# Taming the Shrink-Swell Dragon

## An Elusive Steam Generator Control Problem Is Solved at Maanshan II

03/24/2004

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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).

The load change was simulated from a steady state at zero deviation by placing the LC in Manual, stepping its output by an acceptable increment, and then transferring immediately back to Auto. This placed the controller output apart from the steady plant load by that increment, requiring it to integrate back to its last steady-state value, which matched the load. An increment in controller output in one direction is equivalent to an increment of the same size in load in the other direction.

Take careful note though. To test a liquid-level loop by stepping its set point is a mistake. First, most level loops operate at constant set point all the time, so set-point response is meaningless. Secondly, the steady-state output of a level controller matches the load and is not a function of its set point. Following a step in set point, the LC output will return to its previous steady-state value. This does not require the controller to integrate, as a load change does, and produces a response curve having an integrated error of zero, and hence an area overshoot of 100%. By contrast, the overshoot resulting from a load change is determined by the integral setting of the controller.

Read Also: PID World Tour--The Final Performance

From the load change simulation came the conclusion that the WR gain K should be set to 5, because that was the amplitude ratio of the NR to WR cycles observed in Unit I. This had an immediate stabilizing effect on NR level. As a result of this success, K was then increased to 8, 10 and finally 12, where it remained. This reduced the loop oscillation period by a factor of two, and allowed a commensurate 4-min. reduction in the integral time of the NR controller. This was the fastest and most stable 1E response ever observed at the plant. The NR proportional band was left unchanged at 60%.

#### Differential-pressure Control

Feedwater flow is a product of FRV opening and the square-root of its pressure drop dp. The pressure drop in this plant is regulated by manipulating the speed of the feedwater pumps. This loop is especially important to 1E control, because any variation in valve dp changes feedwater flow, requiring the NR LC to operate the valve by integrating the resulting level deviation. Therefore the dp controller should be tightly tuned. At Maanshan II its proportional band was reduced to 50%, where a lightly-damped oscillation broke out; it was then increased to 75% and left there.

The dp loop gain was expected to change with the number of pumps n being manipulated by the controller, and so the proportional band of the controller was multiplied by n. However, this left the loop overdamped with three pumps running, indicating this was overly cautious. The expected interaction between the dp controller and the three parallel feedwater flow controllers, however, did not create any problems.

The set point of the dp controller at Unit II was programmed to be proportional to plant power generation. This conserves pump horsepower, which varies directly with the product of feedwater flow and FRV dp. A properly executed program keeps the steady-state opening of the FRV approximately constant with generated power.

Figure 1 shows a neutron flux signal used as a feedforward input to the 1E control system. This was implemented in Unit II, along with the dp set-point program. During a rampdown from 14 to 7 power, the NR level was driven down about 12%, where it stayed until the ramp was ended. A constant deviation during a load ramp is common to feedback loops without feedforward (Figure 3), because the controller must integrate a constant deviation in order to ramp its output. However, without feedforward, the level should have risen during the rampdown, as more water was being delivered to the SG than the falling load required. So the low level during the ramp indicated that too much feedforward was actually being applied.

The gain K of the flux feedforward input should be set at m/, where m is the output of the NR level controller. Accordingly, the LC output at the initial and final steady-states were compared, and found to be the same! The reason for this is the programming of dp with power"all of the load change was transferred from the FRV to the dp loop. In other words, the reduction in feedwater flow required to match the plant load was achieved by reducing the dp across the valve, instead of closing it. As a result, the feedforward input from neutron flux actually duplicated what the dp set-point program had accomplished.

To eliminate the duplication, K was set to zero. It can be seen that the two responses in Figure 3 are mirror images of each other. Therefore, the proper amount of feedforward achieved by the set-point program of the dp controller, left the level constant. Because the LC output is the same before and after the ramp, integrated error with K  set to zero is also zero.

#### Nonlinear Filters

To reduce the negative effect of shrink and swell accompanying every load change, nonlinear filters were applied to the deviation of both the 1E and 3E-level controllers. They consist of three zones shown in Figure 1: the center zone has a width of ±z and a gain of kz, and the outside zones have a gain of 1.0. For the level controllers at Maanshan II, z = ±3.0% and kz = 0.4. Minor upsets produced level variations of less than ±3 %t, where kz diminishes the effects of these variations on feedwater flow, allowing the feedforward signals to do their work. Any major upset that drives the level deviation beyond 3% promotes a greater driving force to return the level within the low-gain zone where damping is heavier.

##### Figure 4: When the controller was left in manual too long, an offset cycle developed.

However, the proportional band of the level controllers must be tuned for stable response to a larger upset. Originally, the 3E LC was set for 60% proportional band, which was stable for deviations within the low-gain zone. Eventually, a larger upset caused the deviation to exceed 3% on both sides of set point, promoting an expanding triangular cycle. This behavior is shown in Figure 4. Increasing the proportional band to 100% dampened the cycle and eliminated any recurrence.

At one point, stability of the 1E loop was tested by placing the LC in Manual and stepping its output upward. However, the LC was left in Manual until the level exceeded the low-gain zone, and then returned to Auto. The higher gain of the level controller in this zone quickly turned the level back toward set point, but started a proportional cycle above set point. Integral action brought the cycle progressively back toward set point, and after the low-gain zone was re-entered, it dampened. This response is compared to a simple step load change in Figure 5. It did not require a re-tuning of the level controller. As a result of the WR proportional loop's help, the proportional band of the 1E LC was left at 60%, compared to the 100% setting required for the 3E LC.

#### Conclusion

Feedwater control must be both stable and responsive across the entire plant load. This is particularly problematic at loads below the range of steam and feedwater flowmeters, where single-element level control must be used. With the assistance of proportional feedback from a WR level measurement, the effect of inverse response was mitigated and the single-element loop response time was reduced by a factor of two.

Controlling differential-pressure across the feedwater valves by manipulating pump speed prevented unmeasured load changes from upsetting level, and programming the dp set point, as a function of power, eliminated that source of the disturbance. Interaction between the dp and feedwater flow loops under three-element level control did not surface as a problem.

Nonlinear filters reduced the effects of shrink and swell upon the level loops, but complicated tuning of the level controllers. Their proportional-band settings must be tested for stability following upsets which drive the level deviation out of the low-gain zone on both sides.

### References

1. Shinskey, F. G., Process Control Systems, 4th ed., McGraw-Hill, 1996, New York, pp. 88-90.
2. "Westinghouse Plant Digital Feedwater Control System," Sec. 4.3, Feedwater I&C Maintenance Guide, Electric Power Research Institute, November 1995.
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