Systems and methods of predicting a critical effective k for a nuclear reactor

A method for modeling critical effective k's at a plurality of off-rated core states in an off-rated plant operation of a reactor in a nuclear power plant, the method comprising:

• estimating, for a plurality of off-rated core states, a control rod density, a gadolinium reactivity worth, a Doppler reactivity worth, and a xenon reactivity worth responsive to a control rod pattern, a reactor power plan defining the off-rated core states and one or more reference effective k's;
• calculating a change in the control rod density, a change in the gadolinium reactivity worth, a change in doppler reactivity worth, and a change in xenon reactivity worth, each change being calculated relative to the corresponding received reference value and associated with each off-rated core state;
• determining a plurality of correlations affecting a neutron balance within the reactor at each off-rated core state responsive to the percent core power, the change in the gadolinium reactivity worth, the change in the doppler reactivity worth, the change in the xenon reactivity worth, and the change in the control rod density;
• determining a change in the effective k in response to the determined correlations;
• determining an estimated critical effective k as a function of the determined change in effective k for each off-rated core state;
• comparing an actual critical effective k for one or more of the off-rated core states to the estimated critical effective k for the corresponding off-rated core states;
• selecting a type of plant from the group consisting of a xenon driven plant and a gadolinium driven plant, responsive to the comparing;
• identifying a plurality of coefficients wherein at least one coefficient is identified for each of the determined correlations as a function of an exposure at the off-rated core state, the selected plant type, and a type for the off-rated plant operation;
• and
• selecting a subset of the correlations and coefficients in response to the selected plant type and the type of off-rated plant operation.