Page 161 - Dynamics and Control of Nuclear Reactors

158 CHAPTER 12 Pressurized water reactors

zero for errors in the range 1.0°F. The dead-band includes a 0.5°F lock-up [2].This
avoids a continuous chatter in the control rod motion due to small errors in a small
range adjacent to a 1°F temperature error. Fig. 12.4 shows the magnetic jack control
rod drive mechanism (CRDM) used in Westinghouse PWRs.
The minimum rod speed is 8 SPM (steps per minute) and the maximum speed is
72 SPM. Each step corresponds to a motion of approximately 5/8in.

12.10 Feedwater control for PWR with U-tube steam
generators [2, 4, 5]
U-tube steam generators produce a mixture of saturated water and steam. The water
and steam are separated in the steam separators and driers in the top of the steam
generator. The separated steam goes to the turbine and the separated water flows into
the downcomer, an annular region inside the outer wall of the steam generator. The
water level in the downcomer is measured and controlled. This level remains con-
stant at all power levels.
A phenomenon called shrink-and-swell occurs in U-tube steam generators and it
dictates the type of control used for feedwater. (This phenomenon also occurs in so-
called drum-type boilers in fossil-fuel plants and in BWRs and also necessitates a
similar control strategy).
Consider what happens when the main steam valve opens. Pressure in the steam
generator drops, causing saturated water to flash and the two-phase volume to swell.
This drives more steam-water mixture into the steam separators and driers and, con-
sequently, more liquid water flowing into the downcomer. So, the downcomer level
temporarily increases, signaling a need to decrease feedwater flow. But since the
steam flow has increased to start the transient, this is the wrong direction for feed-
water flow changes. So, feedwater level alone is an inadequate measurement to
determine feedwater flow control. The opposite happens when the there is a reduc-
tion in the steam flow rate resulting in a shrinking of the steam generator level.
Using a controller that uses three measurements to determine control action
solves the problem of shrink and swell. The downcomer level measurement is aug-
mented by measurement of steam flow and feedwater flow rates. The difference
between steam flow rate and feedwater flow rate, along with downcomer water level
error, provides the inputs to a controller as shown in Fig. 12.12.
Such a controller is called a three-element controller. The error signals used in the
controller are defined as
Flow error,E W ¼ Steam flow rate Feedwater flow rate

Level error,E L ¼ Level set point Measured level (12.12)
Since the two error terms have different units, the flow error is divided by the full
power steam flow rate and the level error is divided by the allowable level range.
Thus the error terms are non-dimensional. Note that there is no direct steam pressure