In this study, we derive the one- and two- Point Reactor Kinetics Models (PRKMs) using the actual neutron population and the actual power, which are different from the conventional PRKMs. To obtain analytical solutions for the actual neutron population and power, we use the Eigenfunction Expansion Method (EEM). It is observed that, the trends of power and neutron population may be completely different from each other which confirms the actual power and neutron population can only be calculated with the newly developed formulations. It is also shown that the adjoint flux after the perturbation is the best weight function for an initially critical system that is kept critical after the perturbation whereas for the supercritical perturbed systems, the results of PRKMs are the same as the results of the EEM regardless of whether the weight function is taken as the adjoint flux either before or after the perturbation. (C) 2019 Elsevier Ltd. All rights reserved.