proportional to shaft speed: Q1/Q2 = N1/N2

Law 1b: Speed (N) constant: Flow (Q) is proportional to the impeller diameter (D): Q1/Q2 = D1/D2

The first affinity law states: The flow rate (capacity) of an impeller is directly proportional to a change in speed.

Law 2. Head is proportional to the square of the speed (N) or impeller diameter (D)

Law 2a: Impeller diameter (D) constant: Head (H) is proportional to the square of shaft speed: H1/H2 = (N1/N2)2

Law 2b: Speed (N) constant: Head (H) is proportional to the square of the impeller diameter (D): H1/H2 = (D1/D2)2

The second affinity law states: The head of an impeller varies as the square of a change in speed. The law starts to become a little more complex at this point, but simply means that the ratio of a change in speed multiplied by itself then multiplied by the original head will result in the modified or new head.

Law 3. HP is proportional to the cube of the speed (N) or impeller diameter (D)

Law 3a: Impeller diameter (D) constant: HP is proportional to the cube of the shaft speed (N): HP1/HP2 = (N1/N2)3

Law 3b: Speed (N) constant: HP is proportional to the cube of the impeller diameter (D): HP1/HP2 = (D1/D2)3

The third and final affinity law states: The input horsepower of an impeller varies as the cube of a change in speed. As in our previous example, this time the relationship is now the ratio of the two speeds multiplied by itself three times, then multiplied by the original horsepower:

Example: Assume a pump/motor combination operating on an electrical system with 60 Hertz (60 Hz) power. The pump is capable of 500 GPM at 200 feet of total head with a brake horsepower requirement of 33.5 BHP at a full load motor speed of 3450 RPM. Now assume the frequency is lowered from 60 Hz to 42 Hz. Using the affinity laws, determine the revised speed and revised operating conditions for this unit.


1. Determine the revised speed: 42 Hz/60 Hz = 0.70 (70%) = 3450 RPM × 0.70 = 2415 RPM

2. Determine the revised pumping conditions:

Revised flow rate = (2415 RPM/3450 RPM)1 = 0.70 × 500 GPM = 350 GPM

Revised head = (2415 RPM/3450 RPM)2 = 0.70 × 0.70 = 0.49 × 200′ = 98 feet of head

Revised HP = (2415 RPM/3450 RPM)3 = 0.70 × 0.70 × 0.70 = 0.343 × 33.5 HP = 11.49 BHP

Although this column is primarily oriented to performance changes due to pump speed variations, note the previous relationships also conceptually apply to changes in impeller diameter with a constant speed, illustrated in Laws 1b, 2b, and 3b.

This is because the rim or peripheral speed of the impeller is another determiner applied to pump performance. It should be obvious in the example that a relatively small reduction in pump speed can result in a significant drop in brake horsepower. In the example, with efficiency being equal, a reduction in motor speed of just 30% results in a corresponding drop in brake horsepower of 65.7%.

However, it is a misconception that adding a variable speed drive to a pump will necessarily increase the overall efficiency of the motor or pump. When considering the wire-to-water efficiency of the pump, motor, and VSD as a combined element, each component that is added to the pumping system lowers the wire-to-water efficiency at a respective flow rate because each component has individual losses associated with it.

For example, a bowl assembly with an efficiency of 83% at a specific flow rate may drop to a combined efficiency of 78% with the addition of an electric motor and then drop further to a system efficiency of 75% with the addition of a VSD.

Generally, the loss or correction in efficiency of any one component pales in comparison to the energy reduction or increase due to the impact of the affinity laws. The only way to accurately determine the precise wire-to-water efficiency at various flow rates in the field is to perform production tests at various operating conditions, record the input horsepower at each individual operating condition, and compare the results to theoretical (water horsepower) values.

Variable speed drives are useful in that they not only modify flow and head in accordance with the affinity laws, but generally retain the pump’s characteristic performance curve shape. This provides great rangeability, and therefore, any predictable flow/head combination within the given speed envelope can usually be attained.

Contrary to much of the current hype circulated by many sales personnel, a VSD will usually perform their full energy conserving potential only when an adequate reduction in speed is possible and the pump has a wide band of relatively high operating efficiency. This is the primary reason that VSDs are generally most effective with pumps that exhibit a steeper operating curve than those with a relatively flat curve, although they can be used successfully with either type with appropriate caution.

However, use of a VSD is not limited to just energy conserving applications. Variable speed drives are also used as a means to regulate and stabilize output flow or pressure regardless of the impact on energy consumption.

They are often used to control pressure surges or water hammer caused by the starting and stopping of pumps and sometimes used as soft starters to limit the high inrush currents associated with the starting of electric motors (although there are specific electronic and electrical motor control devices already available for this application that are less expensive and complicated than most VSD devices).

Certainly, variable speed drives are not for every application nor always more desirable than using control valves or conventional on-off pressure control with pressure tanks, but they remain viable options for many water pumping applications.


Next month, we will continue this topic with commonalities between VSD systems and then move to the concepts and design of VFDs in the June issue.

Until next time, as always, work safe and smart.

Learn How to Engineer Success for Your Business
 Engineering Your Business: A series of articles serving as a guide to the groundwater business is a compilation of works from long-time Water Well Journal columnist Ed Butts, PE, CPI. Click here for more information.

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

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