Taming the Shrink-Swell Dragon

The shrink-swell phenomenon in the liquid level of boilers and steam generators can dramatically limit control system's ability regulate level; especially during transient conditions. This is particularly true at low power rates, below the range of steam and feedwater flowmeters, where single-element controls must function.

After a thorough analysis, a control system upgrade provided the means to tame the shrink-swell dragon taking up residence in the steam generators of Maanshan II, a 950-MW pressurized-water reactor nuclear power plant in southern Taiwan. Maanshan II's design is complex, with three parallel steam generators, each with its own feedwater control system, and three feedwater pumps connected through a common header.

The shrink-swell phenomenon is caused by variations in the vapor-liquid ratio in the evaporating section of a boiler or steam generator (SG). In the interest of accuracy, water level is measured over a narrow range at the water surface, although most of the water inventory lies below the taps of the narrow-range (NR) transmitter. It is much like measuring the tip of an iceberg.

When steam is not being generated, the evaporating section is completely flooded with water. As boiling begins, however, vapor bubbles start to occupy some of the space, lifting water into the range of the NR transmitter, indicating a higher level, even though the water inventory may actually be decreasing. As power generation increases, the vapor volume in the evaporating section will increase proportionately, leaving a progressively lower inventory of water. This can be observed in a lower measurement of wide-range (WR) level, which senses the most of the water inventory. Because the WR measurement is less accurate than the NR measurement, and must change with power generation for the same NR lever, it is not normally used for control.

The problems caused by shrink and swell are dynamic as well. When the amount of steam being withdrawn from the SG is suddenly increased, its pressure starts to fall until more heat can be transferred to the water. This drop in static pressure causes the vapor bubbles to expand, lifting more water into the NR area. The swelling-level effect causes the level controller (LC) to reduce feedwater flow at a time when a higher flow is required to match the higher demand for steam. The opposite effect"shrinking level"follows a decrease in steam withdrawal.

In a three-element (3E) feedwater control system, the steam-flow signal is used in a feedforward manner to set the feedwater flow controller (FC) to the same flow. However, in biasing the feedforward calculation, the LC acts counter to the direction of the load change. Thus the LC counteracts the swell effect by reducing flow while the load is increasing, or the shrinking effect by raising flow while the load is decreasing. This action has value because water inventory must be reduced at higher power and increased at lower power.

A single-element (1E) feedwater control system however, has neither a steam nor feedwater flowmeter, but relies on the NR controller to position the feedwater regulating valve (FRV) directly. Without the help of the steam-flow input, the LC will initially drive the FRV in the wrong direction on a change in load.

A second, and perhaps even worse control consequence of shrink and swell is its inverse response, especially at lower power when feedwater temperature is much lower than that of the steam being generated. If the feedwater flow is suddenly increased by the LC, it tends to collapse some of the steam bubbles, causing the NR level to fall, while increasing water inventory at the same time.

Although this reversal of direction of the NR level is temporary, the delay between the opening of the FRV and the eventual rise in NR level could be as long as a minute or more, making the level very difficult to control. Inverse response is quite similar to dead time in its delaying effect on the control loop2.

In Unit I of the Maanshan plant, the NR level under 1E control was observed at one point to be cycling with a period of about seven minutes, with the WR signal cycling at the same period, but leading the NR signal by 1.5-2 minutes. The amplitude of the WR cycle in percent of scale was about 1/5 that of the NR cycle in percent of scale. Could the WR signal be added to the NR controller"something like how a derivative (lead) is added to a PI controller"to make a PID?

The possibility of using the WR level measurement as a "feedforward" input into the 1E control system has been described in detail1 and depicted in the manner shown in Figure 1. The WR signal is filtered by first-order lag f(t), then compared with the no-load set point (the normal WR level when no steam is being generated). Their difference is then multiplied by gain K and added to the output of the LC.

This scheme was added as shown to the 1E system of Maanshan Unit II. Although published information refers to the WR level input as "feedforward,"2 actually it is not"it is a proportional feedback input, because changing the FRV position changes WR level. In essence, this scheme combines proportional control of WR level with PI control of NR level.

With WR gain K set at zero, a 15-min. period of NR level loop oscillation was observed on Unit II, with a proportional-band setting of 60% and an integral time of 8 minutes. These settings were approximately optimum, as the step load response of the loop was a symmetrical (bell-shaped) curve followed by a small overshoot and satisfactory damping, as shown in Figure 2. These features are characteristic of a response curve having a minimum Integrated Absolute Error (IAE).