Method and apparatus for determining nearness to criticality of a nuclear fueled electric power generating unit

A method for determining the closeness to criticality of a nuclear reactor during start-up, comprising the steps of:

• completing a control rod withdrawal step, thereby generating a change in an output signal of a neutron detector;
• measuring the output signal after the completion of the control rod withdrawal step and during a transient portion of the output signal;
• calculating the effective neutron multiplication factor (Keff) based upon the measured output signal and elapsed time between the output signal measurements;
• and
• determining the closeness to criticality of the nuclear reactor based upon the calculated value of the effective neutron multiplication factor Keff,
• wherein the step of calculating the effective neutron multiplication factor (Keff) based upon the recorded output signals and elapsed time between at least two of the recorded signals, comprises the step of:
• calculating the effective neutron multiplication factor (Keff) using the following equations, K eff ⁡ ( t s ) = 1 + β _ 1 + λ eff θ ⁢ ( t )
• where,
• β=effective 1-group delayed neutron fraction,
• λeff=effective 1-group neutron precursor decay constant, θ ⁡ ( t ) = 1 ( t - t s ) ⁢ ⁢ ln ⁡ ( n ⁡ ( t ) - n ⁡ ( ∞ ) n ⁡ ( t s ) - n ⁡ ( ∞ ) )
• and where,
• t=a time after completion of the control rod withdrawal step,
• n(ts)=the value of the output signal measured at a time ts following completion of the control rod withdrawal step,
• n(t)=the value of the output signal measured at a time t following completion of the control rod withdrawal step, and
• n(∞)=the value of the output signal measured after neutron flux stops increasing.