# Understanding the economics of variable speed pumping

During the last decade variable frequency drives have become increasingly popular for controlling pump flow rates. Variable speed drives have many advantages compared to throttle valves when it comes to regulation of flow. They offer large energy savings and, hence, large cost savings if they are applied correctly.

The increasing popularity of the variable speed drive has, however, brought with it a large number of misapplications. In these cases, the end user receives *increased energy bills* instead of savings as a result of installing a variable speed drive. How could this be the case? Read on.

To understand any pumping system, you first must realize that all of its components are interdependent. Sub-optimization on the *component level* can easily lead you astray. When examining or designing a pump system, first ask about the process demand that it is expected to fulfill. For example, do we need to regulate the flow rate continuously or in steps? Can we use on-off batch pumping? What are the flow rates needed and how are they distributed in time? A duration diagram encapsulates the answers to these questions.

#### The duration diagram

A duration diagram in its simplest form shows how many hours during a year that you need a given flow rate (the dashed curve). The solid curve in the same diagram is interpreted differently. Each point on the solid curve tells you how many hours during a year the flow rate exceeds the value on the y-axis.

This diagram is instrumental in understanding your pumping needs. You must be able to deliver the peak flow but, from an economic point of view, it is also important to know at what flow rates you are going to operate *most of the time*.

Given this information, you can proceed with the design of your piping system. If, for example, the maximum flow rate occurs only for short periods of time, it may not pay to install a large diameter pipe. On the other hand, if you are operating at peak flow rates for extended periods of time, then you should take this fact into account when specifying the pipe diameter. When you finish designed your piping system, it is time to calculate your *system curve*.

The system curve tells you how much head, or pressure, you need from a pump to push a given flow rate through your pipe system. The head has two components: the static head and the dynamic head. The static head indicates how far the fluid must be lifted or, if you must pump into a pressurized vessel, the static pressure differential across the pump.

The dynamic head is the frictional force and other point losses to be overcome in moving the fluid at the desired flow rate. Dynamic losses increase with the square of the fluid velocity. So, if you double the flow rate, the dynamic losses increase by a factor of four. Now you should go back to the duration curve to see where on the system curve you are going to operate and for how long.

We now get to the point where we must specify a pump, or pumps, plus suitable means for regulating the flow i f needed. Also, now it is helpful to understand how a pump performs in conjunction with a variable speed drive. Figure 3 shows how the pump's performance curve responds to a change in the frequency delivered to the motor. New curves can be calculated to a good approximation by using the Affinity Laws,

Q_{1}/Q_{2} = n_{1}/n_{2}

H_{1}/H_{2} = (n_{1})^{2}/(n_{2})^{2}

where, n is the speed of the impeller in rpm, Q is the flow rate, and H is the developed head. The broken lines show how a particular point on the original curve moves to form a new curve. Along these lines efficiency remains essentially constant.

A common mistake is to use the Affinity Laws to calculate energy savings. Although this may sometimes be done as a good approximation, it can also lead to major errors. It is important to note that the *operating point* is the intersection of the pump curve and the system curve. In systems without static head, the system curve follows the lines of constant efficiency and pump efficiency remains essentially constant as the pump speed changes.

However, in systems with static head, the system curve does not start from the origin but at some non-zero value on the y-axis corresponding to the static head. Hence, the system curve does not follow the curve of constant efficiency. Instead, it intersects them. In turn, this means that the pump efficiency changes when the speed of the pump changes. This is quite the contrary to a pump system without static head, in which the pump efficiency remains fairly constant with changing speed.

The operating point on the reduced speed curve moves relatively higher and higher on the pump curve as the speed is reduced. Eventually the pump runs at shut-off head if the speed is reduced too greatly.

**The resulting difficulties **

There are two problems connected with this situation. The first is that the pump efficiency goes towards zero when the operating point moves towards shut-off head. The second problem is that the pump then operates in a flow regime where it should not be operated. Severe damage to the pump occurs if it is operated close to shut-off head for extended periods of time even if this takes place at a reduced rate of speed.

The more static head there is in a system, the more dramatic these effects will be. At high static heads, a relatively minor decrease in speed moves the pump operating point into an area where the pump should not be operated continuously. Decreasing the speed even more brings the operating point to the shut-off point. Then the motor is running and consuming energy although generally less than it does at full speed. The flow rate is, however, equal to zero and all of the energy provided to the pump goes into heating the fluid through friction.

A pump system is built to move a certain volume of fluid from one point to another (in circulating systems they are the same). A useful measure for calculating the cost of pumping is the specific energy, E_{s}. Specific energy is defined as the energy required for a specific pump to pump a unit volume of fluid in a specific system. Specific energy is equal to Wh/G, where W = ??? ,H = ????, and G = ?????.

To understand what is happening in a system with static head, plot the specific energy as a function of speed. Assume the pump starts at full speed (Point A) where it is consuming specific energy Wh/G. As the speed is reduced, the specific energy may (Curve A), or may not (Curve B), drop below this level. As the operating point approaches shut-off, specific energy always goes towards infinity. In this example, specific energy rises rapidly at about half-speed.

It is important to understand that this will *always *occur in a system having static head. The speed at which specific energy rises rapidly is a function of the amount of static head. In systems with low relative static head, there might still be opportunities to save energy by reducing the pump speed. In systems with high relative static head--above 50 percent of the total head--there is a distinct possibility that using a variable speed drive will increase the net energy usage, compared to on-off pumping at full speed.

In most instances, pumps are sized and chosen to deliver the peak flow rate with some margin upwards. With duration curves looking like the continuous curve, it is, therefore, common that the* normal* flow rate is around, or less, than 50 percent of the rated flow.

If the system curve exhibits a fair amount of static head and the pump is oversized for most of the pumping needs, then problems can occur. It is not uncommon in such systems to find that the cost of pumping is considerably increased, compared to on-off pumping at full speed, when using a variable speed drive. That the combined efficiency of a variable speed drive-motor package can drop considerably as the load is decreased does not make the situation better. Throttling the flow, however, is still worse!

Consider a variable speed drive used in a system with static head. The useful range of the variable speed drive can be extended if the pump is chosen so that the intersection of its system curve and the full speed pump curve lies to the *right* of the pump's best efficiency point. This extends the area in which the variable speed drive is useful, since the pump efficiency first increases before it starts to fall, as the speed is reduced.

**Understand your pumping needs**

Variable speed drives can give you good control of your flow rate. They generally reduce the operating cost in all systems when compared to throttling valves and in systems with little or no static head without throttling valves. In systems with high relative static head, take extra care when using variable speed drives to avoid the pitfalls of low pumping efficiency and operation in harmful flow regimes. The allowable speed range thus becomes restricted both from operational and economical points of view.