Nuclear reactors are designed to have inherent characteristics of power suppression, namely, to have negative reactivity coefficients for temperature variation. There­fore, an excess reactivity to accommodate temperature variation is required to operate the reactor during a given cycle length. Reactors are designed to be shut down safely by properly controlling the excess reactivity.

[1] Reactivity Coefficients

PWR cores have almost no voids and therefore the void coefficient is not significant (only a small void fraction is assumed in evaluating shutdown margin in core design). Important reactivity coefficients in self-controllability of the reactor core are moderator temperature coefficient and Doppler coefficient.

(1) Moderator Temperature Coefficient

The moderator temperature coefficient is defined as a reactivity variation by the moderator temperature rise of 1 °C. In PWRs, water density decreases as moderator temperature increases, and reactivity varies correspondingly.

Boron in the moderator, used as a means of reactivity control, makes the moderator temperature coefficient less negative because the moderator temperature rise results in a decrease in boron concentration as well as water density. Figure 3.35 shows the dependence of the moderator temper­ature coefficient on boron concentration. A high boron concentration can cause a positive moderator temperature coefficient. Burnable poison rods and gadolinia-added fuel rods can be employed to lower boron concentra­tion and maintain a negative moderator temperature coefficient. Thus, reactor cores are designed to have a negative moderator coefficient during power operation and therefore a moderator temperature rise leads to the nuclear feedback to decrease reactivity.

Rod Cluster Control Assemblies insertion gives a more negative moder­ator temperature coefficient because neutrons with a longer mean free path due to the moderator temperature rise are more easily absorbed in control rods.

The moderator temperature coefficient shifts to more negative values with increasing burnup, as shown in Fig. 3.36. The main reason is the decline of critical boron concentration as burnup proceeds and the produc­tion of plutonium and FPs also contribute to the more negative moderator temperature coefficient as burnup proceeds.