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maximum reactivity worth is fully stuck outside of the core. The negative reactivity (sub-criticality) at the cold shutdown condition is referred to as the "(stuck rod) shutdown margin of the reactor.”

In practice, the core is designed so that the effective multiplication factor, when one control rod of the maximum worth is stuck outside of the core, is always below 0.99 over the core life. Figure 2.3.20 gives an example.

In an ABWR, since two control rods are driven by one control rod drive unit, the shutdown margin is defined as the negative reactivity when two control rods of the highest worth attached to the same control rod drive unit are stuck outside of the core.

  1. Control rod worth

A BWR has its own self-regulation capability provided by the so-called negative feedback mechanisms of Doppler effect, moderator temperature effect and void effect, which mitigate the abnormal power increases (power excursions). However, if a positive reactivity is inserted into the core at critical or near critical condition, there may be an abnormal power excursion depending on the magnitude and insertion rate of the reactivity. Such reactivity transients may occur, for example, when a control rod blade becomes detached from

the coupling for some reason and falls due to its own weight from its stacked position in the core. Such an abnormal power transient may cause mismatching between the energy production and removal, or a rapid increase in fuel temperature (fuel enthalpy increase), which may eventually result in fuel failure (disintegration of fuel or even fuel melt down). If a significant amount of fuel melts, mechanical energy may be released in the form of a pressure wave or water hammer, following the interactions between the high temperature fuel pellets and coolant It may hit, and could possibly damage, the reactor coolant pressure boundary. Therefore, it is very important that the worth of individual control rods be kept sufficiently low, with due consideration to the above mentioned self-regulation mechanisms (the negative feedback effects).

The reactivity worth of individual control rods vary with reactor conditions and the control rod positioning pattern. The withdrawal sequence and its patterns are selected so that the control rods are uniformly distributed in the core for lowering the reactivity worth of individual control rods to maneuver, while ensuring appropriate core performance. To this end, the control rod worth minimizer in the operation monitoring system

Figure 2.3.20 Control rod with the maximum reactivity worth

(Burn up dependence of effective multiplication factor with the maximum reactivity worth control rod or rods belonging to the same hydraulic control unit)

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Chapter 2 Systems of BWR Nuclear Power Plants

(process computer) monitors the withdrawal sequence of the control rods from the core at a cold or hot condition and prevents undesirable withdrawals of the control rods.

  1. Scram reactivity

The scram reactivity is the negative reactivity added by the control rods to scram the reactor. The power control capability depends on not only the magnitude of the scram reactivity (integral worth of fully inserted control rods), but also how fast they are inserted. The relation between the control rod insertion and the negative reactivity added (the "scram reactivity curve" or simply the "scram curve") plays an important role.

The shape of the scram curve largely depends on the relationship between the control rod position and the reactor power distribution. In general, the scram curve would "deteriorate" when the control rods are fully withdrawn and positioned at a distance from the high power density region, i.e., the speedy effects are lost A typical example of a design scram curve is given in Figure 2.3.21.

  1. Reactivity coefficients

Reactivity coefficients are classified into the following three different types:

  1. fuel temperature coefficient (Doppler reactivity coefficient);

  2. moderator void coefficient;

  3. moderator temperature coefficient; and

The integrated coefficient of the above three reactivity coefficients is called;

  1. power coefficient

Each component is discussed in the following.

  1. Fuel temperature coefficient (Doppler reactivity coefficient)

The Doppler effect comes from the increased neutron absorption by U-238 due to broadening of the resonance capture cross section with increased fuel temperature. The Doppler effect plays an important role in safety and dynamic characteristics of nuclear reactors. When the reactor power rapidly increases, the negative feedback reactivity due to the Doppler effect induced by the fuel temperature rise suppresses the power excursion. Therefore, in a nuclear excursion event (caused by a rapid reactivity insertion), the large prompt negative reactivity

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Control rod insertion depth

Figure 2.3.21 Design scram curve (example)

feedback from the Doppler effect will immediately suppress the nuclear excursion. The Doppler effect plays a crucial role in self-regulation and safety of nuclear reactors.

  1. Moderator void coefficient

Void fraction varies with the reactor power and the coolant flow rate and it is the primary factor for changing the moderator average density at normal power operation.

The void reactivity coefficient has a large negative value and suppresses the reactor power increase caused by a reactivity insertion. When the moderator density decreases it has the effect of increasing the neutron leakage to the reflector region and increasing the control rod reactivity worth. These two effects lead to a negative reactivity feedback in the BWR core.

  1. Moderator temperature coefficient

The moderator temperature coefficient varies with the temperature and fuel burn up. It has no significant effect on fast power transients since its magnitude is limited and there is a time delay of heat transfer from the fuel to the coolant

In addition, the coolant water is in equilibrium

2-33

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