A new formula of neutron multiplication during startup of PWR

While withdrawing control rods to extrapolate to critical state during physical startup of reactor, even if reactivity added is equal to 1/3 of the extrapolation value, there exists the possibility that the reactor reaches supercriticality accidentally. Therefore, continuous indication of neutron density level and its change rate is required at all times for the startup safety. The reactor safety requires the development of a method to monitor criticality. In this paper, an accurate analytical solution for point kinetics equations with one-group delayed neutron and extraneous neutron source is introduced to calculate the change of neutron density, which considers that the reactor does not reach steady state before a new reactivity is added. A comparison with the traditional methods indicates the superiority and validity of the developed analytical solution. The results can be used to monitor physical startup of reactor in real time for critical extrapolation.