Pump stations: pressure control and staging

A water booster station, a building's pressure set or a cooling circuit must keep the pressure steady while users open and close taps. The pump cannot know the demand in advance: it measures the pressure and corrects its speed. This is the closed loop of lesson A7, applied to Lab II.

The constant-pressure loop

A pressure transmitter on the discharge measures the head $H$. A PI controller compares it with the set-point and commands the VFD speed:

$$r(t) = r_0 + K_p\,e(t) + K_i \int_0^t e\,d\tau, \qquad e = H_\text{set} - H$$

The booklet leaves the tuning to you. The reference model starts from $K_p = 0.02$ and $K_i = 0.01$ (speed ratio per metre of error), the values preset below. The plant has three lags: the VFD ramp and inertia (about 1 s), the sensor (0.5 s), and a 0.2 s transport delay.

Kp

0.020

Ki

0.010

Pressure set-point

25.0 m

Reference gainsP onlyAggressive

Demand: 120 m³/h until 15 s, then the night minimum (96 m³/h), then from 45 s a morning peak (130 m³/h). The dashed red trace is the same pump at fixed speed, without control.

• Set-point
• With PI control
• Fixed speed
• Pump speed

Largest deviation after an event

2.78 m

Remaining error at the end

0.00 m

Energy used (75 s)

216 Wh

At fixed speed

221 Wh

At fixed speed the network pressure would wander: up to 27.2 m at night when the taps close, down to 24.1 m in the morning peak when they open. With PI control it is back at 25 m within seconds. The pump slows to 96 % speed at night and speeds up to 102 % (51 Hz) for the peak.

Predict first

Press 'P only' (Ki = 0). What does the pressure do after the night-time drop in demand?

It returns exactly to 25 m, just more slowlyIt settles above 25 m and stays thereIt oscillates for ever

Try the aggressive gains: the pressure recovers faster but rings, because the loop gain is now high compared with the lags in the loop. Tuning is a compromise between speed and damping (lesson A7 and the PID playground).

The booster on paper (Tutorial 2.3)

A packaged booster must hold 6 bar at its discharge, whatever the consumption, from a municipal supply. As a head of water, 6 bar is $6 \times 10^5 / (1000 \times 9.81) = 61.2$ m. Two drawings describe it.

The P&ID shows the process: supply, suction isolation valve HV-101, suction gauge PG-101, pump P-101 driven by motor M-101, check valve CV-101, discharge gauge PG-102 and pressure transmitter PT-101, discharge isolation valve HV-102, then the process. PT-101 sends a 4–20 mA signal to the drive VFD-101, whose internal PID sets the motor speed. The control block diagram shows the signals: set-point, error, PID, speed command, pump, network, transmitter, and back.

The PID does not have to live in the drive. It can run in a PLC or DCS that reads the transmitter and sends the drive a 4–20 mA or 0–10 V speed command; today it is more often the drive's built-in PID block, with the sensor wired straight to an analogue input, as here. The course's version of this booster holds 5 bar: at night the pump idles near 20 Hz, and when the morning demand arrives the loop settles it near 40 Hz.

1. Set-point 6 bar
2. Error e = SP − PV
3. VFD PID
4. Speed command 0–50 Hz
5. VFD + motor + pump
6. Building network
7. PT-101 (4–20 mA)
8. PV back to the comparison

• The gauges are local dials for operators; only the transmitter gives the controller a signal.
• If a large valve opens downstream, the pressure drops, the error becomes positive, the proportional term raises the speed at once and the integral term keeps raising it until the pressure is back on 6 bar, at a new, higher speed.
• If the check valve failed open with the pump stopped, water would flow back through the idle pump, spin it backwards and drain the discharge line. The isolation valves let the pump, motor and check valve be removed without draining the system.
• The P&ID says what is controlled and measured; the electrical schematic says how the control is wired. Both are needed.

Several pumps: lead-lag staging

Large stations use several identical pumps in parallel. A lead pump runs on the VFD; lag pumps are added as demand rises. Two facts decide when to add one.

1. Parallel pumps do not add flow. They add flow at the same head, but the system curve demands more head at more flow. On the friction-dominated Lab II network, one pump gives 120 m³/h, two give 134.5 m³/h and three only 137.9 m³/h. On a network with high static head, a second pump adds much more.
2. A pump running far from its best-efficiency point wastes energy. Two pumps sharing a small flow each run at low flow and low efficiency.

Friction-dominated (Lab II)High static head (20 m)

Demand

90 m³/h

79 %Pump 1

offPump 2

offPump 3

• 1 pump
• 2 pumps
• 3 pumps

Least power: 1 pump, 5.33 kW, pump efficiency 75 %.

1 pump

5.33 kW · η 75 %

2 pumps

6.96 kW · η 57 %

3 pumps

9.23 kW · η 43 %

Full-speed capacity: 1 pump 120 m³/h, 2 pumps 135 m³/h, 3 pumps 138 m³/h. All running pumps share one VFD speed; efficiency peaks at 75 % at each pump's best-efficiency flow.

On the Lab II network at 60 m³/h, one pump needs 2.25 kW at 73 % efficiency; two pumps sharing the same flow need 3.17 kW at 52 %. Run the fewest pumps that can meet the demand, near their best-efficiency flow.

In practice the station controller:

• stages up when the lead pump has been at maximum speed for some seconds and the pressure is still low;
• stages down when the speed has been below a threshold for some time;
• uses hysteresis and delays so pumps do not start and stop every minute;
• rotates duty between pumps so they wear evenly, and keeps one as standby.
• trims with the VFD: in the common arrangement the lag pumps run at fixed speed, started direct on line, and only the lead ("trim") pump is on a VFD, filling the gap between them and the exact demand. The course's municipal station runs its trim pump at 30–40 % overnight, ramps it to 100 % at the morning peak, stages in Lag 1, then trims again.

ExplorerGo deeper: derivations and open questions

Loop gain changes with the operating point. The slope $dH/dr$ of the pump at its operating point is the process gain seen by the controller. Compute it at 96 m³/h and at 130 m³/h on the Lab II network. At which demand is the loop closer to instability with fixed gains?

Sleep mode. At very low demand the pump would run below its minimum speed (lesson 1). Drives stop the pump, let the pressure fall to a lower threshold, then restart it. Design the thresholds so that the pump does not start more than 6 times an hour.

Pipe-burst detection. A burst pipe looks like a very high demand. What pattern of speed, flow and pressure would let the controller tell a burst from a busy morning?