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# The energy equation of variable speed drives

It's easy to understand how variable-speed motor drives benefit pumps and blowers from the energy curves that depict their performance.

It is interesting to look at figures from the Energy Information Administration about where energy gets consumed in our economy. These figures reveal that industrial uses account for 31% of all energy use. Industrial motor-driven systems also consume about 25% of all electricity in the U.S. and are the single largest category of electricity use in the country.

Clearly there should be many opportunities for energy savings in motor applications. But figures collected by the U.S. Dept. of Energy show there is a lot of room for improvement when it comes to industrial motors. In its most recent assessment of industrial motor systems, the DoE found about 40% of the companies it surveyed had made no improvements in fan or pump systems. And 52% had not added any kind of controls to more efficiently power variable loads.

Industrial firms often argue against installing energy efficient motor controls on the grounds that such systems are more expensive than their alternatives. The problem with this argument is that most costs associated with large electric motors are in the energy they use over their lives rather than in their up-front costs and installation expenses. Data collected by Siemens in Germany, for example, estimate the purchase price of a 150 hp motor accounts for less than 1% of its overall lifecycle costs. Energy costs account for the rest. The same kind of economics applies to smaller motors. The purchase price and installation costs of a 2-hp motor account for less than 4% of its life cycle cost. Again, energy costs make up the rest.

Thus it is logical on a variety of levels to reduce the energy costs associated with applications run by electrical motors. Variable speed drives are the usual way of approaching this goal. The typical way of controlling ac motor speed is with an inverter. The ac from the grid is first rectified to dc. This dc is then inverted to an ac waveform whose frequency is varied. This variable frequency signal drives the motor at a speed that is proportional to the frequency of the power signal.

VFDs vary motor speed as a means of saving energy in applications where the motor needn't run at full speed at all times. They are energy saving alternatives to mechanical controls such as throttling valves and dampers, which reduce flow rates while the motor still runs at full load speed. Typical uses in this category include ventilating air blowers that only need to run at full speed under the most severe environments, and pumps or compressors in which the volume of pumped fluid can vary.

A point to note is that VFDs can also save energy by recovering energy that would otherwise be wasted. VFDs outfitted with regenerative capabilities can take energy used to brake the motor and recycle it back to the power line.

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### Flow control

It becomes easier to understand the specific amount of savings involved in VFD applications by examining the underlying mathematical relationships between variables such as pressure, volumetric flow rate, speed, and power. In pumps and fans, affinity laws determine how relative speed affects pressure, power, and flow. Specifically, flow is proportional to motor shaft speed; pressure (or head) is proportional to the square of shaft speed; and power is proportional to the cube of shaft speed.

For a specific example of the affinity laws in action, consider a large water fountain operated with a 900 kW pump. The pump must deliver 100% flow during peak hours, 60% flow in the morning and evening, and 30% at night. Suppose we evaluate two means of realizing this flow control: with a mechanical throttle and with a VFD. We can calculate the power required versus the flow rate for both methods. The accompanying graph shows the result. The energy that the VFD saves is the area between the two power curves. The analysis shows a 58% energy savings. This is an actual example wherein the payback time for the VFD was three months and investment in the VFD returned more than four times its cost.

The usual way of calculating potential payback from a VFD pumping system is by analyzing the operating point on a system curve. The curve for a pumping system is the relationship between pressure and flow rate. Factors that affect it include the size and length of piping, number and location of elbows, and so forth. We analyze the operating point of a pumping system by superimposing the system curve with a pump curve that is determined by the physical qualities of the pump. The natural operating point of the system is the point where the system curve and the pump curve intersect. This is the point where the pump pressure matches the system losses.

It is instructive to compare the system curve and operating point under the influence of mechanical throttling with that using VFDs. Throttling basically changes the location and slope of the system curve while the pump curve remains fixed. Contrast this with the situation under VFD control. Here, the VFD changes the pump curve when it varies the pump speed. The system curve remains fixed. One can calculate the energy saved for a given flow rate from the difference between the two operating points.

A similar analysis applies for centrifugal fan applications. Here the system curve shows what kind of venting system the application demands and the amount of pressure necessary to overcome system losses and produce airflow. As with pumps, the natural operating point is at the intersection of the system curve and the fan curve. It gives the actual pressure and flow that will be measured at the fan outlet.

Systems can use mechanical means to modify flow rates without varying the motor speed. One such method is with a damper or control louvers installed on the outlet. Turning the dampers restricts the outlet. The effect of an outlet damper is to move the system curve by increasing the resistance to airflow. Here,

P = K ~ F2

where P = pressure needed for a given flow in the system; K = a system constant representing resistance to airflow, which is affected by the outlet dampers; and F is the desired airflow, cfm. A view of the curve describing input power as a function of flow rate shows that power requirements drop gradually as flow diminishes.

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Another mechanical means is the use of variable inlet vanes that restrict the amount of fluid admitted to the fan inlet. Vanes have the effect of varying the position of the fan curve. Thus the point of intersection between the fan curve and system curve changes with variations in fluid flow. A look at the power curves for these devices reveals that power drops as fluid flow drops, and that the reduction in power is greater than is the case with outlet dampers.

VFDs also change the location of the fan curve, as do inlet vanes. But inspection of the input power curve shows that changes in flow rate with a VFD have a more dramatic impact on input power than changes in flow rate with inlet vanes.

To evaluate scenarios with VFDs and mechanical flow control devices, it is easy to do what-if comparisons of fan speed, pressure, and flow rate using the law of affinity. This can help predict the way a centrifugal fan will function at any operating point based on the original fan characteristics:

### Wasted energy recovery

Many industrial applications are characterized by cyclical acceleration and deceleration. The problem is that there is often a significant amount of energy wasted during deceleration when the application involves a lot of mass. Ditto for applications that involve motor braking, such as down-hill conveyors or hoists. In the age of escalating energy costs, it is frequently beneficial to somehow recover energy lost during deceleration and braking.

When a motor decelerates, it can effectively become a generator due to the dual nature of induction motors. To understand how VFDs can recover energy of this nature, first consider the case where the inverter simply dissipates energy generated during braking and deceleration rather than recycling it. This takes place through use of a braking chopper circuit between the rectifier and the dc link. The braking chopper is basically an IGBT that shunts electrical current generated by the motor to a large power resistor which converts the energy to heat. The chopper automatically actuates when the dc bus voltage exceeds a specified level, depending on parameters of the VFD.

In contrast, regenerative drives contain no braking chopper circuits. The rectifier portions of their circuits replace the rectifying diodes with power transistors, usually IGBTs. These transistors are bidirectional in nature. However, they are configured to effectively act as a diode bridge recifier on the input of the drive in normal motoring operation. When the motor is overhauling and delivering energy back to the drive (regenerating), the IGBTs on the input act to generate a pulsed dc wave form that can be returned to the facility power system.

Of course, regenerative drives cost more than those that implement braking, simply because the power circuitry involved is more complicated. Applications where regenerative drives are warranted include those where motors operate in braking or deceleration a large percentage of the time. Examples might include test stands for life testing of motors or combustion engines, where the unit under test works against a load.

### Resources

Siemens Industry Inc., Alpharetta, Ga., (770) 740-3724, www.usa.siemens.com/motioncontrol

Sizer design tool, www.siemens.com/sizer

VFD info, www.usa.siemens.com/energysavings

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