Even with this increase in variance, the pump probably would still perform satisfactorily. At low flows, the pump curve in Figure 4 exhibits a significant sensitivity of head to flow. This isn’t the case for all pumps. For some, the pump curve at low flows is essentially flat (slope is zero) — that is, at low flows, pump head is independent of flow. For such pump curves, the propagation of variance from static head to pump flow would be much larger.
Pumps with a flat pump curve at low flows likely will experience cycling between no flow and some positive flow. Avoid them if you want a VSD to perform smoothly at low flows. Pumps with pump curves such as in Figure 6 probably wouldn’t exhibit the cycling.
Sensitivity of flow to pump speed
It’s also important to understand the change in flow produced by a given change in pump speed.
Figure 8. Value remains relatively constant over the entire operating range.
Figure 5 presents the sensitivity of flow to pump speed for the range of speeds over which the pump could operate. (The somewhat erratic nature of the graph is the result of digitizing the pump curve.) It shows that the sensitivity increases as the pump speed decreases — that is, at low pump speeds, a change in speed has a larger effect on flow than the same change at high speeds.
Such a change in sensitivity affects the performance of the control loop (flow, level, temperature or other) whose output determines the pump speed. As the sensitivity increases, more oscillations can be expected in that loop. So, to use the same tuning at low flows and at high flows, either tune the loop under a low flow condition or conservatively tune the loop at high flows. The results are essentially the same — the controller is tuned with a lower gain. For the controller to function at low flows, performance is sacrificed at high flows.
While techniques such as scheduled tuning could address this problem, conservative tuning usually can accommodate a change in sensitivity of 3:1. But it’s possible that the change in sensitivity could far exceed 3:1. At low flows, the pump curve in our example exhibits a significant sensitivity of head to flow. However, the pump curve for some pumps is basically flat. For such pumps, the increase in sensitivity would be much larger than 3:1 and could even lead to instabilities in the loop that outputs to the pump speed.
Figure 9. High sensitivity of flow to speed at low rpm could lead to cycling.
Pump curves traditionally are drawn with pump speed as a parameter. This might imply that the flow through the pump is best controlled by varying the pump speed, but it isn’t necessarily the case. Changing the torque may make more sense. VSDs can control either of these variables.
When the input signal to the drive electronics adjusts pump speed, the relationship between flow through the pump and pump speed is important. This can be computed from the pump curve and system curve (Figure 6). The departure from linearity is noticeable — and is consistent with the changes in the sensitivity of flow to speed (Figure 5).
When the input signal to the drive electronics adjusts torque, the relationship between flow through the pump and torque is important. This also can be computed from the pump curve and system curve (Figure 7). The graph exhibits only a slight departure from linearity, making it preferable for PID control as that control equation is linear.
Figure 10. Nearly linear relationship offers advantage for control.
Figure 8 presents the sensitivity of flow to torque for the range over which the pump could operate. The somewhat erratic nature of the graph is the result of digitizing the pump curve. The sensitivity changes only slightly over the operating range.
These graphs were computed from the pump curve (Figure 5), which exhibits significant sensitivity of head to flow at low pump flows. As already mentioned, for some pumps the pump curve is flat at low flows — that is, the head is almost constant at such flows.
Figure 9 shows flow as a function of speed for a pump with a flat pump curve. The departure from linearity is much greater. At low flows this graph is almost vertical, so the sensitivity of flow to speed at low flows will be very large, which could lead to cycling in the flow.
However, even for a pump with a flat pump curve, the relationship between flow and torque is nearly linear (Figure 10). Generally linear behavior leads to better performance from the controls.
So, for a centrifugal pump with a VSD it’s usually preferable to use torque to control flow. This also seems consistent with the future directions for VSD technology.
Cecil L. Smith is president of Cecil L. Smith, Inc., Baton Rouge, La. E-mail him at firstname.lastname@example.org.