The operating point is always where the pump curve intersects the system curve.
Control valves regulate flow by varying friction head — that is, they work entirely through the system curve, as illustrated in Figure 1. It presents system curves for a fully open control valve and a control valve that is 75% open. For the fully open valve, flow is 177 gal/min. As the control valve closes, resistance to flow increases. This raises the friction head component of the system curve, which makes that curve intersect the pump curve at a lower flow — at 75% open, flow is 127 gal/min.
Small variations in both static and friction head occur in any pumping installation. These head variations cause flow variations, which also can be determined from the performance curves.
Suppose the static head is 60 ±1 ft. Figure 2 shows system curves for 59 ft. and 61 ft. and where they intersect with the pump curve. For the fully open control valve, flow is 177 ±2 gal/min; for the 75% open control valve, flow is 127 ±2 gal/min. In each case, a head variance of ±1 ft. leads to a flow variance of ±2 gal/min.
Figure 6. Nonlinear relationship can hamper using PID control.
Closing the control valve doesn’t significantly affect the propagation of variance from head to flow. But as we shall see, this isn’t necessarily the case for variable speed pumping.
Flow regulation with a VSD
With variable speed pumping, the system curve is fixed but the pump curve shifts with pump speed. Some vendors provide pump curves for certain selected speeds; others provide a pump curve only for the rated speed of a constant speed drive. In either case, the affinity laws can be applied to obtain pump curves at other speeds:
Q(N) = QC (N/NC) (2)
H(N) = HC (N/NC)2 (3)
where N is speed, rpm; NC is speed for the pump curve supplied by the manufacturer, rpm; Q(N) is volumetric flow at speed N, gal/min; QC is volumetric flow at speed NC (from the pump curve), gal/min; H(N) is head at speed N, ft.; and HC is head at speed NC (from the pump curve), ft.
Flow decreases in proportion to the pump speed; head decreases in proportion to the square of the pump speed. The affinity laws also state that power decreases with the cube of the pump speed, which strengthens the energy savings arguments by VSD manufacturers.
Figure 3 illustrates regulating flow by varying pump speed. The system curve is fixed. For a pump speed of 3,450 rpm, the flow through the pump is 177 gal/min; for 2,850 rpm, 98 gal/min; and for 2,370 rpm, 0 gal/min. In fact, 2,370 rpm is the minimum pump speed for flow — that is, flow occurs only for speeds above 2,370 rpm.
The minimum speed to obtain flow is easily computed. When there’s no flow, the system head is the static head. The pump curve shows the head delivered by a pump with no flow and running at speed NC. The minimum pump speed to obtain flow is computed using the affinity laws:
Nmin = NC (HS/HC0)½ (4)
where Nmin is minimum pump speed for flow, rpm; HS is static head (from the system curve); and HC0 is head at speed NC and zero flow (from the pump curve), ft.
For our example, NC is 3,450 rpm, HS is 60 ft., and HC0 is 127 ft. The minimum pump speed is 2,370 rpm. So, the VSD must operate over the range of 2,370 rpm to 3,450 rpm. The minimum speed is 69% of the maximum speed; the turndown ratio is 1.46:1. VSDs are easily capable of this.
Figure 7. More linear relationship better matches the PID control equation.
Figure 4 illustrates propagation of variance from static head to flow for pump speeds of 3,450 rpm and 2,450 rpm. At 3,450 rpm, a static head of 60 ±1 ft. gives a flow of 127 ±2 gal/min (just like for the fully open control valve). However, at 2,450 rpm, a static head of 60 ±1 ft. gives a flow of 19 ±6 gal/min. As the pump speed decreases, the variance in flow increases by a factor of three.