The reactivity changes due to changes in temperature and fuel burnup in reactors have been described in this chapter. Control rods, burnable poisons, and chemical shim were introduced as methods to control the reactivity. In the reactor core design, it is necessary to manifest that there is enough margin in such control elements to the total reactivity requirement for control. This is called an evaluation of control reactivity balance.

Table 1.4 shows examples of the control reactivity balance for the PWR and BWR. The total reactivity requirement for control, that is, the core reactivity with all control elements withdrawn from the core, is the excess reactivity. Because the reactivity of the system is reduced due to the consumption of fissile nuclides and the accumulation of FPs with fuel burnup (burnup defect) and also because the tem­perature defect and power defect of the reactivity lead to a negative feedback effect, the excess reactivity is largest at no burnup and cold shutdown. Temperature defect, power defect, reactivity worth of Xe and Sm, and burnup defect are included in the excess reactivity.

The control reactivity worth is estimated by piling up the reactivity worth of the individual control elements; i. e., the control rods, burnable poisons, and chemical shim (for the PWR). The control rod worth is the sum of the reactivity worth values of individual control rods, as a conservative margin, with the exception of the most reactive control rod stuck in the full out position from the core. This is called the “stuck-rod criterion”.

The so-called “shutdown margin” is obtained by subtracting the excess reactiv­ity at no burnup and cold shutdown from the control reactivity worth. The control elements must necessarily provide a shutdown margin.

A suitable design margin is practically evaluated from the accuracy in nuclear design for the excess reactivity and control reactivity worth and it is considered for the control reactivity balance.