The reactor period will dramatically decrease at the beginning of reactivity insertion in the nuclear reactor, which may trigger the protection system of the reactor period and lead to unnecessary shutdown. The instantaneous short reactor period is influenced greatly by the inserting rate of reactivity, but also related with the present delayed neutron precursors, which is difficult to quantify.

This study aims to explore the relationship between the instantaneous short reactor period and the inserting rate of reactivity from a theoretical perspective.

A point reactor model was used to deduce the inserting rate of the reactivity function using the variable factors of reactivity, reactor period, and reactor dynamic parameters, with some conservative assumptions to omit the effect of delayed neutron precursors. The relationship between reactivity insertion rate and transient period of reactor was derived after analysis on the short period phenomenon. Then, the formula of relationship was verified for several transient cases.

The results show that the reactor periods are all larger than the aim reactor periods for all transient cases when using the rate constraint of reactivity insertion in the aforementioned formula. According to the proposed theoretical framework, unnecessary shutdown during an instantaneous short reactor period can be avoided.

A theoretical framework proposed in this study can be applied to the control of rod withdrawal rate during the operation of nuclear reactors.